Mechanical testing of advanced ﬁbre composites · 10.6 Standardisation status 241 10.7 Future trends 243 References 244 11 Fatigue 248 p t curtis 11.1 Introduction 248 11.2 Basic

Mechanical testing of advanced fibre composites

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Mechanical testingof advanced fibre

composites

Edited by

J M Hodgkinson

Cambridge England

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Published by Woodhead Publishing Limited, Abington Hall, AbingtonCambridge CB1 6AH, Englandwww.woodhead-publishing.com

Published in North and South America by CRC Press LLC,2000 Corporate Blvd, NWBoca Raton FL 33431, USA

First published 2000, Woodhead Publishing Ltd and CRC Press LLC© 2000, Woodhead Publishing Ltd, except chapters 6, 8, 11 and 15, Crown copyright.The authors have asserted their moral rights.

This book contains information obtained from authentic and highly regardedsources. Reprinted material is quoted with permission, and sources are indicated.Reasonable efforts have been made to publish reliable data and information, butthe authors and the publishers cannot assume responsibility for the validity of allmaterials. Neither the authors nor the publishers, nor anyone else associated withthis publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book.

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The consent of Woodhead Publishing and CRC Press does not extend tocopying for general distribution, for promotion, for creating new works or forresale. Specific permission must be obtained in writing from Woodhead Publishingor CRC Press for such copying.

Trademark notice: Product or corporate names may be trademarks or registeredtrademarks, and are used only for identification and explanation, without intent toinfringe.

British Library Cataloguing in Publication DataA catalogue record for this book is available from the British Library.

Library of Congress Cataloging in Publication DataA catalog record for this book is available from the Library of Congress.

Woodhead Publishing ISBN 1 85573 312 9CRC Press ISBN 0-8493-0845-3CRC Press order number: WP0845

Cover design by the ColourStudioTypeset by Best-set Typesetter Ltd., Hong KongPrinted by TJ International, Cornwall, England

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Contents

Preface xiList of contributors xiii

1 Introduction 1j m hodgkinson

References 3

2 General principles and perspectives 4s turner

2.1 Mechanical testing in perspective 42.2 Formal framework for mechanical test methods 102.3 Special features of the mechanical testing of composites 132.4 Nature and quality of test data 192.5 Mechanical tests for long-fibre composites 242.6 Concluding comments 33

References 34Bibliography 35

3 Specimen preparation 36f l matthews

3.1 Introduction 363.2 Laminate production 363.3 Quality checking 393.4 Specimen preparation 393.5 Strain gauging 413.6 Summary 42

References 42

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4 Tension 43e w godwin

4.1 Introduction 434.2 Testing equipment 504.3 Specimen details 564.4 Test procedure 624.5 Data reduction 644.6 Material and sample preparation 674.7 Practical example 704.8 Future developments 71

References 73

5 Compression 75f l matthews

5.1 Introduction 755.2 Types of test 765.3 Standards 825.4 Specimen preparation 835.5 Specimen configurations 855.6 Execution and problems 875.7 Typical results 895.8 Conclusions 97

References 97

6 Shear 100w r broughton

6.1 Introduction 1006.2 Test methods 1016.3 Summary of test methods 1186.4 Comparison of data 1186.5 Recommendations and concluding remarks 118

Acknowledgements 122References 122

7 Flexure 124j m hodgkinson

7.1 Introduction 1247.2 Three-point and four-point flexure tests 1257.3 Comparison of recommended test methods 1287.4 Failure modes 1337.5 Typical data 1337.6 Steel versus soft lined rollers 138

vi Contents

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7.7 Through-thickness flexure 1407.8 Conclusions 141

References 141

8 Through-thickness testing 143w r broughton

8.1 Introduction 1438.2 General issues 1448.3 Tensile test methods 1468.4 Compression test methods 1568.5 Shear test methods 1608.6 Concluding remarks 167

Acknowledgements 167References 168

9 Interlaminar fracture toughness 170p robinson and j m hodgkinson

9.1 Introduction 1709.2 Terminology and typical values 1709.3 Overview of test methods and standards 1739.4 Mode I testing 1789.5 Mode II testing 1949.6 Mixed mode I/II 2009.7 Multidirectional laminates 2049.8 Conclusions 206

References 207

10 Impact and damage tolerance 211p j hogg and g a bibo

10.1 Introduction 21110.2 Impact testing 21110.3 Damage tolerance – compression after impact (CAI) tests 22810.4 Boeing test methods and related variants 22910.5 Data interpretation 23510.6 Standardisation status 24110.7 Future trends 243

References 244

11 Fatigue 248p t curtis

11.1 Introduction 24811.2 Basic test philosophy 249

Contents vii

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11.3 Machines and control modes 25411.4 Presentation of data 25611.5 Monitoring fatigue damage growth 25611.6 Potential problems 26111.7 Fatigue life prediction 26411.8 Post-fatigue residual strength 266

References 266

12 Environmental testing of organic matrix composites 269g pritchard

12.1 Introduction 26912.2 Why environmental testing? 26912.3 Environmental threats to composites 27012.4 Standard tests 27112.5 Sample conditioning 27512.6 Experimental approaches 27612.7 Determination of sorption behaviour 27812.8 Lowering of Tg by absorbed liquids 27912.9 How do composites perform in adverse environments? 28012.10 Diffusion of liquids into composites 28412.11 Classification of absorption categories 28812.12 Edge corrections 289

References 291

13 Scaling effects in laminated composites 293c soutis

13.1 Introduction 29313.2 Background 29413.3 Investigation of failure 29413.4 Practical application examples 30413.5 Specialised scaling techniques in composites 30813.6 Concluding remarks 311

References 312

14 Statistical modelling and testing of data variability 314l c wolstenholme

14.1 Introduction 31414.2 Importance of looking at data plots 31414.3 Basic statistics 31614.4 Distribution of sample statistics 31714.5 Testing for differences between samples 317

viii Contents

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14.6 Comparing several samples simultaneously 32514.7 General linear model (GLM) 331

References 339

15 Development and use of standard test methods 340g d sims

15.1 Introduction 34015.2 Development of test methods 34115.3 Validation of test methods 34315.4 Sources of standards and test methods 34715.5 Harmonisation of composite test methods 35215.6 Recommended mechanical test methods 355

References 355Bibliography – selected ISO standards 356Appendix – contact details for standards organisations 357

Index 359

Contents ix

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Preface

Mechanical property data are essential in the design process if structuresare to perform as intended – reliably and cost-effectively for their full life.However, there are no data without testing at some stage. But what testsshould be carried out to give the required data? How, precisely, should thetests be conducted, and who says so? What does the data actually mean?How reliable are the data produced? Are data obtained from small testspecimens meaningful when large structures are being designed? Whateffect will the operating environment have? Fortunately most, if not all ofthese questions have been answered in the case of isotropic solids, giving astarting point for the development of mechanical test methods for morecomplex materials such as advanced fibre composites. This book attemptsto set out the current position with regard to these potentially highlyanisotropic materials, which are finding repidly increasing applicationsdespite their complexity.

The expression ‘advanced fibre composites’ probably means differentthings to different people. To many it might encompass only carbon and asmall group of thermoplastic fibres including aramid and polyethylene, tothe exclusion of glass fibres. However, in some industrial applications, glassfibres, whilst not necessarily being deemed as advanced in any particularsense, are the only fibres which can fulfil the specific design and environ-mental requirements. So perhaps the term ‘advanced’ in this context isreally application driven. As far as this book is concerned much of the dis-course surrounds high modulus, high strength fibre/plastic matrix compo-sites, but not exclusively so, it is high performance which is the key. It hasbeen left to the author(s) of each chapter to judge for themselves, from theirown interests and experience, precisely what to include. It is in any casequite clear that, for most of the mechanical test methods described, rela-tively minor modifications allow perfectly good results to be obtainedacross the whole range of fibre/matrix combinations, from the most exoticto the most humble.

This book has developed out of a short course of the same title which

xi

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has normally run on a yearly basis at Imperial College (London Univer-sity) since 1989.The course has now seen over 250 delegates ‘graduate’; theyhave come from a wide variety of industry sectors and from all over theworld. The course has been supported by experts in their field from QueenMary and Westfield College (London University), the National PhysicalLaboratory, the Defence and Evaluation Research Agency and City Uni-versity. I am indebted to these colleagues, and those from Imperial College,who have not only taught on the course but have also given up a great dealof valuable leisure time providing their copy for the book. A special thank-you goes to Professor Geof Pritchard, the only contributor to the book whohasn’t taught on the course, which has a section on Environmental Effectsbut, in comparison to the book chapter, is probably woefully inadequate.

In recognition that not everybody has the same interests in life, this bookis organised in chapters dealing with particular types of test (tension, com-pression, shear, etc.), allowing the reader to ‘dip in and out’ as he/she wishes.It is my hope that the reader finds the book both informative and interest-ing and that it encourages best practice as it is currently known, across thevarious industrial sectors making use of fibre-reinforced plastic matrix composites.

It is as well to remember that a bad test is not worth doing and that eventhe best test can be done badly. It is all in the detail.

JM Hodgkinson

xii Preface

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List of contributors

Dr G A BiboBritish Aerospace Australia41-45 Burnley StreetRichmondVictoria, 3121Australia

Dr W R BroughtonNational Physical LaboratoryTeddingtonMiddlesexTW11 0LW

Professor P T CurtisStructural Materials CentreBuilding A7, Room 2008FarnboroughHampshireGU14 6TD

E W GodwinCentre for Advanced Composite MaterialsImperial CollegePrince Consort RoadLondonSW7 2BY

Dr J M HodgkinsonCentre for Advanced Composite MaterialsImperial CollegePrince Consort Road

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xiv List of contributors

LondonSW7 2BY

Professor P J HoggDepartment of MaterialsQueen Mary & Westfield CollegeUniversity of London327 Mile End RoadLondonE1 4NS

Professor F L MatthewsCentre for Composite MaterialsImperial CollegePrince Consort RoadLondonSW7 2BY

Professor G PritchardYork HouseMoseley RoadHallowWorcestershireWR2 6NH

Dr Paul RobinsonDepartment of AeronauticsImperial CollegePrince Consort RoadLondonSW7 2BY

Dr G D SimsNational Physical LaboratoryTeddingtonMiddlesexTW11 0LW

Dr C SoutisDepartment of AeronauticsImperial CollegePrince Consort Road

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List of contributors xv

LondonSW7 2BY

Dr S TurnerDepartment of MaterialsQueen Mary & Westfield CollegeUniversity of London327 Mile End RoadLondonE1 4NS

Professor L C WolstenholmeSchool of MathematicsCity UniversityNorthampton SquareLondonEC1V 0HB

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In the mind of the general public the term ‘composite materials’ is largelyeither misunderstood or not understood at all. There is a reasonable ideaof what might be expected of some other materials and what they might beused for. Steel is used for fabricating the skeleton of many buildings (orinside the concrete) and for most automobile body shells; copper is usedfor electrical wiring; aluminium is used a lot in aeroplanes; plastics (of what-ever colour) are used for almost everything. However, even with theseisotropic homogeneous materials there is little real understanding of whythey are used for particular applications. This is not an unreasonable situa-tion. Most people have more to concern themselves about in their lives thanwhy a specific screw could be made from steel, brass or a plastic. It doesnot matter whether people understand, or not. Quite rightly the expecta-tion is that the goods that they purchase, or make use of in some way, arefit for purpose. This is where the mechanical and other types of materialstesting comes in.

In order to design a structure or component so that it is efficient and fitfor purpose, the shape of each subcomponent needs to be decided upon,taking into account the material it is to be made from. This means thatcareful consideration must be given to the intimate relationship betweenhow the component is supposed to perform in service and the propertiesof the material from which it is made. This can be a tricky balancing acteven with isotropic homogeneous materials but substantially more difficultwhen attempting to make use of materials which are not isotropic and nothomogeneous.

How does one go about deciding what a material is capable of, mechani-cally speaking? Well, first one needs to know what the beast one is dealingwith is made of, and in this book we are concerned with what are generallytermed advanced fibres in a plastic matrix. The fibres involved in the dis-cussion are carbon, aramid and glass, normally continuous rather than shortfibres. The resins considered are epoxies and a variety of thermoplastics.For the most part, but not exclusively, we are concerned with laminates of

1Introduction

J M HODGKINSON

1

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these fibres and resins. Given any knowledge of the way that homogeneousmaterials react to the application of loads of varying types, it does not takemuch thought to come to the conclusion that these fibre-reinforced plasticsare an entirely different breed, and that considerable thought and experi-mentation might be needed to describe, adequately well, their mechanicalproperties.

This is what this book is all about. We need to be able to establish howthese materials react to all types of loading, be they tensile, compressive orshear, of short-term or long-term duration, or cyclic, in the presence of highor low temperatures, or other environments which might significantlymodify their behaviour, in the same way that we can for homogeneousmaterials. Designers can then make use of the information to create struc-tures which perform within the design requirements. These structuresinclude large parts of military and civil aircraft, racing cars, automobiles,buses, coaches, lorries, railway and military vehicles, boats, ships and othermarine vehicles, a wide variety of sports, home, office, recreational and otherleisure goods and, increasingly, civil engineering structures.

The tests which can be carried out to ascertain the behaviour of these materials depend on testing machines which have been designed and built, not necessarily with this particular range of materials in mind,but are generally adequate for the purpose. Quite frequently it is the subtesting equipment (i.e. testing jig), specimen design and other experimental arrangements which address the special reqirements of thesematerials.

Subsequent chapters in this book describe the specimen design and howthe tests might be carried out, as far as possible to best practice, under dif-ferent loading regimes, with due regard given to the statistical analysis ofthe data produced and progress in the development of test methods frominitial conception to full international acceptance.

During the period of this book’s development there have been numer-ous initiatives by standards organisations worldwide to update existingmethods and produce new standard test methods to satisfy (or at least toattempt to satisfy) the particular requirements of advanced fibre-reinforcedplastic matrix composite materials. The ‘push’ for these better, or new, testmethods to be developed, refined, written into standardised form and finallyadopted, preferably at international level, has come from the ‘grass roots’,largely (but not exclusively) driven by the aerospace industry.

Although it is clear that many other organisations were involved in thesedevelopments in the 1980s and 1990s (and might have been equally con-cerned about the dearth of appropriate standardisation for this class ofmaterials), a key catalyst appears to have been the Composites ResearchAdvisory Group (CRAG), which set about in the early 1980s to attempt todefine what the best practice should be over a range of test methods. The

2 Mechanical testing of advanced fibre composites

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Group reported the results of its preliminary deliberations in 1985 and ina final report1 in 1988, but by this time numerous sections of industry,research organisations and university researchers (primarily but not exclu-sively in the UK) were making use of the recommendations. The CRAGrecommendations were proposed to the British Standards Institution andsubsequently had a considerable effect in the development of new interna-tional standards. From start to finish the process has taken the best part of20 years to establish a fairly coherent and comprehensive body of standardsat international level. One is tempted to suggest that this is an extraordi-narily long time. It is also a time during which the influence of the aero-space industry on the future of composite materials has diminishedsomewhat. At least we are left with the legacy of the standards.

References

1. P T Curtis (ed.), CRAG Test Methods for the Measurement of the EngineeringProperties of Fibre Reinforced Plastics, Royal Aircraft Establishment, TechnicalReport 88012, February 1988.

Introduction 3

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2.1 Mechanical testing in perspective

2.1.1 Overall objectives of mechanical testing

Humanity’s utilization of materials has always been supported by testingactivities, which have developed over the centuries from crude tests of thefitness-for-purpose of service items to the modern science-based proceduresthat support all aspects of the science and technology of materials and theirutilization. There is now a mutual dependency between advances in scien-tific knowledge and test method development, with first one and then theother providing an enabling facility for further progress in the developmentof versatile evaluation programmes capable of supporting various essentialindustrial operations. In the particular case of mechanical tests those oper-ations include:

• quality control• quality assurance• comparisons between materials and selection• design calculations• predictions of performance under conditions other than those of the test• indicators in materials development programmes• starting points in the formulation of theories.

This list is a simplification, in that some of the functions overlap andseveral are linked by lateral connections which become effective at variousstages in the conversion of materials into end-products. But, in isolation,these functions make different demands on the data, and therefore, theresources that are deployed need to be matched carefully to the demandsof particular circumstances. For instance, quality control can usually beachieved by the use of simple test procedures provided that they reflect relevant mechanical characteristics of the product; the simplicity of the test procedure and precision of the data are usually deemed far more

2General principles and perspectives

S TURNER

4

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important than scientific rigour and accuracy whereas, in contrast, the pri-orities would be reversed for a procedure used to generate data for a designcalculation.

Some test methods are multipurpose via a variety of operating proce-dures.Thus, a conventional tensile test operated under fixed conditions mayserve a quality control function whereas, operated with controlled variationof influential factors such as temperature and straining rate, it may providea first-order estimate of load-bearing capability. On the other hand, sometest methods are uniquely dedicated to a single purpose and the data theyyield could be misleading if used in a wider context.

There is another complication in materials testing. The property valuederived from a mechanical test varies with the state of internal order of thetested item, which for many classes of material is sensitive to the produc-tion route and other factors. Each sample or test specimen is then unique,and derived data must be regarded as relating just to it, rather than to thematerial in general. The corresponding properties of the latter, or of othersamples, have to be inferred.There are, therefore, far-reaching ramificationsfor the scope of test programmes, evaluation strategies, the mode of uti-lization of the data, design procedures and so on.

The variations in material state are commonly in the molecular or atomicorders which, after the processing stage, slowly change towards a state ofgreater order. In a fibre composite the molecular reordering process gen-erally occurs in the matrix and at the fibre–matrix interfaces. However, thedominating source of variation is the spatial distribution of the fibres, whichmay change inadvertently during the manufacturing stage, or may bechanged deliberately by the fabricator to induce a particular mechanicaleffect. Thus the trains of inference that, for a simple class of material, leadfrom test specimens, to sample, to material and finally to end-product, aremore tenuous and less reliable and may even be inappropriate for long-fibre composite systems.This occurs to the point where ‘test specimen’ tendsto be replaced by ‘test coupon’, the concept of sample is largely discardedin favour of items such as subelements and substructures and ‘material’ isreplaced by ‘structure’.1 These changes are functional rather than cosmetic,signifying a testing strategy linked more closely to engineering than tophysics, though the testing of structures, substructures and so on supple-ments rather than replaces the testing of coupons.

The suite of tests used for the evaluation of the mechanical properties orattributes of a material expand in range and complexity with the severityof the anticipated service but also as the class of material changes fromisotropic to anisotropic and from homogeneous to heterogeneous. Thus,numerous methods are deployed to measure the mechanical properties oflong-fibre composites. In most cases they are elaborated variants of the teststhat have traditionally been used for other classes of material, for example,

General principles and perspectives 5

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metals and plastics, and they are described in standard test methods, thescope of which is variously international, national, industrial sector andcompany. However, whilst the technical details of such standard testmethods are always explicit, the underlying rationale is generally unstatedthere; and in the absence of such statements, the special stipulations on testconfigurations and procedures can seem to be demanding, costly andirksome. In comparison, other classes of material may seem to be simplerin general characteristics and more amenable to rational evaluation butthose classes may well have seemed correspondingly difficult to evaluateduring their novelty and development phases. For example, the testing ofthermoplastics during the period 1940 to 1970 was fraught with misleadingtest data and imperfect rationale. It finally transpired that the initial con-fusing multiplicity of test methods could be reduced and rationalisedthrough the agency of refinements to the theories of mechanics and throughthe testing of ‘critical basic shapes’ that function as a formal set of sub-structures. There is some evidence that the same rationalisation process istaking place in the field of long-fibre composites, but a reliable comparisonis elusive because the market environment for thermoplastics was, andremains, very different from that in which long-fibre composites exist.

There is, of course, an extensive literature on the manufacture, proper-ties and service performance of composites, but only a small proportion ofit relates either directly or peripherally to mechanical testing. A short bib-liography at the end of this chapter cites a number of text books which areintended to complement the present work. The list includes one text(Brownlee) which sheds precomputer light on the subject of practical statistics.

2.1.2 Service-pertinent mechanical properties of long-fibre composites

Long-fibre composites are generally required to function as load-bearingstructures. It follows that elastic modulus, strength, ductility and fracturetoughness are particularly important properties. The property values andgeneral chartacteristics manifested by long-fibre composites and other,similar materials are the resultants, via various combination rules, of theproperties of the separate constituents. However, the realities of practicalsituations may violate the rules, so that a datum derived from a partic-ular test procedure may be a biased or invalid indicator of the property,or attribute, that the test ostensibly measures. The apparent interlaminarshear strength of a long-fibre composite derived via flexure of a short beam is one such vulnerable quantity, because the beams often fail by acombination of several fracture/rupture processes that frustrate anyattempt to assign a proper value to the postulated property. There is, also,


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a more fundamental issue. The polymeric nature of most matrix materialsintroduces viscoelastic characteristics into the mechanical behaviour ofcomposites such that, depending on local circumstances, the concepts ofelastic modulus, strength and ductility may have to be expanded to embracephenomena such as creep, stress relaxation, creep rupture and fatigue, andattributes such as impact resistance. Any modern textbook discussion of the mechanical properties of the matrix materials (i.e. plastics) is likely to include this extended range of topics. Corresponding treatments, includ-ing this one, of long-fibre composites tend to concentrate on the fourprimary properties and pay less attention to ‘time-dependent’ or ‘rate-dependent’ aspects of those properties – except for fatigue, which has beenstudied comprehensively.

The relative neglect of some features of the mechanical behaviour may have arisen mainly because viscoelastic characteristics are reflected inonly some composite structures in some stress fields whereas, in contrast,anisotropy is a dominant feature of many structures, with modulus andstrength often varying much more with stress axis than with elapsed timeor straining rate. Additionally, the superposition of viscoelasticity on toanisotropy introduces formidable analytical difficulties and increases thetesting burden two-fold or three-fold, so the long-standing tendency forlong-fibre composites to be regarded as anisotropically elastic rather thananisotropically viscoelastic is explicable as a pragmatic compromise.However, that compromise offers no universally safe solution to load-bearing calculations, since a large composite structure might creep to an un-acceptable degree because of unpredicted creep in a single element.

At the present time the vast majority of applications for long-fibre com-posites have little reason to consider time-dependent effects; this situationmay change when such materials are used more extensively in, for example,heavy civil engineering applications, where design lives of 50 years or moreare required. Little is known about the time-dependent behaviour of long-fibre composites, although it is generally recognised that any effects arelikely to manifest themselves when the materials are subjected to shear orthrough-thickness loading. It is highly likely that new test methods will needto be developed to tackle measurement of the viscoelastic properties of thisclass of materials, because those presently available appear to be inade-quate in a number of ways.2

Strength is often loosely related to the elastic modulus, both being similarly sensitive to the volume fraction of the fibres and their alignmentrelative to the stress field. Ductility, or toughness if the item is a sub-structure or a structural element, is a more complex matter. For a homo-geneous material it is inversely related to modulus; a rough working rule isthat steps taken to enhance the modulus, for example, by modification ofthe composition, tend to diminish the toughness and vice versa; and similar


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correlations arise for long-fibre composites, but the simple inverse rela-tionship is distorted and partly obscured.This is primarily because the ratio-nale breaks down when the dimensions of the stress field irregularity nearthe crack tip are similar in magnitude to the scale of the heterogeneity.

This particular detail exemplifies a general point that the mechanicalevaluation of composite samples does not lie exclusively within the formalframework defined by continuum mechanics; their heterogeneity and theiranisotropy dictate a larger repertoire of tests than would suffice for asample of a more conventional material. Thus, for example, for long-fibrecomposites, modulus and strength measurements in flexure and uniaxialcompression are as important as, and sometimes more important than, testsin tension and can be regarded as complementary to them, whereas forhomogeneous samples they often play only a supplementary role.

The mechanical properties depend on several variables of the composition:

• properties of the fibre• surface character of the fibre• properties of the matrix material• properties of any other phase• volume fraction of the second phase (and of any other phase)• spatial distribution and alignment of the second phase (including fabric

weave)• nature of the interfaces.

Mechanical properties also depend on the many details of the processingstage, particularly those affecting the degree of adhesion between fibre andmatrix and the physical integrity and overall quality of the final structure.If the mechanical properties of the fibre and the matrix are known,mathematical models enable the corresponding properties of samples with particular fibre volume fractions and fibre spatial arrangements to be calculated, but the models are imperfect. The fibre alignments in testcoupons and service items generally deviate from the ideal states assumedfor the models, and the properties deviate correspondingly from the calcu-lated predictions. The effectiveness of the coupling between the phases ina composite is also an influential factor. It is neither fully quantified nor properly understood. Good coupling seems to be desirable where a composite with high moduli is the objective and also, in many cases, wherehigh strengths are required. The lines of reasoning are less clear wheretoughness is the objective. Poor coupling is advantageous in that localdecoupling between fibre and matrix can arrest, or deflect, a growing crackand extensive decoupling is an effective mechanism for energy absorption.On the other hand, a decoupled fibre may act as a stress concentrator andpromote failure.


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2.1.3 Mechanical testing strategy for long-fibre composites

Despite the complications of heterogeneity, interfaces and anisotropy, theproperty data for long-fibre composite test coupons conform in manyrespects to the conventional definitions for homogeneous isotropic materi-als, apart, that is, from additional subsidiary definitions and nomenclatureto accommodate the anisotropy and special property definitions, wherethere is no homogeneous isotropic counterpart, for example, the interlam-inar shear strength. Even so, the almost infinite variety of possible spatialarrangements of the fibres and fibre volume fractions raises doubts aboutwhether any particular combination of matrix and fibre should be regardedas a typical and characterising material state. The different fibre–matrixassemblies are each unique, so that, even more so than for processing-sensitive homogeneous materials, a tabulation of property values derivedfrom one structural assembly has a restricted field of relevance. On theother hand, since the mechanical testing of a long-fibre composite is a costlyprocess, there usually has to be a pragmatic compromise between the desir-ability of test data for several different structures and the need for testingeconomy. Evaluation programmes are therefore often constrained by finan-cial considerations, although the potentially harmful effects of such con-strains may be offset by the adoption of a different testing strategy.1

The spatial distribution and alignment of the reinforcing phase are oftenso arranged as to satisfy a particular service requirement, and sometimesto attain an unusual combination of attributes in an end-product. Dataderived either from test coupons cut judiciously from such structures, orfrom special subelements tested in their entirety,1 may reflect the load-bearing capability of the complete structure. Such data are unlikely to haveany claim to generality but, in addition to their direct relevance to a par-ticular structure, they should give an insight into the range of values of the‘property’ that could be manifest in service and thereby provide quantita-tive options in design calculations. On the other hand, conventional datafrom specimens consisting of uniaxial arrays of fibres, and from lamellaewith specific fibre alignments, have some general downstream utility via themathematical models mentioned previously. Preferential alignment offibres in one direction tends to confer property deficiencies such as lowstrength and modulus in a transverse direction. Similarly, stacks of lamel-lae with different fibre alignments are prone to out-of-plane distortions.Testprogrammes for such specimens, or samples, should include checks on thepossible deteriorations and imperfections. Additionally, deficiencies in theproduction processes may give rise to inadvertent variations in fibre align-ment, and so on, and the behaviour of the test coupon, or end-product, maytherefore deviate from what might be expected and/or may vary from itemto item.


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2.2 Formal framework for mechanical test methods

The foundation of satisfactory test methods for the measurement ofmechanical properties is the theory of mechanics. That theory became wellentrenched for homogeneous isotropic elastic materials during the nine-teenth century and was progressively extended later to accommodate inhomogeneity, anisotropy and anelasticity, all of which are characteristicfeatures of long-fibre composites. If the material under investigation is vis-coelastic, it is convenient for a mechanical test to be regarded as consistingof the application of an excitation and the observance of the response ofthe test piece, with the relationship between the two defining a property.This seemingly cumbersome approach, or something similar, is an inescap-able consequence of the nature of viscoelasticity; it requires that the simpleelastic constitutive equations relating stress to strain be replaced by con-volution integrals but, when the viscoelasticity is not dominant, some ofthose integrals can be replaced by simple weakly time-dependent coeffi-cients. Irrespective of the types of excitation and response, in most mech-anical tests, forces are applied and displacements ensue. In a few, thedisplacements are imposed, athough that necessarily requires the priorapplication of forces. Mechanical properties derived from such tests haveto be defined in terms of the relationships between the stresses and thestrains. Translation from force to stress, and from displacement to strain, isrelatively straightforward if the tested item is homogeneous and isotropic,but more complex if it is heterogeneous and/or anisotropic.

The basic assumption of linear elasticity theory is that the response to anexcitation is a linear function of all the components of the excitation tensor,Equation [2.1]:

sij = cijklekl [2.1]

where sij and ekl are the stress and strain tensors, respectively, with cijkl being the stiffness coefficients. Each suffix has possible integral values1, 2 or 3.

Alternatively (Equation [2.2]),

e = sijklskl [2.2]

where sijkl represents the compliance coefficients.Because of symmetry in the stress and strain tensors, only 21 of the 81

stiffnesses and compliances are independent, and that number is reducedfurther if there are symmetries in the material (i.e. if the material is not fullyanisotropic), see Table 2.1.

The most general case, with 21 independent elastic coefficients, is socomplex as to be virtually unmanageable in both the analytical and exper-imental aspects. However, this extreme situation rarely arises in practice


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because the fabrication processes impose some order, either from deliber-ate intent or inadvertently. If the material is isotropic the relationshipsbetween the stress and the strain are relatively simple and the coefficientsreduce to the two moduli of isotropic elasticity theory.

Elasticity theory relates to a continuum but composites are hetero-geneous and therefore the equations are an imperfect representation.However, they suffice in many cases provided that the scale of the inter-phase discontinuities is small relative to the size of the test specimen. Stip-ulations on the size of test specimens in the standard test methods coveringmodulus and strength ensure that the heterogeneity does not distort thederived data, but there are difficulties at the micromechanical level, forinstance in estimates of the stress field at the tip of a crack.

The case usually considered analytically is orthotropy, which is conferredapproximately by a uniaxial array of fibres in long-fibre composites, by uniaxial drawing of fibres and films and by other directional processing ofthermoplastics. The stress–strain relationship for an orthotropic system isgiven by Equation [2.3]:

where the cij are the stiffness coefficients, the first suffix denotes the direc-tion of the normal to the surface to which the stress or strain relates andthe second suffix denotes the strain axis or the line of action of the stress;g is the shear strain, t is the shear stress, s is the tensile stress and e is thetensile strain. See Fig. 2.1 for clarification.

The strain–stress relationship is similar and is expressed as Equation[2.4]:

sssttt

eeeggg

11

22

33

23

31

12

11 12 13

21 22 23

31 32 33

44

55

66

11

22

33

23

31

12

0 0 0

0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

=

c c c

c c c

c c c

c

c

c


Table 2.1. Classes of symmetry.

Type of material symmetry Number of independent elastic coefficients

None (triclinic) 21One plane of symmetry (monoclinic) 13Three planes of symmetry (orthotropic) 9Transversely isotropic (one plane of isotropy) 5Isotropic 2

[2.3]

MTA2 11/22/2000 9:10 AM Page 11


where the sij are the compliance coefficients. In Equations [2.3] and [2.4],e11, e22 and e33 are the principal strains and s11,s22 and s33 are the principalstresses.

The compliance matrix can be rewritten in terms of the more familiarengineering/physical constants Eii, nij and Gij, Equation [2.5]:

1 0 0 0

1 0 0 0

1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

11 21 22 31 33

12 11 22 32 33

13 11 23 22 33

32

31

12

E E E

E E E

E E E

G

G

G

- -- -- -

n nn nn n

eeeggg

sssttt

11

22

33

23

31

12

11 12 13

21 22 23

31 32 33

44

55

66

11

22

33

23

31

12

0 0 0

0 0 0

0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

=

s s s

s s s

s s s

s

s

s

3

1

2

3

2

1

s33

s11

s22

t31

t32

t13

t12

t21

t23

2.1 Principal directions and stress components for an orthotropicmaterial.

[2.4]

[2.5]

MTA2 11/22/2000 9:10 AM Page 12

where G12 is the in-plane shear modulus (see plane number 3 in Fig. 2.1)and nij is Poisson’s ratio for transverse strain in the j direction when thespecimen is stressed in the i direction.

Because the matrix materials are viscoelastic, those stiffness and compli-ance coefficients that relate to deformations in the matrix vary with rate ofstraining, duration of loading and so on, and are therefore viscoelastic func-tions similar to those that describe the mechanical behaviour of plastics and on which there is an extensive literature. In contrast, there is a relativedearth of information on the time dependence of the stiffness and compli-ance coefficients relating to long-fibre composites and a general ignoranceabout the nature of the interactions between them. Despite its imperfec-tions, the existing formal framework contains justifications for the variousconstraints and stipulations that have been imposed on test configurationsand test procedures for long-fibre composites.

2.3 Special features of the mechanical testing

of composites

2.3.1 Features arising from the theory of anisotropic elasticity

The principal precautions that are necessary during the mechanical testingof long-fibre composites are in relation to:

• generation of a uniform stress field in the critical reference volume• avoidance of overwhelming ‘end-effects’• attainment of adequate loading levels without damage or failure near

the loading points• appropriate specimen dimensions related to the scale of structural

inhomogeneities• tension–shear coupling.

The first four precautions apply similarly to the testing of homogeneousisotropic materials and give rise to various stipulations about specimendimensions, test configurations and machine specifications, although heterogeneity and anisotropy entail more severe constraints and introduceadditional considerations. Some of these complications reflect a greaterstringency in Saint Venant’s Principle when the specimen is a composite. Inits original form, for isotropic materials, it states that any differences in thestress states produced by different but statically equivalent load systemsdecrease with increasing distance from the loading points, the differencesbecoming insignificant at distances greater than the largest linear dimen-sion of the area over which the loads are acting. In an anisotropic


MTA2 11/22/2000 9:10 AM Page 13

specimen, the region of uniform stress is approached much more gradually.It has been shown that the decay length, l, is of the order:

[2.6]

where b is the maximum dimension of the cross-section. For rectangularstrips subjected to traction at their ends, Equation [2.7]:

[2.7]

where l is the distance over which a self-equilibrated stress applied at theends decays to 1/e of its end-value.

The ratio E11/G12 may have a value lying between 40 and 50 for a unidi-rectional composite with a carbon-fibre volume fraction of 0.6. The valuewould be about 3 for an isotropic specimen and if Equation [2.7] is validfor the anisotropic case, as it should be, the respective decay lengths are inthe ratio of about 3.5 :1.

Other difficulties arise when the test configuration is such that the prin-cipal directions of the stress and strain tensors do not coincide with the sym-metry axes of the specimen. This can easily be shown for a thin laminate(e.g. a single lamella) for which a state of plane stress can be assumed,such that:

s33 = 0, t23 = 0, t31 = 0 [2.8]

and

e33 = s33s11 + s32s22 [2.9]

which is therefore not an independent coefficient, in which case, Equation[2.4] reduces to Equation [2.10]:

[2.10]

An important feature of Equations [2.3], [2.4] and [2.10] is that thenormal and shear components are uncoupled; in other words, normalstresses do not induce shear strains and shear stresses do not induce normalstrains, but this situation prevails only when the coordinate system for thestress field coincides with the symmetry axes. For a lamella whose materialaxes are aligned at an angle q in the 1–2 plane to the stress axis, the rela-tionship in Equation [2.10] becomes:

eeg

sst

11

22

12

11 12

21 22

66

11

22

12

0

0

0 0

=s s

s s

s

lp

ª ÊË

ˆ¯

b EG2

11

12

12

bEG

11

12

12Ê

Ëˆ¯


MTA2 11/22/2000 9:10 AM Page 14

where

[2.12]

in which m and n are cosq and sin q, respectively. The other terms have asimilar form.

The normal and shear modes are now coupled. That is, a tensile stressinduces some shear and a shear stress induces some tensile strain.

The expression for may be rearranged into Equation [2.13]:

[2.13]

to give the in-plane variation of tensile modulus for this simple system ofanisotropy.

The consequences of Equation [2.11] and similar relationships are important:

• if the principal axes of the stress field do not coincide with the symme-try axes of the specimen, extraneous forces and deformations will arise;e.g. flexed coupons may additionally twist and tensioned coupons mayexhibit in-plane shear.

• if a laminate consists of unidirectional lamellae lying at various anglesto each other, deformation mismatches occur at the interfaces becauseof the different degrees of tension/shear coupling in the various lamel-lae. The severity of the effects will depend on the stacking sequence,the degree of asymmetry, the test modes, the clamping arrangementsand so on, and may be sufficient to cause delamination, especially at theedges.

In summary, the principal practical consequences of anisotropy are:

1 severe ‘end-effects’, which extend in the direction of higher stiffness (afunction of both the specimen geometry and the anisotropy)

2 premature failure in grips or at other loading points3 premature delamination at free edges, or other unintended failure

modes.They tend to arise from the interactions between the macrostruc-ture of the composite and even the simplest system of external forces.

4 property imbalances between, say, a tensile modulus (or strength) dominated by the properties of the fibre and a shear modulus (orstrength) governed largely by the properties of the matrix.

1 4 1 1

0

4

0 45 90 0

2 24

90E E E E E E= + - -Ê

Ëˆ¯ +

cossin cos

sinqq q

q

s11

s m s m n s s n s114

112 2

12 664

222= + +( ) +

eeg

sst

x

y

xy

x

y

xy

s s s

s s s

s s s

=11 12 16

21 22 26

61 26 66


[2.11]

MTA2 11/22/2000 9:10 AM Page 15

These consequences entail special constraints on test configurations,specimen geometries and stacking sequences in laminates. They also some-times induce behaviour in subelements, substructures and structures that isunique to anisotropic systems.

2.3.2 Features arising from practical realities

The results from experimentation are sometimes erroneous because therequirements to ensure accurate data are onerous and not always achiev-able. Additionally, errors arise from imperfections originating in the fab-rication stage. The possible defects include imperfect alignment anddispersion of the fibres, broken and kinked fibres, incompletely wettedfibres, voids and general mismatches between the constituents.

The tensile modulus along the fibre direction of a composite containinga unidirectional, parallel array of fibres provides a simple example of theeffect that fabrication defects can have on properties. The modulus can beestimated using the ‘Rule of Mixtures’ equation:

[2.14]

where Ec is the Young’s modulus of the composite, Ef the Young’s modulusof the fibre and Em the Young’s modulus of the matrix, with j being thevolume fraction of the fibres.

In practice the simple Equation [2.14] usually has to be modified to:

[2.15]

where ho is the efficiency factor for fibre orientation and hl the efficiencyfactor for fibre integrity (length and effective length).

Usually Ef >> Em so that:

Ec � hohljEf [2.16]

the upper bound of which is:

Ec = jEf [2.17]

and lower values of Ec reflect the fabrication deficiencies mentioned above.Research indicates that the properties of the fibres can be utilized with anefficiency of about 85% for modulus and about 70% for strength. With thisas an upper bound, the simple tensile test procedure on this type of couponprovides a first-order assessment index of the quality of composite attain-able from a particular fibre–matrix combination.

The situation is much more complex for other stress fields and/or otherfibre–matrix assemblies, where the matrix and the interface may be sourcesof weakness. The interlaminar shear strength, the shear modulus, the prop-erties in the transverse direction and those under uniaxial compression are

E E Ec = + -( )h h j jo l f m1

E E Ec f m= + -( )j j1


MTA2 11/22/2000 9:10 AM Page 16

all sensitive to the properties of the matrix and reflect the potential defi-ciencies of fibre composites. For such situations a third efficiency factor hasto be incorporated into any analogue of Equation [2.15], to quantify theeffectiveness of the fibre–matrix coupling. It follows, therefore, that the first-order assessment by tensile testing is insufficient for many purposes andanything other than the most elementary evaluation programme shouldinclude tests in at least one additional and fundamentally different defor-mation mode.

A popular test procedure which utilizes a different deformation modepurports to measure the interlaminar shear strength, by three-point flexureof a short beam. The span/depth ratio of the beam is so chosen that thebeam should fail by interlaminar shearing rather than by tensile failure. Inpractice, failure is often mixed mode because the properties vary from pointto point and therefore critical stresses may arise simultaneously at severalpositions; it is not unusual for evidence of tensile failure in the tension faceof the beam, fibre buckling in the compression face of the beam and inter-laminar shear at a mid-plane, all to be found in one specimen. Additionally,the configuration dimensions favourable for shear failure are such that theshear stress prevailing at the instant of failure cannot be calculated withhigh precision or accuracy. Even so, in principle the failure should be eitherat a fibre–matrix interface or in the matrix, and hence the measured valueshould not exceed about 60 MNm-2 for any of the plastics–matrix compo-sites currently available. When higher values than this are reported, it isprobable that some fibres were misaligned and had an orientation compo-nent out of the plane of the laminate, so that the measured breaking forcewas partly attributable to the stretching and possible fracture of some fibres.In such cases the tensile properties should correspondingly be lower thannormal for the particular fibre volume fraction and fibre disposition.

A similar role can be played by uniaxial compression tests, but they arefraught with practical difficulties associated with the transfer of force fromthe actuator to the test specimen. Irrespective of whether the ends of thespecimen are clamped or free, a compromise has to be found between theideal long slender specimen which tends to buckle under axial loading andthe short wide specimen that is mechanically stable but yields data distortedby frictional or mechanical constraints at the thrust plates. Apart from theassociated inaccuracies and imprecisions, the lateral strains are tensile incharacter and can cause phase separation in some composite structureswhen the coupling is weak; axially aligned fibres may become unsupportedcolumns which then tend to buckle with damage developing progressively,whereas under tensile stress the fibres would contribute fully to the strengthand modulus along that axis.

Irrespective of the deformation mode and the anisotropy, elastic modulusis a bulk property and, provided the dimensions of the specimen are much


MTA2 11/22/2000 9:10 AM Page 17

greater than the scale of the inhomogeneity, it is amenable to measurementand calculation. Strength and ductility, to some degree, are ‘local’ proper-ties and therefore susceptible to structural discontinuities; consequently, theproperty values tend to be more variable and the test methods less soundlybased than those for modulus. In particular, the methods used for the measurement of fracture toughness are not entirely satisfactory, mainlybecause the fractures seldom progress as a single crack and the criticalregion (i.e. the crack tip) is of the same order of magnitude as the scale ofthe heterogeneity.

2.3.3 Samples and specimens for mechanical tests

The samples from which specimens are taken for test purposes are usuallyin one of three forms: pultrusions, filament-wound tubes and flat sheets, allof which may be tested in their entirety, or used as a source of smaller testpieces. The first two forms were chosen partly for fabrication convenienceand partly for their correspondence to important industrial productionprocesses.

In pultrusions, the fibres are mainly aligned along the pultrusion axis; infilament-wound tubes the fibres may be aligned circumferentially or alongspirals (often opposed, balanced spirals), and in other filament woundshapes the fibres can be placed to optimum effect. Also, these fabricationprocesses facilitate good consolidation of the structure and relatively void-free end-products.

Commercially produced flat sheets fall into four classes, with radicallydifferent fibre dispositions:

• randomly oriented fibres (mainly random in the plane of the sheetrather than three-dimensionally random)

• layers of uniaxially oriented fibres variously aligned with respect to areference axis

• layers of woven fabric variously aligned with respect to a reference axis• sandwich structures.

The four classes of sheet, the pultrusions and the filament-wound structuresoffer various anisotropy options, ranging from isotropic in the plane toseverely anisotropic and even some reinforcement in the third direction,which relate to a range of downstream composite structures. It is obviouslyimperative that any quoted properties data be qualified by a clear descrip-tion of the volume fraction and spatial arrangement of the fibres in thestructure, substructure, element, subelement or coupon that is tested. Forthe singular case of laminates consisting of unidirectional laminae arrangedwith their fibre-alignment axis varying from layer to layer, which are


MTA2 11/22/2000 9:10 AM Page 18

popular for research purposes, there is an agreed notation which describesthe stacking sequence, see Table 2.2.

The properties of coupons cut from laminates vary with the stackingsequence, the alignment of the specimen axis in relation to the pattern offibre orientation and, to a lesser degree, the in-plane position of the specimen. Some companies (e.g. in the automotive and aircraft industries)have in-house sheet cutting patterns designed so as to minimize the cost of specimen preparation and simultaneously to maximize the informationderivable from each sheet. Local agreements on collaboration sometimesresult in a group of companies adopting the same lamination and sheetcutting patterns. Similarly, the properties of pultrusions, filament-woundstructures and coupons cut from both sources depend on the fibre disposi-tion, but the testing emphasis is on structures (e.g. tubes, small pressurevessels, etc) for which there are special standard tests, rather than coupons,although filament-wound rings are tested in several standardised configu-rations such as diametral compression of an intact ring, flexure of a curvedsegment cut from the ring, torsion of a cut but otherwise complete ring andso on.

2.4 Nature and quality of test data

The factors that have to be considered in assessing the quality of mechani-cal properties data include the following:


Table 2.2. Laminate code.

Guide to the notation Examples of stacking sequence code

Orientation of each lamella is expressed indegrees between the filament axis and the x-axis

Positive angle is clockwise looking towardsthe layup tool surface

Lamellae are listed in sequence, starting from layup tool surface

Successive layers of different orientation are +45,-45,0,90 = +45/-45/0/90separated by/

Subscripts denote repeat lamella orientation +45,-45,0,0,90 = +45/-45/02/90The beginning and end of a code are marked +45,-45,0,90 = (+45/-45/0/90)T

by brackets, after which subcript T 90,0,45,45,0,90 = (90/0/45)S

indicates that total laminate is shown and 90,0,45,0,90 = (90/0/45)S

subscript S indicates that only one half of a symmetric laminate is shown

MTA2 11/22/2000 9:10 AM Page 19

• precision• accuracy• authenticity and typicality• relevance to the test objectives• physical significance.

Precision and accuracy are easily amenable to statistical analysis but arenot unambiguously separable in a small set of data. The last three factorsare not so readily quantifiable because of the possible uniqueness of eachtest coupon, or service item, although experimentation dedicated to par-ticular issues can circumvent that difficulty in principle, if not always in practice.

Similar values of a notional property are generated by replicate tests, butthere is usually some scatter. The resultant distribution of values in a set iscompounded of varabilities related to:

• precision of the measurements• accuracy of the measurements• variations in the structure of the test coupons in the set.

Overall, the interspecimen variability is an indicator of the quality of thedata, but it cannot identify the separate causes unless the test programmehas been specifically designed to do so.

The mean value and a measure of the width of the distribution (e.g. thestandard deviation) characterise the distribution of values in a set of inde-pendent measurements. They constitute only estimates of the mean value,and so on, of the distribution for all members of the population. Alterna-tive characterising indicators are the median and the range. The mediangives less weight to extreme values than the mean does and is thereby asuperior measure in some circumstances; the range is less quantitatively jus-tifiable than the standard deviation as a measure of the variability.

The standard deviation is the square root of the variance, and that is givenby Equation [2.18]:

[2.18]

where s is the standard deviation of a set of results, n the number of specimens in the set and xi the individual values.

The symbol s denotes the standard deviation of the data from the testson a set of specimens, and the standard deviation of the entire populationis usually denoted by s. Apart from their direct role as a measure of thevariability in a set of data, the variance and the standard deviation enableinferences to be drawn about:

sn

xx

nii2 2

21

1=

--

( )È

ÎÍÍ

˘

˚˙˙

ÂÂ


MTA2 11/22/2000 9:10 AM Page 20

• confidence limits for a set of data• reliability of apparent differences between sets of data• combined uncertainty of measurements when there are several sources

of variability• separate variabilities when several factors have affected a set of data• goodness of fit when correlation between a dependent and an indepen-

dent variable is derived.

Variance and standard deviation say nothing about the physical significance of a set of data, the difference between sets, correlations and so on, and in isolation they are likely to be misleading if the distributionof property values is multimodal, because what may then actually be variation would be presented as variability. They are also ineffectual if the criterion of acceptability is a boundary value rather than a mean value, because the number of requisite test results increases disproportion-ately as the probability level approaches the upper or lower limit of unityor zero.

Some experimental and service situations are fraught with both extreme value and multimodality difficulties, as explained later in thissection.

Multimodality arises when the individual specimens in a set do not all respond similarly to the imposed excitation. This is commonly en-countered in certain types of strength test, where the failure may be variously due to shear at an interface, tensile failure in fibres, compressionbuckling of fibres and so on. The overlapping distributions of strengthvalues associated with the different processes can be identified and quantified by several techniques ranging from the construction of simplehistograms to elaborate numerical manipulation, but ideally any such analysis should be supported by visual evidence of the different modes ofbehaviour.

The standard deviation may be converted into confidence limits on themean value via the expression:

[2.19]

where L is the confidence limit for some specified probability level (usually95%), se is the estimated true standard deviation (i.e. s above), n is thenumber of specimens and t is the Student’s t.

t/ decreases as n increases, as shown in Table 2.3 for 95% confidencelimits.

Thus, for example, if the mean value, , has been derived from a set often specimens there is a 95% probability that the true mean value (i.e. froman infinite set of specimens) will lie within the range = 0.715se.x

x

n

± =Ltn

s e


MTA2 11/22/2000 9:10 AM Page 21

Similarly, judgements can be made as to whether an observed differencebetween the mean values from two sets of data are statistically significantvia the calculation of t from the expression:

[2.20]

where

[2.21]

and the suffixes 1 and 2 denote the two sets. Reference to the standard tabulation of Student’s t then gives the level of significance of the observeddifference.

The identification of individual variances when several are affecting theoverall variability in a set of data relies on a procedure referred to, unsur-prisingly, as the analysis of variance.Where there are several influential vari-ables, which may not be completely uncoupled, and where the effects ofeach one cannot be varied methodically and independently of the others(i.e. in the usual industrial situation), it is necessary in the interests of testingeconomy and statistical efficiency that the test programme be appropriatelydesigned.

Correlation coefficients are also limited in what they signify unless they are supported by physical evidence. Lifetime curves (e.g. fatigue and creep rupture data) are particularly challenging because the regres-sion curve is often nearly horizontal. At any particular level of severity the number of cycles or the time to failure is highly variable, typically two decades on a logarithmic scale. A shallow slope tends to worsen thevariability because a small variation in the applied severity converts into a large change in lifetime. The practical concerns are the severity levelbelow which no failures occur, the investment in testing that will enable thatlimiting level to be determined with a high degree of confidence and the

s e2 1 1

22 2

2

1 2

1 12

=-( ) + -( )

+ -n s n s

n n

tx x n n

n n=

-+

1 2 1 2

1 2s e


Table 2.3. Variation of t / with n.

n n n

5 1.24 8 0.84 15 0.5556 1.05 9 0.77 20 0.477 0.93 10 0.715 30 0.37

tn

tn

tn

n

MTA2 11/22/2000 9:10 AM Page 22

risks entailed in extrapolating experimental data to times significantlylonger than the duration of the tests. A nearly flat, featureless regres-sion curve based on unimodal sets of lifetimes observed at different sever-ity levels may suddenly change slope as a second failure mode suddenlyintervenes.

Statistical analysis of data embraces techniques ranging from simple estimates that entail nothing more that mental arithmetic to elaborate calculations requiring modern computing power. The latter are now muchin vogue as a support for scientific experimentation, but they should beregarded with some circumspection because their superiority over the ele-mentary methods rests mainly on their ability to extract more informationfrom scattered data and not on an enhanced ability to provide a rationale.Thus, enhanced confidence limits on a set of data do not in themselvesendow the result with a physical significance, justify an extrapolationbeyond the range of the data, signify that an observed correlation is evi-dence of a causal relationship or imply that other inferences may be drawnfrom the data. That reservation is not intended to discredit statistical analy-sis nor is it an endorsement of the view of a very famous physicist who said,‘If your experiment needs statistics, then you should have done a betterexperiment.’ With regard to the latter, it is undoubtedly true that an elab-orate statistical analysis cannot improve the data derived from a poorly conducted or poorly designed experiment. However, in some instancesimpeccable experimentation nevertheless yields high variability and statis-tical analysis may then be the only route to the extraction of informationfrom the data.

The value of such analysis varies with the circumstances. Commercialbenefits can accrue from minor differences in the properties of competingmaterials but, on the other hand, an observed difference may be statisti-cally significant but physically unimportant and even a perfect correlationdoes not alone signify a causal relationship. Overriding all other consid-erations, however, is the fact that the penalties for malfunction in servicemay be severe. Therefore, validation test programmes for service items orprospective service are necessarily cautious and expensive. Apart from theprecautions that have to be taken to ensure that tests are properly con-ducted, any data that indicate the enhancement of a property must be inter-preted with caution because the advantage of a favourable trend in oneproperty with respect to some independent variable may be completelyoffset by the disadvantage of a simultaneous unfavourable trend in anotherproperty. For example, precise uniaxial alignment of fibres maximises theattainable tensile modulus in that direction but the modulus in a transversedirection, the transverse strength, the torsional rigidity and the interlami-nar shear strength are all adversely affected; the implications for testingstrategy and evaluation costs are obvious.


MTA2 11/22/2000 9:10 AM Page 23

2.5 Mechanical tests for long-fibre composites

2.5.1 Primary properties

An extensive infrastructure of test methods and procedures has had to bedeveloped to support the composites business, but the great variety of com-posite structures, the complexities of the properties, the diversity of serviceapplications and the immediacy of particular commercial pressures haveresulted in the developments often being arbitrary and narrowly specificrather than interconnected elements of a coherent evaluation system. Thus,the particular role of any one test method as part of the testing infrastruc-ture is often obscure, and the test may seem to be merely one of an agglom-eration of methods rather than one of a coherent system. Even a cursoryinspection of the established standard test methods reveals that there areconflicting recommendations for some test procedures, coexisting minorvariants of some methods and some owing more to expediency than toscience. There are also some major omissions from the repertoire of com-monly used tests. Even so, a logical pattern of test procedures and inferen-tial steps can be discerned under the conflicts and confusions of the finedetail, which provides a unifying framework against which any inconsis-tencies and deficiencies can be set in proper perspective. This chapter seeksto set that perspective.

It is generally agreed that a minimum requirement for the assess-ment of the three primary properties of a long-fibre composite (modulus,strength and ductility) are those parameters listed in Table 2.4, or other,very similar parameters. Table 2.4 quite properly stipulates moduli intension, flexure and uniaxial compression, which would provide a super-fluity of tests for an isotropic homogeneous sample, but which are neces-sary for a long-fibre composite sample for the reasons touched upon earlier.On the other hand, the minimum requirement falls far short of compre-hensively quantifying the stiffness and strength tensors, and it neglects theviscoelastic aspects of behaviour. In fact, despite the list giving the minimumrequirement, no single investigating body is likely to carry out all of thosetests as a general routine procedure because various sectors of the indus-try have different objectives for their evaluation programmes. With someoversimplification it can be said that manufacturers of fibres are mainlyinterested in the mechanical properties manifest in fibre-dominated situa-tions (e.g. the properties in tension and flexure of samples containing uni-axial arrays of fibres). Manufacturers of resins tend to rely mainly on thosetests that entail compression and shear modes of deformation, which aresensitive to the quality of the fibre–matrix coupling.The downstream indus-tries need to supplement the data of Table 2.4 with data directly related toservice situations.


MTA2 11/22/2000 9:10 AM Page 24

Several of the properties listed in Table 2.4 might be cited as essentialconstituents in an evaluation of a homogeneous single-constituent ma-terial, and the same test machines might be used for both that class of ma-terial and long-fibre composites. Thus, for tensile and uniaxial compressiontesting, irrespective of the class of material, the primary requirements arethat the testing machine should be ‘axial’ (i.e. the force should act along thelongitudinal axis of symmetry), the specimen should be long and slender,the strain should be measured on a gauge section sufficiently remote fromthe grips to ensure that they exert no influence on the result (i.e. with dueallowance for Saint Venant’s Principle) and, for strength measurements,fracture should occur within that section. The additional stipulations fortests on composites are secondary in nature although important neverthe-less; they include specified minimum dimensions for test bars, to ensure thatthey are larger than the scale of the inhomogeneities and the size of anylikely defect, testpiece grips commensurate with the overall properties andadditional measurements related to the anisotropy, and so on.

In practice, tensile machines are seldom axial, which can severely distorta tensile property datum if the testpiece has a high modulus and/or is notductile. Extensometers tend to slip. Alternatively, strain gauges can inter-fere with the local strain. Testpieces tend to slip from the grips, or breakthere rather than within the gauge length. In addition, specimen size maybe dictated by extraneous factors such as the availability of adequatesamples, the cost of fabrication of test coupons, the load capacity of testmachines and so on. Furthermore, even though the breaking force and


Table 2.4. Primary mechanical properties essentialfor an evaluation of a long-fibre composite.

Tensile modulusCompressive modulus (uniaxial)Flexural modulusShear modulus (in plane)Lateral contraction ratiosa

Tensile strengthCompressive strength (uniaxial)Flexural strengthApparent interlaminar shear strength

Fracture toughnessb (various modes)

a In principle these quantities need not be measuredprovided the various corresponding moduli areknown.b There is as yet no firm consensus about whichdeformation modes are the most informative inrelation to service.

MTA2 11/22/2000 9:10 AM Page 25

ultimate extension of long-fibre composites may be measured accurately,the conversion of those quantities into failure stress and failure strain,respectively, are arbitrary and unreliable procedures because of the het-erogeneity. All that may be claimed is that the notional failure stress andnotional failure strain may be measured precisely.

Flexure is a popular deformation mode for modulus measurementsbecause it requires simpler apparatus and test specimens than tension.However, if the specimen is inhomogeneous, or if the properties vary otherwise through the thickness of the beam, the flexural response to transverse forces cannot properly be translated into a modulus because of the way in which the stiffness of the beam is dominated by the outerlayers.This is generally termed ‘stacking sequence dependence’. In a tensiontest on a composite coupon with a laminated structure the properties of individual layers contribute in parallel and without bias (apart fromtension–shear coupling) to the overall property. The force–deflection relationship defines a notional modulus which reflects the fibre align-ments in the individual lamellae irrespective of the stacking sequence.In a flexure test, on the other hand, the contribution of each lamelladepends on its disposition with respect to the neutral axis and hence thedatum generated in the test is the stiffness of the particular beam ratherthan a modulus.

The practical constraints on the dimensions of specimens in flexural testscorrespond to those implicit in the Bernoulli–Euler elastic beam theory,with modifications necessitated by the high ratio of the Young’s modulusto the shear modulus. The relevant equation for a homogeneous, isotropicspecimen subjected to three-point flexure is Equation [2.22]:

[2.22]

where d is the deflection at the mid-point of the beam, P is the load at themid-point, L is the span, b is the width, h is the thickness, with E and Gbeing the flexural and shear moduli, respectively.

Equation [2.22] is approximately valid for long-fibre composites if the substituted values of the moduli are appropriate for the particularanisotropy. Various modifications to the second term within the brackets(which are multiplying factors not very different from unity) have been proposed to allow for the heterogeneity; but even as it stands, the equationsets an approximate lower limit for the span/thickness ratio if shear is notto contribute significantly to the deflection of the beam. For example, theYoung’s modulus of a unidirectional composite with a carbon-fibre volumefraction of 0.60 may be 120 GNm-2 and the shear modulus may be only 3GNm-2, so that the span/thickness ratio should satisfy the condition:

d = +ÊË

ˆ¯

PLbh E

EhGL

3

3

2

241


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[2.23]

if the shear correction is to be less than 1% of the measured value. Thisratio is higher than the 16 :1 normally regarded as sufficient for an isotropicmaterial. A ratio of 60 :1 is recommended by ASTM (American Society forTesting and Materials) for carbon-fibre reinforced resins. At the otherextreme, the span/thickness ratio is variously specified as between 3 :1 and5 :1 for the short-beam shear test, to favour interlaminar shear failure, butthe high transverse forces that are required to flex a thick beam can causeexcessive distortion or damage near loading points and thereby change theeffective span. The damage can be limited and a tendency for fibres tobuckle out of the compression face of the test piece can be reduced by theuse of larger radii for the loading and support anvils. However, the greaterthe radii, the greater the uncertainty about the effective span, and ASTMD790-86, for instance, recommends that the radii should be no greater thanfour times the beam thickness.

Apart from its uses as an alternative, or as a supplement, to tension,flexure is often the only practicable deformation mode for macrocompos-ite structures such as laminated honeycomb sandwich panels. Local crush-ing and indentation at loading points are a common difficulty with suchspecimens, and flat loading pads usefully replace cylindrical anvils.

The specific details of tensile, flexural and other mechanical tests varyfrom company to company within a country, from country to country andwith the nature of the sample. Most of the variations dictated by the natureof the sample are necessary for technical reasons, for instance, to accom-modate specimens in which the axis of fibre orientation does not coincidewith the stress axis, although others appear to have no more justificationthan casual prejudice. Similarly, the specifications for end-tabs, which havebeen used almost universally to reduce the probability of failure initiatingat the grips during a tensile test, vary widely. End-tabs can also facilitateaccurate alignment of the specimen in the test machine, provided that theyare symmetrical and properly positioned on the specimen, but if they aredeficient in these respects they can cause misalignment and introduce stressconcentrations.

In the absence of systematic evidence to the contrary, one must assumethat the various specified test procedures might yield different values for modulus and strength on specimens of the same composition. Some light was shed on the issue in a paper by Sottos et al.,3 who compared theresults obtained on one fibre–resin formulation in four different lami-nate layups by use of three standard test methods with permitted variants.In the case of tensile modulus and tensile strength there were 17 sets ofdata, with five specimens in each set. The coefficients of variation for the

Lh

2

240100>


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modulus measurements varied from 0.013 to 0.120 with a mean value of0.068. For the strength they varied from 0.041 to 0.140 with a mean valueof 0.075. Such coefficients of variation compare unfavourably with cor-responding data for other classes of material (e.g. thermoplastics and thermosets) but they are similar to the coefficients reported elsewhere forother composite materials. For instance, values of 0.079, 0.080, 0.083 and0.100 were tabulated by Johnson4 for tensile modulus measurements on a polyester resin with four different volume fractions of glass fibre and Owenet al.5 reported even higher levels of variability for sheet moulding compounds. It seems likely that relatively high coefficients of variation arean inherent characteristic of composite materials in general, probablycaused by local variations in fibre volume fraction, fibre alignment and voidcontent.

Sottos et al.3 concluded that ‘with one or two exceptions, the differentstandards do, in fact, give data which are probably not significantly differ-ent’. They did, however, note that the recommended use of only five spec-imens for each data set was barely adequate for discrimination between themean values when the coefficients of variation are at the level found in theirtest programme. Taking the mean values of the coefficients of variation astypical for this type of measurement and on the basis of a normalised dis-tribution, one might expect 95% confidence limits in the region of 0.08 to0.10 for sets of five specimens.

The specifications for the other types of test listed in Table 2.4 are simi-larly varied, and the sparse published information on variability suggestssimilar coefficients of variation, though Sottos et al.3 reported lower meancoefficients of variation of 0.043 for ‘modulus’ and 0.056 for strength mea-sured in flexure. In general, the possible disparities in measured propertyvalues arising from the different specimen dimensions have not been quan-tified, nor, until recently, has there been much advocacy of the merits ofinternational standardisation. It seems that the active groups have a vestedinterest in perpetuating their use of whatever procedures had been adoptedinitially, probably because it enables them to make the best current use oftheir archive data, which are often extensive and which, in the absence ofa science-justified database, are a pragmatic basis for materials selectionand end-product design.

If high variability is an inherent characteristic of fibre–composite materials and if, because of that, the various standard tests do not give obviously different results, except possibly via the generation of large sets of data, there is no reason for them all to be retained unless there areindependent grounds for their retention. On the other hand, by a parallelargument it should not matter if they are retained because the dispari-ties could be largely ignored. Substantial savings in evaluation costs could be achieved if this matter were to be resolved. However, little effort


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is expended on the acquisition of facts about the relative merits of thevarious standard procedures and the comparative variabilities, partlybecause of vested interests and partly because the statistically sound testprogrammes that would be necessary would be costly and rather tedious to conduct.

2.5.2 Engineering properties data

The test programme implied by Table 2.4 has been expanded in scope byarbitrary procedures to satisfy various downstream requirements whichvary from company to company.Table 2.5 lists the tests stipulated by a largecommercial aeroplane manufacturer in the USA as being necessary in the‘initial testing’ phase.

The call for ‘open hole’ tests reflects reservations about the reliability ofthe theories of failure and about the relevance and relative paucity of theempirical evidence from conventional fracture toughness tests. The protag-onists of such tests sometimes seem to be preoccupied with a search forauthentic and/or definitive data which is perpetually frustrated by a pre-ponderance of mixed-mode failures in their experiments. The same is trueof short-beam shear testing. However, since most service failures are alsomixed mode, it may be that the use of data generated through an empiri-cal matching of laboratory configurations to service situations would be abetter option than the use of arbitrary and unreliable data generated in aformally correct way. It could also be argued that a fracture which featuresall possible failure mechanisms indicates that the ultimate properties offibre, matrix and interface were well balanced in the item and were beingfully utilised in the composite structure.

The inclusion of the sixth and seventh items in the list of Table 2.5 is a pragmatic response to the fact that in-service conditions can be arduousand may induce severe deteriorations in the structure and performance thatare not revealed, or implied, by the data generated by traditional mechan-


Table 2.5. Primary engineering properties forpreliminary selection of composite materials.

Tensile strength at room temperatureUniaxial compression at room temperatureInterlaminar shear at room temperature

Open hole tension at room temperatureOpen hole compression at 93°C

Hot /wet compression strengthEdge-plate compression strength after impact at

room temperature

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ical tests. It also compensates for the disparity which exists between theproperties measured in a traditional evaluation programme and the attri-butes that are required of a serviceable end-product.

Apart from the limitations mentioned above, the tests listed in Tables 2.4and 2.5 generate only so-called ‘single-point’ data. These may be useful forquality control and materials selection purposes, but are of limited utilityin design calculations for load-bearing service, for which creep, creeprupture, fatigue and other phenomena are relevant considerations. The pre-viously mentioned partial failure of the composites testing community torecognise that viscoelastic behaviour is likely in some circumstances hasbeen corrected, in that the automotive, aerospace and chemical plant indus-tries demand creep, creep rupture and fatigue data, overlain by informationon the degenerative effects of various environments.

The list of topics of concern to end-users is formidable; the main head-ings of a list emanating from an automotive company in the USA are givenin Table 2.6 as an example.

Despite the inclusion of long-term data in the wants lists, the dearth ofdata in this area of durability persists. This leads directly to a common formof data misuse, namely short-term modulus and strength data being used ina design context of long-term load-bearing capability without an appropri-ate allowance being made for the ‘elapsed time’ effect. The errors are notserious when the fibres dominate the response, because the time depen-dence is then slight, but when the stress field is such that the matrix is influ-ential, the neglect of time dependence may lead to inadequate load-bearingcross-sections and a short service lifetime.


Table 2.6. Primary data and design data as envisaged by the automotiveindustry.a

Elastic and strength properties at various temperatures in the range -40°C to150°C

Effect of loading rate on tensile and compressive properties in the range 1.67 ¥ 10-3 s-1 to 1.67 ¥ 10s-1

Long-term material propertiesb

Environmental effects on long-term propertiesEnergy absorption upon impactManufacturing effectsc

Characterisation of joints and fasteners

a This information is extracted from a document emanating from one companyin the USA, but it is very similar to the data requirements stated by German,French and British automotive companies.b Creep, fatigue, residual strength after fatigue, effect of notches and holes onthose properties.c Properties in ribs, bosses, at knit-lines, etc.

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Because impact is a common service hazard, impact testing featuresincreasingly in evaluation programmes. Current test practices for compos-ites loosely follow the standardised procedures recommended for unrein-forced plastics, but the specimen dimensions and other details of the testconfiguration were chosen either arbitrarily or in attempts to simulate com-monly encountered structural features.

The test configurations are:

• bars in tension• beams in flexure• plates in flexure.

The impact is variously by swinging pendulum, falling dart, driven dart,spring-driven projectile and air-driven projectile, all of which deliver rela-tively low velocity impacts, and do not simulate aggressive service impacts.They do correspond, however, to the casual service hazard of a minorimpact that may cause only slight direct damage but nevertheless leave theitem prone to premature failure by a different mechanism during subse-quent service. There have been a number of notable studies which havecovered quasi-static through to ballistic impact.6

Many of the early impact studies, most notably by Adams7 of the University of Wyoming, USA, made use of the flexed beam methods, butthe flexed plate configuration has now become the more popular. Theformer methods enable the measured quantity to be related to the overallanisotropy of the plate from which the beams have been cut, whereas thelatter almost automatically identifies the easiest failure path and corre-sponds more closely than the flexed beam to the situation prevailing duringa casual impact on a service item. However, the response to impact of aconventional laboratory test piece may, nevertheless, be very different fromthat of a service structure. Apart from a tenuous geometric similaritybetween the flexed plate test configuration and service impacts, a usefulpractical advantage is that the preparation of the test specimens is relativelyundemanding, because results are generally not so sensitive to the qualityof the edges as those from flexed beams.

Various shapes and sizes of specimen, support and impactor have beenemployed and, similarly, so have various impactor velocities and incidentenergies. The use of a circular support constitutes a perpetuation of thegeneral practice that has been established and standardised for unreinforcedplastics. The use of a square aperture seems to have been encouraged bythe manufacturers of test machines in the USA; it may be felt that a squareaperture corresponds more closely than a circular one to the majority ofpanels in service. Another unresolved issue is international standardisationof the size of the aperture, the striker and so on, the details of which stronglyaffect the apparent impact resistance and the mode of failure.


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Each of the dimensional factors affects the stress field at and near thepoint of impact. The analysis for a flexed laminated plate is beset withuncertainties and the theoretical stress field will be distorted by the onsetof even minor damage, so that comparisons between data emanating fromdifferent sources are likely to be unreliable until standardised test practicesare established. Additionally, a distinction has to be drawn between thestrain energy imparted to the entire structure (test specimen or serviceitem), which can be measured, and the local strain energy density initiat-ing and subsequently sustaining the failure processes, which cannot be measured.

Impact tests at low incident energy provide insights into the mechanicsof fracture. The data obtained set the impact resistance of composites inperspective relative to that of other classes of material; for example, in oneof the standard flexed plate configurations an incident energy of 1–2J suf-fices to damage a 16-ply laminate slightly and less than 10 J creates exten-sive damage, whereas in the same test configuration many unreinforcedthermoplastics have impact resistances in the region 60–80 J. The slightdamage incurred in a superficially innocuous impact may weaken a struc-ture directly, by introducing stress concentrators and local weaknesses, orindirectly, through the creation of pathways for the subsequent ingress ofwater or solvents. The mechanical deterioration attributable to the damagemay be assessed in various ways, for example strength in flexure of sand-wich structures, or tensile and compressive strength, but the currentlypopular method is edge compression of a plate.

In that test a rectangular plate is impacted transversely at low incidentenergy and then subjected to in-plane compression by force applied alongone edge. The initial impact, which has not yet been standardised interna-tionally, is such as to produce ‘barely visible damage’. However, that crite-rion is subjective, and the visible damage is known not to correlate well withthe amount of damage as assessed by ultrasonic absorption, or with theresidual strength of the damaged structure. Quite extensive internal delam-ination can occur with no apparent damage at the surface. Therefore, theseveral variants of the ‘damage tolerance test’ all stipulate relatively largeplates to reduce the possibility of the internal damage extending to theedges, and this large size entails edge supports for the plate during the com-pression phase and a large load-capacity test machine.

The collapse load cannot be translated into a specific physical propertybecause practical factors limit the attainable precision in an edge-loadingconfiguration. Also, prior damage can only be known accurately by dissec-tion, and so on. Thus, the test is arbitrary and data emanating from varioussources may not be directly comparable, so that the links between experi-mental data and service performance are tenuous and largely unquantifiedat present.


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The cost of comprehensive evaluations such as that implied by Table 2.6is high and, in consequence, the downstream demand for data is rarely metin full, so that there is some uncertainty over which sector(s) of the indus-try should bear the main burden of the testing. There is a tendency for thedata demands of a user industry to be excessive and, correspondingly, thereis a tendency for information supplied by a materials producer to be thebare minimum and to be selectively biased to the advantage of the partic-ular product. It is likely that the pragmatic compromise that always has tobe achieved is determined more by the politics of the marketplace than byscientific rationalisation. Even so, the financial penalties for using inappro-priate data can be severe. Overdesign is expensive and inefficient. Under-design leads to malfunction, so that reliable design data are a primerequirement for most projects. Those properties tend to be dominated bythe properties of the matrix and the fibre–matrix interface to varyingdegrees.

2.6 Concluding comments

A survey in 1987 of the then-current range of standardised, or semi-standardised, mechanical tests8 concluded that the existing system of standardised test methods was deficient in three respects:

• there were too many variants of some tests and a dearth of hard evidence about the effects of the variations on the reliability of the generated data

• some tests were not fit for their intended purpose• some important phenomena and properties were neglected by the

testing community.

Some tests for modulus and strength were deemed to be fit for theirintended purpose; some (modulus and strength in uniaxial compression,modulus in shear, interlaminar shear strength, impact resistance, fatigueresistance) were deemed marginally or conditionally fit-for-purpose; others(damage tolerance, fracture toughness) were deemed not fit-for-purposeand some (creep, creep rupture) were seldom carried out. This unsatisfac-tory state of affairs was attributed in the report to the fragmented natureof the industry, poor interaction between academy and industry and a col-lective failure to establish an adequate infrastructure. Little has changed inthe intervening years but even so, imperfect though the testing infrastruc-ture might be, each test event contributes a datum to the hierarchy of infor-mation that supports each downstream operation.

An apparent insufficiency of information/data is common to all classesof material, because evaluation programmes may be curtailed by con-straints on costs, test procedures may be inappropriate for the intended


MTA2 11/22/2000 9:10 AM Page 33

purpose and circumstances may be such that direct testing cannot cover therequirement when, for instance, a specified load-bearing lifetime is muchlonger than the allocated product development time. Such testing insuffi-ciencies are common in industry, particularly when the materials are novel,or the applications are innovative, but there is a set of procedures that partlycompensate for them. In general, limited laboratory test data can be‘adjusted’ or extended by one or more of the following procedures to matchthem to the data demands for particular end-products or components inspecific service:

• interpolation between data measured at standardised excitation levelsand ambient conditions

• extrapolation of durability data to longer times than the duration of thetests, or to other frequencies

• acceleration of failure processes by exposure to aggressive environ-ments

• allowance for likely changes of state in an end-product during its servicelifetime.

Provided there is an established justifying rationale, even single-pointdata of the type listed in Table 2.4 can be used in a wider context than thatimplicit in the defined scope of the tests, especially if results can be inter-preted in the light of previously established correlations with service performance.

For long-fibre composites, although adjustment for the fibre volume frac-tion, for the spatial distribution of the fibres and for component size andshape is commonplace via the combination of simple tests and mathemat-ical models, some of the ground rules for the adjustment procedures men-tioned above have not yet been firmly established. Further consolidation ofthe prediction procedures is hampered by the high cost of the enabling testsand the validating stage, by the large number of possible combinations ofmatrix type, fibre type, fibre volume fraction and spatial arrangement, by adearth of certain classes of critical data and by the ineffectual informationpathways available. The ineffectual pathways were identified and remedialaction was proposed in the survey referred to earlier.8

Testing is usually the first stage in the process of the prediction of serviceperformance. However, inaccurate, incomplete or inappropriate test datawill almost inevitably lead to questionable predictions and a consequentialtendency for overdesign in prospective load-bearing structures.

References

1. R Martin, ‘Composite structures: a dual approach to design’, Materials World,1995 3(7) 320–2.


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2. P J Hogg, ‘Designing for creep in composites’, Proceedings of the InternationalConference on Designing Cost-effective Composites, The Institution of Mechani-cal Engineers, London, UK, 15–16 September 1998, Professional EngineeringPublishers, 1998, 93–106.

3. N R Sottos, J M Hodgkinson and F L Matthews, ‘A practical comparison of stan-dard test methods using carbon fibre reinforced epoxy’, Proceedings of the SixthInternational Conference on Composite Materials, Imperial College, London, UK,20–24 July 1987, eds F L Matthews, N C R Buskell, J M Hodgkinson and JMorton, Elsevier Applied Science, London, 1987, Vol 1, 1.310–20.

4. A F Johnson, Engineering Design Properties of GRP, British Plastics FederationPublication No 215/1, 1978.

5. M J Owen, A M Tobias and H D Rees, ‘Design limits for polyester SMCs’,Plastics and Rubber Processing and Applications, 1984 4(4) 349–54.

6. W J Cantwell and J Morton, ‘Comparison of the low and high velocity impactresponse of CFRP’, Composites, 1989 20 545–51.

7. D F Adams and J L Perry, ‘Instrumented Charpy impact tests of several unidi-rectional composite materials’, Fibre Science and Technology, 1975 8 275–302.

8. P J Hogg and S Turner, The Mechanical Testing of Long-fibre Composites:Harmonisation and Standardization in the UK, Report for the Department ofTrade and Industry, UK, January 1988 (Copies are available from Prof. P J Hogg,Materials Department, Queen Mary and Westfield College, London).

Bibliography

1. K A Brownlee, Industrial Experimentation, London, HMSO, 1957.2. C A Dostal (ed), Engineered Materials Handbook, Vol 1: Composites, ASM

International, Materials Park, Ohio, 1987.3. J M Whitney, I M Daniel and R B Pipes, Experimental Mechanics of Fiber

Reinforced Composite Materials, SESA Monograph No 4, Society for Experi-mental Stress Analysis, Brookfield Center, Connecticut, 1982.

4. L A Carlsson and R B Pipes, Experimental Characterization of Advanced Composite Materials, Prentice Hall, Englewood Cliffs, New Jersey, 1987.


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3.1 Introduction

There are a number of subsidiary, but vital, issues that are complementaryto the main activity of mechanical testing. These issues, taken together, con-stitute the preparatory work required to produce test specimens of ade-quate quality. If insufficient attention is given to any of these activities, theresults from a particular test could be invalidated. The following remarksrelate to the use of specimens of high performance composites fabricatedfrom continuous preimpregnated fibres, the subject of this text. The fourstages considered are: laminate production; quality checking; specimenmanufacture; application of strain gauges. The final three stages would, ofcourse, apply to any material.

3.2 Laminate production

Thin sheets, known as laminates, usually 1 or 2mm thick for coupon speci-mens, are manufactured from layers of fibres preimpregnated with partiallycured (if epoxy-based) resin prepreg. The matrix is usually an epoxy, butBMI (bismaleimide) and thermoplastic prepregs are also used. It should benoted that the following discourse relates mainly to epoxy prepregs (owingmainly to their popularity). It should, however, be pointed out that thepreparation of laminates with thermoplastic matrices is in many ways a similar but more straightforward process, because the plastic resin is not required to cure, but simply ‘melts’ at a suitably high temperature andresolidifies when cooled.

A single prepreg layer is usually 0.125 or 0.25mm thick and the fibres areeither continuous and parallel (unidirectional), or in the form of a wovenfabric. The prepreg is supplied as ‘tape’, normally 0.3m wide (but suppliershaving width preferences, woven materials being generally wider than uni-directional products), sandwiched between protective layers of paper orplastic and wound on a reel. If epoxy, the prepreg should be kept in a freezer

3Specimen preparation

F L MATTHEWS

36

MTA3 11/22/2000 9:16 AM Page 36

until it is required; if thermoplastic, low temperature is not a requirementbut it is advisable to store the material in a clean, light-free environment.Shelf-life (for epoxies) is normally around 18 months and will be clearlystated by the supplier; thermoplastics, on the other hand, generally degradevery slowly at ambient temperatures. If the prepreg has exceeded its life-time it can probably still be used for a further six months, at least. However,its suitability should be checked by moulding a test panel, or by checkingthe cure state of the matrix resin using differential scanning calorimetry(DSC).

Appropriate lengths are cut from the reel and placed on top of each otherwith the fibres in each layer oriented relative to one another in a prede-termined sequence. Hand tools, such as a ‘Stanley’ knife drawn against ahard edge, are usually satisfactory for cutting. Fabric prepreg can be cutusing shears or scissors. Where available, a rotary knife or water jet couldbe used. The protective layers are removed before each layer is placed onthat previously laid down, and the layer carefully smoothed out to preventair entrapment. It is essential that the layers are aligned with reference toa datum, since even a few degrees’ misalignment can cause a dramatic effecton mechanical properties. With properly prepared prepreg the edge of theprotective backing sheets can be used as a reference. Care must be takento ensure that twisted or knotted fibre bundles, or prepreg areas contain-ing gaps between bundles, are not included in the laminate.

Following completion of the layup, the stack of prepreg layers is preparedfor curing in the case of epoxies, or consolidation for thermoplastics. Theepoxy resin, which forms the matrix of the composite, is formulated forautoclave curing; the whole curing process lasts several hours and involvesa combination of vacuum, raised temperature (to 120 or 175°C for epoxies,often higher for thermoplastics) and raised pressure.The prepreg layers arecontained within a sealed ‘blanket’ as illustrated in Fig. 3.1.

To prevent the laminate sticking to the base and caul (pressure) plates,the latter can be coated with release agent, or layers of release fabric or apolymeric film are inserted between the plates and the prepreg. A dis-advantage of the second approach is that an impression of the fabric is lefton the surface of the laminate, thus making it difficult to detect the fibreorientation in the surface layers with the naked eye.

As an alternative to autoclave curing it is possible to use a heated press,in which case it is necessary to monitor separately the state of resin gela-tion, or a press-clave. The latter device, illustrated in Fig. 3.2, is placed in aheated press, in combination with a separate high pressure supply and avacuum source.A heated press, with facilities for rapid cooling of its platens,would be used for processing advanced thermoplastic prepregs. Clearly thesize of the laminate that can be produced will be determined by the size ofpress available.

Specimen preparation 37

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Sealingtape

Melinex

Pressure plate

Vacuum bagging material Laminated composite plate Air breather cloth

Peel ply

Vacuum connection

3.1 Arrangement for producing laminates by autoclaving.

Baseplate

Pressure vessel Pressure connectionDiaphragm

Top plateLaminate, etc.FrameVacuum connection

Vacuum connection

Top plate

MelinexBleed clothPeel ply

LaminatePeel plyPerforated PTFE

Peel ply

Frame

Baseplate

3.2 Layout of a press-clave.

MTA3 11/22/2000 9:16 AM Page 38

3.3 Quality checking

The manufacturing process, if not properly controlled, can introduce defectsinto the laminate. Typical defects are voids (small cavities in the resin),delaminations (unbonded areas between layers) or, unusually, longitudinalcracks (lack of bonding between fibre and matrix).

Voids can be caused if the prepreg is not allowed to warm to room tem-perature before laying-up, thus introducing moisture into the prepreg stack.Delaminations can be caused by entrapped air or the inclusion of pieces ofbacking sheet. Longitudinal splitting and delamination can occur in multi-directional laminates as a result of thermal stresses induced during cool-down from the curing temperature.

All the above defects will degrade mechanical properties, particularly in compression, shear and flexure. It is, therefore, important that their presence is detected so that faulty laminates can be discarded.

The standard method of detection is to use ultrasonic C-scan, which isgood at detecting inclusions, porosity and delaminations, or, possibly, X-raytechniques, which can detect through-thickness cracks.

3.4 Specimen manufacture

Specimens, as defined by the relevant standard, or test to be carried out,are cut from the laminates using a diamond-tipped saw. The normal bladehas 600 grit, but a cleaner cut, with less damage to the laminate, is obtainedwith 800 grit. In the latter case the blade can become clogged with debrisand frequent cleaning may be required. Laminates produced by autoclav-ing will have a feathered edge which must be removed.

It is clearly vital that edges produced after trimming, which effectivelyact as a datum for subsequent specimen cutting, are correctly aligned withthe fibres in the layers. A commonly used method for establishing the 0°direction of a cured laminate prior to cutting is to split off a narrow stripof material along this direction (in multidirectional laminates this can bedone if the 0° layer is made slightly wider), but it has been shown that thisapproach may not be sufficiently accurate, and a preferred method1 is tomark the outermost ply by scoring across in the 90° direction in a non-stressed region.

High temperatures are generated during dry cutting, which can causelocal degradation and damage at the machined edge. This can be largelyprevented by the use of a coolant (water), but subsequent drying-out stepsmust be taken to remove any absorbed liquid from the specimen. Gener-ally, specimen blanks are machined oversize, final dimensions beingachieved by grinding.

Drilling is readily achieved with tungsten carbide or diamond tipped bits,


MTA3 11/22/2000 9:16 AM Page 39

the laminate being supported by a (sacrificial) backing plate. It is advisableto use a drill bit tip angle of 55–60° for thin laminates and 90–100° for thicksections, rather than the usual 120°. Other operations are best achieved bygrinding. Clearly, appropriate support is needed for thin laminates ifthrough-thickness shaping is to be carried out. Kevlar fibre-reinforcedmaterials need special attention. Owing to the nature of the fibre it is difficult to avoid a ‘furry’ edge. Specially adapted impregnated wheels canbe obtained for cutting. Another alternative is to use a high pressure waterjet.

For many tests, for example tension and compression, it is often neces-sary to bond end-tabs to the specimen; this is done to diffuse the grippingloads and prevent failure at the specimen ends. According to the particu-lar requirements, the tabs may be of aluminium alloy, GFRP (glass-fibrereinforced plastic) or CFRP (carbon-fibre reinforced plastic). When thetabs are of composite, the preferred method is to stick strips to the trimmedlaminate before cutting into specimens. This approach is not only quicker,but it also ensures alignment of tabs and specimen.When the tabs are metalthis approach cannot be adopted and the tabs must be bonded to indi-vidual specimens, using a jig to give accurate positioning. Surfaces whereend-tabs are to be bonded should be abraded in order to remove surfacecontamination, whilst taking care not to damage the outermost fibres. Thisis done most easily, particularly if the laminate surface is rough, by grit blast-ing, the only objection to this method being that the surface may itselfbecome contaminated, either by grease carried by the grit or embedmentof the grit. Surfaces not needing to be abraded can be protected by maskingwith self-adhesive tape. The grade of grit used, typically 80–120 grade, doesnot appear to be critical if care is taken to avoid excessive abrasion and damage to the composite. The dust left behind on the material after grit blasting is most easily removed by flushing under running water.If the water lies on the surface in an unbroken film, a good standard of surface cleanliness is indicated. The amount of water absorbed by thelaminate will be small, particularly if the material is dried immediately afterwashing.

After drying, the surfaces are solvent wiped and bonded. Commercial‘two-tube’ epoxy resin has been found to be suitable for bonding end-tabsto be used for tests at room temperature and should be applied sparinglyto both bonding surfaces. The joint, when assembled, can be contained in a simple vacuum bag which will apply an adequate clamping force andremove entrapped air. The tab material can be located by using small pegsinserted in notches cut through the tab and test materials. An alternativeto low temperature curing adhesive is to use bonding film which is curedunder elevated temperature and pressure, although in some cases this cancause thermal stresses sufficient to split a 0° laminate. Whatever adhesive


MTA3 11/22/2000 9:16 AM Page 40

is used it should be tough, with a greater failure strain than that of the mate-rial under test. CRAG2 specifies that it should have a shear strength greaterthan 30MPa. Special adhesives would be preferred for fatigue testing orhigh temperature work. An incidental advantage in using GFRP end-tabsis that the material is translucent and any gaps in the glue film can be seenby visual examination. Even if the joint is strong enough to withstand speci-men failure loads, gaps in the glue line can result in uneven stresses in theunderlying composite and cause premature failure.1

The crucial issue when bonding is to ensure that both the specimen andthe tabs are properly prepared. Composites need to be degreased andabraded to remove all traces of release agent transferred during moulding.This procedure should be followed by wiping with a solvent. Similar pro-cedures should be followed when making bonded joints. In addition todegreasing, aluminium alloy tabs need to be etched in chromic acid or phosphoric acid.

3.5 Strain gauging

All mechanical tests will involve the measurement of displacements orstrains, as defined by the appropriate standard. When strain gauges arecalled for, it is important to follow the recommended procedures.The lengthof the gauge may be specified by the relevant standards, but should alwaysbe significantly shorter than the gauge length of the specimen. Compositescan cause particular difficulties not encountered with metals.3

The issues that must be addressed are as follows:

1 High gauge resistances are desirable because high voltages (2–4V) withlow current can then be used; this improves hysteresis effects and zeroload stability.

2 If possible, use gauges with lead wires attached, or solder wires to thegauge before installation; this should avoid soldering damage to thecomposite.

3 Ideally the pattern of the autoclave scrim cloth should be removedbefore gauge installation; this is particularly important if contact adhe-sives are used.

4 Corrections may be necessary to gauge transverse sensitivity effects;errors of over 100% between actual and measured strains can beobtained.

5 Gauges must be precisely aligned; errors of 15% can result from a 2°misalignment. There is no universally acceptable way of ensuring align-ment. The scrim cloth pattern can be misleading. Sometimes C-scan after installation can be useful, or checking with failure surfaces after fracture.


MTA3 11/22/2000 9:16 AM Page 41

6 Dummy gauges are the preferred method for temperature compensa-tion but, again, precise alignment is needed. It is necessary to mount thedummy gauges on an ‘identical’ piece of laminate, with the same orien-tation relative to the fibres as used for the active gauges.

3.6 Summary

In summary, it is essential that careful and consistent procedures are fol-lowed at every stage of specimen production. Failure to do so will throwdoubt on the validity of any data generated.

References

1. P W Manders and I M Kowalski, ‘The effect of small angular fiber misalignmentsand tabbing techniques on the tensile strength of carbon fiber composites’, 32ndInternational SAMPE Symposium, Anaheim, CA, USA, eds R Carson, M Burgand K J Kjoller, Society for the Advancement of Material and Process Engineering, Covina, CA, USA, 1987.

2. P T Curtis (Ed), CRAG Test Methods for the Measurement of the EngineeringProperties of Fibre Reinforced Plastics, Royal Aircraft Establishment, Farnbor-ough, UK, Technical Report 88012, 1988.

3. M E Tuttle and H F Brinson, Resistance Foil Gauge Technology as Applied toComposite Materials, Report No. VPI-E-83-19, Department of EngineeringScience and Mechanics, Virginia Polytechnic Institute and State University,Blacksburg, VA 24061, USA, June 1983.


MTA3 11/22/2000 9:16 AM Page 42

4.1 Introduction

Put simply, the purpose of a tensile test is to determine the ultimate tensilestress (UTS) and tensile modulus (E) of a material, and with additionalinstrumentation Poisson’s ratio may also be measured. However, a closelyobserved test of a material under controlled conditions should provide agreat deal more information about the way it behaves under load. A com-posite may split or delaminate, for instance, and studying the material as itis subjected to increasing load may give an insight into the ways in whichdamage initiates and develops. Finally, the nature of failure is seen; it maybe brittle, with no warning, or it may be preceded by obvious audible orvisible signs. All such information is useful; knowledge of the UTS and the way in which failure occurs is vital if serious use is to be made of thematerial.

Mechanical testing began being carried out on a scientific basis in thesecond half of the nineteenth century when metals were the commonestengineering material. The use of high performance composite materials, asdistinct from ‘reinforced plastics’, as major load-carrying materials beganalmost a century later, and it follows that the test methods initially used totest composites were based very closely on ‘metallic’ techniques. Testing of metals is not a particularly difficult task, being aided by the strain-hardening isotropic homogeneous nature of the material. At its simplest, apiece of stock material can be pulled in a testing machine and fail in its mid-length: locally reducing the cross-section of the testpiece (‘waisting’) canensure that failure occurs away from the grips. The inadequacy of estab-lished tensile testing techniques when used with composites became ap-parent in the 1960s, and emphasised how different the behaviour of composites could be from that of metals. The key differences are that com-posites, by definition, are inhomogeneous and may, as a result of their two-phase nature, exhibit weakness under a particular loading mode, whilsthaving high strength under other modes.Thus a waisted specimen could fail

4Tension

E W GODWIN

43

MTA4 11/22/2000 11:42 AM Page 43

because the low shear strength of the material results in the wider, orthicker, part of the specimen simply shearing away from the body of thespecimen before reaching the tensile failure stress.

The variety of specimens in use at that time is seen in the proceedings ofthe first ASTM (American Society for Testing and Materials) sponsoredconference on testing and design of composite materials (ASTM STP 460).1

These are illustrated in Fig. 4.1. The names given to the designs are evoca-tive (dog-bone, waisted, bow-tie) but the specimens themselves showedvarious failings which have been widely reported. Although in its time theelongated bow-tie was described2 as being the only design of GFRP (glass-fibre reinforced plastic) specimen to fail consistently in the gauge length,that too has become obsolete. The ratio of UTS to ultimate shear strengthwas then roughly 4 :1. By 1974 it had been calculated that, for a ratio of 16 :1 (a value somewhat less than today) a radius of 1000 mm was neededto achieve an acceptable ratio of shear/tensile stresses in the specimen. Theshouldered and waisted designs, which clearly owed their origins to metalstesting, have ceased to be used and, of the geometries in use at that time,only the parallel-sided end-tabbed type remains in use today. The charac-teristics of the tab material may be radically different from that of the testmaterial, being chosen to provide adequate gripping and protection of theunderlying material. This, of course, exemplifies composites design, which isa matter of building up rather than machining down to size. Moreover, theproperties of the material may be varied as required within the thicknessof the material.

It is important to understand that, where composite materials are con-cerned, there are two separate, and possibly distinct aims when carrying out a materials test. The first is to establish fundamental material proper-ties for subsequent use with structural analysis and design techniques.Theseproperties, sometimes referred to as ‘single ply data’, are obtained fromwell-aligned unidirectional fibres loaded in a variety of directions. If thefibres are aligned in the loading direction, this represents something of anultimate test condition where the stresses developed will be higher than ispossible with any other layup of the same fibres; conversely, if the fibres areat 90° to the loading direction, the testpiece is weak and requires carefulhandling. The second aim is to determine the properties, or investigate thebehaviour, of an existing material. This is likely to involve testing materialwith fibres lying at a number of angles to the principal loading direction. Inmany cases this may require a clear understanding of laminate analysistechniques, and of the behaviour of non-axial fibres in a laminate, if sensi-ble use is to be made of the results of the test.

Again, there are two fundamental problems to be addressed in mechani-cal testing, irrespective of the material under test. The first of these is to minimise and, ideally, to eliminate undesirable interactions between


MTA4 11/22/2000 11:42 AM Page 44

the means of load application and the test material. This is particularly relevant in the case of composite materials where loads, frequently very largeloads, have to be introduced into the body of a material through an inherently weak phase (the matrix) without overloading the outer layersof fibres. Depending on the construction of the material, these outer

Tension 45

76.2 R 57.2

12.7 19.1114.3 between grips at start of test

215.9

End of test material 30° bevel ± 45° tab material 4.8 Ø

4.8 Ø

6.4 Ø

6.4 Ø

12.7

12.7

12.7

12.7

69.9 76.2254.0

53.8 6.4 R

19.1

12.7

12.7

19.1

19.1

292.1

57.2 57.2215.9

76.2 R

228.6

45° bevel

50.8254.0

12.7

57.2

31.8 R 6.4

50.8203.2

19.1

(a)

(b)

(c)

(d)

(e)

(f)

(g)

57.2

4.1 Tensile test specimens being used in 1969.1 (a) ASTM D 638plastics specimen; (b) straight-sided, tabbed (Dastin); (c) long-neck, bow-tie (Dastin); (d) tabbed, shouldered, for 90° fibres(Hoggart); (e) tabbed, straight-sided, 0° fibres; (f) tabbed, straight-sided (Elkin); (g) tabbed, dog-bone (Rothman and Molter). R =radius, ∆ = diameter.

MTA4 11/22/2000 11:43 AM Page 45

fibres may account for most of its strength and, because of their position, aresusceptible to damage.The second is that of producing as nearly pure a stateof stress, in this case tensile stress, as possible.Actually, it may be argued thatsuch a stress state is never achieved in practice and that the nearest approxi-mation occurs when a very long, very thin filament is tested. However, asthere is a requirement to test bulk samples of material, then the object ofspecimen design must be to minimise the problems outlined above, whilstproducing the best approximation to a pure stress within the testpiece.

Testpiece specifications and testing procedures are detailed in a numberof published standards, or guides, four of which are summarised in Table 4.1and illustrated in Figs. 4.2 and 4.3. These are ASTM D3039,3 BS2782,4

CRAG5 and ISO 527.6 This is a very small selection from the standardswhich are available, but studying them serves to demonstrate how manydetails vary from one standard to another. They reflect a range of opinionsabout how a specimen should be designed and how a test should be carriedout. It is assumed that tests will be carried out in accordance with one ofthese procedures wherever possible, but situations can arise where, for onereason or another, a standard design of specimen cannot be used. This


±45° composite tabs

15.056.0

1.0 7° (90° optional)1.5(a)

(b)

(c)

(d)

250.0

25.02.0

175.0

1.5

25.0

±45° composite tabs

50.0Edge of grips

15.0 (0° matl.)25.0 (90° matl.)

10.0 (0° material)20.0 (90° material)

250.0



0.5 to 2.0

Composite orlight alloy tabs

50.0 100.0 to 150.0

200.0 to 250.0

0.5 to 2.0

4.2 Current tensile specimens for use with aligned (0° and 90°) fibre-reinforced material: (a) ASTM D 30393 (0°); (b) ASTM D 30393 (90°);(c) ISO 5276 (0°); (d) CRAG5 methods 300 (0°) and 301 (90°).

MTA4 11/22/2000 11:43 AM Page 46

chapter aims to give some background to the reasons leading to one choiceof detail or another, and it is intended that it should act as a guide to atesting technique that will enable valid tests to be carried out in such cases.If excessive reference appears to be made to the ASTM standard, thisshould not be seen as a sign of bias, rather that ASTM generally gives moreinformation than most other standards for the rationale behind details ofspecimen design and testing procedure. Such additional information andguidance are often invaluable to the practitioner, and are a welcome featureof the ASTM standards series, which other standards organisations mightemulate to their own credit.

Whilst the majority of tensile tests are directed towards establishingtensile modulus, ultimate tensile stress and lateral contraction ratio(Poisson’s ratio) under tensile load, simple modifications to the specimenenable a number of other factors to be investigated. Notch sensitivity andbolt-bearing tests are two examples, and the Composites Research Advi-sory Group (CRAG)5 gives recommendations for testpiece dimensions.Tensile loading regimes are also used for two popular forms of shear test.One of these is the lap shear test which, in turn, can be modified to inves-tigate the behaviour of adhesive and mechanically fastened joints.The otheris the ±45° shear test.

Tension 47

Unbonded abrasive cloth tabs

25.0

2.5

250.0

(a)

(b)

(c)

45.01.0 to 10.0

200.0 (min)

25.0 (Strength measurements)

12.5 (Modulus measurements)

3.0 (min)

Composite orlight alloy tabs

20.0 (min)10 t (typ)

50.0 (min) 100.0 (min) or W(1+1/tan�)

�

1.0 to 4.0 0.5 to 2.0

4.3 Current tensile specimens for use with non-0° fibre-reinforcedmaterial: (a) ASTM D 3039;3 (b) ISO 527;6 (c) CRAG5 method 302.

MTA4 11/22/2000 11:43 AM Page 47

Tab

le 4

.1.

Co

mp

aris

on

of

sele

cted

det

ails

of

stan

dar

d t

ensi

le t

est

met

ho

ds.

a

Sta

nd

ard

AS

TM

D30

39B

S 2

782:

par

t 3:

met

ho

dC

RA

G m

eth

od

s 30

0 &

C

RA

G m

eth

od

302

ISO

527

320

E,

EN

61

301

Ap

plic

abili

tyB

alan

ced

sym

met

ric

Co

mp

osi

tes

Un

idir

ecti

on

al fi

bre

-M

ult

idir

ecti

on

al t

ape

or

Fib

re r

ein

forc

ed

com

po

site

s in

corp

ora

tin

g m

at,

rein

forc

ed p

last

ics

wo

ven

fib

re-r

ein

forc

ed

po

lym

ers

‘No

t re

info

rced

wit

h

clo

th,

wo

ven

ro

vin

gs

0°(M

eth

od

300

)m

ater

ials

. M

ust

be

no

rmal

ly s

uit

able

co

nti

nu

ou

s o

r in

clu

din

g p

rep

reg

s.90

°(M

eth

od

301

)ax

ially

ort

ho

tro

pic

.fo

r m

ult

idir

ecti

on

al

dis

con

tin

uo

us

mat

eria

ls’.

hig

h m

od

ulu

s fi

bre

.

Th

ickn

ess

(t)

1.0

(0°

UD

) ±4

%1.

0 to

10.

0 ±

0.5

1.0

±0.

04 (

Met

ho

d 3

00)

1 to

41

±0.

2 (0

°)2.

0 (9

0°U

D)

"M

ach

ined

if

nec

essa

ry2.

0 ±

0.04

(M

eth

od

301

)2

±0.

2 (9

0°)

2.5

(Oth

er)b

"

Wid

th (

W)

15 (

0°U

D)

±1%

25 ±

0.5

for

stre

ng

th10

to

20,

un

ifo

rm9t

min

. 10

tty

pic

al15

±0.

5 (0

°)25

(90

°U

D a

nd

oth

er)

12.5

±0.

5 m

od

ulu

s o

nly

abso

lute

min

20

25 ±

0.5

(90°

)

Ove

rall

len

gth

(L)

250

±4%

(0°

UD

an

d

200

(min

)10

0 to

150

+2L

TG

reat

er o

f (1

00 +

2LT)

150

±1

+2L

Tc

oth

er)

Gau

ge

(fre

e) l

eng

th

or

[w(1

+1/

tan

q) +

2LT]2

Gau

ge

len

gth

50

175

(90°

UD

)11

0m

inIf

q<

15°

L=

(w/t

anq

+2L

T)

Gau

ge

len

gth

10

to 5

0w

her

e q

=fi

bre

an

gle

Tab

len

gth

(L T

)56

(0°

UD

)45

(m

in)

50 (

min

)50

(m

in)

5025

(90

°U

D)

Tab

th

ickn

ess

1.5

No

t le

ss t

han

3m

m0.

5 to

2.0

0.5

to 2

.00.

5 to

2.0

Tab

mat

eria

l0°

/90°

GFR

P, c

om

mo

nly

Sim

ilar

to t

hat

un

der

G

RP

fo

r h

ot/

mo

ist

+/-4

5°G

FRP

reco

mm

end

edap

plie

d a

t +/

-45°

test

con

dit

ion

sE

mer

y cl

oth

(O

ther

)Li

gh

t al

loy

‘sat

isfa

cto

ry’

for

amb

ien

t co

nd

itio

ns

MTA4 11/22/2000 11:43 AM Page 48

Tab

en

d7°

or

90°

(0°

UD

)90

°90

°90

°90

°(9

0°U

D)

Tab

ed

ge

7m

m

wit

hin

gri

ps

Test

ing

sp

eed

Failu

re w

ith

in 1

to

10

mm

min

-1(r

ou

tin

e To

cau

se f

ailu

re w

ith

in

2.0

mm

min

-1(0

°)10

min

, o

r st

rain

te

sts)

30 t

o 9

0s

1.0

mm

min

-1(9

0°)

rate

=0.

01m

in-1

, o

r 2

mm

min

-1fo

r d

isp

lace

men

t =

det

erm

inat

ion

of

2m

mm

in-1

elo

ng

atio

n/m

od

ulu

s

Gri

ps

Sel

f-al

ign

ing

S

elf-

tig

hte

nin

g

Hyd

rau

lic p

refe

rred

reco

mm

end

edsu

gg

este

d

Bas

is f

or

0.1–

0.3%

ch

ord

Lin

ear

po

rtio

n o

f cu

rve

0–0.

25%

ch

ord

0–0.

25%

ch

ord

0.05

–0.2

5% c

ho

rdm

od

ulu

s25

–50%

ult

imat

e st

rain

or

tan

gen

t o

r se

can

t re

com

men

ded

calc

ula

tio

nif

ult

imat

e st

rain

at

‘re

qu

ired

lev

el o

f b

ut

no

t m

and

ato

ry<0

.6%

stra

in’

No

tes

No

t ap

plic

able

to

m

ater

ials

wit

h

un

idir

ecti

on

al

rein

forc

emen

t: u

se

ISO

527

aA

ll d

imen

sio

ns

in m

m.

bU

D =

un

idir

ecti

on

al fi

bre

s, ‘

oth

er’

=b

alan

ced

sym

met

ric

or

ran

do

m-d

isco

nti

nu

ou

s re

info

rcem

ent.

c10

0 ±

1 +

2LT

for

fila

men

t w

ou

nd

tes

t p

late

s.

MTA4 11/22/2000 11:43 AM Page 49

4.2 Testing equipment

4.2.1 Testing machines

There are two classes of testing machine: those which apply a deadweightload to the testpiece, generally by hydraulic means, though formerly usingweights and levers, and those which induce a load by applying a controlleddeflection to the testpiece using a jack. It is important to appreciate the dif-ference between the ‘soft’ characteristics of load control and the ‘hard’loading provided by displacement-controlled loading. When the specimenweakens, under displacement control there will be a fall in load, whereasunder load control an uncontrolled failure will occur as the machine triesto maintain load on a weakening testpiece.This can be dangerous and tendsto preclude study of the mechanics of failure. Servohydraulic machinesallow either of these loading regimes to be applied, as well as offering the availability of fatigue, programmed, strain-controlled and high-rateloading, but their high cost and relatively limited working distance tend tomilitate against them as a choice for general testing work. This leaves thescrew-jack type of machine in a pre-eminent position. Certainly the use ofthis type of machine is assumed in most standards, which specify loadingrate in terms of displacement per unit time.

The mechanical side of testing machines (grips, loading frames, etc.) hasnot changed greatly over the years. The same cannot be said of control anddata-logging equipment, of which the latter would now be expected to becomputer-based, and the former may also involve extensive use of micro-electronics. Testing machines are robust and do not normally wear outquickly. Their replacement cost is high, so a large amount of older equip-ment is still in use. It is, therefore, appropriate to assume that the reader ofthis chapter may not necessarily be using ‘state-of-the-art’ testing machines.Whilst microprocessor control can offer a wider range of control optionscompared with older machines and computer data logging greatly facilitatesdata acquisition and subsequent data reduction, much testing is still carriedout using machines with a limited range of testing speeds and data may stillbe recorded only on a paper chart.

4.2.2 Data acquisition

Typical standards require that the load indicating system should have anaccuracy of 1% or better, and should be ‘substantially free from inertia’,3 aclear reference to mechanical chart recorders. Current equipment, usingcomputer-based data acquisition systems, does not suffer from inertia assuch, but the rate at which data are collected is important. Unless datapoints are collected at a suitable rate, important information may be lost in


MTA4 11/22/2000 11:43 AM Page 50

the interval between points. It is not uncommon to find that the maximumload displayed (instantaneous measurement) and the maximum loadrecorded for a test can vary by much more than 1%. A sophisticated data-gathering algorithm might be expected to adjust the rate of data collectionin conjunction with varying rates of change in load or strain, and so on.Most testing machine software is intended to be used in routine testing andpermits automatic calculation of information such as elastic modulus, andstatistical analysis of the results. However, it is often found that such systemsare not particularly suitable for research work or other non-routine testing.If a pen recorder is used, or if stress and strain data are to be taken manu-ally from a printed graph, it is advisable to scale the load and strain axes sothat the graph has a gradient of roughly 45°, as this will give the greatestprecision of measurement on each axis.

4.2.3 Grips

Composite materials are usually gripped using some form of ‘friction grip’,where the load is transferred to the specimen through gripping faces whichare roughened with serrations or a cross-cut pattern. A fine-scale roughen-ing is recommended for use with composites in order to spread the grip-ping force over the largest possible area and to minimise damage to thespecimen. An alternative, if only coarse grips are available, is to interposeabrasive covered cloth between the grip face and the specimen. In the eventof grips having to be specially manufactureds for use with composites, therecommended methods for producing a gripping surface are to use eitherspark erosion or an electrodeposited abrasive surface.

Parallel clamping grips, positively closed by manual or hydraulic means,allow the operator to control the gripping force on the specimen. Ideally,this should be no more than is necessary to grip the material under test untilmaximum load is reached. It has been observed in composites compressiontestpieces that an excessive clamping force distorts the outer fibres of thetest material at the edge of the end-tab, causing a reduction in failure load,7

and the same may be found to apply to tensile tests. On the other hand,insufficient force will permit the specimen to slip, which generally leads tothe surface in contact with the grip being torn off. This material then fillsthe serrations of the grip, with the consequence that no increase in clamp-ing force is sufficient to grip the specimen, which has then to be removedand the grip surfaces cleaned. The position of the specimen can be adjustedboth laterally and transversely. By attaching micrometer heads to the bodyof the grips it is possible to adjust the position of the specimen, relative tothe axis of the machine, with a high degree of accuracy.

Wedge grips, sometimes referred to as self-tightening grips, have grippingfaces which slide on inclined planes, so that the gripping force increases with

Tension 51

MTA4 11/22/2000 11:43 AM Page 51

axial load. Such grips are widely recommended, although there is a body ofopinion (including ISO 527)6 which regards the lack of control over thethrough-thickness clamping force as undesirable. It has also been observedthat worn wedge grips can allow the jaw faces to slide at different rates,resulting in very large and undesirable shear stresses and a consequent ten-dency to bend the specimen. This should not happen if the alignment pins,specified by some standards, are used. An advantage with wedge grips isthat the small gripping force at the start of a test can allow the testpiece tomove slightly and thus correct any initial misalignment.

4.2.4 Alignment

The lack of any yielding mechanism in composites means that even smallmisalignments, and the resultant bending, may result in large local stresses,so that accuracy of alignment is important if reliable results are to beobtained. It has already been noted that misalignment can be caused byinadequate grips. Alignment of the grips relative to each other is deter-mined by the machine on which they are mounted. Testing machine manu-facturers adopt one of two approaches to this. One is to mount the grips asrigidly as possible in a stiff testing frame and thus ensure that alignment is‘built in’ to the machine; the other method is to mount one of the grips ona universal joint and allow it to self-align. Which method is preferable isprobably a matter of personal choice, as neither is without its faults. Thefirst requires that the machine should be built, and as importantly, main-tained, to a high standard of accuracy. Maintenance of accuracy may not beeasy to guarantee after the machine has seen a large amount of service, par-ticularly in view of the large loads to which it is likely to have been sub-jected. The second method may give a false reassurance of accuracy, asalignment may be hampered in practice by friction in the universal joint,whilst flexibility in the load path may encourage a tearing failure across thespecimen.

Alignment of the testing machine can be checked using the method recommended by ASTM3 and ISO6. A specimen 25mm wide (Fig. 4.4) is instrumented with three strain gauges, two of which are positioned at theouter edges of one face, whilst the third is in the centre of the reverse face.If alignment is perfect, all three gauges will give the same reading. Bendingof the specimen, as a result of misalignment, causes differences between theoutputs of the gauges. To eliminate any effects resulting from misalignmentof the gauges, the specimen should be loaded in four positions. Starting withthe initial position (1) these are: (2) rotated back-to-front only; (3) rotatedend-for-end only; and (4) rotated back-to-front and end-for-end. The per-missible limit for bending is that the sum of 4/3 the strain difference acrossa face plus the strain difference between the face and the mean strain


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should be less than 3%6 or 5%3 of the mean strain. ASTM3 recommendschecking alignment during modulus tests by the use of back-to-back transducers.

Bending of the specimen will also occur if the fibre layers are not equallyspaced, for instance as a result of poor consolidation, when the effectivestiffness of the material will vary through its thickness, resulting in bendingunder tensile load.8 A similar effect may occur if the form of reinforcementvaries through the thickness of the material; in these cases strains shouldbe measured on both faces of the material if the modulus is being determined.

4.2.5 Strain measurement

The choice of strain measurement technique is normally between exten-someters and strain gauges, both of these methods having their advantagesand disadvantages.

The major problem with contacting extensometers, as far as the specimenis concerned, is that, in order to minimise errors, point contact is required.This is generally achieved on a flat specimen by the use of curved knife-edges and the concern is that high contact stresses may damage the outerfibres of a composite and lead to premature failure. It follows that contact

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W

W/2

L

W/8

L/2

SG 1 &SG 2

SG 3

Strain gauge 1Strain gauge 3Strain gauge 2

4.4 Specimen recommended by ASTM D 30393 and ISO 5276 forchecking test machine alignment.

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forces should be kept as low as possible consistent with avoiding slippage.It is necessary to support the weight of any but the lightest clip gauge,because allowing it to hang from the specimen is likely to cause bendingand impose relatively large contact stresses. Extensometers built into thetesting machine avoid this problem. To avoid damaging the extensometerit should be removed, or released from the specimen, prior to failure, as thesudden, almost explosive, release of the large amount of elastic energystored by many composites specimens can easily wreck even the mostrobust extensometer, as could be imagined from Fig. 4.5.

Two-axis extensometers are available which measure lateral contractionfor Poisson’s ratio determination, but it should be noted that the lateralstrains concerned may be very small. Poisson’s ratios of less than 0.01 are not uncommon in composites. Non-contacting extensometers are also available. These avoid any contact damage and are sufficiently remotefrom the specimen to allow them to be used up to failure, but may not have sufficient resolution for use with stiff testpieces. A new generation ofnon-contacting extensometers, based on video technology and digital signal


4.5 Explosive failure of aligned unidirectional (0°) carbon-fibrereinforced plastic (CFRP).

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processing, appear to offer solutions to many problems connected withextensometry.

The alternative to the extensometer is the electrical resistance straingauge. The magnitude of change in resistance is generally about twice themagnitude of the strain change causing it, but even so it will be clear thatvery small resistance changes are being considered and they are generallymeasured using a form of Wheatstone bridge circuit. Strain gauges aredesigned and calibrated for use on specific metals, which means that errorswill result when they are used on composites.These are described in detail,9

and referred to in Chapter 3, but a summary of possible errors is given here.Although the major sensitivity of the gauge is along its length, there is

also a small sensitivity to transverse strain, which is allowed for during man-ufacture, by calibration to suit the Poisson’s ratio of the metal on which thegauge would normally be used. Inaccuracy will occur when the gauge is usedon other materials, especially composites, which can have very differentvalues of Poisson’s ratio, dependent on layup and testing direction relativeto the fibre directions. This error can be compensated for if the gauge iscalibrated against an extensometer on a sample of the material on which itis intended to be used.The calibration will, of course, vary considerably withthe orientation of the gauge relative to the composite.

Humidity and temperature changes leading to differing strains betweenthe composite and the gauge itself can be minimised by the use of ‘dummy’gauges, mounted on material identical to that under test and in the sameatmosphere, in one arm of the bridge circuit. Self-heating of the gaugearising from the voltage drop across it, when in use, can also cause prob-lems. Although this is small, the area available for heat dissipation is alsosmall, and the resultant power density can be surprisingly large.This heatinggives rise to spurious ‘apparent strains’, which should eventually reach anequilibrium condition. The problem is less apparent on materials with goodthermal conductivity, but ‘thermal drift’ remains a problem when straingauges are used on composites. If a pulsed power supply is not used, theproblem can be alleviated by using high resistance gauges (350W andabove), excited with as low a voltage as possible (typically 1 to 2V), and byusing gauges with an active length of at least 3mm, and preferably 6mm ormore, to give as large an area as possible for heat dissipation. Large gaugesare preferable anyway as they are easier to align, and average out localstrain variations. The latter can be important on material with a woven orbraided reinforcement where strains may vary over the weave pattern. It isrecommended that at the very least one repeat of the weave pattern shouldbe covered by the gauge.An analysis of the problems to be considered whenstrain gauges are used with such materials is available.10 Local strain varia-tions have also been known to cause premature failure of strain gauges.Correct alignment of the gauge is important, and it has been shown9 that

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significant errors can be caused as a result of careless application of strain gauges to composites. Although it is unlikely to be relevant to mostcomposites, strain gauges can significantly reinforce weak or low modulusmaterials.

Strain gauges are available as single gauges, or in ‘rosettes’ aligned at 30°,45° or 90° to each other, either closely spaced or stacked. It is left to theuser to decide whether or not the benefit of accurate alignment outweighsthe possible thermal problems resulting from using stacked gauges.

To avoid damaging the composite when attaching leads to the straingauge, it is advisable to solder flying leads to the gauge before bonding itonto the test material. To ensure a good bond between the composite andthe gauge, the area may be lightly grit-blasted, or manually abraded, whilsttaking care only to abrade the resin-rich outer layer, and not to damage thefibres.The latter method is likely to be ineffective if the surface of the mate-rial is excessively rough. In extreme cases it may be necessary to fill thesurface with resin before attaching strain gauges.

Despite all the problems outlined above, it should be stressed that straingauges are still an effective way of measuring strains, often the only prac-tical method on complex structures, and are an accepted method of strainmeasurement on coupon tests. They are preferred by CRAG,5 because theygenerally give more reliable results than extensometers. Although straingauges remain attached to the specimen up to failure, it may be found thatthey themselves fail before the failure strain of the composite is reached.They present a simple means of detecting bending of the specimen by moni-toring the outputs of gauges positioned on each face of the material.

4.3 Specimen details

4.3.1 General

A typical specimen is shown in Fig. 4.6, with related nomenclature. Thenomenclature is not necessarily universal. The term ‘gauge length’, forinstance, is used by many sources for the region given here as ‘free length’.It is a pity that this term is not more widely used, since it would then allow‘gauge length’ to define the distance between extensometer contact points.The terms ‘testpiece’, ‘test coupon’ and ‘specimen’ are often used inter-changeably, although there is an implication that ‘testpiece’ and ‘specimen’are generic terms, whilst ‘coupon’ refers specifically to a sample cut fromexisting material.

Any testpiece, or specimen, should be representative of the body of mate-rial from which it is removed. It should include a region of uniform stressover which strain measurements can be made (the gauge length) and inwhich, it is hoped, failure will occur. As far as this chapter is concerned, this


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failure should be in a recognisably ‘tensile’ manner. The material should beflat, at least if fundamental materials properties are to be determined,although, where ‘industrial type’ laminates are concerned, it may be neces-sary to test the material ‘as supplied’. Tensile specimens typically lie in therange 10–30 mm wide with a length of 200–250 mm, the narrowest speci-mens being used for unidirectional material. The specimen should be longenough to avoid end effects (i.e. effects caused by load discontinuities asso-ciated with the region of load introduction, in accordance with SaintVenant’s Principle). ASTM D30393 recognises this by adding twice thewidth to the gauge length (but there is an ambiguity here, and it appearsthat what is meant is free length). Specimens with a woven or braided rein-forcement must be wide enough to contain a reasonable number of unitcells of the reinforcement. Where high strength materials, or thick samples,of ‘real’ laminates are being tested, the size of the specimen may be limitedby the maximum load capacity of the testing machine.

In order to avoid failure at the ends of the specimen, where loads areapplied, end-tabs are generally used to protect and reinforce the material.We have already seen that waisting and other machining of the testpieceare discouraged. Through-thickness machining is only applicable, in anycase, for material with unidirectional reinforcement, because such machin-ing of a multidirectional material would alter its effective composition.Even unidirectional material is altered to some extent by the removal ofthe resin-rich outer surface, and machining is also likely to damage the out-ermost remaining fibres of the specimen. In practice, it appears that theformer effect predominates. The earlier version of CRAG method 300 useda specimen waisted through the thickness. This was found to give highervalues for strength and stiffness than other methods using unwaisted test-pieces11 and, apparently to avoid this inconsistency, the specimen has beensuperseded by an unwaisted design.

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'Square-ended' end-tab

End tab thickness

Gauge length

Tapered end-tab

Thickness

Width

Tab bevel angle

Freelength

End tablength

Widthwise waisting

Shoulder

Through-thicknesswaisting

4.6 Tensile specimens and nomenclature.

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4.3.2 Dimensions

It has already been mentioned that unidirectional material is generallytested in order to obtain fundamental laminate properties. It follows fromthis that the material is generally prepared specifically for this purpose andmay be manufactured to any chosen thickness which, in general, is as nearas possible to either 1 or 2 mm. Too thin a laminate may give unrealisticresults because the resin-rich surface means that the material will be rela-tively thick per layer of reinforcement. If too thick a laminate is used (i.e.a laminate containing more plies), its strength may exceed that of the adhe-sive joints between the specimen and end-tabs. A thick specimen is alsomore likely to suffer from poor consolidation and hence from the problemswith bending referred to in the literature.8 Multidirectional material is oftenthicker than unidirectional and may, in some cases, require machining to afinished thickness. BS 27824 specifically refers to this by setting a maximumspecimen thickness of 10mm, stipulating that anything greater than thisshould be machined down to 10mm and that material should be removedfrom one face only. Through-thickness machining of testpieces is a con-tentious matter, as it may alter the effective composition of the material, ifonly by removing the resin-rich layer which normally exists on the surfaceof composites. There is also the possibility of residual stresses within thematerial being released, leading to undesirable distortion of the specimenafter machining.

Edge effects are unlikely to affect the behaviour of unidirectional mate-rial, and a relatively narrow testpiece may be used.The recommended widthhas commonly been 10mm but there is now a tendency towards 15mm,which is the dimension specified by the current versions of both ASTMD30393 and ISO 5276. For transverse properties (i.e. unidirectional lami-nates tested in the 90° direction), the width in both cases is 25 mm with aspecified thickness of 2mm. Such specimens are delicate and susceptible tobreakage when being handled, which no doubt in part accounts for thelarger recommended dimensions.

When samples are machined from material with a multidirectional rein-forcement, the specimen geometry may be determined by the layup itself,needing to be wide enough to contain a representative sample of the rein-forcement. Multidirectional reinforcements can also give rise to through-thickness tensile stresses at free edges, so that the width of the specimenshould be sufficient to ensure that the region affected is only a small pro-portion of the total width. It is difficult to find definitive advice when thematerial to be tested contains angled fibres, but the CRAG5 recommenda-tion that some angled fibres originating under an end-tab should run to thefree edge of the testpiece appears likely to give a conservative resultbecause, in practice, such fibres are likely to be more constrained. Woven


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and braided materials are special cases of multidirectional laminates andthe specimen should, at the very least, be wide enough to contain a rea-sonable number of weave repeats, although it is likely that a width of 30mm would be more than adequate in this respect. More serious problemsare likely to come as a result of fibre waviness and edge effects. Becausewoven and braided materials contain out-of-plane fibres, severe edge effectscan be encountered leading to through-thickness stresses which are capableof causing delamination at the specimen edges.

The testing of laminates with fibres at angles of other than 0° and 90° isbeset with problems. It is necessary to take great care when the results arebeing interpreted, and a good understanding of laminate analysis tech-niques is required, especially if few or no 0° fibres are present. Materialswith mat or continuous strand reinforcement, being relatively weak com-pared with unidirectional material, present few problems in testing.

4.3.3 End-tabs

Although not universally specified, end-tabs are used on the vast majorityof specimens. Their purpose is to provide a compliant gripping surface, tofeed loads into the underlying test material, and to protect the outer fibresof the specimen. During the evolution of composites specimen design,various materials have been used, including stainless steel, aluminium alloyand composites in various forms. The requirements are that the materialused should be soft enough to be indented and firmly gripped by the jawsof the test machine, whilst being strong enough to transfer load into thebody of the specimen. This suggests a combination of shear strengththrough the thickness, with sufficient axial tensile strength. The tab shouldnot be so stiff as to prevent natural deformation of the specimen. Stainlesssteel is no longer specified (as it used to be by the ASTM) and the choicenow is between aluminium alloy and composite. The most common tabmaterial is probably E-glass laminate, although CRAG5 suggests using light alloy except when testing in hot, moist conditions. The significantadvantage of composite tabs over metallic versions is that they and the specimen can be co-machined to size, which is far easier than bonding individual tabs to premachined specimens, and generally results in a betterfinished testpiece.

There is no satisfactory common cutting process which can be used onboth soft metal tab material and composite. Specimens with composite end-tabs can be prepared by bonding, with an appropriate adhesive, strips ofend-tab material (once properly described, if rather grandly, in BS2782 asparallelepipedic strips of material) to the test material before cutting, seeFig. 4.7. Attaching tabs in this way, rather than individually after cutting,helps to maintain them in good alignment. End-tabs with 0°/90° fibres are

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easily produced using commercially available laminates with woven rein-forcements, material widely used in the electronics industry. Some standardsorganisations specifically refer to this tabbing material as ‘printed circuitboard substrate’.

ASTM at one time specified that the inner plies of composite tabs shouldbe aligned with the outer layers of the specimen in order to avoid unwantedshear stresses, but the most recent version of ASTM D 3039,3 in commonwith the current ISO 527,6 has revived the use of end-tabs with reinforce-ment at ±45°. Use of such a material is not mandatory; for instance, it is permissible to use material identical to that under test.ASTM D 30393 spec-ifies the use of unbonded abrasive tabs when testing material with non-unidirectional reinforcement, see Fig. 4.8.

The reason for specifying the relatively inconvenient ±45° material, whichmust be either layed up specifically for this purpose or cut (with consider-able waste) from 0°/90° woven material, is that it imposes less constraint onthe specimen in both the longitudinal and lateral directions. It has been sug-gested12 that there is a decreased tendency for unidirectional specimens tosplit when tested using ±45° tab material. An improvement in measuredstrength of 18% was also reported when specimens with taper-ended ±45°tabs were compared with others having square-ended 0°/90° tabs.

The use of end-tabs which finish abruptly at their inner end (referred toas square-ended or 90° bevel-ended tabs) is often criticised for introducing


4.7 Specimen preparation. End-tab material has been attached to apanel of the test material. The waste section (foreground) showspegs used to align the tab material. The trimmed specimen(background) is instrumented with a biaxial strain gauge rosette.

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a stress concentration into the testpiece, and to alleviate this various ‘soft-ening’ techniques are used. The traditional method is to finish the ends ofthe tabs with a shallow bevel. ASTM3 currently recommends tabs with abevel end of 7° to 10° where wedge grips are used, square-ended tabs beingacceptable with non-wedge grips; ASTM add the rider that use of the spe-cified tabs ‘does not guarantee success for every existing or future materialsystem’. ASTM used to recommend the almost universal use of tabs bev-elled at 5° but it has been found that strain mismatch at the tip of the tabcan induce peeling stresses large enough to detach the tab, frequently takingwith it the outermost fibres of the specimen,13 as shown in Fig. 4.9. This isa case where a preconception, based on metals experience (i.e. the gradualchange of section to minimise stress concentrations), fails to apply whenused with composites. The ‘square-ended’ tab, as well as being simpler tomanufacture, gives better results. Even so, there have been attempts to‘soften’ the transition between the tab and the body of the specimen. For-merly, BS 27824 recommended that some 5mm of the tab should be allowedto protrude beyond the edge of the grips, the idea being that the unclampedportion of the tab would be more compliant than the portion held withinthe grips.

This contrasted with other standards, CRAG5 for instance, which specifythat the edge of the tab should be level with the edge of the grip. This isfine in principle but fails in practice because many testing machine manu-facturers chamfer the last few millimeters of the grip jaws so that the degreeof softening, if any, is entirely dependent on the design of the jaws. In viewof this it is perhaps surprising that only recently has the practice beenadopted of gripping the specimen with the tab-end a specified distance

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4.8 ASTM D 30393 specimen of 9-ply, 90°/0° CFRP. The specimen hasfailed in the centre of the free length, an ideal failure.

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inside the jaws. In the case of ISO 5276 this distance is 7 mm, whilst ASTM3

requires that the grips extend 10–15mm beyond the beginning of thetapered portion of the tab. This method provides no softening at all but is,at least, reproducible.

4.4 Test procedure

Before the test is commenced, details of the material should be recorded,including fabrication details (stacking sequence and cure cycle), resin, fibrevolume fraction, fibre details (type, manufacturer, diameter, surface treat-ment, etc.). If the specimen has undergone environmental conditioning, thisshould be described, together with details of the testing environment. Thetesting machine should be described, giving details of calibration date, grip-ping equipment, data-acquisition method and associated details. Details ofstrain measuring equipment or, if strain gauges are used, gauge factor, size,resistance and so on should be given.

The dimensions of the specimen can then be measured, normally takingan average of three readings each of width and thickness. The opportunitycan also be taken to examine the quality of the specimen; those with ob-vious notches or other machining damage should be discarded. ASTM D30393 specifies the use of a ball-ended micrometer for thickness measure-ment, with a flat-anvil instrument to be used for width measurements, andrecommends that the accuracy of the micrometer should be within 1% ofthe dimension being measured, which typically equates to ±2.5mm, where


4.9 Early ASTM D 3039 specimen design (5° tab tip) in 8-ply 0° CFRP.The tapered end-tabs have detached owing to peeling stresses atthe tip of the tab. The through-thickness stresses were sufficientlyhigh to detach the outer layer of carbon fibres.

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thickness is concerned. The principle that accuracy in testing should beginwith the measurement of the testpiece is excellent but, in practice, this isperhaps an excessively high degree of precision, and immediately promptsthe (unresolved) question as to what allowance should be made for therough resin-rich surface found on many laminates. ISO 5276 requires theuse of a micrometer reading to 0.02 mm, a common toolroom standard.

Whether such measuring equipment is used in practice or not, clearly itis necessary to use a device which will give a similar standard of accuracy,whilst not exerting sufficient force to deform the specimen. Calipers andmicrometers with an electronic digital display are becoming popular, if onlybecause they are easy to read without taxing the eyesight, but perhaps theiruse should not be encouraged, because they do not have a fixed zero reference and, therefore, despite having adequate precision, do not give aguaranteed standard of accuracy. Having taken such care with measure-ment, it may be found that the standard requires measured stresses to be ‘normalised’ (i.e. scaled) to the value that would have been obtained ifmaterial of a specified nominal thickness had been tested.

After measurement and inspection, the specimen can be mounted in thegrips. If one of the grips is articulated, this should be tightened first toprevent the specimen being subjected to large bending and twisting loadsduring tightening. Care should also be taken to avoid axially stressing thespecimen whilst the grips are being tightened. ISO 5276 requires that anyinitial prestress should cause a strain of no more than 0.05%. The centre-line of the specimen should be aligned with the axis of the testing machineso as to eliminate bending and asymmetric loading. If an extensometer is being used, this should be attached to the centre of the specimen and the initial gauge length measured. A small preload may be applied to thespecimen before the extensometer is attached. Adequate guards should beplaced round the specimen, or test machine, if there is any possibility of anexplosive failure. The test can then be commenced.

It used to be customary to specify loading rate in terms of testing machinespeed (grip separation rate). Low speeds were not recommended in theinterest of avoiding creep effects (if not boredom on the part of the operator), whilst high speeds were believed to lead to inaccuracy owing toviscoelastic effects. A problem that arises when specifying testing rate inthis way is that the relationship between machine speed and the rate at which the specimen is extended is unknown, owing to lost motion in the machine, slippage of wedge grips and so on. It has been estimated thatthis can result in an actual strain rate 10–50 times lower than that calcu-lated from the machine speed.3 It has been the custom of the CRAG5

guides simply to require that failure should occur within a specified time(30–90s), with the preferred time being at the lower end of the range. Thelatest version of ASTM now also specifies a time-to-failure, in this case

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1–10min – a radical difference from CRAG. This is given as a preferredalternative, the other options being a displacement rate of 2mm min-1

or a strain rate of 0.01 min-1. ISO 5276 specifies a displacement rate of 2mmmin-1 for the testing of laminates with unidirectional (0°) reinforce-ment and 1 mmmin-1 when testing material with 90° reinforcement.

4.5 Data reduction

4.5.1 Stress–strain curve

The stress–strain curve shown in Fig. 4.10 includes all the features likely to be found in a loading curve, including evidence of changes in stiffness,progressive failure and so on. Many composite materials, particularly if they contain a large proportion of 0° fibres, have substantially linearstress–strain characteristics, but it is not uncommon for the curve to shownon-linearities at the start of the test. This is generally dismissed as beingdue to the specimen ‘settling down’ in the grips, machine backlash beingtaken up, slippage and so on.

The value of the load–displacement curve should not be underestimatedhere for, whilst it gives little information about specimen behaviour, it cancontain useful information about such anomalies as gripping problems. Inthe days when data were recorded on paper charts, it was common toproject the lower (linear) end of the load–displacement curve back to theaxis and establish a false origin which could then be used as a basis forelastic modulus calculation (generally using a secant modulus at 0.0025strain), but the practice of discarding the lower portion of the curve in thisway is not now encouraged.


0.25% tangent

B

0.05%–0.25% secant

% StrainA

Str

ess

0.1 0.2 0.3 0.4 0.5 0.6

CD

4.10 Tensile stress–strain curve showing typical detail.

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4.5.2 Elastic modulus

Three options are available when calculating the elastic modulus from anon-linear loading curve. The first of these is to take the modulus as beinga tangent to the initial part of the curve, the second is to construct a tangentat a specified strain level and the third is to construct a secant (‘chord’ inASTM) between two points given as A and B in Fig. 4.10, and typically atstrain values of 0.0005 and 0.0025,6 or 0.001 and 0.003.3 [It should, perhaps,be noted here that there appears to be no universal agreement on the termused to express the value of a strain. Absolute values (e.g. 0.0025 strain) are becoming more common but, in the interests of avoiding decimals, theuse of either microstrain or percentage strain is useful, in which case theequivalent value is expressed as 2500 mstrain or 0.25% strain, respec-tively.] Modulus values are given in these cases as ‘initial tangent modulus’,‘B% tangent modulus’ and ‘A%–B% secant (chord) modulus’, respectively.The use of computer-aided linear regression methods may be allowedinstead of a two-point basis for calculating these values.6 If the material isbrittle and fails at a strain of less than 0.006, ASTM D 30393 recommendsusing a strain range of 25–50% of the ultimate.

4.5.3 Poisson’s ratio

Poisson’s ratio can be calculated, if longitudinal and transverse strain dataare available, using the same upper and lower strain limits used for themodulus calculation. Transverse data are generally low in value and may beseriously affected by spurious signals (noise) in the instrumentation. In thiscase, taking the ratio of regression fits to the graphs of transverse and lon-gitudinal strain, which are obtained using simple computer graph-plottingsoftware, should give reliable results.

4.5.4 Failure

Other information available at the conclusion of a test is the failure modeof the specimen and the location of failure. It is normal to regard failureswithin the end-tab, shown in Fig. 4.11, or within a specified distance of thetab, Fig. 4.12, as being influenced by the grips, and therefore invalid. ASTM3

requires that the method of load introduction into the material should bere-examined if a significant number of failures occur in this way. BS 27824

requires that specimens which have slipped in the grips, broken in or within10mm of the grips, or given ‘manifestly inconsistent results for evidentreasons’ should be discarded and replaced, whilst CRAG5 requires thatspecimens should fail ‘in the central region’ to be valid for design purposes.It is generally taken that if all the specimens tested fail at, or close to, the

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4.11 Early ASTM D 3039 specimen (5° tab tip) of 8-ply, 0° CFRP,showing failure within the end-tabbed region, leading to splittingof the specimen.

4.12 CRAG5 method 302 specimen in woven CFRP, showing failureclose to the end-tab.

grips, the stresses obtained should be treated as ‘lower-bound values’. Thepractice of disregarding such failures is a contentious one, carrying as it doesthe suggestion of censorship of undesirable results, and it would seem to bebetter to adopt the practice given in ISO 5276 which requires a statementin the test report about whether any test specimens have been rejected andreplaced, together with the reasons for doing so.

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ASTM D 30393 recommends using a three-part code when describingfailures, where the first part indicates failure type (splitting, edge delami-nation, explosive, etc.), the second part indicates the failed area (in thegauge length, under the tabs, etc.) and the final part gives the location (top,bottom, left, right, etc.). Since it is possible to observe a variety of failuremodes in apparently identical specimens from the same material, or evenwithin a single testpiece (see Fig. 4.13), and also quite common to observefailure at more than one place in the specimen, it is important that fulldetails of failures are given when the results are reported. It should also bemade clear whether ‘failure stress’ refers to the first observed drop in load(point C in Fig. 4.10) or to the stress preceding complete failure (point D).It is normal to present data for each specimen (maximum stress, modulus,etc.) and not uncommon to include stress–strain data for each test. A morecomplete list of information to be included in the report is given in ASTMD 3039.3

4.6 Material and sample preparation

Sample preparation is covered elsewhere in this book (Chapter 3) but, atthe risk of repetition, it is worth stressing those aspects which are particu-larly relevant to tensile testing.

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4.13 CRAG method 302, quasi-isotropic specimen. One face shows 45° failure (upper), the opposite face shows transverse failure(lower). The light appearance at the edge of the end-tab isevidence of partial debonding.

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If the material is being prepared specifically for the determination ofaligned fibre properties, then great care should be taken to ensure correctalignment of the fibres. Misalignment of fibres relative to the specimen axis,shown schematically in Fig. 4.14, results in a reduction in the effective widthof the testpiece, and it has been shown that a misalignment of 1° can reducethe measured strength of a unidirectional laminate by over 30%.12 Mis-alignment of the specimen within the testing machine, or grips, leads to theeffect suggested schematically in Fig. 4.14, and has a less significant effecton strength, but also leads to high scatter. The results of these effects areshown in Fig. 4.15.

Note that cutting a testpiece so that its fibres are misaligned relative tothe test axis is not the same as loading a testpiece with a similar misalign-ment. The former case results in a reduction in the effective width of thetestpiece whilst the latter may largely be alleviated by compliance in thetestpiece, the testing machine and (as already noted) the testpiece self-aligning as it settles in the grips.


Effectivewidth

4.14 Schematics showing the effects of a 1° misalignment of thespecimen in the test machine (left) and a 1° error in machining(right), showing reduction in effective width.

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The major advantage of using composite tabs has already been men-tioned, namely, the ability to co-machine the tabs and test material. Machin-ing is most easily carried out using an abrasive-edged cutting wheel whichcan be used dry with suitable dust extraction facilities, or water lubrication.Dry cutting may be criticised because of the risk of overheating the mate-rial, whilst an objection to wet cutting is the possibility of moisture absorp-tion. It is important that the cut edges are free from notches and othercutting damage, and they may need to be finished by manual abrasion or agrinding operation. Early versions of ASTM D3039 recommended cuttingthe testpiece 3 mm oversize, before grinding to the finished width, but thelatest recommendation is that final dimensions are reached using ‘water-lubricated sawing, milling or grinding’.

Figure 4.16 shows how the strength of a specimen is affected by thequality of surface finish. Manual abrasion here consisted of nothing more

Tension 69

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ned

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mis

alig

ned

with

wed

ge g

rips

Test

ed 1°

mis

alig

ned

with

hyd

raul

ic g

rips

4.15 Effects of misalignment on measured strength.

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than rubbing the specimen edges on coarse (80 grit) aluminium oxide paperuntil all cutting marks were removed, a relatively crude and quick process.320 grit silicon carbide paper is recommended by CRAG.5 Manual abrasionhas been shown elsewhere13 to give an improvement of some 20% in mea-sured strength. It is sometimes stated that polishing the edges of a speci-men in this way ‘increases the strength of the specimen’, although in factwhat has been observed is a reduction in the decrease in strength causedby cutting. Edge polishing should be carried out carefully to avoid radius-ing the edge of the specimen, or introducing local variations in width, bothof which may lead to increased scatter in test results.

4.7 Practical example

A panel was layed up from eight plies of unidirectional Hexcel T300/914carbon/epoxy prepreg, taking care to maintain the fibre alignment. Whencured, the material was end-tabbed to the then current ASTM D3039-76 specification using woven GFRP (0°/90° alignment), machined with a 5° bevel on the outer edge. Five specimens were cut and tested using a displacement rate of 5mmmin-1. Strains were measured using an


2000

1000

Ulti

mat

e te

nsile

str

engt

h (M

Pa)

As

cut

Abr

aded

Gro

und

04.16 Effect of surface finish on specimen strength.

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extensometer with a gauge length of 150 mm. Individual results are listedin Table 4.2.

Three things are significant here. The first is the large variability in theresults as shown by the standard deviations, over 10% in the case of failurestress.The second is the variety of failure modes, four being apparent in fivetests. The final point is that the highest ultimate stress was given by a test-piece in which the test material did not fail. This emphasises the need totest more than one sample. Should this result be considered in isolation, itwould normally be regarded as a lower bound value as the test material didnot fail. Set in the context of four other tests, it is clear that this particularsample happened to be taken from an unusually strong part of the panel.Of course, if all five testpieces had not failed properly, then it would be validto regard the set of tests as giving only a lower bound result. Incidentally,if there is a certain vagueness in the descriptions of the failures, this isbecause it is often impossible to identify the exact point of failure, and thesudden release of load as the specimen fails can cause secondary failureselsewhere in the testpiece.

4.8 Future developments

The design of test specimens continues to evolve. Often this is because tech-niques that were formerly adequate fail to work satisfactorily with new,higher strength materials. We have seen end-tabs with square ends, 5° and7° bevel ends, in a variety of materials from stainless steel to ±45° compos-ite. Stainless steel tabs attached with cyanoacrylate adhesive were once usedwith specimens waisted in width and thickness, true descendants of the fully

Tension 71

Table 4.2. Tensile test results for a unidirectional (0°) CFRP.

Specimen Failure stress Elastic modulus Failure mode and locationnumber (MPa) (GPa)

1 1618 125.8 In tab region at one end andcracked across 10mm fromother tab

2 1760 138.4 End-tabs peeled off, nomaterial failure

3 1364 122.1 Failed at centre of gaugelength

4 1541 146.2 Failed close to end-tab5 1391 138.7 Specimen split, likely end-tab

failure

Mean 1535 ± 164 143.2 ± 10

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machined metal specimen. Waisting is currently out of fashion, althoughthere has been a tentative revival of through-thickness waisting. The splitting-off of the outer plies inherent with these specimens is regarded aseffectively resulting in a specimen with integral end-tabs.

All these details, together with width, thickness, testing rate and so on,have been specified by published standards at one time or another. Speci-fications are often accompanied by a clause to the effect that ‘tests whichare carried out on specimens of different dimensions, or on specimens whichare prepared under different conditions, may produce results which are notcomparable’.6 Two questions are prompted by this. First, if these details areso important, how can they be allowed to vary between standards? Second,if results are only valid if comparisons between materials are made withina single method, what exactly is being measured? Over 100 years ago DavidKirkaldy, who pioneered the scientific approach to mechanical testing,believed that the objective of testing should be to produce ‘Facts not Opin-ions’, and he had the phrase carved above the entrance to his testing labo-ratory.14 Yet it seems that where composites are concerned, opinions abouthow a test should be conducted may frequently obscure the facts of mate-rials behaviour.

Now that the preferred form for the test material is, almost universally,a parallel-sided strip, the only significant changes that can be made to thetestpiece are the details of the end-tabs. As these are intimately involved inthe transition from the various forces at the end of the testpiece to the stressin the gauge length, it seems logical that work should continue towardsunderstanding, and then minimising any adverse influences between thetabs and the testpiece. Preliminary experiments15 suggest that radiusing theinner edge of the tab may successfully reduce stresses at the tab tip.Anotherfactor to be investigated is the effect of an unbonded area at the end of the tabs.

A radical alternative to the traditional specimen for gaining single-plystrength data has been described.13 Rather than all unidirectional material,the test material consists of nine layers of fibres laid alternately at 90° and0°, with 90° fibres on the outside. The 0° fibres are thus protected fromdamage, whilst it is claimed that the cross-plied material is more represen-tative of real composite structures. The ASTM D 30393 ‘multidirectional’specimen shape, with unbonded abrasive end-tabs, was used (Fig. 4.8). Theequivalent unidirectional strength is calculated simply by multiplying thestrength of the cross-plied laminate by the ratio of unidirectional and cross-plied Young’s moduli, the strains to failure being common to both. It wasdemonstrated that this method gives a higher value for strength, with lowerscatter compared with the traditional ASTM fully unidirectional specimen.Whether this technique becomes adopted as a standard method remains tobe seen.


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Current specimen designs have attracted criticism because they do notsatisfy the criterion that ‘a specimen can characterise a material only whenminor changes in dimensions do not result in a change in failure mode ormeasured strength’.13 Some standards organisations are adopting a less dog-matic attitude towards specimen design, to the degree that ASTM3 nowdescribes it as being ‘to a large extent an art rather than a science’. Yet thefinished specimen will be used as part of a scientific investigation of mate-rial behaviour, with none of the freedom of opinion often implied by ‘art’.There remains a driving force to examine current test procedures, to analysewhat is and is not essential, to simplify specimen manufacture and, mostimportant, to evolve test procedures which produce results which aredependable in characterising the material under test, preferably without theneed to adhere to a rigidly defined test method.

References

1. Proceedings of the First Conference on Composite Materials:Testing and Design,ASTM STP 460, New Orleans, LA, 11–13 February, 1969.

2. S Dastin, G Lubin, J Munyak and A Slobodzinski, ‘Mechanical properties and test techniques for reinforced plastic laminates’, Proceedings of the FirstConference on Composite Materials: Testing and Design, ASTM STP 460, NewOrleans, LA, 11–13 February, 1969, 12–26.

3. ASTM D3039M, ‘Standard test method for tensile properties of polymer matrixcomposite materials’, American Society for Testing and Materials, 100 BarrHarbor Drive, West Conshohocken, PA 19428, USA, Vol 15.03, 1997.

4. BS 2782: Part 3: Method 320A-F, British Standards Institution, UK, 1976.5. P T Curtis (ed), CRAG Test Methods for the Measurement of the Engineering

Properties of Fibre Reinforced Plastics, Royal Aircraft Establishment, Farnbor-ough, UK, Technical Report 88012, 1988.

6. BS EN ISO 527 Part 5, Tensile Test for Unidirectional FRP Composites, 1997.7. J Haeberle, ‘Strength and failure mechanisms of carbon fibre-reinforced

plastics under axial compression’, PhD Thesis, Imperial College, London University, 1992.

8. C Zweben, W S Smith and M W Wardle, ‘Test methods for fiber tensile strength,composite flexural modulus, and properties of fabric-reinforced laminates’, Pro-ceedings of the Fifth Conference on Composite Materials: Testing and Design,ASTM STP 674, New Orleans, LA, ed SW Tsai, 1979, 228–62.

9. M E Tuttle and H F Brinson, ‘Resistance-foil strain-gage technology as appliedto composite materials’, Journal of Experimental Mechanics, 1984 24(1) 54–6.

10. S T Burr, P G Ifju and D H Morris, ‘A method for determining critical straingage size in anisotropic materials with large repeating unit cells’, ExperimentalTechniques, 1995 September/October, 25–27.

11. N R Sottos, J M Hodgkinson and F L Matthews, ‘A practical comparison of standard test methods using carbon fibre reinforced epoxy’, Proceedings of theSixth International Conference on Composite Materials and Second EuropeanConference on Composite Materials, London, Elsevier Applied Science, 1987.

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12. P W Manders and I M Kowalski, ‘The effect of small angular fiber misalign-ments and tabbing techniques on the tensile strength of carbon fiber compos-ites’, 32nd International SAMPE Symposium, Anaheim, CA, eds R Carson, MBurg, K J Kjoller and F J Riel, SAMPE Covina, CA 1987, 985–1007.

13. L J Hart-Smith, ‘Generation of higher composite material allowables usingimproved test coupons’, 36th International SAMPE Symposium, 1991.

14. Carved above the door of Kirkaldy’s Testing and Experimenting Works, 99Southwark Street, London, 1873.

15. K Bultheel, ‘Factors influencing the behaviour of tensile tests’, Eupoco MSc Dissertation, The Centre for Composite Materials, Imperial College, London,UK, June 1999.


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5.1 Introduction

Most lightweight structures and substructures include compressionmembers, which may be loaded in direct compression, or under a combi-nation of flexural and compressive load. The usual design process for light-weight structures attempts to introduce loads as pure compression and puretension. The flexural loading of framework or sandwich constructions, forexample, is transformed into essentially pure compression and tensionloading of struts or facings. Composite materials are especially adaptablefor such designs owing to their high orthotropy.

The axial stiffness of compression members can only be controlled by thecross-sectional area. It is, therefore, proportional to the weight.The bendingstiffness of axially compressed struts or panels is of particular importance,since in-service buckling must normally be avoided. This stiffness can bealtered by geometric means, for example, the use of tubes rather than rods,sandwiches rather than plain plates, corrugation or the deployment of T-stiffeners.The stresses in a member of a given geometry can only be reducedby increasing the effective cross-section under load. It follows that high spe-cific stiffness and strength in both tension and compression are desirablefeatures for the ideal lightweight construction material. Fibre-reinforcedplastic matrix composites are particularly valued for their high tensilestrength. However, the comparatively low compressive strength of somecomposites, for example those reinforced with aramid fibres, reduces theirpotential applications.

Ideally, fibrous composites would fail in compression using the full poten-tial of the reinforcement. However, high modulus, highly anisotropic carbonand organic fibres are relatively weak in compression compared with inter-mediate modulus carbon or glass fibres. The ratio of compressive to tensilestrength is low for the highly anisotropic fibres, but the compressive strengthof glass fibres is probably higher than their tensile strength. For all this, theexperimental evidence shows that the compression failure of composites

5Compression

F L MATTHEWS

75

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containing fibres of high compressive strength is dictated by fibre bucklingrather than fibre compression failure.

Early attempts to predict microbuckling failure of composites modelledthe fibres as plates on an elastic foundation and significantly overpredictedthe critical stress. More recent non-linear models have been developedwhich fit the experimental data, making use of reasonable boundary con-ditions and input data.There is, however, no universal model which predictscompressive failure from the properties of the constituents. The situation iscomplicated by the difficulties surrounding the experimental determinationof compressive strength for a given composite system and the mechanism(s)responsible for triggering compressive failure.1–4

It is probably fairly easy to be cynical about the results from many ‘round-robin’ exercises, but the spread of results obtained has a cause or causes,one of which is usually the difficulty in performing the particular testmethod at all.A relatively recent round-robin into the compression strengthtesting of composite laminates5 was conducted with the cooperation ofseven European laboratories, each using their own testing procedures.The influence of composite production was eliminated by each labora-tory manufacturing one batch of material to be shared with the other six participants. Figure 5.1 shows the results sorted into categories of materials tested. If one wished to use this chart as a data base, it quicklybecomes apparent that literally any compressive strength within the meas-ured range could be assigned to any of the material systems examined.The range of results encompasses a factor of 2 for almost all of the systems.

An alternative way of presenting the data is shown in Fig. 5.2, where theresults are sorted into categories of the participating laboratories. A defi-nite trend is now apparent, with the test results revealing a high dependenceon the laboratory carrying out the test. Some laboratories generated gen-erally higher results than others throughout the range of materials tested,even though all of the laboratories were known to be experienced in com-pression testing of composites and used standard test methods. It is clearthat the test results are dependent on individual local testing practice, whichincludes parameters such as test method, actual testing experience andspecimen preparation techniques.

5.2 Types of test

There are three basic methods of introducing a compressive load into aspecimen, as illustrated in Fig. 5.3: direct loading of the specimen end,loading the specimen by shear, and mixed direct and shear loading. Directloading of the specimen end, as specified for instance in ASTM (American


MTA5 11/22/2000 1:00 PM Page 76

Society for Testing and Materials) D695M-91,6 is not suitable for highstrength composites. Because of the low transverse and interlaminarstrengths of these materials the specimens fail by end crushing, oftenreferred to as ‘brooming’, and/or longitudinal splitting.

Shear loading of the specimen end, which is usually tabbed in the samemanner as for a tension specimen, is the most common method. Shape,material and precision of the end-tabs are likely to infuence the failuremode and strength result.

One of the first fixtures to be developed using this principle is known asthe Celanese fixture, which has its origins at the Celanese Research Center.7

The specimen is held in conical wedge grips which are accommodated intapered sleeves. An outer cylinder maintains alignment of the parts. Whenload is applied to the sleeves it is transmitted to the specimen by shear,through friction between the specimen and the grips. A schematic diagramof the arrangement is shown in Fig. 5.4(a), with Figs. 5.5(d) and 5.6(b)showing the assembled and disassembled jigs. This fixture needs careful

Compression 77

2000

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0

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4

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76

T40

0/63

76

HTA

7/63

76

HTA

7/98

2

IM40

0/52

45

5.1 Test results from a European round robin on compressionstrength testing of carbon-fibre reinforced plastics (CFRP), sortedinto categories of material. �, lab 1; �, lab 2; �, lab 3; �, lab 4; �, lab 5; �, lab 6; �, lab 7.

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2000

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lab 1 lab 2 lab 3 lab 4 lab 5 lab 6 lab 7

5.2 Test results from Fig. 5.1 sorted into categories of participatinglaboratories. �, T800/5245; �, T800/924; �, T800/6376; �, T400/6376; �, HTA7/6376; �, HTA7/982; �, IM400/524.

Transverse load

Direct end loading

Shear loading

Mixed shear/direct loading

5.3 Load introduction methods for compression tests.

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adjustment to the thickness of the specimen if non-uniform load distribu-tion on the cones is not to lead to distortion of the sleeves and friction withthe outer cylinder. If precise overall specimen thickness dimensions are notadhered to, the conical wedges form a line contact with the outer sleeves,resulting in jig/specimen instability and, consequently, lower bound strength values.

A fundamental modification of the Celanese fixture was developed bythe Illinois Institute of Technology Research Institute (IITRI).8 Here, flat-

Compression 79

5.4 Diagrammatic representation of (a) Celanese, (b) IITRI jigs.

(a) (b) (c) (d)

5.5 Several compression test jigs, fully assembled and on the samescale: (a) IITRI, (b) ASTM D 695 (modified), (c) ICSTM, (d) CRAG(Celanese).

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(a)

(b)

(c)

5.6 Several disassembled compression jigs with specimens mounted,not to same scale: (a) IITRI, (b) CRAG (Celanese), (c) ASTM D 695(modified).

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sided tapered grips, which fit into matching pockets in massive steel blocks,are used rather than conical ones, so that specimens of different thicknessescan be easily accommodated. The steel blocks are aligned by pillar guidesand linear bearings. A schematic diagram of the IITRI jig is shown in Fig.5.4(b) and the assembled and disassembled jigs are shown in Fig. 5.5(a) and5.6(a). The weight of this fixture, at approximately 250N, does reduce theease of use quite significantly.

Wyoming University modified Celanese fixture9 uses trapezoidal wedgegrips similar to the IITRI fixture. This approach leaves the jig far less sus-ceptible to the problems caused by specimen thickness variability, to whichthe original design using conical shapes is subject. It should be noted thatin all the above-mentioned fixtures the specimen end is loaded through-thickness in order to generate the shear load.

A typical representative fixture for mixed shear and end loading is theconfiguration originally proposed by Purslow and Collings and later modi-fied by Port10 at what was the Royal Aircraft Establishment (now known asthe Defence Evaluation and Research Agency, DERA, Farnborough, UK).The specimen is bonded into slots in aluminium end-blocks, shown sche-matically in Fig. 5.7(b). The amount of shear loading depends on the prop-erties of the adhesive as well as on the thickness of the bond layer.

In the modified ASTM D 695 method,6,11 load is applied in a similar wayas shown schematically in Fig. 5.7(a), with the assembled and disassembledjig and specimen being shown in Fig. 5.5(b) and 5.6(c). A certain amountof the load is introduced to the specimen by shear through the end-tabs,depending on the stiffness of the tabs and bond layer. An additional align-ment device is recommended. Although the specimen requires carefulpreparation, parallelism of the specimen ends being particularly important,and the test jig is of remarkable simplicity, cheap to manufacture and easyto use. Owing to the transverse constraint of Poisson’s deformation, thespecimen may experience some transverse loading which, in turn, leads tofriction between the support faces and the specimen.

A variation of the RAE method is the fixture developed at BirminghamUniversity.12 Here, an RAE-type specimen with a waisted gauge section isclamped within steel cubes at its ends rather than being bonded, as shownin Fig. 5.7(c). Thus, the specimen end is loaded directly and a portion of theload is transmitted by shear, depending on the clamping force. Mounting ofthe specimen is very simple.

A further refinement of the Birmingham jig has been developed at Imperial College in London, UK.13 In addition to some modifications to the blocks in which the specimen is located, the whole fixture is placed in a four-pillar die set, thus ensuring good alignment. The fixture is shown in Fig. 5.5(c) and Fig. 5.8. Again, mounting and demounting of thespecimen is very simple.

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5.3 Standards

Of the methods referred to above, some have been adopted by the variousstandards organisations. The Celanese jig, in slightly modified form, is spe-cified by the German standard DIN 29971 and by CRAG (CompositesResearch Advisory Group).14 The method is adopted within the ASTM D3410 standard15 which, in addition, also embraces a version of the IITRI testjig. Of the others only the ASTM D 695 method,6 originally established for


(a) (b) (c)

5.7 Diagrammatic representation of (a) ASTM D 695 (modified), (b) RAE, (c) Birmingham test arrangements.

Die set

Upper grip

Testpiece

Side restraint

(optional)Clamping block

Clamping screws

Lower grip

(exploded view)

Hardened and ground

loading plate

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0/990° GRP

2

Dimensions

(in mm)

Ground flat

Strain gauges

1 2 10

40width 10

1.7

Standard specimen Improved specimen

Weakly bonded

area

(e.g. PTFE tape)

5.8 Imperial College (ICSTM) jig.

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unreinforced plastics, has been taken up, but with a modification to the specimen.

There are, of course, many company standards. The Boeing Aircraft Cor-poration use the modified ASTM D 695 and British Aerospace use theirown variant of the wedge action-type of fixture. Figure 5.9 shows this jigpartially disassembled. This jig combines features of the Celanese andIITRI fixtures and can be regarded as a synthesis of the two jigs. The IITRIwedge grips are contained in Celanese-type circular tapered sleeves. Theouter cylinder which aligns the sleeves is an open frame rather than a closedshell, allowing access to the specimen. Quick release retaining pins easehandling of the jig.

On the international scene, much work has been done in the develop-ment of an ISO standard for compression. This will be known in the UK asBS EN ISO 14126, indicating that it is adopted not only as the internationalstandard but also has European and British status. Crucial elements of thisnew standard will also be adopted within the ASTM D 3410.

5.4 Specimen preparation

Specimen preparation is covered in more detail in Chapter 3. However, afew points are worth re-emphasis here. In order to ensure repeatability,special attention must be paid to the preparation of the specimens and a

Compression 83

5.9 British Aerospace compression jig, a variant of the Celanese testmethod.

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consistent procedure should be adopted.This includes laminate production,together with a quality check using, for example, ultrasonic C-scan, machin-ing of the specimens from the laminate in the correct orientation to thefibre direction, moisture conditioning, measurement of dimensions andapplication of strain gauges.

When using tabbed specimens the preferred approach is to adhere thetab material to the laminated panel before cutting individual specimens.This should ensure correct alignment of the end-tabs and hence minimisethe effects of eccentric loading. The need to prepare the laminate and tabmaterial properly prior to bonding cannot be overemphasised; failure to doso could well result in premature failure. Where the tab material is a fibre-reinforced plastic, the above approach is relatively straightforward andcutting of the specimens poses no problem. However, cutting the laminatewith metal end-tabs preadhered is not really an option; it is necessary tocut specimens from the laminate and then attach the end-tabs individually.Even greater care must then be taken to ensure correct alignment betweenspecimen and end-tabs.

A typical assembly procedure when composite end-tab material is usedis illustrated in Fig. 5.10 and a prepared plate is illustrated in Fig. 5.11. Inthe latter, surfaces ‘a’ and ‘b’ are made square and at right angles by cuttingon a diamond saw bench. It is not always necessary to grind surface ‘a’ but


End-tab Adhesive layerSilicone rubber shim

CompositeDouble-sidedadhesive tape

Adjustable alignment blockFlat ground plate

5.10 Laminate/end-tab plate assembly.

Surface 'a'

Surface 'b'

Surface 'c'

5.11 Plate ready for cutting into individual specimens.

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if the specimen is to be end loaded, these surfaces must be as flat and par-allel as possible and machine grinding becomes, in effect, mandatory. Thewhole plate can be dealt with in a single operation. In order to removemachining defects, surface ‘b’ should also be ground. It might be possibleto do this manually by rubbing individual specimens on different grades ofemery paper secured on a flat surface. However, best results in terms ofdimensional tolerances will be achieved by machine grinding. Surface ‘c’should be dealt with in a similar way to surface ‘b’.

Where they are to be used, strain gauges should be affixed to both facesof a specimen. This allows comparative strains to be measured through-out the test and gives an early indication of any specimen bending (macrobuckling).

5.5 Specimen configurations

There are three basic specimen types: short unsupported gauge length, longsupported gauge length and sandwich constructions. The use of sandwichspecimens is relatively rare, owing to the additional expense and difficultyof their manufacture. It follows that the former two specimen configura-tions are those in more general use.

Methods which propose the use of short unsupported specimens are gen-erally appropriate for the measurement of the properties of unidirectionalmaterials. Although specimens with other laminate layups may also betested with these methods, it should be noted that the gauge length,however short, is unsupported and buckling failure is highly likely. Detailsof the specimen shapes recommended in CRAG 400, ASTM D 3410 andASTM D 695 are shown in Fig. 5.12, which shows the now superseded ASTM D 3410 Celanese specimen, which had end-tabs with bevelled edges,with an angle of 9°, as well as the currently recommended specimen. Thespecimen to be used in the IITRI jig is identical to that used for theCelanese test, and for both jigs the specimen may be used without end-tabswhere appropriate. Also shown are both types of specimen included inASTM D 695.

The ICSTM method also uses short, unidirectional tabbed specimens,although it too can accommodate untabbed specimen shapes. Typicaldimensions of tabbed specimens are shown in Fig. 5.8, including the origi-nal and modified versions. The modified specimen was found to give moreconsistent results. Cross-ply GRP (glass-reinforced plastic) was adopted asthe preferred end-tab material.

Very few recommended test methods now advise the waisting of speci-mens. However, this used to be considered to be an acceptable means ofensuring failure in a particular region of the specimen. In some circum-stances waisting can be considered as an optimised form of tabbing, but it

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W

W

LT LT

LT LT

LT

LT

GL

GL

GLGL

(a)

hA

h

h

A

A

(b)

W h W

(c) (d)

9°

5.12 Specimen configurations for (a) ASTM D 3410, Celanese andIITRI; (b) CRAG 400, Celanese; (c) ASTM D 695; (d) modifiedASTM D 695 methods. W = specimen width, LT = end-tab length,GL = gauge length, h = specimen thickness, A = end-tabthickness.

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must be carried out with extreme caution and care, both in the actualmachining operation and in order to maintain a symmetric specimen, other-wise bending will be introduced causing premature failure. Port10 showedthat interfacial splitting due to excessive shear stresses can be avoided whenthe specimen is waisted following the taper contour equation, which givesthe minimum gauge length:

[5.1]

where glmin is minimum gauge length, H is the nominal specimen thickness,h is the minimum specimen thickness, Sc is the compressive strength and Sis

is the interlaminar shear strength.A further variant on waisted specimens, for which good results are

claimed, has been proposed by workers16 at the Defence Research Agency(DRA) Farnborough, UK (now known as the Defence Evaluation andResearch Agency, DERA). In their approach a co-cured laminate is pro-duced by sandwiching unidirectional material between layers oriented at±45°. The latter are subsequently machined away in the gauge section togive a specimen with integral end-tabs.

To avoid constraint at the ends, multidirectional specimens are usuallymuch longer than unidirectional and, hence, have to be supported by anantibuckling guide. The CRAG method 401 is typical.14 Specimen detailsare given in Fig. 5.13, together with the recommended jig design.

Sandwich specimens are usually designed to be tested as sandwich beamsrather than sandwich columns, and are loaded in four-point bending.17,18 Thetop cover composite sheet is the specimen to be tested.A metal honeycombcore and a bottom cover sheet with greater stiffness and strength ensurethat the specimen fails on the upper, compressive, side. In this way very thinspecimens can be tested. The high costs incurred in the manufacture of thistype of specimen have led to the development of a reusable sandwich beam.19

Here, the core in the test section is made of Plexiglas and a CFRP sheetused as the tension face. On the compression side, rather than being bonded,the specimen is clamped between two aluminium end caps.

A form of sandwich column specimen uses the matrix resin as the corematerial. Excellent results are claimed for this specimen when tested in theIITRI jig.20

5.6 Execution and problems

Carrying out a compression test, or any other test for that matter, shouldbe simple without sacrificing repeatability and reproducibility of the testresults. These two terms can be used to characterise a test method and canbe distinguished in the following way:

glHh

hSSmin ln= Ê

Ëˆ¯

ÊË

ˆ¯

c

is

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Repeatability Reproducibilitysame method same methodidentical material identical materialsame lab different labsame equipment different equipmentsame operator different operatordifferent sessions different sessions

As the main parameters influencing compression test results the followingare suggested:


W

LT

LT

GL

Specimen

h

End-tab 0.5–2 mmlight alloy (or GRPfor hot /wet tests)

b 0.16b

5.13 CRAG multidirectional specimen with testing jig. Dimensions: W = 9h minimum, typically 10h (absolute minimum = 20mm); LT = 40mm minimum; h = 2–4mm, depending on laminateconfiguration; GL = not less than W (1 + 1/tanq) or 100mm,whichever is greater. q is the angle that the off-axis fibres makewith the long axis of the specimen.

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• Test method 1 method of load introduction2 geometry of the test piece3 mechanical properties of tabbing

• Laboratory/operator 4 method of laminate and specimen production

5 condition of testing hardware• Operator 6 care taken in performing the test

7 assessment of results.

The test method and ways of laminate and specimen production havebeen addressed above; the need for standardisation has been stressed. Thecondition of testing hardware, for example parallelism of loading surfacesand the calibration of the load cell, can obviously influence results and canbe regarded as being part of the ‘operator influence’, which naturally is noteasy to define and is often held responsible for a number of effects. In par-ticular, the assessment and interpretation of failure modes and test resultsare important in this context and depend on the experience of the tester.For example, partial loading of the rig will produce misleading results unlessthe stress–strain curves are examined critically. The aim of a test methodshould be to keep the influence of the operator as small as possible. Table5.1 attempts to summarise the effects in compression testing and is a faircheck list for potential testers.21

Failure to address the issues listed can lead to a variety of problems, eitherin execution of a test or in interpretation of evidence and results; some ofthese have already been mentioned.Whichever method is adopted, it is vitalthat the operator gains experience before using any data that are gener-ated. Clearly the simpler the test jig, the quicker an efficient and reliableprocedure can be established.

One crucial item that should always be checked is the failure mode. Basi-cally, the ideal failure occurs within the gauge section. However, sometimesfailure may initiate close to the gauge length end of the end-tab and propa-gate into the gauge length. Such failure would be considered as valid, butany specimen failing within the grip/tab region should be regarded asinvalid and the test repeated.

5.7 Typical results

There are a fairly large number of published sources reporting research andexperimentation into the various compression test methods and quotingresults found. ASTM D 3410 quotes a number of key references whichsupport its conclusions in adopting the specific methods which it recom-mends. These works are cited in the reference list.17,22–26 In addition, therehave been several major projects carried out at Imperial College to examine

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compression test methods. Largely, the data obtained from these projectssupport the results from research carried out elsewhere, although there isclear evidence that improvements in test technique can deliver highervalues of compression strength. The background, experimental details andresults from the various Imperial College test programmes are given in thefollowing sections.

5.7.1 Background

Staff and research students in the Centre for Composite Materials at Impe-rial College have been involved in a number of test programmes with thetheme of investigating test methods for composite materials since 1985.These programmes have compared different test methods recommendedby various standards organisations and company standards, in addition to


Table 5.1. Factors influencing the results of compression tests.21

Test method Testpiece preparation

Method of load introduction Method of laminate productionshear prepreg layup proceduremixed end/shear curing cycleend curing device (autoclave, pressclave,

heated press)Testpiece geometryMethod of specimen productionwidth

bonding surface preparationunsupported lengthtabbing adhesive propertiesthicknesssymmetry of tabbingTabbing materialalignment when machiningaluminiumspecimen surface finishsteel

GRPCFRP

Equipment Operator influence

Calibration Measurement of testpiece dimensionsload cell micrometer, vernier, etc.transducers, etc. removal of resin pimplesstrain gauges

AccuracyCare taken in carrying out the test

parallelism of testing machine checking alignment

surfaces‘zero load’ at test start

alignment of compression rigAnalysis of test data

assessment of failure modesclassification of valid/non-valid failurescheck of unlikely resultsmethod of modulus determination

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the development of new test methods. Several programmes have examinedcompression test methods.

5.7.2 Experimental details and results

5.7.2.1 Programme 1

The first programme27 included CRAG method 400, ASTM D 3410(Celanese), and both the standard and modified versions of ASTM D 695.Unidirectional and multidirectional laminates of XAS carbon and E-glassfibres both in 913 epoxy were investigated, these materials being suppliedas prepreg by Ciba Geigy (now Hexcel).

Tables 5.2 and 5.3 show the specimen dimensions and conditions used for the various tests. In the main, 2mm thick (16-ply) laminates were used because the CRAG method insists on this thickness, although sometests were carried out on 3mm thick material.

Two different and relatively inexperienced operators carried out the tests,one on the CFRP, the other on the GFRP (glass-fibre reinforced plastic).The same test machine was used, but there was a 12 month gap betweenthe two sets of experiments. The results are given in Tables 5.4 and 5.5.

All of the stress–strain curves for unidirectional and 0°/90° CFRP andGFRP specimens were linear to high strains. However, the stress–strain

Compression 91

Table 5.2. Dimensions and test conditions adopted for compression tests onunidirectional XAS/913 carbon/epoxy. The D 695 specimen was also used formultidirectional tests.

ASTM D 695M ASTM D 3410 CRAG 400

modified standard(Celanese) (Celanese)

Material thickness 2 2 2 2Gauge length 5 80 12.7 10Overall length 75 80 139.7 110Width 10 19/12 6.35 10End-tab thickness 2 — 1 1End-tab material carbon/ antibuckling steel aluminium

epoxy guideEnd-tab profile 90° — 9° 90°Strain — extensometer strain gauge strain gauge

measurementTest speed 1.0 1.0 1.3 1.3

(mmmin-1)

All dimensions in mm.

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Table 5.4. Compressive modulus and strength data for different layups of CFRPusing several test methods.

Test type Fibre orientation Elastic modulus Strength(GPa) (MPa)

CRAG Uni 106 (4.4) 1003 (100)ASTM D 3410 Uni 101 (11.5) 1082 (99)ASTM D 695 (mod) Uni — 1198 (180)ASTM D 695 Uni 107 (7.4) 744 (73)ASTM D 695 0/90 72 (3.1) 675 (56)ASTM D 695 ±45 18 (0.5) 199 (6)

Standard deviation in brackets.

Table 5.5. Compressive modulus and strength data for different layups of GFRPusing several test methods.

Test type Fibre orientation Elastic modulus Strength(GPa) (MPa)

CRAG Uni 43.6 (2.7) 1230 (188)ASTM D 3410 Uni 44.5 (4.5) 642 (46)ASTM D 695 (mod) Uni 37.4 (2.2) 592 (45)ASTM D 695 0/90 24.1 (1.1) 616 (39)ASTM D 695 (90/+45/0/-45)2S 23.0 (1.7) 539 (21)ASTM D 695 (+45/0/-45/0)2S 27.6 (2.5) 633 (76)

Standard deviation in brackets.

Table 5.3. Dimensions and test conditions adopted for compression tests on E-glass/epoxy. The D 695 specimen was also used for multidirectional tests.

ASTM D 695M ASTM D 3410 CRAGStandard

Material thickness 2 3 2Gauge length 80 12.7 10Overall length 80 139.7 110Width 19/12 6.35 10End-tab thickness — 1.5 0.8End-tab material antibuckling guide 0° E-glass aluminiumEnd-tab profile — 9° —Strain measurement extensometer strain gauge strain gaugeTest speed (mmmin-1) 1.0 1.26 3.25

All dimensions in mm.

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curves for the remaining layups were non-linear from the start of the test.

The results for compressive elastic modulus are quite reasonable acrossthe different test methods and layups, the unidirectional CFRP rangingfrom 101GPa to 107GPa and unidirectional GFRP from 37.4GPa to 44.5GPa.

The problems associated with the use of the Celanese jig in order toobtain acceptable strength data have been mentioned previously. These arelargely due to difficulties in ensuring perfect alignment. This is reflected inthe results obtained here. Whilst the strength results for the CRAG andASTM D 3410 unidirectional carbon specimens are quite similar, they arewell below what should be expected for this type of material. In fact theyare lower than that obtained with the modified version of the ASTM D 695method. The strength results for the standard D 695 unidirectional speci-mens are considerably lower owing to premature failure by crushing of theunsupported ends of the specimen, these results being only marginallygreater than those for the 0°/90° specimens. As expected, the ±45° orienta-tions using the D 695 jig gave a very low result.

The strength data for unidirectional GFRP are widely different for theCRAG and ASTM D 3410 and D 695 specimens, with the CRAG resultsbeing higher than those achieved for the CFRP material and both ASTMresults being of the same order as the D 695 tests on 0°/90° and quasi-isotropic layups of both carbon and glass. This large discrepancy betweenthe CRAG and ASTM D 3410 results, which on the face of it are obtainedusing essentially the same equipment, must be put down to misalignmentand stability problems, and operator inexperience.

5.7.2.2 Programme 2

A series of experiments conducted on unidirectional CFRP (XAS/914C)supplied by Ciba Geigy (now Hexcel) gave comparative data for severaltest methods,21 the results being shown in Fig. 5.14. It should be noted thatall testpieces, apart from those used in the Birmingham method, weretabbed with square, non-tapered GRP tabs.

There are clear trends, with indirect methods yielding low results com-pared with methods where the load is partly introduced by shear and partlythrough the end of the specimen. Slight changes in specimen clampingresulted in changes of up to 30% of the measured compressive strength.The results suggest that too much variation is possible.

The ICSTM method gave the highest results with the improved testpiece,employing debond inserts, showing a substantial increase over the standardspecimen. Overall, the results, other than for the ICSTM jig, broadly agreewith information published by other workers.

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5.7.2.3 Programme 3

Tables 5.6 and 5.7 give results obtained for unidirectional AS4/PEEK (poly-ether ether ketone) (APC-2) using the ICSTM method21.

The results given in Table 5.6 are for specimens machined from a 4mmthick plate, with Table 5.7 giving results for the improved specimen, shownin Fig. 5.8, which had 5 mm adhesive cellulose tape placed under the end-


scatter

2000

1800

1600

1400

1200

1000

800

600

400

200

0

Ulti

mat

e co

mpr

essi

ve s

tres

s (M

Pa)

1 2 3 4 5 6 7 8 9 10 11 12

CR

AG

(1)

CR

AG

(2)

CR

AG

(3)

IITR

I

AS

TM

(1)

AS

TM

(2)

BI

BA

e(1)

BA

e(2)

BA

e(3)

ICS

TM

(1)

ICS

TM

(2)

5.14 Results of compression tests on XAS/914C using differentmethods and specimen configurations.21 CRAG(1), standardCRAG specimen and fixture, several operators; CRAG(2), oneoperator, remachined grip surfaces, careful adjustment of thegrip collets to the individual testpiece; CRAG(3), as CRAG(2),additionally tab tip debonding by bending the testpiece; IITRI,standard IITRI specimen and fixture, several operators; ASTM(1),modified ASTM D 695, testpiece 2mm thick, end cap on one end;ASTM(2), as ASTM(1), testpiece 1mm thick; BI, Birminghammethod specimen tested in ICSTM rig; BAe(1), BAe standard rigand specimen, one operator; BAe(2), specimen fully gripped, 5mm non-grit-blasted section under the tab tip; BAe(3),specimen partially gripped, 5mm non-grit-blasted section underthe tab tip; ICSTM(1), standard ICSTM specimen and fixture,several operators; ICSTM(2), improved specimen.

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tab tips as a debond insert. The specimens were instrumented with 2 mmstrain gauges and the test speed was 1.5mm min-1.

Unlike the results for XAS/914C, the strength of the machinedAS4/PEEK specimen is considerably lower than that of the improved speci-men, 1133MPa as opposed to 1511MPa, although the scatter is lower forthe machined specimen results. The explanation is to be found in the highfailure strain and high shear strength of the PEEK matrix. The debondinsert had the same effect as in the thermoset system, separating stress concentrators. The fracture surfaces were similar to those of the thermoset

Compression 95

Table 5.6. Compression data on AS4/PEEK (APC-2), machined specimen(ICSTM method).

Specimen Thickness Width CSA UCS Modulus(mm) (mm) (mm2) (MPa) (GPa)

1 1.97 9.95 19.60 1101 120.32 1.98 9.97 19.74 1111 118.23 1.97 9.96 19.62 1153 117.74 1.99 9.96 19.82 1149 127.75 2.00 9.92 19.84 1152 125.7

Statistics Mean sn -1 Cv (%)

UCS 1133 25.1 2.2Modulus 121.9 4.5 3.7

UCS is the ultimate compressive stress, CSA is the cross-sectional area.

Table 5.7. Compression data on AS4/PEEK (APC-2), with debond insert (ICSTM method).

Specimen Thickness Width CSA UCS Modulus(mm) (mm) (mm2) (MPa) (GPa)

1 2.23 9.98 22.26 1353 127.12 2.22 9.95 22.09 1456 128.53 2.22 9.91 22.00 1358 126.04 2.22 9.96 22.11 1597 125.45 2.23 9.94 22.17 1493 125.4

Statistics Mean sn -1 Cv (%)

UCS 1511 119.7 7.9Modulus 126.5 1.3 1.1


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system but with less splitting and brushing. This similarity suggests fibremicrobuckling failure for both materials.

5.7.2.4 Programme 4

Again using the ICSTM method, data were obtained for a unidirectionalE-glass fibre reinforced nylon (ICI ‘Plytron’).21 The material was suppliedin the form of pultruded panels with nominal fibre volume fractions of 23%,29% and 35%.

The standard specimen configuration was used incorporating the sameGRP end-tabs as in the tests on CFRP. The test speed was 3mm min-1.Results are given in Table 5.8.


Table 5.8. Compression data on ICI ‘Plytron’ with different levels of fibrevolume fraction. ‘B’ in the column ‘Failure’ indicates bifurcation of the strainsignals.

Nominal Specimen Thickness CSA UCS Modulus FailureVf (%) (mm) (mm2) (MPa) (GPa)

23 1 1.95 18.93 721 23.2 B2 1.94 19.26 542 20.0 —3 1.94 18.86 696 22.4 B4 1.96 19.40 519 20.8 —5 1.96 19.46 624 20.0 B

29 1 1.86 18.49 770 25.6 B2 1.89 18.79 727 24.0 —3 1.88 18.65 823 26.4 B4 1.90 18.87 850 28.0 B5 1.87 18.61 635 23.2 —

35 1 1.99 19.76 991 30.4 B2 1.97 19.44 924 31.2 B3 1.95 19.38 892 32.0 B4 1.94 19.26 937 32.8 B5 1.93 19.16 1006 32.8 B

Statistics Vf Mean sn -1 Cv (%)

UCS 23 620 89.8 14.529 761 85.0 11.235 950 47.5 5.0

Modulus 23 21.3 1.45 6.829 25.4 1.91 7.535 31.8 1.04 3.3


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The magnitude of stresses responsible for tab tip debonding depends onthe ratio of composite stiffness to tab stiffness, and for a given tab stiffnessthe stresses are strain independent. Debonding of the tab tips occurred inall cases, mostly in a symmetric fashion, between 1% and 2.5% strain. Sincethe failure strain of glass fibre composites is high, tab debonding does notcause immediate failure but acts as a stress relief.

Strain gauges located front and back on the specimens were able to detectthe onset of tab debonding as a bifurcation of the strain signals. As seen in Table 5.8 most of the specimens exhibited this behaviour, suggestingmacroinstability of the testpiece. Normalisation of the bending stiffness ofthe specimen (modulus of elasticity multiplied by the square of the test-piece thickness – to which Euler buckling is proportional) and plottingversus the ultimate compressive stress resulted in a linear relationship fortests where bifurcation occurred, again suggesting macroscopic instability.It is clearly important to design the specimen specifically for the materialto be tested.

The composite examined here did not exhibit significant stiffnessdecrease, but the relatively high stresses achieved by reducing stress con-centrations did introduce the problem of macrobuckling, as was observedwith CFRP.

5.8 Conclusions

Of the methods discussed here, the ICSTM jig is one of the simplest to use.It also gives the highest mean strengths, together with low scatter. However,although a simple method is important and desirable, other techniques cangive higher than usual strengths provided adequate care is taken, the opera-tor is experienced and, also, some modifications are made to the speci-mens.21 It is clear that whichever method is used, great care must be takenwith specimen preparation, operator training and in the execution of thetest.

References

1. C Soutis and N A Fleck, ‘Static compression failure of carbon fibre T800/924Ccomposite plate with a single hole’, Journal of Composite Materials, 1990 24(5)536–58.

2. C Soutis, ‘Measurements of the static compressive strength of carbon fibreepoxy laminates’, Composites Science and Technology, 1991 42(4) 373–92.

3. B Budiansky and N A Fleck, ‘Compressive failure of fibre composites’, J MechPhys Solids, 1993 41 183–211.

4. C Soutis and R Tenchev, ‘A property degradation model for fibre microbuck-ling failure in composite laminates’, Sci Eng Composite Materials, 1995 4(1)27–34.

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5. W t’Hart, R Aoki, H Bookholt, P T Curtis, I Krober, N Marks and P Sigety,‘Garteur compression behavior of advanced CFRP’, AGARD 73rd Meeting of Structures and Materials Panel – Workshop on Advanced Composites in Military Aircraft, San Diego, CA, October 1991.

6. ASTM D 695M-91, ‘Standard test method for compressive properties of rigidplastics’, Vol 8.01, Annual Book of ASTM Standards, 100 Barr Harbor Drive,West Conshohocken, PA 19428, USA, Vol 8.01, 1994.

7. G C Grimes, Experimental Study of Compression–Compression Fatigue ofGraphite/Epoxy Composites,ASTM STP 734, ed. C C Chamis,American Societyfor Testing and Materials, 1981, 281–337.

8. R M Lamothe and J Nunes, ‘Evaluation of fixturing for compression testing ofmetal matrix and polymer/epoxy composites’, in Compression Testing of Homo-geneous Materials and Composites, ASTM STP 808, eds R Chait and R Papirno,American Society for Testing and Materials, 1983, 241–53.

9. J S Berg and D F Adams, ‘An evaluation of composite material compressiontest methods’, J Composites Technology and Research, 1989 11 41–6.

10. K F Port, The Compressive Strength of CFRP, Royal Aircraft Establishment,Farnborough UK, Technical Report 82083, 1982.

11. D H Woolstencroft, A R Curtis and R I Haresceugh, ‘A comparison of test techniques used for the evaluation of the unidirectional compressive strengthof carbon fibre reinforced plastic’, Composites, 1981 12 275–81.

12. A J Barker and V Balasundaram, ‘Compression testing of carbon fibre-reinforced plastics exposed to humid environments’, Composites, 1987 18(3)217–26.

13. J G Haeberle and F L Matthews, ‘Studies on compressive failure in unidirec-tional CFRP using an improved test method’, Proceedings of ECCM-4,Stuttgart, EACM and GARE, eds J Fulles, G Gruninger, K Schulte,A R Bunselland A Massiah, Elsevier Applied Science, September, 1990, 517–23.

14. P T Curtis, CRAG Test Methods for the Measurement of the Engineering Prop-erties of Fibre-reinforced Plastics, Royal Aircraft Establishment, Farnborough,UK, Technical Report 88012, 1988.

15. ASTM D 3410/D 3410M-95, ‘Standard test method for compressive propertiesof polymer matrix composite materials with unsupported gage section by shearloading’, Annual Book of ASTM Standards, 100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Volume 15.03, 1997, 116–31.

16. P T Curtis, J Gates and C G Molyneux, An Improved Engineering Test Methodfor the Measurement of the Compressive Strength of Unidirectional Carbon-fibreComposites, DRA Farnborough, UK, Technical Report 91031, 1991.

17. N R Adsit, ‘Compression testing of graphite/epoxy’, in Compression Testing ofHomogeneous Materials and Composites, ASTM STP 808, eds R Chait and R Papirno, American Society for Testing and Materials, 1983, 175–86.

18. ASTM D 5467–93, ‘Standard test method for compressive properties of unidi-rectional polymer matrix composites using a sandwich beam’, Annual Book ofASTM Standards, 100 Barr Harbor Drive,West Conshohocken, PA 19428, USA,Vol 15.03, 1997.

19. M B Gruber, J L Overbeeke and T W Chou, ‘A reusable sandwich beam conceptfor composite compression test’, Journal of Composite Materials, 1982 16162–71.


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20. A S Crasto and R Y Kim, ‘Compression strengths of advanced composites froma novel mini-sandwich beam’, SAMPE Quarterly, 1990 22(3) 29–39.

21. J G Haeberle, Strength and Failure Mechanisms of Unidirectional Carbon-fibreReinforced Plastics under Axial Compression, PhD Thesis, Imperial College,University of London, UK, December 1991.

22. K E Hofer and P N Rao, ‘A new static compression fixture for advanced composite materials’, Journal of Testing and Evaluation, 1977 5(4) 278–83.

23. R P Pendleton and M E Tuttle, Manual on Experimental Methods for Mecha-nical Testing of Composites, Society for Experimental Mechanics, Bethel, CT,USA, 1989.

24. T A Bogetti, J W J Gillespie and R B Pipes, ‘Evaluation of the IITRI compres-sion test method for stiffness and strength determination’, Composites Scienceand Technology, 1989 32(1) 57–76.

25. D F Adams and E Q Lewis, ‘Influence of specimen gage length and loadingmethod on the axial compression strength of a unidirectional composite materials’, Experimental Mechanics, 1991 31(1) 14–20.

26. D F Adams and E M Odom, ‘Influence of specimen tabs on the compressivestrength of a unidirectional composite material’, Journal of Composite Materi-als, 1990 25(6) 774–86.

27. J M Hodgkinson, An Experimental Comparison of ASTM, BSI and CRAG Standard Test Methods for the Determination of Mechanical Properties of Com-posite Materials, The Centre for Composite Materials, Technical Report 90/02,Imperial College, London, 1990.

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6.1 Introduction

An intrinsically low resistance to shear deformation, particularly in material planes dominated by matrix properties, is a severe weakness in fibre-reinforced plastic composites. Relatively low values of shear stiffness and strength often compromise material performance, forcingdesigners to arrange laminate stacking sequences in order to maximiseshear resistance. The resultant effect of shear property optimisation is that other mechanical properties are frequently compromised. Small tan-gential stresses can lead to severe reductions in the load bearing capacityof composite structures; hence the need for accurate methods for measur-ing shear properties.

Considerable experimental and analytical effort has been expended in the development of in-plane and through-thickness (out-of-plane) shear test methods for the determination of shear modulus and strength of fibre-reinforced polymer composites. One of the principal difficulties in the development of a test method for the measurement of shear properties is the provision of a pure shear stress state in the specimen.Ideally, for quantitative shear measurements, the shear test method shouldprovide a region of pure and uniform shear stress in the test section of the specimen throughout the linear and non-linear response regimes.This region should be one of maximum shear stress relative to all otherregions of the specimen. In addition, a unique relationship should existbetween the applied load and the magnitude of the shear stress in the testsection.

The difficulty of inducing pure shear increases with increasing anisotropyand inhomogeneity of the material. As these characteristics increase, thecomplex stress states arising at or near the loading zones become moredominant, particularly for continuous unidirectional laminates containing

6Shear*

W R BROUGHTON

100

* Crown copyright

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Shear 101

high modulus and high strength fibres. In these materials, it is difficult toobtain adequate regions of uniform shear stress free of extraneous stresscomponents within the specimen, even if the production of the specimenand test alignment are perfect. In addition, extraneous tensile and com-pressive stress components have a marked effect on the shear strength ofthese materials. Tensile stresses induce premature failure, whereas com-pressive stresses delay the onset of failure.

The difficulties encountered in producing a state of pure shear in com-posite specimens have resulted in a limited number of these methods beingincorporated into national and international standards. There is no univer-sal method suitable for the accurate evaluation of the shear properties forthe extensive range of material architectures encountered in compositetechnology. All the shear methods, standardised or otherwise, have physi-cal and geometrical limitations.

Most shear tests have been developed with the objective of maximis-ing shear stress and minimising extraneous induced stresses. It is pos-sible to measure the shear stress–strain response of a composite in the presence of non-shear stresses, provided the magnitude of the shear stress is considerably larger than the other stress contributions. Accept-able shear moduli measurements can be obtained from a range of testmethods.

Full characterisation of the shear properties of a composite lamina orlaminate requires the measurement of shear modulus and shear strength inthe 1–2, 1–3 and 2–3 planes. Because in-plane and through-thickness shearproperties are not necessarily equal, test methods have been developed toinduce both in-plane and through-thickness shear loading. Here, we areonly concerned with in-plane shear test methods.

In the assessment of shear test methods, consideration will be given tothe shear properties attainable, shear and normal stress distributions in thetest section, specimen fabrication and test apparatus requirements, datareduction procedures and data reproducibility.

6.2 Test methods

In this section six commonly used methods for the determination of shearproperties are considered:

• uniaxial tension of a ±45° laminate• uniaxial tension of a 10° off-axis laminate• two-rail and three-rail shear tests• the V-notched beam (or Iosipescu) shear specimen• twisting of a flat laminate• torsion of a thin-walled tube.

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6.2.1 ±45° tension test

The application of uniaxial tension to a balanced and symmetrical ±45°laminate is a relatively straightforward method for determining the in-plane shear characteristics (modulus and strength) of continuous alignedfibre-reinforced systems. The method, widely used in the aerospace/defenceindustry, is available as BS EN ISO 14,129,1 which is a joint interna-tional (ISO) and European (EN) standard, and as ASTM D 3518.2 The testprocedures described in these standards are based on ASTM D 3518 andutilise a 250 mm long rectangular specimen with width 25 mm and thickness2mm (see Fig. 6.1). It is recommended that for materials constructed withlayers thicker than 0.125 mm, the laminate should consist of 16 layers (i.e.[±45]4S).

The specimen is machined to the required size using diamond cuttingequipment, for example, a circular wheel. The use of a liquid coolant suchas water is recommended to prevent the build-up of heat in the test speci-men, which could cause material damage. The surfaces and edges should befree from scratches, pits, sink marks and flashes. Edges should be groundparallel to remove machining defects.

Providing failure does not occur within the grip region, specimens can betested with or without end-tabs. End-tabs, if used, should be constructedfrom a cross-ply or fabric laminate fabricated in glass fibre/resin, or fromthe material under test, with the fibre axes of the fabric set at ±45° to thespecimen axis. The end-tabs are adhesively bonded to the specimen with ahigh elongation adhesive and have a recommended length of 50mm. Thiscorresponds to an overall gauge length (between grips) of 150mm. The tab material thickness should be between 0.5mm and 2.0mm, with a tabangle of 90°.

y

y

x

150

Tab materialorientation

25 45°45°

45°

45°

Transverse strain gauge

JawsSpecimenLongitudinal strain gaugeTab

50

250

6.1 Schematic of the ±45° tensile specimen.

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Shear 103

When a ±45° laminate is loaded in uniaxial tension, a biaxial state of stressis induced within each of the +45° and -45° lamina (i.e. layers).3,4 Thenormal stresses s11 and s22 in the lamina coordinate system depend on boththe applied tensile stress sxx and the induced shear stress txy, whereas theshear stress t12 is related only to the applied tensile stress sxx, such that:

[6.1]

This analysis assumes that there is no interlaminar shear coupling. The corresponding in-plane lamina normal strains e11 and e22 and shear strain g12

are given by Equation [6.2]:

[6.2]

where exx and eyy are the normal strains parallel and perpendicular to thespecimen axis, respectively. In order to determine the in-plane shearmodulus, G12, strains need to be measured both parallel and perpendicularto the specimen axis using either strain gauges or extensometers. The usualapproach when using strain gauges is to bond two separate gauges adhe-sively to the specimen as shown in Fig. 6.1. Alternatively, biaxial rosettegauges may be adhesively bonded to the specimen. The test speed given inthe ISO standard is 2 mmmin-1.

The in-plane shear modulus of the unidirectional lamina, given by Equation [6.3]:

[6.3]

is obtained from the initial slope of the shear stress–strain curve (t12 versusg12) over a strain range of 0.1–0.5%,1 as shown in Fig. 6.2. The specimengeometry has been selected to ensure that the shear modulus is unaffectedby edge effects, end effects or the biaxial state of stress within individuallaminae.

In-plane shear strength, S12, is expressed as:

[6.4]

where Pmax corresponds to the applied load at failure, and b and h are thewidth and thickness of the specimen, respectively.

The ±45° tensile test provides an acceptable method for determining in-plane shear modulus, but caution must be exercised in interpreting the ulti-mate shear strength and strain results.This is due to the fact that the laminaeare in a state of biaxial stress and not pure shear. Normal stresses of a

SP

bh12 2= max

G xx

xx yy12

12 12

12 122=

-( ) =--

se e

t tg g

" '

" '

e ee e

g e e11 22 122= =

+= -xx yy

xx yy;

ss

t ss

t ts

11 22 122 2 2= + = - = ±xx

xyxx

xyxx; ;

MTA6 11/22/2000 1:05 PM Page 103


similar magnitude to those of the shear stresses act along the shear planes,resulting in the onset of mixed-mode fracture. Multiple-ply cracking, fibrerotation and edge or internal delaminations occur prior to final fracture,with the onset of fracture being delayed due to the constraint imposed onthe lamina by adjacent layers. True failure is difficult to determine, withmost standards specifying the shear strength as corresponding either to theultimate load generated during the test or to a specified strain level. It isrecommended in the ISO standard that the test be terminated at g12 = 5.0%.The peak load at or before 5% strain is taken as the shear strength.

6.2.2 10° off-axis test

The 10° off-axis tensile test is a method commonly employed for shear char-acterisation of fibre-reinforced polymer composites.The test consists of uni-axially loading a unidirectional laminate in tension with fibres oriented at10° to the load axis (Fig. 6.3). A biaxial stress state is induced in the mate-rial’s principal coordinate system when subjected to uniaxial tensile load.The 10° angle was chosen to minimise the effects of longitudinal and transverse stress components s11 and s22 on the shear response. At an angleof 10° the shear strain approaches a maximum value.3–6

The in-plane normal and shear stresses and shear strain (in the materialprincipal coordinate system) developed within the specimen in the absenceof end constraints are given by Equations [6.5] and [6.6]5:

6.2 Typical shear stress–strain curve for the ±45° specimen.

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Shear 105

s11 = sxx cos2 q ; s22 = sxx sin2 q ; t12 = 1–2sxx sin2q [6.5]

[6.6]

Substituting q = 10° into Equation [6.5] yields the relative magnitudes ofthe in-plane longitudinal, transverse and shear stresses along the 10° plane:

s11 = 0.970sxx; s22 = 0.030sxx; t12 = 0.171sxx [6.7]

where sxx is equal to the applied load, P, divided by the cross-sectional area, bh, of the specimen. A three-element rosette adhesively bonded at the centre of the specimen, as shown in Fig. 6.3, is used to measure thestrains.The structural strains for such a rectangular rosette with three straingauges (gauge 1 = 0°, gauge 2 = 45° and gauge 3 = 90° to the loading axis)are:

exx = e1; eyy = e3; gxy = 2e2 - e1 - e3 [6.8]

The in-plane strain along the 10° plane is determined by substituting thestructural axes strains from Equation [6.8] into Equation [6.6] and settingq = 10°. The resulting equation is:

g12 = 1.879e2 - 1.282e1 - 0.598e3 [6.9]

Alternatively, the structural axes strains may be measured using a three-element 60° delta rosette (gauge 1 = 0°, gauge 2 = +120° and gauge 3 =-120° to the loading axis). The structural axes strains are given by Equation[6.10]:

[6.10]e e ee e e

ge e

xx yy xy= =+ -

=-( )

12 3 1 3 22 2

32

3; ;

g e e q g q12 2 2= -( ) +xx yy xysin cos

y

x25

150

Tab materialorientation

Strain gauge rosette

SpecimenTaby Jaws

250

50

45°10°

45° 21

12

3

6.3 Schematic of 10° off-axis specimen.

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Similarly, the in-plane strain along the 10° plane is determined by substi-tuting the structural axes strains from Equation [6.10] into Equation [6.6]and setting q = 10°. The resulting equation is:

g12 = 1.313e3 - 0.456e1 - 0.857e2 [6.11]

This test method is not registered either as an ISO or ASTM standard;thus there are no commonly used or agreed specifications for specimendimensions and specimen preparation. A satisfactory approach would be tocomply with Part 5 of the International Standard ISO 527.7 This interna-tional standard specifies ‘the test conditions for the determination of thetensile properties of unidirectional fibre-reinforced polymer composites’.Based on ISO 527-5, the 10° off-axis specimen would have a width of 25mm, length 250mm and thickness 2 mm (i.e. Type A). It is recommendedthat the 10° unidirectional coupon be tabbed in accordance with ISO 527-5, identical to the procedure employed for the ±45° tension test. Specifica-tions relating to specimen dimensions are contentious issues remaining tobe resolved.

The in-plane shear modulus of the unidirectional laminate is obtainedfrom the initial slope of the shear stress–strain curve over a strain range of0.05–0.25%.7 Finite element analysis indicates that the axial strain variationis very sensitive to out-of-plane bending and twisting eccentricities.5 Thiseffect can be kept to a minimum by ensuring that the bending strains in thewidth and thickness are less than 3%, as specified in ISO 527-5. Tests areconducted at a speed of 1 mmmin-1.

The test has the advantages of adaptability to conventional tensile testing(including cyclic and environmental conditions), uniformity of through-thickness shear stress, no residual stresses and ease of manufacturing.However, as demonstrated above, it is necessary to measure three strainsat a point and to transform stresses and strains to another coordinatesystem. Small orientation errors in machining the specimen angle and straingauge alignment can produce large errors in shear measurements. This mis-orientation (recommended to be within ±0.5°) is not critical when measur-ing shear strain at failure, because strain peaks are relatively insensitive tosmall errors at a 10° load angle.

The main concern with this test method is the non-uniformity of the stressfield near the grips, which is caused by end constraints preventing rotation,thus inducing moments and shear forces at the ends. Using long specimens(aspect ratios of 10 or greater) promotes a state of uniform shear stress inthe centre of the specimen and thus reduces the error in shear moduluscaused by the end constraints. However, a complex correction factor is stillrequired to calculate the true shear modulus.7

Failure of 10° off-axis specimens occurs due to the combination of trans-verse tensile and shear stresses. As a consequence, the method tends to

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Shear 107

underestimate the ultimate shear strength and strain. The onset of failureis catastrophic, with a single straight crack developing early, propagatingrapidly across the gauge-section and separating the specimen into two sec-tions.A recent development has been the use of oblique end tabs for testingthese specimens.8,9 Numerical and experimental analyses have shown thatalthough a state of homogeneous shear stress is produced, transverse tensilestresses are still present.

6.2.3 Rail shear test

A third method for determining in-plane shear properties of fibre-rein-forced polymer composites is the rail shear test. This test method is usedextensively throughout the aerospace industry, with in-plane propertiesdetermined by imposing edgewise shear loads on the laminate using a two-rail (Fig. 6.4) or three-rail fixture (Fig. 6.5). The two test configurations (i)two-rail shear and (ii) three-rail shear and associated test specimen geome-tries are specified in ASTM D 4255,10 a standard guide for testing in-planeshear properties of composite laminates. This standard guide covers thedetermination of in-plane shear properties of continuous and discontinu-ous aligned materials (0° and 90° orientations), symmetric laminates andrandomly orientated fibrous laminates.

Tensile orcompressive load

Fixture boltsSpecimen

Strain gauges

Rails

76

120.2

25

51

152

12.7

6.4 Two-rail shear fixture and specimen.

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The two-rail shear test involves clamping the long sides of a rectangularspecimen between two pairs of rigid steel loading rails, with the other sidesremaining unconstrained (Fig. 6.4). The loading rails are usually bolted tothe test specimen. A tensile force is applied to the rails, which induces anin-plane shear load on the specimen. ASTM D 4255 specifies a specimenlength of 76 mm and a width of 152mm. A strain gauge, adhesively bondedto the specimen at 45° to the longitudinal axis of the specimen, is used tomeasure shear strain.

The shear strength, Sxy, and shear modulus, Gxy, can be calculated usingthe following equations:

[6.12]

[6.13]

where Pmax is the ultimate failure load, L the specimen length along the railsand h the specimen thickness. The variables DP and De45 are the change inapplied load and strain (for +45° or -45° strain gauge) in the initial linearregion of the stress–strain curve.

The three-rail (symmetric) shear test, developed to produce a closerapproximation to pure shear, consists of three pairs of rails clamped to the

GP

Lhxyxy

xy

= =DD

DD

tg e2 45

SPLhxy = max

Tensile or compressive load

Centre rail slidesthrough guide

Strain gauges

6.5 Three-rail shear fixture and specimen.

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Shear 109

test specimen, usually by bolts (Fig. 6.5). The two outside pairs of rails areattached to a base plate, which rests on the test machine. A third (middle)pair of rails are guided through a slot in the top of the base fixture. Themiddle pair of rails are usually loaded in compression rather than tension,since the former does not require fastening the base fixture to the testmachine. Shear modulus is measured at the centre of both test sectionsusing strain gauges bonded at 45° to the specimen’s longitudinal axis. Thespecimen width and length are 137mm and 152mm, respectively.10

The shear strength, Sxy, and shear modulus, Gxy, can be calculated usingEquations [6.14] and [6.15]:

[6.14]

[6.15]

where the variables have been defined previously.It is recommended that laminates be 1.27–3.17 mm (i.e. 0.050–0.125

inch) thick.10 Thin laminates tend to buckle at low loads, while thicker lam-inates may have shear strengths in excess of the rail clamping capac-ity. Specimen dimensions for both rail shear tests are shown in Figs. 6.4 and 6.5. Specimens are bolted to the rails using 9.5mm bolts. The bolts are inserted through the specimen via 12.5mm diameter drilled holes.The holes are oversized to ensure that the shear load is introduced into thelaminate via frictional forces between the specimen and the steel loadingrails. It is important that there is no bearing contact in the direction ofloading between the bolts and the specimen. If the torque is too low,the specimen will slip and the bolts will begin to bear on the specimen,and if the torque is too high, then spurious failures may be induced by thehigh local through-thickness compressive stresses. The recommendedtorque on each bolt is 100 Nm, and the bolts may need to be retightenedduring loading. Specimen preparation and testing are time consuming andexpensive.

In reality, it is difficult to machine specimens to the required toler-ances, and in many instances bearing contact initiates premature failurealong the bolt line, rather than in the specimen centre. In addition,delaminations are commonly introduced during the drilling of holes. Thesedefects act as stress raisers, adding further to the uncertainties in strengthvalues measured using the two- and three-rail tests. The uncertainties asso-ciated with the results from this particular test were highlighted when the ASTM conducted round-robin tests; consequently ASTM D 4255 is only a guide.

GP

Lhxyxy

xy

= =DD

DD

tg e4 45

SP

Lhxy = max

2

MTA6 11/22/2000 1:05 PM Page 109


The existence of free edges causes the stress distribution in the laminateto deviate from an ideal shear state. Stress singularities exist near loadedcorners, and axial and transverse stresses are also present. Numerical analy-sis has shown that the length to width ratio can have a major effect on stressdistributions and is laminate dependent.3 Specimen dimensions, as specifiedin ASTM D 4255, ensure that a uniform shear stress distribution exists over a large region in the specimen centre, producing valid shear modulivalues for all laminates, except those with an inherently high effectivePoisson’s ratio (e.g. ±45° angle-ply). In these laminates, a non-uniform shearstress distribution exists with large normal stresses present at the edges.The two loading configurations are only suitable for shear moduli deter-mination. Although the three-rail shear test provides a better approxima-tion to pure shear, problems associated with the two-rail shear method (i.e.significant normal stresses and non-uniform shear stress distribution) arenot eliminated.

Large transverse tensile stresses present in the vicinity of the loadedcorners invariably cause premature fracture in unidirectional laminateswith fibres parallel to the rails (0° orientation). The onset of failure, in theform of longitudinal cracks, is often difficult to locate visually as the initia-tion site is obscured by the rails. This fibre orientation is associated with alarge scatter in test data and low strength. Transverse (fibres perpendicularto the rails) and cross-ply (0/90) laminates fail over a wider region at com-paratively high strains.3 Failure is associated with multiple-ply cracking,which is considered to be representative of subcritical failures observed inindividual plies within laminates subjected to shear. It is worth noting that it is difficult to drill holes in unidirectional laminates without causinglongitudinal splitting.

6.2.4 V-notched beam (Iosipescu) test

The V-notched beam test, originally developed by Iosipescu11 for charac-terising the shear properties of metals, was subsequently adapted for usewith fibre-reinforced plastic composites as ASTM D 5379,12 followingexperimental and analytical work conducted mainly by Adams andWalrath.13 The test method employs a double edge-notched, flat rectangu-lar specimen, which is shown, together with what is often referred to as the‘Wyoming’ test fixture, in Fig. 6.6. Two 90° angle notches with a notch rootradius of 1.3 mm are cut at the edge mid-length with faces orientated at ±45°to the longitudinal axis, to a depth of 20% of the specimen width (i.e. 4mm).The specimen length and width are 76mm and 20mm, respectively, with thethickness being between 3 and 4mm, although greater thicknesses can betested. Specimens with a thickness less than 3 mm require adhesively

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Shear 111

bonded tabs, typically 1.5mm thick, to prevent out-of-plane bending ortwisting, which may lead to premature failure. Local crushing, which canoccur near the inner loading regions, is also avoided by the use of tabs. Testspecimen dimensions may be reduced if required.

Shear strain is measured by bonding two biaxial strain gauges, one oneach opposite face of the specimen, to the centre of the specimen, in thearea between notches. The strain gauges should have a gauge length of 1mm or 2 mm, to keep within the region of uniform stress, and are alignedat ±45° to the longitudinal axis of the specimen. Although a special testfixture is required, testing is relatively straightforward.

In principle, this procedure induces a state of pure shear stress at the mid-length of an isotropic specimen, by the application of two force couples. Astate of constant shear force is induced through the mid-section of the testspecimen, with the induced moments cancelling exactly at the mid-length,thereby producing a state of pure shear at this location.3

Early finite element and experimental analyses suggested that there was indeed a uniform shear stress over most of the gauge section betweenthe notch roots, despite the shear stress concentrations at these locations.The stress concentration was found to be a function of notch angle, depthand root radius and material orthotropy, which died rapidly on moving away from the notch tip. It was also claimed during the development of thestandard14 that, although transverse normal stresses were developed in the test section, they were compressive and redistributed as inelastic failure (longitudinal cracking) occurred at the notch roots, leaving the test

6.6 V-notched beam test fixture and specimen.

MTA6 11/22/2000 1:05 PM Page 111


section essentially free of transverse normal stresses at loads approachingfinal failure.

However, more recent investigations have demonstrated that the shearstress distribution in the test section of both isotropic and anisotropic specimens is not uniform.3,15–17 Furthermore, shear and normal stress distri-butions have been shown to be highly dependent on the orthotropy ratioExx/Eyy, notch geometry and loading boundary conditions.The average shearstrength, Sxy, and shear modulus, Gxy, can be calculated using Equations[6.16] and [6.17]:

[6.16]

[6.17]

where Pmax is the ultimate failure load, w is the distance between the notchesand h is the specimen thickness. The variables DP, De45 and De-45 are thechange in applied load and +45° or -45° normal strains in the initial linearregion of the stress–strain curve. To minimise potential effects of out-of-plane movement or twisting of the specimen, it is recommended that thestrain data used for determining shear modulus be the average of the indi-cated strains from each side of the specimen. Misalignment of as little as1.4° from normal may cause a 6% difference in observed modulus betweenthe two faces.18,19 Numerical studies15–17 show that for specimens with sharpnotches, correction factors need to be employed to calculate the actualshear modulus value. ASTM D 5379, however, specifies a notch root radiusof 1.3mm in order to minimise the shear stress concentration at the notchroots, and thus promote a more uniform shear stress distribution along thenotch-root axis. ASTM D 5379 does not specify the use of correctionfactors; however, the use of large radii is not entirely successful in promot-ing a uniform shear stress distribution.

Various failure modes, shown in Fig. 6.7, may be encountered with thefailure process being highly dependent on the microstructure of the mate-rial. In some cases, a mixed mode of failure has been observed. For example,in continuous unidirectional (longitudinal, or 0°) specimens, damage initi-ates at the notch roots with two symmetric cracks propagating parallel tothe fibres on the opposite sides to the inner loading points. The shear stressconcentration at the notch root is primarily responsible for crack initiation,with crack growth in the principal tensile stress plane being prevented bythe aligned fibres. Axial splitting produces stress relief at the notch roots,resulting in a more uniform and symmetric shear stress distribution aboutthe notch-root axis.15 Further loading causes these axial cracks to arrest and

GP

whxyxy

xy

= =-( )-

DD

DD

tg e e45 45

SPwhxy = max

MTA6 11/22/2000 1:05 PM Page 112

Shear 113

the formation of numerous short interfacial cracks in the gauge section.Thislast event produces final failure with the peak load being used to calculateshear strength.

A more ideal shear stress state exists in the transverse or 90° specimens.The shear stress value is a minimum at the notch root and increases alongthe notch-root axis to a maximum value at the specimen centre. However,these specimens fail prematurely because fracture initiates by a combina-tion of shear and transverse tensile stresses at the notch roots. Cracks prop-agate in an unstable manner along the notch-root axis, which is the path of

(b)

(d)

(f)

(h)

(j)

(a)

(c)

(e)

(g)

(i)

6.7 Typical failure modes for V-notched beam test (* denotesunacceptable modes). (a) Unreinforced thermoplastic-shearyielding, (b) Unreinforced thermoset-brittle tensile*, (c) 0°continuous unidirectional, (d) 90° continuous unidirectional*, (e)woven fabric-intralaminar, (f) woven fabric-interlaminar, (g) ‘long’fibre/thermoplastic-shear yielding, (h) ‘long’ fibre/thermoplastic-brittle tensile*, (i) sheet moulding compound (SMC), (j) choppedstrand mat (CSM).

MTA6 11/22/2000 1:05 PM Page 113


least resistance. Transverse specimens invariably fail at significantly lowerstresses than those measured for the corresponding longitudinal specimens.The failure mode for transverse specimens does not represent shear failure,and these specimens are therefore unsuitable for measuring shear strength;longitudinal specimens should be used in preference.

A number of investigators, in particular Conant and Odom,19 have modi-fied the recommended ASTM fixture in an attempt to prevent misalign-ment of the two fixture halves, to improve the accuracy of specimen centering relative to the jig and to provide lateral constraint to the speci-men and wedges to prevent their displacement perpendicular to the planeof loading. Without doubt the major problem associated with the ASTMfixture is reliance on load application via the moving part of the jig, whichis supported by a single off-set post and bearing arrangement. Such a systemnot only allows rotation (about the post) of the moving part of the jig rela-tive to the fixed part but also assumes no deflection within the bearing itself. Such an assumption is not supported by experimental evidence, asthere is clear movement visible to the naked eye, particularly at high loads.Conant and Odom19 introduced two linear bearings operating on shafts,each passing through both parts of the jig, constraining the fixture to linearmotion in the plane of the specimen.The bearings were adjustable to obtainzero play, further preventing out-of-plane movement. A simpler arrange-ment could be provided by attaching the two sides of the basic Wyomingfixture within a four-bearing subpress.20

6.2.5 Plate-twist test

This test method, which was initially developed to measure the shearmodulus of plywood (ASTM D 3044),21 has proved to be satisfactory formeasuring shear moduli ranging from 0.29 GPa (chopped glass-fibre rein-forced polyurethane) to 88.2 GPa (steel). The test method is unsuitable fordetermining in-plane shear strength.22

In the plate-twist test, shown in Fig. 6.8, a square plate is supported on the two corners of one diagonal and load is applied at a constant rate to the corners of the opposite diagonal. The stress state induced in the plate is essentially pure shear. The total load is recorded as a func-tion of the resultant displacement. The plate should be square or rectan-gular in shape with the diagonals being of equal length and the length tothickness ratio should be ≥35 to minimise through-thickness shear effects.This test method is unsuitable for materials which are not transverselyisotropic or homogeneous through the section (e.g. multidirectional lami-nates including 0°/90° cross-plies). For these materials, the shear modulusproduced under flexural loads is no longer equivalent to the in-plane shearmodulus.

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Shear 115

The shear modulus, G12, can be determined from the displacement of theloading points (DdP):22

[6.18]

and from the displacement at the plate centre (DdC):

[6.19]

where a and b are the plate edge dimensions, h is the plate thickness andDP is the change in load (total) for a change in displacement, d. A practi-cal difficulty with the test has been the positioning of the loading points,which are normally in-board, rather than at the actual corner, as assumedin the analysis. This mispositioning leads to an error of several per cent inthe shear modulus value. A correction factor, K, has been introduced intoEquations [6.18] and [6.19] to account for in-board loading:23

[6.20]

where r is the ratio of L, the test span diagonal length, and d, the plate diag-onal length. The correction factor is relatively insensitive to variations inthe Poisson’s ratio, n, over the range 0.25–0.40.22 The analytical solution asgiven by Equation [6.20] produces K values almost identical to those cal-

K r r r r r( ) = - - -( ) -( )3 2 2 1 12 2ln

GPabK

h12 3

38

=DDdc

GPabK

hp12 3

34

=DDd

6.8 Plate-twist test.

MTA6 11/22/2000 1:05 PM Page 115


culated by Sims et al.22 using a polynomial line fit to finite difference data(i.e. less than 1% discrepancy for r > 0.8).

The plate twist method, which has recently become an international stan-dard, (ISO 15, 31024), recommends a standard plate specimen 150 mm ¥ 150mm and an in-board ratio of 0.95, with other plate dimensions beingoptional.The maximum thickness requirement for non-standard plate spec-imens should meet the requirement of 35h £ a £ b. The modulus is deter-mined over the displacement range of 0.1h to 0.3h, with a maximumallowable plate deflection of 0.5mm.

There are many advantages in the use of a plate specimen, particularlyfor moulded plastics and fibre-reinforced plastic composites. For thesematerials, plate specimens more closely represent the properties of actual products than moulded-to-size dumbbell and beam specimens orhoop-wound tubes. As the technique is non-destructive (most shearmethods result in the destruction of the test material during testing), aplate-twist specimen can also be sectioned into tensile or compressioncoupon specimens along the principal material directions to assess thematerial’s anisotropy. This guarantees that the shear modulus relatesdirectly to any other property measured from the plate. An additionalbonus is that the test results represent the shear response over a relativelylarge area, which means variations in microstructure across the plate areaveraged.

6.2.6 Torsion shear of a thin-walled tube

The torsion of a thin-walled circular tube is a method of directly applyingshear load to fibre-reinforced plastic composites, and from an appliedmechanics viewpoint it is the most desirable method for shear characterisa-tion. In this test, an approximate state of pure shear stress is induced in a thin-walled circumferentially wound cylindrical tube subjected to puretorque about the longitudinal axis of the specimen. The shear stress is uni-formly distributed around the circumference and along the specimenlength. Because the wall thickness is small compared with the mean radiusof the tube, the through-thickness shear gradient is negligible.

The specimen should have a gauge length to diameter (L/D) ratio >1, anda wall thickness to diameter ratio (h/D) of 0.02, or less.3 This serves topromote a uniform shear stress state at the specimen mid-length and pre-vents either local or global shear buckling. ASTM D 544825 recommendsthin-walled hoop-wound cylindrical specimens 140 mm long with a diame-ter of 100 mm and wall thickness of 2mm. Specimens are adhesively bondedto close concentrically fitting circular end fixtures, which are inserted at eachend of the specimen. The ends of the specimen are overwound with addi-tional material and tapered to promote failure within the gauge length. The

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Shear 117

bond lengths at the ends should be 20 mm. The end fixtures attached to thespecimen are mounted concentrically in the test machine, and a monotonicload is applied at constant torque speed of 2°/min. Axial stresses resultingfrom specimen shear deformation can be prevented by allowing free axialdisplacement. An example of a carbon fibre-reinforced epoxy specimenwith tapered end reinforcement is shown in Fig. 6.9.

Shear strain is measured by means of two bonded triaxial strain gauges(0°/45°/90°), diametrically opposite each other, at the centre of the speci-men. The strain gauges have a gauge length of 6 mm. The longitudinal andtransverse strain gauges are monitored to ensure there are no significantbending forces applied to the specimen during the test set-up and nobending loads present during the test. Data reduction is relatively straight-forward, with the in-plane shear stress and shear modulus calculated usingEquations [6.21] and [6.22]:3,25

[6.21]

[6.22]

where T is the applied torque, Ro the outer radial boundary and Ri the innerradial boundary of the cylinder. Shear strain is determined from the averageof shear strains measured using the ±45° strain gauges. Failure initiates atthe outer radius, with the in-plane shear stress at failure, Sxy, calculated bysubstituting the applied torque at failure into Equation [6.21].

The main disadvantage of this method is the cost and difficulty associ-ated with tubular specimen fabrication and testing. Prohibitive material andfabrication costs and the need for specialised testing and gripping equip-

Gxyxy

xy

xy= =-( )-

DD

DD

tg

te e45 45

tp

xyTR

R R=

-( )2

4 4

o

o i

225

1.7–

3.5

15°10

50

50 125 50

6.9 A thin-walled hoop-wound cylindrical specimen.

MTA6 11/22/2000 1:05 PM Page 117


ment have restricted the use of this test method. However, the method isfrequently used to generate reference data for comparison with other testmethods because the stress state within hoop-wound cylinders loaded intorsion approaches an ideal state of uniform shear.

6.3 Summary of test methods

The advantages and disadvantages of each test method are summarised inTable 6.1.

6.4 Comparison of data

A comparison of typical in-plane shear moduli obtained from a wide rangeof fibre-reinforced plastics tested using the plate-twist and the V-notchedbeam tests is shown in Table 6.2. As expected, the two sets of data are ingeneral agreement, because the materials tested are essentially homoge-neous in the through-thickness direction.

In-plane shear modulus and ultimate failure stress (i.e. shear strength)data obtained from a variety of test methods for both unidirectional carbon-fibre and glass-fibre composites are presented in Tables 6.3 and 6.4, with thecoefficient of variation (%) shown in brackets. The results clearly show thatthe shear moduli measured using the ±45° tension and two-rail shear testsare consistently higher than the values determined with the V-notchedbeam test.

The ±45° tension test consistently yields higher shear strength values thanthe other two methods.As a consequence of fibre scissoring, ultimate failureis delayed, with failure being mixed mode. However, damage in the form ofply cracking initiates at low strain levels, and therefore it is recommendedthat the test be terminated at g12 = 2.0%.

6.5 Recommendations and concluding remarks

The plate-twist test is capable of being used in conjunction with the V-notched beam test to measure the shear properties of fibre-reinforcedplastic composites. The range of materials which can be tested is diverseand not limited by the relative magnitude of property values. Testing is relatively straightforward, requiring only minimal instrumentation. Theplate-twist is a non-destructive test allowing specimens to be re-used forfurther tests.

Where material properties vary throughout a composite structure as aresult of variations in fibre orientation and so on arising from the manu-facturing process, the V-notched beam test can provide local values of shearmoduli and in many cases the shear strength. The need to determine the

MTA6 11/22/2000 1:05 PM Page 118

Shear 119

Tab

le 6

.1.

Ad

van

tag

es a

nd

dis

adva

nta

ges

of

shea

r te

st m

eth

od

s.

Test

Ad

van

tag

esD

isad

van

tag

es

±45°

ten

sio

n t

est

Sh

ear

mo

du

lus

and

str

eng

th o

bta

inab

leS

trai

n l

imit

oft

en r

equ

ired

fo

r st

ren

gth

Sp

ecim

en p

rep

arat

ion

is

stra

igh

tfo

rwar

dO

nly

su

itab

le f

or

con

tin

uo

us

alig

ned

fib

res

Sta

nd

ard

tes

t eq

uip

men

t (n

o s

pec

ial

load

ing

jig

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MTA6 11/22/2000 1:05 PM Page 119


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MTA6 11/22/2000 1:05 PM Page 120

Shear 121

failure mode occurring in each case is emphasised in Fig. 6.7. Further devel-opmental work is required to eliminate specimen instability, and thusprovide small front-to-back differences (1–2%) in shear strains andimproved repeatability.

The plate-twist and V-notched beam tests are complementary, offeringdesigners and engineers the means of characterising the shear properties ofan extensive range of composite materials.These two methods are relativelycost effective from both a fabrication and testing perspective, with datareduction being straightforward.

Table 6.2. Typical shear modulus (GPa) values.

Material description Plate-twist V-notched beam

Chopped glass-fibre/polyurethane 0.29 —Polymethyl methacrylate (PMMA) 1.20 1.56Polyether ether ketone (PEEK) 1.30 1.14Glass-fibre random mat/polypropylene 1.69 —Glass-fibre chopped strand mat (CSM) 2.16 —Glass-fibre/polyester pultrusion 3.04 3.20Sheet moulding compound (SMC) 4.80 4.69Glass-fibre square weave fabric/epoxy 5.00 5.03Unidirectional XAS/914C carbon-fibre/epoxy 5.08 5.61Unidirectional AS4/3501-6 carbon-fibre/epoxy 5.40 5.48Unidirectional carbon-fibre/PEEK (APC-2) 5.84 5.72

Table 6.3. Shear modulus (GPa) data for unidirectional fibre-reinforced systems (cv %).

Test method Carbon-fibre/epoxy Glass-fibre/epoxy Carbon-fibre/PEEK

V-notched beam 4.31 (12.3) 5.86 (2.9) 5.19 (7.6)±45° tension 4.83 (2.4) 6.99 (8.0) 6.57Two-rail 4.75 (4.1) 6.79 (4.6) —

Table 6.4. Shear strength (MPa) data for unidirectional fibre-reinforced systems (cv %).

Test method Carbon-fibre/epoxy Glass-fibre/epoxy Carbon-fibre/PEEK

V-notched beam 50.3 (13.8) 90.9 (1.7) 50.0 (10.2)±45° tension 115 (2.8) 167.4 (11.6) 58Two-rail 67.9 (5.9) 85.4 (3.28) —

MTA6 11/22/2000 1:05 PM Page 121


Acknowledgements

This chapter was written with the support of the Materials MeasurementProgramme, a programme of underpinning research financed by the UnitedKingdom Department of Trade and Industry. The author acknowledges thecontributions of his colleagues Dr Graham Sims and Mr William Nimmo atthe National Physical Laboratory, and Dr Paul Hogg, Queen Mary andWestfield College.

References

1. BS EN ISO 14,129: Fibre-reinforced Plastic Composites – Determination of In-plane Shear Modulus and Strength by ±45° Tension Test Method, 1997.

2. ASTM D 3518: ‘Standard test method for in-plane shear response of polymermatrix composite materials by tensile test of a ±45° laminate’, Annual Book ofASTM Standards, 100 Barr Harbor Drive,West Conshohocken, PA 19428, USA,Vol 15.03, 1997, 151–7.

3. S Chaterjee, D Adams and D W Oplinger, Test Methods for Composites, a Status Report. Volume III: Shear Test Methods, US Department of Trans-port, Federal Aviation Administration, Report DOT/FAA/CT-93/17, III,National Technical Information Service, Springfield, VA 22161, USA, June 1993.

4. R Byron Pipes, R A Blake Jr, J W Gillespie Jr, and L A Carlsson, Test methods,Delaware Composites Design Encyclopedia, Volume 6, eds L A Carlsson and J W Gillespie Jr, Technomic Publishing, Lancaster, PA, USA, 1990.

5. C C Chamis and J H Sinclair, ‘Ten-deg off-axis test for shear properties in fibercomposites’, Experimental Mechanics, 1977 17(9), September, 339–46.

6. M-J Pindera, G Choksi, J S Hidde and C T Herakovich, ‘A methodology for accurate shear characterisation of unidirectional composites’, Journal ofComposite Materials, 1987 21 1164–84.

7. ISO 527: Plastics – Determination of Tensile Properties. Part 5 – Test Conditionsfor Unidirectional Fibre-reinforced Plastic Composites, 1994.

8. F Pierron and A Vautrin, ‘The 10° off-axis tensile test: A critical approach’,Composites Science and Technology, 1996 56 483–8.

9. F Pierron and A Vautrin, ‘A new methodology for composite shear strengthmeasurement using the 10° off-axis tensile test’, Proceedings of ECCM-7 (Euro-pean Conference on Composite Materials), Volume 2, Institute of Materials,London, UK, Woodhead Publishing, May, 1996, 119–24.

10. ASTM D 4255: ‘Standard guide for testing in-plane shear properties of composite laminates’, Annual Book of ASTM Standards, 100 Barr HarborDrive, West Conshohocken, PA 19428, USA, Vol 15.03, 1997, 199–208.

11. N Iosipescu, ‘New accurate procedure for single shear testing of metals’, Journalof Materials, 1967 2(3) 537–66.

12. ASTM D 5379: ‘Standard test method for shear properties of composite materials by the V-notched beam method’, Annual Book of ASTM Standards,100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Vol 15.03, 1997,235–47.

MTA6 11/22/2000 1:05 PM Page 122

Shear 123

13. D F Adams and D E Walrath, ‘Current status of the Iosipescu shear testmethod’, Journal of Composite Materials, 1987 21 494–507.

14. D W Wilson, ‘Evaluation of the V-notched beam shear test through an interlaboratory study’, Journal of Composites Technology and Research, 199012(3) 131–8.

15. W R Broughton, M Kumosa and D Hull, ‘Analysis of the Iosispecu shear testas applied to unidirectional carbon-fibre reinforced composites’, CompositesScience and Technology 1990, 38 299–325.

16. H Ho, M Y Tsai and J Morton, ‘Numerical analysis of the Iosipescu specimenfor composite materials’, Composites Science and Technology, 1993 46 115–28.

17. F Pierron, New Iosipescu Fixture for the Measurement of the In-plane ShearModulus of Laminated Composites: Design and Experimental Procedure,Internal Report No. 940125, École des Mines de Saint-Étienne, DépartementMécanique et Matériaux, France, January 1994.

18. E M Odom, D M Blackketter and B Suratno, ‘Experimental and analyticalinvestigation of the modified Wyoming shear test fixture’, ExperimentalMechanics, 1994 34(1).

19. N R Conant and E M Odom, ‘An improved Iosipescu shear test fixture’, Journalof Composites Technology and Research, 1995 17(1) 50–5.

20. J M Hodgkinson, Imperial College of Science, Technology and Medicine,London, UK, March 1999, private communication.

21. ASTM D 3044, ‘Standard test method for shear modulus of wood-based structural panels’, Annual Book of ASTM Standards, 100 Barr Harbor Drive,West Conshohocken, PA 19428, USA, Vol 4.10, 1998, 479–481.

22. G D Sims, W Nimmo, A F Johnson and D H Ferriss, Analysis of Plate-twist Testfor In-plane Shear Modulus of Composite Materials, NPL Report DMM(A)54,1992.

23. B Gommers, I Verpoest and P Van Houtte, ‘Further developments in testing and analysis of the plate twist test for in-plane shear modulus measurements’,Composites Part A, 1996 27 1085–7.

24. ISO 15,310: Fibre-Reinforced Plastic Composites – Determination of In-planeShear Modulus by the Plate Twist Method, 1999.

25. ASTM D 5488: ‘Standard test method for in-plane shear properties of hoopwound polymer matrix composite cylinders’, Annual Book of ASTM Standards,100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Vol 4.10, 1998,248–259.

MTA6 11/22/2000 1:05 PM Page 123

7.1 Introduction

The use of flexural tests to determine the mechanical properties of resinsand laminated fibre composite materials is widespread throughout indus-try owing to the relative simplicity of the test method, instrumentation andequipment required. It is also possible to use flexure tests to determine theinterlaminar shear strength of a laminate (using a short beam), and this isdealt with in Chapter 8, and to investigate the properties of laminate facedsandwich beams with either honeycomb or foam cores. By careful designof the sandwich beam it is possible to assess not only the flexural and shearstiffness of the construction, but also the shear modulus and shear strengthof the core, the tensile and compression moduli and strength of the facings,and to evaluate the bond between core and facings. Flexure may also beused to evaluate the interlaminar fracture toughness of laminates, asdescribed in Chapter 9 of this book, and to assess the stiffness, strength andfatigue behaviour of more complex structures. In this chapter the discus-sion will be restricted to the flexural testing of simple laminated beams.

There is a wide variety of standard test methods for flexure described bythe National and International Standardization bodies. The details of thetest methods recommended vary from one organisation to another, somebeing very precise, others allowing a wide degree of choice. Few of the avail-able recommended test methods were developed specifically with high per-formance fibre-plastic laminated composites in mind, having been originallyproposed for the mechanical testing of homogeneous solids. Amongst theexceptions here are those methods described by the American Society forTesting and Materials (ASTM),1 the Composites Research Advisory Group(CRAG)2 and the recently introduced International Standard.3 Theseorganisations have all made some attempt to address the particular needsof these heterogeneous non-isotropic materials.

Although it is frequently found that flexure tests give results which arevery similar to those from other tests (tension and compression, for

7Flexure

J M HODGKINSON

124

MTA7 11/22/2000 1:14 PM Page 124

example) which are recommended for the acquisition of design data, it isgenerally recognised that test methods applying flexure as a means ofloading do not produce results of design data quality. Data obtained fromsome flexure test methods have to be treated with caution, if not scepticism,because it is possible to achieve results which are a function of the methodused, not reflecting in any way the properties of the material it was intendedto measure. In general, flexure type tests are applicable to quality controland material selection where comparative rather than absolute values arerequired. As such, these types of test continue to be used widely becausetheir relative simplicity allows a rapid assessment to be made with aminimum of fuss and technical expertise.

7.2 Three-point and four-point flexure tests

For flexure tests there is no involvement with end-tabs, or (normally)changes in the specimen shape, tests being conducted on simply supportedbeams of constant cross-sectional area. The two methods most usually usedfor the determination of flexural properties of laminates are the three-pointand four-point tests illustrated schematically in Figs. 7.1 and 7.2, respec-tively. A flat rectangular specimen is simply supported close to its ends andeither centrally loaded in three-point bending or by two loads placed sym-metrically between the supports, giving four-point bending. Also shown inFigs. 7.1 and 7.2 are the shear force and bending moment diagrams relatedto the particular loading regimes.

Clearly stress concentrations exist at the loading points but in four-pointloading, between the inner loading points, there is a constant bendingmoment. Figure 7.3 shows the variation in normal stress, caused by bendingmoment, and shear stress, caused by shear force, assuming a rectangularspecimen cross-section.

In Figs. 7.1 to 7.3 the material properties are assumed to be uniformthrough the thickness because they are in unidirectional composites orisotropic materials. Under these circumstances the normal stress varies lin-early from a maximum in compression on one surface to an equal maximumin tension on the other surface, passing through zero at the mid-plane, whichis usually called the neutral axis. The maximum normal stress is given byEquation [7.1]:

[7.1]

where M is the bending moment, with b and h being the specimen widthand thickness, respectively.The distribution of shear stress is parabolic, witha maximum at the neutral axis and zero at the outer surfaces of the beam;the maximum value is given by Equation [7.2]:

s =6

2

Mbh

Flexure 125

MTA7 11/22/2000 1:15 PM Page 125

[7.2]

where Fs is the shear force on the specimen cross-section.The flexural response of the beam is obtained by recording the load

applied and the resulting strain. The strain can be measured by bonding astrain gauge to the tensile surface of the beam, or by measuring the dis-placement at the centre of the beam and assuming that beam theory4

applies, so that strains can be calculated. The bending moment, M, is a func-tion of the measured load and specimen geometry, so that the applied stress

t =32

Fbh

s


P

h

S

L

Fs = P /2

Fs = P /2

M = PS/4

Shear force diagram

Bending moment diagram

7.1 Three-point flexure test, together with shear force and bendingmoment diagrams.

MTA7 11/22/2000 1:15 PM Page 126

can be calculated from Equation [7.1] and the full stress–strain behaviourof the beam in bending can be obtained.

The states of stress in specimens subjected to three- or four-point bendingtests are somewhat different and may lead to differences in the results. Thebending moment in a three-point bend test increases linearly from zero atthe supports to a maximum under the central loading point, as shown inFig. 7.1, whereas the shear force (and hence the interlaminar shear stress atthe midplane) is uniform along the length of the beam. In four-pointbending the bending moments increase linearly from zero at the supportsto a maximum at the loading points and are constant between these points,as shown in Fig. 7.2. The shear force and interlaminar shear stress are zero

Flexure 127

P

h

Si

L

Fs = P /2

So

Fs = P /2

Shear force diagram

M = P(So - Si)/4

Bending moment diagram

7.2 Four-point flexure test, together with shear force and bendingmoment diagrams.

MTA7 11/22/2000 1:15 PM Page 127

between the loading points, so that this central portion of the beam is subjected to a pure bending moment. From the point of view of the stateof stress, the four-point test is the more desirable of the two methods butthe three-point test is easier to carry out.

The flexural strength is the stress on the surface of the specimen at failure,which should be accompanied by the breaking of fibres, rather than inter-laminar shear. The strength is calculated using the maximum bendingmoment, corresponding to the failure load, in Equation [7.1], and assumesa linear stress–strain relationship up to failure. True flexural failure isencouraged by the use of a large loading span to specimen thickness ratio,because the span of the beam has no influence on the interlaminar shearstress but a large span results in a higher bending moment, promoting lon-gitudinal failure. Unfortunately large span-to-thickness ratios produce largedeflections, under load, which make it necessary to take account of hori-zontal forces developed at the supports when calculating the appropriatebending moment.

7.3 Comparison of recommended test methods

The aim here is to draw attention to some of the inconsistencies (and pos-sible pitfalls when carrying out tests) which exist between some of the flex-ural test methods which have been published. It is clearly not possible toconsider all of the national standards, so the comparison will be limited to those which give a good example of general recommended practice forthe testing of fibre-reinforced plastics materials. These include those fromthe American Society for Testing and Materials (ASTM D 790M-93),1 the


h

b

|sc|= |st|= 6M/bh2

tt = 3Fs/2bh

sc

st

Cross-section Normal stress Shear stress

7.3 Variation of normal stress and shear stress in a flexure test.

MTA7 11/22/2000 1:15 PM Page 128

Composites Research Advisory Group (CRAG),2 BS 2782 method 10055

and ISO-14125.3

A detailed reading of these recommendations reveals that prior to thepublication of ISO-14125 there was no agreement on virtually any aspectof the test method to be used between the three organisations. Areas ofconflict include: specimen dimensions, span-to-thickness ratios, the use ofthree- or four-point loading arrangements, loading and support nose radii,loading rate, minimum overhang of specimen length beyond the supportpoints and the calculations to be used when making allowance for large displacements.

7.3.1 Specimen dimensions and testing arrangement

The ASTM and BSI specifications allow a wide freedom of choice in termsof specimen dimensions, as long as the cross-section is rectangular and spe-cific span-to-thickness (S/h) ratios are adhered to. The ASTM specificationallows a series of different S/h ratios (16 :1, 32 :1, 40 :1 and 60 :1) in boththree- and four-point bending, BSI just one (16 :1), and that in three-pointloading only. ASTM offers two arrangements for four-point loading, withthe loading points set at either 1/3 or 1/4 of the support span. The ASTMhave attempted to satisfy the requirements of a range of industries with anumber of reinforced materials in mind, whilst the BSI standard is restrictedto textile glass-fibre reinforced plastics. On the other hand, CRAG, whichis also restricted to the three-point loading arrangement, requires a partic-ular (2mm) laminate thickness, and specifies S/h ratios dependent on laminate layup and the type of fibre used. This is clearly aimed at high performance materials. Table 7.1 summarizes the dimensional possibilitiesfor specimens within the ASTM, CRAG and BSI specifications. Table 7.2gives the possibilities for support and loading nose radii, span-to-thicknessratios and loading (or strain) rate.

The ASTM specification includes a series of tables which indicate theappropriate specimen width, length, support spans (and loading span for

Flexure 129

Table 7.1. Dimensional possibilities for flexurespecimens in several specifications.

Specification Thickness Width Length(mm) (mm) (mm)

ASTM D790M 1–25 10–25 50–1800BSI 2782 1–50 15–80 20hCRAG 2 10 100

MTA7 11/22/2000 1:15 PM Page 129

four-point testing) and rate of crosshead motion (based on the strain rateof 0.01mmmm-1) for the full range of specimen thicknesses and span-to-thickness ratios allowed. This is all very well but, given the range of possibilities, it is not clear under which set of conditions a particular type of material should be tested in order to obtain meaningful results.The CRAG document is far more specific and includes advice on material type, fibre alignment and appropriate span-to-thickness ratio given in Table 7.3.

ISO-14125, perhaps understandably, appears to be an amalgamation ofthe previous three, although there were undoubtably influences from other national organisations in its drafting. It covers both three- and four-point (in this case only the 1/3 option is available) bending methods, tightens up on specimen thickness, length and width possibilities,is coherent in terms of loading and support nose radii and loading rate,and advises on what types of material should be tested under specific span-to-thickness ratios. Tables 7.4 and 7.5 give the specimen dimensionalpossibilities for three- and four-point bending tests, respectively, in this International Standard.


Table 7.2. Possibilities for support and loading nose radii, span-to-thicknessratios and loading rate in several specifications.

Specification Support Loading Span-to- Strain ratenose radius nose radius thickness (mmmm-1) or(mm) (mm) ratio failure time

ASTM D790M 3–1.5h 3–4h 16, 32, 40, 60 :1 0.01 and 0.1BSI 2782 2 5 16 :1 0.01CRAG 3, 5 5, 12.5 16, 20, 25, 40 :1 Failure time

30–180s

Table 7.3. Advice in the CRAG specification on S/h ratios for particular fibretypes.

Reinforcement Fibre alignment to beam axis Span-to-thickness ratio

Unidirectional carbon 0° 40 :1Unidirectional carbon 90° 25 :1Woven carbon 0°/90° 25 :1Unidirectional glass 0° 20 :1Unidirectional glass 90° 20 :1Woven glass 0°/90° 20 :1Woven Kevlar 0°/90° 16 :1

MTA7 11/22/2000 1:15 PM Page 130

7.3.2 Calculations

7.3.2.1 Flexural modulus

In each of the specifications the flexural modulus is defined in the same way,such that for a three-point bending test:

[7.3]

where Ef is the flexural modulus, S is the support span, m is the slope of theload/deflection curve, with b and h being the width and thickness of thebeam, respectively.

ES mbh

f =3

34

Flexure 131

Table 7.4. Recommended specimen dimensions for different material types forthree-point flexure in ISO-14125.

Material Length Span Width Thickness(mm) (mm) (mm) (mm)

Class I 80 64 10 4Class II 80 64 15 4Class III 60 40 15 2Class IV 100 80 15 2

Class I: discontinuous fibre-reinforced thermoplastics.Class II: mat, continuous mat, fabric and mixed format reinforced plastic. DMC(dough moulding compound), BMC (bulk moulding compound) and SMC(sheet moulding compound).Class III: Transverse (90°) unidirectional composites. Unidirectional (0°) andmultidirectional composites with 5 < E11/G13 ≤ 15 (for example, glass-fibresystems).Class IV: Unidirectional (0°) and multidirectional composites with 15 < E11/G13

≤ 50 (for example, carbon-fibre systems).

Table 7.5. Recommended specimen dimensions for different material types forfour-point flexure in ISO-14125.

Material Length Support span Loading span Width Thickness(mm) (mm) (mm) (mm) (mm)

Class I 80 66 22 10 4Class II 80 66 22 15 4Class III 60 45 15 15 2Class IV 100 81 27 15 2

NB Classes as given in Table 7.4.

MTA7 11/22/2000 1:15 PM Page 131

As was mentioned previously, ASTM D 790 offers two options for thefour-point flexure test. In the first the loading span is 1/3 of the supportspan, in the second it is 1/2 of the support span. ISO-14125 offers only thefirst of these options. The flexural modulus is given by Equations [7.4] and[7.5]:

[7.4]

[7.5]

It can be seen from Equations [7.3]–[7.5] that the precise measurement ofthe support span and specimen thickness are crucially important, as theyare both raised to the power 3.

7.3.2.2 Maximum stress

The maximum stress at the outer surface of the beam in three-point bendingis also defined in the same way by each of the specifications considered here,such that:

[7.6]

where s is the stress on the outer surface of the specimen and P the appliedload.

ASTM D 790, BSI 2782 and ISO-14125 each consider what correctionshould be applied to the stress equation if the beam experiences largedeflections (greater than 10% of the support span). Table 7.6 shows the discrepancies which exist in these recommendations. CRAG makes nocomment on a correction. It will be noted that whilst these corrections aresimilar, they are not precisely the same.

s =32 2

PSbh

Option 2 fES mbh

= 0 173

3.

Option 1 fES mbh

= 0 213

3.


Table 7.6. Different ways of correcting for large deflections in a three-pointbend test.

Specification Corrected stress equation

ASTM D790

BSI 2782 and ISO-14125

D is the deflection of the beam at the centre of the support span.

s

s

= + -ÊË

ˆ¯

= +ÊË

ˆ¯

32

16 4

32

14

2

2

2 2

2

2

2

PSbh

DS

hDS

PSbh

DS

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The maximum stress at the outer surface of a beam tested in four-pointflexure with the loading span 1/3 of the support span is given by both ASTM D 790 and ISO-14125 as:

[7.7]

and in the case of ASTM, where the loading span can be 1/2 of the supportspan, the maximum stress is given by:

[7.8]

Again, corrections are recommended for large deflections and those givenby both the ASTM and ISO documents are given in Table 7.7.

It is, perhaps, interesting to note from Tables 7.6 and 7.7 that for the three-point bend test correction the BSI standard has been adopted by ISO asopposed to that from the ASTM standard, whereas in the case of the four-point bend test ISO have been happy to adopt the ASTM correction.

7.4 Failure modes

Whilst a wide range of failure modes might occur under flexural loading,dependent on the particular test method used and the type or layup ofmaterial under test, these are broadly very similar for three- or four-pointflexure tests. The types of failure likely to be observed are shown in Fig. 7.4,not all of which might be considered as acceptable flexural failures, thoseincluding evidence of interlaminar shear being particularly suspect. Cer-tainly for specimens with axially aligned fibres one would not expect to seeinterlaminar shear accompanying failure, as this would suggest that thespan-to-thickness ratio used in the test was too low.

7.5 Typical data

A number of investigations have been conducted at Imperial College into various aspects of the flexural behaviour of laminated composites.

s =34 2

PSbh

s =PSbh2

Flexure 133

Table 7.7. Ways of correcting for large deflections in four-point bend tests.

Standard Corrected stress equation

ASTM D790 and ISO-14125(loading span 1/3 of the support span)

ASTM D790(loading span 1/2 of the support span)

s

s

= + -ÊË

ˆ¯

= -ÊË

ˆ¯

PSbh

DS

hDS

PSbh

hDS

2

2

2 2

2 2

14 7 7 04

34

110 9

. .

.

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These were carried out over a number of years by different research students.

7.5.1 Programme 1

The first of these projects6 was a comparison of the three test methods1,2,5

referred to above (i.e.ASTM D 790, CRAG and BS 2782).At the time therewas a general dissatisfaction with test methods for advanced fibre com-posite materials, and it was anticipated that the data from these three testmethods might well be quite different. Since the choices of specimen shapeand test arrangements are quite wide, and vary from standard to standard,a 2 mm thick laminate was decided upon (CRAG only allows this thick-ness); all other testing factors were followed for the particular standardbeing investigated. The material used was Ciba Geigy (now Hexcel)XAS/913 CFRP (carbon-fibre reinforced plastic), with unidirectional and avariety of other layups being tested. Here only the unidirectional data willbe discussed; it is presented in Table 7.8, together with the other test para-meters. In each case at least five specimens were tested.

The results for flexural modulus are reasonably consistent, in the range


Tensile fracture ofouter surface

Compression fractureof outer surface

Tensile fracture withinterlaminar shear

Compression fracturewith interlaminar shear

Interlaminar shear

Tensile fractureof fibres

7.4 Schematic of possible failure modes in three- and four-pointflexural tests.

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Flexure 135

Tab

le 7

.8.

Test

co

nd

itio

ns

ado

pte

d f

or

a co

mp

aris

on

bet

wee

n d

iffe

ren

t te

st m

eth

od

s an

d t

he

flex

ura

l m

od

ulu

s an

d s

tren

gth

res

ult

so

bta

ined

fo

r X

AS

/913

CFR

P.

Met

ho

db

hS

/hL

Load

Su

pp

ort

Load

ing

Es m

ax

(mm

)(m

m)

(mm

)ro

ller

rolle

rra

te(M

Pa)

(MP

a)ra

diu

sra

diu

s(m

mm

m-1

)(m

m)

(mm

)

AS

TM

252

1650

3.2

3.2

0.9

59.0

1370

3-p

oin

t±5

%±4

.1%

AS

TM

252

3280

3.2

3.2

3.4

103.

214

403-

po

int

±4.2

%±3

.2%

AS

TM

252

4010

03.

23.

25.

310

1.7

1490

3-p

oin

t±4

.4%

±7.3

%A

ST

M25

260

150

3.2

3.2

12.0

116.

715

603-

po

int

±4.5

%±6

.2%

AS

TM

252

20/6

015

03.

23.

213

.313

2.4

1607

4-p

oin

t±7

.7%

±6.5

%A

ST

M25

230

/60

150

3.2

3.2

12.0

144.

914

414-

po

int

±7.2

%±6

.7%

BS

I15

216

502

51.

073

.714

603-

po

int

±7.0

%±5

.3%

CR

AG

102

4010

05

12.5

5.0

114.

917

203-

po

int

±1.9

%±6

.4%

MTA7 11/22/2000 1:15 PM Page 135

100–117GPa, as long as the span-to-thickness ratio is greater than the 16 :1 allowed under the ASTM and British Standards. At a span-to-thickness ratio of 16 :1 the elastic modulus measured is approximately one-half of the correct value. Clearly such a low span-to-thickness ratio is inappropriate for these extremely stiff materials. On the other hand thereis a suspicion that large span-to-thickness ratios may lead to somewhathigher strength values being recorded. Note here the somewhat highervalues obtained with the CRAG specimens and the high span-to-thicknessratio ASTM specimens. It appears that the 16 :1 span-to-thickness ratio isentirely satisfactory for the measurement of strength in these materials.

Whilst it true that there are other influences at play in this series of exper-iments, for example differences in specimen width, overhang and load andsupport roller radii, by far the most important factor is the span-to-thickness ratio used.

One final observation is that the results from the four-point tests are notconvincingly better than those from three-point tests. The flexural modulusis rather high in both cases examined here, although the strengths recordedare similar to those from three-point tests.

Figure 7.5 shows typical failures for the unidirectional specimens testedunder the various regimes of the programme. It should be noted that all ofthe three-point flexure specimens failed by complete and brittle fracture ofthe specimen, across the width, under the central loading roller, exceptthose tested at a span-to-thickness ratio of 16 :1. For these specimens therewas evidence of damage under the central roller on both tension and compression surfaces; however, there was no complete fracture of the specimens.The four-point bend specimens also fractured in a brittle manneracross their width – fractures which appear to have initiated under thecentral loading rollers, causing not only width-wise fracture but also interlaminar failures between these central rollers.

7.5.2 Programme 2

A second programme of three-point flexure tests7 involved three differentCFRP materials from Hexcel: XAS/913, XAS/914 and HTA/6376.The layuptested in all cases was unidirectional, with both axial and transverse speci-mens being investigated.The tests were carried out according to the CRAGrecommendations for specimen dimensions, roller diameters and testingrate. Five specimens were tested in each case.

The results are shown in Table 7.9, where it can be seen that the flexuralmodulus and strength values for XAS/913 (axial) are very similar to thoseof the previous study using the CRAG test. It appears from these resultsthat XAS/914 (axial) has a similar flexural modulus to that of XAS/913(axial). This might be expected since the composite has the same fibre in


MTA7 11/22/2000 1:15 PM Page 136

Flexure 137

7.5 Typical failures for unidirectional three- and four-point flexurespecimens: (a) ASTM 3-point, 16:1; (b) ASTM 3-point, 32:1; (c)ASTM 3-point, 40:1; (d) ASTM 3-point, 60:1; (e) CRAG 3-point,40:1; (f) BSI 3-point, 16:1; (g) ASTM 4-point, 1/4 points, 40:1.

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each case, the resin having little influence on the modulus value. Thestrength of XAS/914 (axial) is, however, significantly greater, with thestrength of HTA/6376 (axial) being greater still and with a slightly increasedflexural modulus. The scatter in the axial data is quite low, but for the transverse data it is greatly increased. Given the degree of scatter in theflexural modulus data between the three materials, it would be difficult to suggest that there was much difference.Although the transverse strengthdata are subject to a similar degree of scatter, it does appear that theHTA/6376 material is superior to the other two. All of the fractures were brittle, across the width of the specimens, under the central loadingroller.

7.6 Steel versus soft lined rollers

It has been mentioned previously that the loading rollers introduce a for-midable stress concentration in flexure tests, even under four-point loading.A means of mitigating this effect is to line the rollers with a soft plastic orrubbery material, or even replace the steel rollers with plastic ones. Thismakes the specimen effectively useless for the measurement of flexuralmodulus unless a strain gauge is used, because there is significant contactdeflection of the relatively soft roller material when load is applied.However, this approach does introduce the possibility of a more ‘realistic’flexural failure. ISO 14125 allows this option, suggesting that ‘a thin shim,or cushion, between the loading member and the specimen may be used to discourage failure of the compressive face of the specimen’. What ISOactually proposes is that a 0.2mm thick shim of polypropylene has beenfound to work well in this respect.

Hexcel T300/913 CFRP specimens, 2mm thick (150 mm long and 25 mmwide) with unidirectional axially aligned fibres, were tested8 in three- and


Table 7.9. Flexural modulus and strength data for several CFRPs with eitheraxial or transverse unidirectional fibres.

Material Flexural modulus Flexural strength(GPa) (MPa)

XAS/913 (axial) 113.0 ± 2% 1642.5 ± 2%XAS/914 (axial) 112.3 ± 2% 1786.9 ± 2%HTA/6376 (axial) 119.5 ± 5% 1924.8 ± 5%XAS/913 (transverse) 9.7 ± 11% 99.8 ± 16%XAS/914 (transverse) 8.3 ± 22% 83.0 ± 26%HTA/6376 (transverse) 10.0 ± 5% 109.1 ± 12%

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four-point flexure according to ASTM D790. A first series of experimentsinvestigated the effect in three-point loading (S/h of 60 :1) of varying thediameter of the central steel loading pin, whilst keeping the steel supportpin diameters constant at 6 mm. The results shown in Table 7.10 indicate, asmight be predicted, that as the loading pin diameter is increased from 6 mmto 16mm (all allowed in the standard for this thickness of material), themeasured strength increases monotonically.

A second series of experiments was carried out on specimens from thesame 2mm thick laminate, with specimens of the same size as the first seriesof experiments, in three-point loading (S/h 60 :1) and both options of four-point loading allowed under the ASTM standard (in both cases the outersupport span was 120mm, with the inner loading span being either 60mmor 40mm). The support and loading rollers were always 6mm in diameter(the only diameter allowed under the standard) and were either steel orplastic. The results are shown in Table 7.11. It is clear that the strength measured using the plastic pins is significantly higher in all cases.

The failure modes were quite different, dependent upon whether the pinsused were steel or plastic. When plastic pins were used no damage wasnoted on the compression side of the specimen, but multiple fibre failureoccurred on the tension side in both three- and four-point loading, givingthe surface a brush-like appearance, as shown in Fig. 7.6. Failure using thesteel pins was catastrophic and occurred across the width, under the centralloading pin(s), for three- and four-point loading arrangements, as noted previously.

Flexure 139

Table 7.10. Influence of steel loading pin diameteron the flexural strength of T300/913 CFRP in three-point flexure.

Pin diameter (mm) 6 8 10 16Strength (MPa) 1685 1726 1757 1766

Table 7.11. Flexural strength of T300/913 CFRP using steel and plastic loadingpins.

Experiment Failure stress (plastic Failure stress (steelpins) (MPa) pins) (MPa)

Three-point loading 1955 1685Four-point loading (1/2 span) 1640 1519Four-point loading (1/3 span) 1832 1590

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7.7 Through-thickness flexure

Chapter 8 of this book covers test methods for the measurement of through-thickness elastic and strength properties of composite laminates. It does,however, seem more appropriate to introduce here a novel approach tothrough-thickness testing in flexure.

Mespoulet9 designed a beam-type specimen, shown in Fig. 7.7, which con-sisted of a central region of composite machined from a 160-ply, 20mmthick unidirectional laminate of Hexcel T300/914 CFRP, the compositebeing bonded to epoxy resin ‘arms’ in a jig into which the liquid epoxy waspoured and allowed to cure.The length of the central composite section was17mm, and its cross-section was waisted by grinding to give 4mm ¥ 4mmat the centre and 8 mm ¥ 8mm at the arms. The orientation of the fibres in the central region when under test could be in the 1–3 or 2–3 direction(i.e. not along the axis of the specimen), dependent upon how the specimenwas orientated with respect to the loading jig.

Eight specimens of were tested in four-point flexure with an outer span


7.6 Brush-like appearance of fractured CFRP specimen tested usingplastic loading and support pins in four-point loading.

MTA7 11/22/2000 1:15 PM Page 140

of 80mm and an inner span of 40mm (i.e. at an effective span-to-thicknessratio of 20 :1) to determine the through-thickness (1–3) failure stress, whichwas found to be 105 MPa. Specially designed in-plane transverse tensionspecimens in this same programme, testing thick laminates, gave a failurestress of 96.9MPa. It should also be noted that in-plane transverse tensionspecimens from a 2 mm thick laminate of equivalent material (XAS/914),using the CRAG recommendations failed at 83 MPa (see Table 7.9).

7.8 Conclusions

Whilst it has to be admitted that data from flexure tests will always beviewed (with good cause) with a certain amount of suspicion, the test doesprovide a relatively straightforward, easy to use and economical techniquefor qualifying materials. This chapter has concerned itself with laminatedbeams of one sort or another; there are, however, a wide range of othertypes of beam and structure which the technique can be used for, withsuccess. Even within the restricted remit of this book, the flexure techniquehas been shown to be a useful adjunct to the overall testing portfolio, findinguse not only in the description of in-plane and out-of-plane laminate prop-erties (both in this chapter), but also in shear behaviour (chapter 6) andinterlaminar fracture behaviour (chapter 9).

This is a testing technique which should not, and will not, be dismissedlightly.

References

1. ASTM D790M-93, ‘Standard test methods for flexural properties of unreinforcedand reinforced plastics and electrical insulating materials’, American Society forTesting and Materials, Annual Book of ASTM Standards, Vol. 08.01, 1993.

2. P T Curtis (ed), CRAG Test Methods for the Measurement of the EngineeringProperties of Fibre-reinforced Plastics, Royal Aircraft Establishment, TechnicalReport 88012, February 1988.

Flexure 141

40

4 ¥ 48

8 epoxy specimen

1.515

80100

epoxy

7.7 Through-thickness flexure specimen. Dimensions are inmillimetres.

MTA7 11/22/2000 1:15 PM Page 141

3. International Standards Organisation (ISO-14125), Fibre Reinforced PlasticComposite – Determination of Flexural Properties, 1998.

4. A Morley, Strength of Materials, 9th Edition, Longmans, London, 1940.5. British Standards Institute, BS 2782, British Standard Methods of Testing Plas-

tics, Part 10, Glass reinforced plastics, Method 1005, Determination of FlexuralProperties. Three Point Method, 1977.

6. N R Sottos, J M Hodgkinson and F L Matthews, ‘A practical comparison of standard test methods using carbon fibre reinforced epoxy’, Proceedings of theSixth International Conference on Composite Materials and Second EuropeanConference on Composite Materials, Imperial College, London, Elsevier AppliedScience, 1987.

7. P Francotte, J M Hodgkinson and R Keunings, Experimental and TheoreticalAnalysis of the General and Micromechanical Behaviour of Composite Materials,Report of joint project between Imperial College and Université Catholique deLouvain, 1993.

8. R Grothaus, J M Hodgkinson and K Kocker, ‘Interpretation of flexural tests usingWeibull strength theory’, Proceedings of the 3rd International Conference onDeformation and Fracture of Composites, The Institute of Materials, Guildford,UK, March 1995, 269–76.

9. S Mespoulet, Through-thickness Test Methods for Laminated Composite Ma-terials, PhD Thesis, Centre for Composite Materials, Imperial College, LondonUniversity, UK, January 1998.


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8.1 Introduction

Interlaminar (out-of-plane) stresses, combined with inherently lowthrough-thickness (T-T) strength properties, especially in tension, are primarily responsible for damage initiation and eventual structural failureof layered composite materials. T-T properties of laminated composite are essentially matrix dominated and, as a result, are often significantlylower than the in-plane stiffness and strength properties of the ma-terial. There is also a tendency to associate interlaminar stresses with ‘thick’sections; however, interlaminar stresses and strains may be induced in ‘thin’ laminates through the application of membrane loads (i.e. in-planeloads).

Engineering structures are often unavoidably complex, consisting of anumber of geometric features which induce interlaminar stresses andstrains. High stress gradients are present in regions such as free edges(stress-free boundaries), curved edges (e.g. bolt holes), ply termination,thickness changes (e.g. ply drop-off or taper) and bolted or bonded joints.Until recently, the general tendency has been to use two-dimensional (2-D)(plane stress) analysis to evaluate structural response to three-dimensional(3-D) loading configurations. Three-dimensional finite element analysis,now in common use, frequently requires a full complement of in-plane andT-T properties, especially for those ‘difficult but real’ aspects of designwhere the composite, to perform its function, has to be shaped (e.g. flanged)and connected (e.g. bonded) to the remainder of the system. The need forT-T data poses a major problem; with the exception of shear, there are no recognised national or international standards available for generatingreliable design data. As a consequence, designers and engineers rely on in-plane data or ad hoc tests to determine structural performance. Thisapproach is clearly unsatisfactory, as the use of the data will result in eitherunderdesigned or overdesigned structures.1–3

8Through-thickness testing*

W R BROUGHTON

143

* Crown copyright

MTA8 11/22/2000 1:19 PM Page 143

Research has been undertaken worldwide into test methods and designprocedures for in-plane properties of fibre-reinforced plastic composites.As a result, a supporting infrastructure of test methods is beginning to beestablished on an international basis, and these are discussed in other chapters of this book. Considerably less research and development of testmethods suitable for the measurement of T-T properties has been under-taken, but there has been a continuing interest for many years and the avail-able literature has been critically reviewed.1,2,4

This chapter evaluates the current status of test methods for mea-suring T-T properties under tensile, compressive and shear loading.Each method is examined in terms of the level of standardisation, elastic and strength properties obtained, material suitability, material thicknessrequirements, specimen fabrication, test apparatus, methods of data measurement and data reduction procedures. Consideration has also beengiven to both the practicality of using the test method in an industrial environment, in terms of ensuring ‘fitness for purpose’, and to the degreeof uniformity of stress distributions throughout the test geometry. In most cases, the issue of test geometry and associated dimensions is still to be resolved.

8.2 General issues

A problem with many T-T test methods is the need to fabricate thicksamples in order to machine specimens in the T-T direction. Fabrication ofspecimens with thicknesses of the order of 20 mm or greater is expensiveand often difficult, with process induced stresses becoming increasinglyimportant as the thickness is increased. Residual stresses, which are stronglyinfluenced by processing history, can have a significant effect on the engi-neering properties of laminated structures by inducing warpage, fibre buck-ling, matrix microcracking and delaminations. Residual stresses arise fromresin chemical shrinkage, as a result of curing and differences in thermalcontraction between adjacent plies on cooling the laminate from the curetemperature. The net effect is that the residual strength properties of a laminate are likely to be diminished.

The most familiar problem associated with processing thermoset-basedcomposite systems is material degradation, induced through exothermicchemical reaction of the matrix. The risk of material degradation existswhen the dissipation of liberated heat through thermal conduction is slow.In this case, the internal temperature may be elevated to levels that induceirreversible thermal damage. A second concern relates to the complex tem-perature and degree of cure gradients that develop in thick sections duringthe curing process. These gradients may induce a non-uniform state of curethrough the laminate thickness. Non-uniform curing can produce poor con-


MTA8 11/22/2000 1:19 PM Page 144

solidation, leading to undesirable volume fraction gradients and entrappedvolatiles or voids.

Defects such as voids can significantly degrade matrix-dominated prop-erties. Interlaminar shear strength diminishes by approximately 7% foreach 1% increase in void content, for void contents in excess of 2%.5,6

Increasing the size (thickness) of a testpiece will lower the ‘apparent’ inter-laminar shear and tensile strengths, as the number of critical flaws can beexpected to increase with additional material. Thus, the detrimental effectof voids on interlaminar properties can be expected to be more evidentwhen testing thick sections.

The existence of size effects on interlaminar strength implies a need forexercising caution when using test coupon data as allowable design stresses(design allowables) for large composite structures, particularly where onlya small volume of material is subjected to interlaminar tension. Interlami-nar tensile data may result in a significant overestimation of structuralstrengths, especially if larger structures have higher levels of inherentdefects than the test specimens.5

The assessment of test geometries for laminated composite materialswould be incomplete without consideration being given to the influence of end and edge effects, and stress concentrations on stress uniformity.Saint Venant’s Principle, often neglected when developing mechanical testmethods for measuring homogeneous isotropic elastic materials, is funda-mental for determining a suitable gauge length, where a uniform stress andstrain state are induced, and local effects caused by clamping of the speci-men may be neglected. For fibre-reinforced plastics loaded along the T-Taxis, the characteristic decay length over which the end effects are signifi-cant (greater than 1%) is, in general, smaller than for isotropic materials.The characteristic decay length can be determined in terms of geometricand material parameters.7 It should also be added here that, whereas thetest methods discussed in this chapter may be suitable for the measurementof strength in unidirectionally oriented fibre-reinforced laminates, it doesnot follow that the same specimen shapes could measure the true strengthfor multidirectional materials, where the edge effects, evidenced by inter-laminar stresses, are more severe.

Stress concentrations at the specimen ends (loading zones) will often leadto premature failure in these regions. To ensure failure occurs within thegauge length, a number of tensile and compressive test methods employwaisted specimens, with the radius being either circular or elliptical. Highstresses and strains can be expected at the intersection between the gaugelength and the necking radius. These stresses will almost certainly inducepremature failure in these zones. The use of large radii (20–30 mm) com-bined with plastic deformation of the composite should reduce the stressconcentration to almost unity.

Through-thickness testing 145

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A major problem of measuring T-T properties involves the testing of relatively thin laminates (<10mm thick). To facilitate testing of thin lami-nates, two or more layers of the composite material may need to be bondedto form a sandwich construction. It is important that the positions of bond-lines do not correspond to geometric features which act as stress concen-trators and that material properties remain unaffected by the adhesivejoints (i.e. similar properties to those of the integral/monolithic material).

8.3 Tensile test methods

This section provides an evaluation of direct and indirect loading configu-rations commonly used for measuring T-T tensile properties of fibre-reinforced plastic composites. Test methods considered include:

• square section block• square section block with plain radius or elliptically waisted profile• square section waisted block with a parallel gauge section• I-section• C-section• closed ring.

The first three of these test methods are direct loading configurations,with the load introduction being via metallic end-loading bars.1,3,4 Thisapproach assumes that loading bars can be successfully bonded to the speci-mens using commercially available adhesives, which may be the situationfor thermoset resin-based systems, but is not in the case of fibre-reinforcedthermoplastics. Difficulties encountered in transferring load to fibre-reinforced thermoplastics have necessitated the development of the I-section for measuring T-T tensile strengths.8

Applied bending moments in sections of significant curvature can alsoproduce direct T-T tensile stresses. Such bend test specimens include semi-circular and semi-elliptical curved beams.9,10 Typical examples of bend speci-mens are the C-section and closed-ring specimens. These test geometriesoffer a means of determining the ‘apparent’ interlaminar tensile strength of‘thin’ composite sections.

8.3.1 Square section block

The simplest approach is to load a parallel-sided square block directly viaadhesively bonded metallic loading bars with the tensile load applied alongthe T-T axis. This cross-sectional shape is preferable, as the geometry facili-tates the measurement of lateral strains, which are required for the deter-mination of Poisson’s ratios. Circular cross-sections are incompatible withlateral strain measurements for anisotropic materials.


MTA8 11/22/2000 1:19 PM Page 146

Reliable elastic property measurements can only be guaranteed when the state of stress over the entire gauge length is sufficiently uniform, andalthough T-T dimensions of 150mm or greater (similar to the length rec-ommended for in-plane tests) will facilitate this precondition, the cost ofproducing such thick laminates is usually prohibitive. Specimens with alarge T-T dimension are also far more prone to process and machine-induced damage, so that residual strength can be expected to decrease withthickness. The use of short specimens with a length-to-width ratio of 2 : 1,or even lower4 where special precautions are taken to reduce end effects,should guarantee a relatively uniform stress state at the specimen mid-section, making them suitable for elastic property determination.

Short square section blocks when loaded in tension are only suitable for measuring elastic constants. Failure consistently occurs at the adhesivejoints between the specimen and the metallic loading bars for all but theweakest materials, thus invalidating the strength data obtained. The resultspresented in Table 8.1 demonstrate that rectangular specimens 15 mmsquare, machined from 20mm and 40 mm thick laminates, are capable ofproviding reliable elastic property data. Table 8.1 presents T-T test resultsfrom waisted and unwaisted specimens fabricated from unidirectionalT300/924 carbon-fibre reinforced epoxy composite with a fibre volume frac-tion, Vf, of 60%. Work in 1998,4 including both finite element and experi-mental evidence on T300/914 unidirectional carbon/epoxy, reports that 6mm square section specimens of thickness as low as 6 mm can also be usedto determine elastic constants with an acceptable degree of accuracy, pro-vided end effects and loading misalignments are minimised.


Table 8.1. T-T tensile properties of unidirectional T300/924 carbon fibre/epoxy.1

Test method E33 (GPa) n31 n32 S33 (MPa)

15mm square block 9.9 ± 0.1 0.019 ± 0.002 0.55 ± 0.01 n/a(40mm thick)

15mm square block 9.9 ± 0.4 0.020 ± 0.002 0.51 ± 0.01 n/a(20mm thick)

25mm square, plain n/a n/a n/a 78 ± 7radius block waisted to16mm (40mm thick)

25mm square, radius 9.5 ± 0.1 0.020 ± 0.01 0.47 ± 0.01 71 ± 6waisted block withparallel-sided gaugesection (38mm thick)

E33 = Through-thickness elastic modulus, n31 and n32 = axial and transversethrough-thickness Poisson’s ratios, respectively by, S33 = through-thicknessstrength.

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A major disadvantage is in the number of strain gauges (four biaxialrosettes) required for the highest accuracy measurement of axial and trans-verse strains. A biaxial strain gauge with an active length of 2mm is bondedto each face of the specimen at the mid-section, with gauges aligned parallel and perpendicular to the loading direction to measure axial andtransverse strains, respectively. A nine channel data acquisition system is required to monitor and record strain measurements and applied load. Elastic moduli are obtained from the linear-elastic region of thestress–strain curve. The T-T elastic modulus is the average value of the fouraxial measurements. Poisson’s ratio values in the two transverse directionsare the average values calculated from axial and transverse strain mea-surements for the two sets of opposing faces. Strain averaging accounts forpossible bending strains caused by small deviations in specimen or loadalignment. Strain gauge numbers could possibly be reduced if there was suf-ficient confidence in the quality and alignment of the specimen. Axial andtransverse extensometers may also be used to measure the T-T elastic prop-erties of 40 mm thick material. However, difficulty may be encountered inmounting these devices to the specimens.

Specimens are usually machined roughly to size using a water-lubricateddiamond wheel cutter and then surface ground to final size with a toleranceof ±0.1mm, although ±0.01mm is achievable and preferable. It is essentialto ensure that all faces are flat and parallel to the opposite surface, and perpendicular to adjacent surfaces. Reusable stainless steel or aluminiumloading bars are bonded to the ends of the specimen using a high strength,two part epoxy adhesive. Room temperature curing adhesives shouldpreferably be used to avoid residual stresses at the adherend interface. Theloading bars have their ends machined square to match the cross-section ofthe test specimen. Immediately before bonding, the adherend surfaces arelightly abraded and cleaned with a solvent (e.g. acetone). During the curingprocess the specimens need to be held in a gluing fixture to ensure properalignment between the loading blocks and the loading axis, and to maintainpressure on the bonding surfaces. Specimens are usually left for at least 24hours before testing to ensure that the adhesive is fully cured. Loadingshould be at a displacement rate of 1.0 mmmin-1, with at least five speci-mens tested from each batch of material.

The method is relatively straightforward, requiring no special loadingfixture, unless the specimen dimensions are relatively small (e.g. 6mmsquare specimens).3,4 Although such small specimens allow thinner lami-nates to be characterised, particular care is required during handling. Speci-men fabrication is uncomplicated and economical, but care is needed toensure that misalignment at both the fabrication and testing stages is mini-mised. Data reduction is straightforward, with the applied stress given byEquation [8.1]:


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[8.1]

where P is the applied force and A the specimen cross-sectional area.The procedures for bonding of end-loading bars and axial load transfer

to the specimen must be accurate; all sources of misalignment should beminimised. Small misalignments will induce bending, resulting in differen-tial strains on opposing faces of the specimen. An offset of 0.1mm in theloadline has been calculated to induce an error of ±10% between oppositefaces of a block 12mm in length and 6mm square4 and a design of loadingjig has been proposed, which ensures automatic correction for any mis-alignment in the load train.

8.3.2 Waisted block (circular and elliptical)

As previously mentioned, short rectangular columns of uniform cross-section are unsuitable for generating T-T strength data, as failure invariablyoccurs at the specimen ends. An alternative approach is the use of waistedspecimens which may be of circular or elliptical profile.1,3,4 The reduction incross-sectional area promotes failure at the specimen mid-thickness.

Using specimens with a large circular radius or elliptical fillet reduces thestress concentration in the vicinity of the fillet root. Examples of specimenswith circular and elliptical profiles are shown in Fig. 8.1. The plain waisted

s =PA


8.1 Waisted block specimens. (left) Circular or plain waisted, (right)elliptical.

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(or circular) specimen shown has a nominal T-T dimension of 40 mm, a filletradius of 30mm and 25mm square ends. The gauge section is 32mm long,with a cross-section approximately 16 mm square at the specimen mid-thickness.1 Similar but significantly smaller specimens, of both circular andelliptical profile, have also been developed;4 with a total length of 17 mmand 4 mm square gauge section of length as little as 2 mm, a carefullydesigned elliptically waisted specimen can give the true elastic and strengthproperties of fibre-reinforced/plastic matrix laminated composites.

Specimens are machined to the required profile by wet grinding.Reusable stainless steel or aluminium loading bars are bonded to the endsof the specimen. The bonding procedure, loading configuration (Fig. 8.2)and test conditions are similar to those employed for rectangular blockspecimens. Specimens have a tendency to fail at the bondline between thecomposite and the loading bars when the interlaminar strength is higherthan the tensile strength of the adhesive bond. Proper specimen designshould effectively eliminate this possibility. Alignment is critical for low-failure strain systems, as bending stresses produced through eccentricloading can result in premature failure. Care should be taken to minimiseor eliminate the possibility of misalignment during bonding and testing.Mespoulet4 gives examples of successfully applied bonding arrangementsand alignment jigs for carrying out tensile tests.

Data reduction is simple, with the applied stress given by Equation [8.1].T-T tensile failure should occur in a plane orthogonal to the loading direction at the specimen mid-thickness. Provided the adhesive joints havesuperior strength and fatigue performance to the composite material, thewaisted block specimens could be used under cyclic loading conditions.


8.2 Typical T-T tensile loading configuration.

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Environmental testing could also be performed with the same provisionthat the adhesive joints can withstand the environmental conditions.

8.3.3 Waisted block with parallel-sided gauge section

Test geometries suitable for measuring both tensile and compressive, T-Telastic and strength properties have been developed by the Defence Evalu-ation and Research Agency (DERA, Fort Halstead, UK) and ImperialCollege.1,4 These geometries both employ waisted rectangular specimens ofas little as 17mm in thickness, with a constant cross-section along the gaugelength of the specimen (Fig. 8.3). In the case of the DERA specimen theoverall thickness is 38mm, with base dimension 25mm square, reducing toa 12mm long gauge section with a rectangular cross-section of 10mm (2–3plane) by 16 mm (1–3 plane) via large radii fillets (12mm). This test geom-etry is intended to achieve an acceptable uniformity of stress, both alongand across the specimen gauge length and to avoid significant stress con-centrations adjacent to the gauge length.

The Imperial College specimen4 is supported by finite element analysiswhich shows that the design is also acceptable for both elastic constant andstrength determination. With a total thickness of 17mm and ends 8mmsquare, reducing via an elliptical waisting to a 2mm long and 4 mm squaregauge section, it aims to test unidirectionally reinforced material.

For both specimens, preparation is identical to that employed for otherwaisted test geometries with reusable metallic loading bars bonded to theends of the specimen. The loading configuration and test conditions (Fig.8.4) are similar to those employed for short rectangular block specimens.For the highest accuracy, a biaxial strain gauge with an active length of 2mm is bonded to each face of the specimen at the mid-section, with gauges


8.3 Waisted block (DERA) tensile specimen.

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aligned parallel to and perpendicular to the loading direction.A data acqui-sition system is required to monitor continuously eight strain gauges andthe applied load. In principle, the number of strain gauges could be reducedto avoid data replication, provided the induced bending loads are minimal.T-T tensile failure invariably occurs at the specimen mid-thickness, not inthe vicinity of the fillet.

Discounting the problem of misalignment, which can be managed by theuse of suitably designed bonding and loading jigs, this test method is rela-tively straightforward to perform. Machining and instrumentation of speci-mens are, however, fairly labour intensive and expensive. Data reduction is simple, with the applied stress being given by Equation [8.1]. The main advantage is that the test geometry is suitable for producing a fullstress–strain response under both tensile and compressive loading condi-tions and is potentially suitable for fatigue and environmental testing, pro-vided the adhesive joints have strength and fatigue performance that issuperior to the composite material and can withstand the environmentalconditions.


8.4 Tensile loading of waisted specimen (courtesy of DERA, FortHalstead, UK).

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8.3.4 I-section specimen

The bonding of loading bars to fibre-reinforced thermoplastics (e.g.glass-fibre reinforced polypropylene) is an extremely difficult task. Roomtemperature curing epoxy adhesives have been found to be unsatisfactory.It is recommended that surface treatments, such as corona discharge orflame treatment, be used.

An alternative approach, developed at the National Physical Laboratory,8

uses an I-section specimen (Fig. 8.5), where the load is applied via the topand bottom flanges by two sets of hardened stainless steel stirrups. Theinside surfaces of the flanges rest directly on the stirrup surfaces. This testgeometry is particularly suited to testing relatively thin laminates (of the order of 20 mm thick). Specimens have a nominal width of 5 mm. The10mm gauge section is plain radius waisted, with a radius of curvature of 5mm. The cross-section is 5mm square at the specimen mid-thickness.

The test is simple and economical, and there are no problems associatedwith alignment or adhesive bonding. A special loading fixture (loading stir-rups) is required, but the overall costs involved are relatively low comparedwith bonded configurations. The flange thickness was found to be sufficientto ensure failure occurred within the gauge length. Ideally, the fillet radiusshould be larger, to minimise the high stresses and stress gradients in thisregion, but this is not practicable for 20mm thick laminates.

8.3.5 C-section and closed ring specimens

As previously mentioned, applied bending moments in sections of signifi-cant curvature can also produce T-T tensile stresses. Prime examples are


8.5 I-section tensile specimen.

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the closed ring and semicular (C-section) specimens (Figs. 8.6 and 8.7).These test geometries are only suitable for measuring T-T tensile strength.Specimens of both configurations can be sectioned from tubular structuresand are representative of a number of structural features (e.g. bends and elbows). The two configurations are, however, only compatible with alimited range of materials, such as continuous aligned and multilayered lam-inates (including woven fabrics), where a clearly defined plane of failureexists. Indirect loading cannot be applied to discontinuous or random mat reinforced systems, because these materials tend to fail in transversetension. Machining specimens is relatively inexpensive and straightforward;however, fabrication of the laminated sheet structure is moderately expen-sive when accounting for the initial costs of producing mandrels and mould-ing dies. The advantage of these methods is that the required laminatethickness is 10mm or less.

Materials are formed using a cylindrical mould (or mandrel), typically 50mm in diameter. Specimens 20–25mm wide are then sectioned from thecylinders. Two types of failure can occur, flexural failure involving the outerlayers of the section and delamination failure near the specimen mid-plane (or radial neutral axis). Flexural failure involves tensile fractureand/or compressive failure at the appropriate surfaces. Caution is requiredwhen differentiating between the two modes of failure, because it is notunusual for flexural failure to be accompanied by delamination failure in the outer layers. The resultant failure mode is dependent upon the thickness-to-radius (h/R) ratio of the curved section, the fibre/matrix systemand the layup configuration. Chandler et al.11 have predicted that a transi-tion between delamination and flexural failure should occur at a criticalthickness-to-radius ratio. Subsequent research indicates that the thickness


A A

B

B

Region ofdelamination

8.6 Closed ring specimen.

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for aligned and woven fabric C-sections with a radius of 25 mm should be5mm and 7.5 mm, respectively.

These structures have a tendency to deform (i.e. straighten) duringloading. In straightening, tangential tensile and interlaminar shear stressesare introduced into the curved structures. The influence of these stresses onthe interlaminar tensile strength needs to be accounted for in the calcula-tions. The use of thick specimens tends to reduce geometric deformationrather than eliminate the effect altogether. Low h/R ratios will often resultin flexural failure and significant deformation prior to failure. Large struc-tural deformation creates difficulties in measuring the onset of failure.

Special loading fixtures are required for both test geometries.The fixturesare manufactured from hardened stainless steel to reduce grip wear due tofrictional effects and to prevent environmental attack. Before a specimenis mounted, contact surfaces should be lubricated with graphite, or frictionreducing inserts such as PTFE (polytetrafluoroethylene) should be used. Aspecial test fixture for loading C-section specimens in tension has beendesigned and manufactured by DERA (Farnborough, UK).The fixture con-sists of a matching pair of loading arms which are held in the top and bottomgrips of a test machine (Fig. 8.7). The specimen ends are clamped in eachloading arm by tightening a central bolt.This secures the specimen betweenthe ‘flat’ of the central mechanism and the load bar in the outer ‘yoke’.The test fixture is designed to induce simple bending within the specimenwithout introducing complicated off-axis end loads/moments or offsetloads. In order to achieve this objective, the fixture allows free end rotationof the specimen whilst the load is applied. Shear components within thelaminate are expected to cancel out, resulting in a ‘pure’ interlaminar tensilefailure mode near the apex of the specimen.1

A major disadvantage of the use of indirect methods for inducing inter-laminar tension is the considerable influence that combined stress states


8.7 C-section tensile fixture and specimen (courtesy of DERA,Farnborough, UK).

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have on structural deformation and failure. Failure mechanisms are oftencomplex and the associated analysis is usually rather elaborate. These configurations are also prone to process-induced damage (e.g. poor compaction). Fractographic evidence suggests that mixed-mode failure containing both tensile and shear components occurs in preference to interlaminar tensile failure. Failure is caused by a combination of tensileand shear stresses in the vicinity of the specimen ends, a region of maximumstresses, and not along the mid-plane at the specimen apex.At present, thereis insufficient evidence to support the use of either test method.

8.4 Compression test methods

The determination of in-plane compressive properties of fibre-reinforcedplastic composites is particularly difficult, as explained in Chapter 5. Theproblems relating to T-T compression testing are also rather complex, withfailure being dependent upon the specimen geometry, material microstruc-ture and loading configuration. Ambiguities and uncertainties in the inter-pretation of fracture may result from competition between several failuremechanisms (e.g. interfacial failure, fibre microbuckling and plastic defor-mation) prior to final fracture.These mechanisms are often interactive, withprogressive damage leading to local stress redistribution. As a result, theoverall stress–strain state within a structure alters continuously with pro-gressive failure. However, the loading arrangement itself is far simpler thanfor in-plane specimens.

This section is essentially confined to the evaluation of the followingwaisted and unwaisted configurations:

• square section block• square section waisted block with either a circular or elliptical profile• square section waisted rectangular block with a parallel gauge section.

Details of suitable test specimen geometries are given in the section onT-T tension. Specimen preparation, instrumentation requirements and datareduction, using Equation [8.1], are similar to those for tension. However,caution needs to be exercised to ensure flatness and parallelism of bothspecimens and loading platens.

8.4.1 Square block

The most basic approach is to load a rectangular block directly betweentwo flat and parallel hardened steel platens, with the specimens located at the centre of the platens in closely fitting recesses (although these are optional), with the compressive load being applied along the T-T axis.12

A four-pillar die set is often used, as this ensures uniform loading to theends of the specimen.There are no national or international standards avail-


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able, but International Standard ISO 60413 is a potential precursor.This stan-dard specifies a method for the determination of compressive properties ofplastics with the displacement rate (speed of testing) set in accordance withthe purpose of the measurement (modulus or strength), the material spec-ification (brittle or ductile) and the specimen length.A length-to-width ratio£0.4 is recommended to avoid the possibility of compressive buckling.

This test geometry provides consistent and reliable elastic property datafor both monolithic and layered (sandwich construction) materials, and isamenable to standardisation for this purpose as shown in Table 8.2, whichgives data obtained for unidirectional T300/924 carbon fibre-reinforcedepoxy (for a Vf of 60%). The rectangular block data presented in Table 8.2were obtained from 15mm square rectangular blocks, machined from 20mm and 40 mm thick laminates. Elastic and strength properties wereapproximately the same for both T-T dimensions, meaning negligible endeffects. The use of specimens with a length-to-width ratio of 2 : 1 shouldensure a relatively uniform stress state at the specimen mid-section andprevent compressive buckling. Strength values were consistent to within±10% and in reasonable agreement with the strength data obtained using


Table 8.2. T-T compressive properties of unidirectional T300/924 carbonfibre/epoxy.1

Test method E33 (GPa) n31 n32 S33 (MPa)

15mm square block 10.0 ± 0.1 0.022 ± 0.001 0.52 ± 0.01 263 ± 3(40mm thick)

15mm square block 9.9 ± 0.1 0.020 ± 0.001 0.56 ± 0.01 256 ± 6(20mm thick)

Layered square block 10.0 0.02 0.52 258 ± 3(40mm thick)





E33 = Through-thickness elastic modulus, n31 and n32 = axial and transversethrough-thickness Poisson’s ratios, respectively, S33 = through-thicknessstrength.

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the waisted block geometries. This test method is, however, unsuited to measuring T-T strength, as failure invariably initiates at the specimen ends, independent of material anisotropy and degree of homogeneity (seeFig. 8.8). The presence of stress concentrations in these regions causes pre-mature failure, hence the lower strength value. This method is relativelyinsensitive to material flaws, such as porosity.

Significantly smaller (6mm square section, with a thickness of 6 mm)T300/914 carbon/epoxy specimens have been investigated,4,14 giving quitesimilar results to those in Table 8.2.

Preparation and testing of the short block specimens are straightforwardand economical, although care is required to ensure that the specimen endsare machined flat and parallel. The technique requires no special fixture.The use of a high precision die set ensures uniform axial loading. Com-mercial units are available at a reasonable price. As with the tensile test, amajor drawback relates to the number of strain gauges required for thehighest accuracy measurement of axial and transverse strain. The numberof strain gauges could be reduced if there is confidence about the flatnessand parallelism of the specimen and loading platens. Extensometers are notparticularly suitable for measuring axial and lateral strains.

8.4.2 Waisted block (circular and elliptical)

This relatively straightforward approach can be used to measure both T-Ttensile and compressive strengths of monolithic and sandwich construc-tions. Testing can be considered uncomplicated, requiring no special fixture.The use of a high precision die set will ensure uniaxial loading over theentire specimen cross-section. Compared to rectangular blocks, specimenfabrication is expensive and labour intensive.As with tension, a large radiusfillet (30 mm), or elliptical profile, reduces the stress concentration in thevicinity of the fillet root, although the stress state within the gauge lengthis less uniform than an equivalent sized rectangular prism.


8.8 Failed fabric specimens: (left) DERA, (centre) plain radius, (right)square block.

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Consideration needs to be given to specimen dimensions in order to mini-mise end effects and avoid the possibility of compression buckling. Alength-to-width ratio of 2 : 1, as used for the test geometry in Fig. 8.1, hasproved to be satisfactory for an extensive range of composite materials.Thistest geometry may be scaled down by a factor of 2, with minimal effect oncompressive strength.The results in Table 8.2 show that the influence of endeffects increases slightly with reduction in thickness.

Shear is the predominant cause of failure in all fibre-reinforced plasticcomposites, independent of the material microstructure or loading configu-ration. Failure is often instantaneous and catastrophic, resulting in diagonaland interlaminar cracking, with failure modes generally remaining unaf-fected by a reduction in specimen size. For 2-D woven fabrics, two orthog-onal fracture planes can be observed at 45° to the T-T axis.

8.4.3 Waisted block with parallel-sided gauge section

This versatile test geometry can be used to measure both T-T tensile andcompressive elastic and strength properties.1,4,14 The specimens are sub-jected to direct compressive loading between two hardened steel parallelplatens at a constant displacement rate (Fig. 8.9). The test geometry (Fig. 8.3) may be scaled down by a factor of 2, with minimal effect on eitherelastic property or strength data. It has been observed that the failure modefor most composites remains unaltered as a result of reducing specimenthickness. A reduction in specimen thickness to 15 mm or less makes handling (strain gauging and testing) more difficult. The accompanying


8.9 Compression fixture with DERA specimen (courtesy of DERA, UK).

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reduction in cross-sectional area has a tendency to induce compressivebuckling, particularly for thermoplastic-based systems.

Preparation and testing of these specimens are fairly expensive and labour intensive, considerable effort being required to machine specimensto size and to install strain gauges. Specimen preparation and instrumenta-tion requirements and associated problems are similar to those encoun-tered for tension. The technique requires no special fixture, although theuse of a high precision die set ensures uniform axial loading. As withtension, a major drawback is in the number of axial and transverse straingauges required. These could be reduced in number if there was sufficientconfidence in the flatness and parallelism of the specimen and loadingplatens. Extensometers are not particularly suitable for measuring axial andlateral strains.

Shear failure consistently occurs at the radius root, independent of the material microstructure. This is due to the presence of stress concen-trations. Failure is usually instantaneous and catastrophic, with diagonalcracking occurring along the shear planes and between layers. Failuremodes generally remain unaffected by a reduction in specimen size. Linearelastic finite element stress analysis1 has shown that for isotropic materialsthe stress concentration in the vicinity of the fillet is approximately 1.6. Incontrast, the stress concentration at the mid-section of specimens witheither a circular or elliptical profile is close to unity,1,4 provided the radiusof curvature is large. This partially explains the lower strength valuesobtained using this test geometry. It is worth noting that plastic deforma-tion and microdamage formation tend to reduce stress concentrations. Bar-relling frequently occurs, resulting in failure of the adhesive bond betweenstrain gauges and the composite, thus preventing the measurement offailure strains. Fibre-reinforced thermoplastics are particularly prone to thismode of failure.

8.5 Shear test methods

At a first glance, there appears to be a multitude of test methods of varyingcomplexity for the evaluation of interlaminar shear properties. On closerinspection, the number of test methods that can be used effectively for T-T shear characterisation is limited, with all techniques demonstrating defi-ciencies. A major difficulty is in producing a state of pure shear stress,particularly in the T-T direction. The problem is compounded by theimpracticality of producing thick sections with similar dimensions to thoseemployed for in-plane testing. This difficulty increases with materialanisotropy and inhomogeneity. Additional problems associated with com-plexity and cost of specimen fabrication and testing and poor reliability oftest data considerably reduce the number of test methods suitable for either


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quality control or design purposes. This section provides an overview ofthree test methods that are used extensively throughout the compositeindustry for evaluating T-T shear properties:

• short beam• double-notch• V-notched beam (Iosipescu).

The short beam and double-notch methods have been widely adoptedfor characterising the interlaminar failure resistance of fibre-reinforcedplastic composites. Owing to their simplicity and the low costs involved inspecimen fabrication and testing, the two methods are often used for qualitycontrol purposes. The V-notched beam test is suitable for determining boththe in-plane and T-T shear moduli and shear strengths of most polymermatrix composites, provided a suitable shear failure occurs.

Standards exist for all three methods:

• short beam, BS EN ISO 14,13015

• double-notch, ASTM D 384616

• V-notched beam, ASTM D 5379.17

The double-notch method, which consists of loading a non-symmetricallynotched composite coupon in uniaxial tension or compression, is alsoincluded in BS 499418 and BS 6464.19 ASTM D 384616 specifies compressiveloading, and the two BSI standards specify tensile loading.

8.5.1 Short beam

The short beam method is one of the simplest tests to conduct and is used widely for measuring the ‘apparent’ interlaminar shear strength of continuous aligned and fabric-reinforced composites. The test consists of ashort beam specimen of rectangular cross-section loaded in three-pointbending so that an interlaminar shear failure occurs (Fig. 8.10). The speci-men is supported by two cylindrical rollers which allow lateral motion, andthe load is applied through a central roller located at the specimen mid-length. The support and loading rollers are 6mm in diameter. For alignedmaterials, the fibre axis is parallel with the length of the specimen. Flexurefixtures with an adjustable span facility can be purchased from test machinemanufacturers or produced in-house at a relatively low cost. Tests are con-ducted at a displacement rate of 1 mmmin-1 using standard mechanical testequipment.

Specimen preparation is straightforward and only a small amount ofmaterial is required. The standard specimen thickness, h, is nominally 2mmwith a width, b, and overall length, L, of 10 and 20mm, respectively.15 Inaccordance with the ISO standard, short beam specimens sectioned from


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materials of non-standard thickness should have an overall length of 10 hand a width of 5h. In all cases the loading span, S, is 5h ± 0.3mm. The smallloading span-to-thickness (S/h) ratio has been adopted to increase the levelof shear stress relative to the flexural stress in the test specimen to encour-age interlaminar shear failure. Interlaminar shear failures are difficult toattain at S/h > 5. The four-point bend test has been considered as an alter-native method.

According to classical beam theory, the shear stress distribution in shortbeams loaded in three-point flexure is distributed parabolically through thespecimen thickness. The stress is a maximum at the mid-plane and zero atthe upper and lower surfaces. Finite element analysis has shown that the T-T shear stress distribution is severely skewed near the load and reactionpoints and varies along the beam length. The maximum interlaminar shearstress, tmax, is in fact positioned between the mid-plane and the uppersurface, close to the loading zone, and is larger than predicted by classicalbeam theory.20,21

Data reduction is straightforward, with the maximum interlaminar shearstress given as:15

[8.2]

where P is the load applied by the central loading cylinder, with b and hbeing specimen width and thickness, respectively.

The method is suitable for use with fibre-reinforced plastic composites,with both thermoset and thermoplastic matrices, providing an interlaminarshear failure is obtained. Interlaminar shear failure has been observed foraligned glass-fibre and carbon-fibre reinforced systems. Most other materi-als (e.g. chopped strand mat) tend to fail on the tensile face, with crackspropagating through the specimen thickness.

The short beam test cannot give results which are acceptable as theabsolute material shear strength, because failure is influenced by flexural

t max =34

Pbh


PFibre direction

3

1

P2–

L2–L

2–P

2–

8.10 Short beam loading configuration.

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and contact stresses. Failure frequently results from a combination of high shear and transfibril compression gradients present in the upperportion of orthotropic beams, near the concentrated central load. Thesurface under the central loading zone is subjected to compression, and thecomposite may undergo localised buckling. This effect will be particularlysevere for aramid-reinforced composites, and thermoplastic-based systems,which have a low resistance to compression loading.

It should be emphasised that the result obtained is not an absolute value.For this reason the term ‘apparent’ interlaminar shear strength is used todefine the quantity obtained. Test results from different sized specimens, orfrom specimens tested under different conditions, are not directly compa-rable.15 Despite these difficulties, the simplicity of the test, combined witheconomic costs, has ensured its popular use for quality control and as amaterials screening tool. The four-point bend arrangement has been con-sidered as an alternative method, but test data have failed to demonstrateimproved reliability.

In conclusion, the short beam method is inappropriate for generatingdesign data, although there has been a tendency to use the measurementsas design allowables.

8.5.2 Double notch

An alternative approach for measuring interlaminar shear strength is toapply uniaxial tensile or compressive load to a non-symmetrically notchedspecimen of rectangular cross-section. Various double-notch geometrieshave been suggested, including those specified in ASTM D 3846,16 BS 499418

and BS 6464.19 The specimen, shown in Fig. 8.11, is machined with two par-allel offset notches, one on each face of the specimen, cut across the entirewidth of the specimen. The notches are equally spaced on either side of thespecimen mid-length. A water-lubricated diamond cutting tool should beused to machine the notches. Failure of the specimen occurs in shear, alongthe mid-plane between the two notches. The main advantage of using thedouble-notch method is that relatively thin laminates (2.5–10 mm thick) canbe tested. This advantage is counteracted by the difficulty encountered inaccurately machining the notches to the required depth of half the speci-men thickness (i.e. mid-plane).

In principle, the entire load is transmitted by shear forces, distri-buted along the central plane between the notches. Linear-elastic stressanalysis has shown that the shear stress distribution along the mid-plane between the notches is non-uniform, but tends to become moreuniform as the notch separation increases.20 Shear stress concentra-tions exist at the notches. The T-T shear strength, Sxz, is given by Equation[8.3]:


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[8.3]

where Pmax is the failure load, L the distance between notches and b thespecimen width.

T-T shear strength, as determined by the test method specified in ASTMD 3846,16 is measured by applying a compressive load to a double-notch specimen at a displacement rate of 1 mm min-1.The specimen must to be sup-ported along its entire length to minimise out-of-plane deformation. Speci-mens are nominally 79.5 mm in length and 12.7mm wide. The two parallelnotches are 6.4mm (0.25 in) apart and between 1mm and 1.6mm wide. Testspecimen geometry and loading configuration are given in Figs.8.11 and 8.12,respectively.

The method specified in ASTM D 384616 is relatively straightforward toperform, requiring a support fixture of moderate cost.The method providesconsistent strength data, with interlaminar failure regularly occurring alongthe mid-plane joining the two notches. T-T shear strength data is generallyconsistent with results obtained using the V-notched beam method. Speci-men preparation and testing are relatively straightforward, although thequality of machining the notches has a significant effect on strength data.Notch depth must be accurately machined. Fractographic examination ofthe failure surfaces reveals shear dominated mixed-mode failure.

BS 499418 specifies a method for tensile loading 3mm thick double-notchcoupons with an overall length of 200mm and a width of 25mm. The twonotches are 12.5 mm apart and equidistant from the specimen mid-length.No particular details are available on the notch width. Since this structureis not laterally supported, the coupon bends. Without lateral support, thisout-of-plane bending results in premature failure. Shear strengths using this

SPbLxz = max


Notch depth is1/2 specimen

thickness

6.4 mm

36.3 mm

2.54 to 6.60 mm

10.0 mm

79.5 mm

notch width1.02 to 1.65 mm

8.11 Double-notch specimen for determination of T-T shear strength.

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method have been found to be lower than corresponding tests performedin compression.

No allowances have been made in either the ASTM or BS standards toaccount for the non-uniformity of the stress distribution between thenotches, the effect of bending or the local stress concentration at the fibreends associated with the notch geometry. The close agreement betweenstrength measurements, shown in Table 8.3, obtained using the double-notch (ASTM D 3846)16 and V-notched beam shear tests for a wide rangeof materials indicates that the strength calculations do not need to beadjusted to account for stress concentrations present at the notches ofdouble-notch specimens. Non-linear stress analysis conducted at theNational Physical Laboratory has shown that the stress concentration at thenotches is close to unity for an isotropic double-notch specimen loadedaccording to ASTM D 3846.16 This analysis would need to be extended toanisotropic solids in order to substantiate the experimental observation.Specimen alignment, as with all tests, can be regarded as critical to test performance.


8.12 Compression fixture with double-notch shear specimen.

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8.5.3 V-notched beam shear

Details of test procedure, specimen geometry and preparation for this testmethod can be found in Chapter 6 on shear testing. Providing adequatematerial thickness is available (at least 10 mm), this method can be used tomeasure shear modulus and shear strength (Table 8.3) in all three materialplanes (i.e. X-Y, X-Z and Y-Z) for a diverse range of composite materials.22

T-T specimens are machined from 20 mm thick panels to the requireddimensions according to ASTM D 5379.17 Differences between shearmoduli, caused by out-of-plane deformation, could be as high as 10% for abatch of nominally identical specimens.To ensure maximum accuracy, shearmodulus is determined from the average strain response of back-to-backbiaxial rosettes. At present, the standard requires only one specimen froma batch to be tested in this manner, provided the amount of twist for thistestpiece is no greater than 3% (for further details see Chapter 6 on sheartesting).


Table 8.3. Typical T-T shear properties.

Material and test method Gxz (GPa) Gyz (GPa) Sxz (MPa) Syz (MPa)

UD carbon-fibre/epoxyShort beam n/a n/a 108 ± 6 n/aDouble notch n/a n/a 75 ± 12 n/aV-notched beam 5.3 ± 0.2 2.9 ± 0.3 111 ± 2 64 ± 9*

CSMShort beam n/a n/a 13.4 ± 3.0* [13.4 ± 3.0]*Double notch n/a n/a 38.3 ± 4.7 [38.3 ± 4.7]V-notched beam 1.64 ± 0.09 [1.64 ± 0.09] 40.7 ± 1.7 [40.7 ± 1.7]

2/2 twill glass-fibrefabric/epoxyShort beam n/a n/a 52.5 ± 0.6* [52.5 ± 0.6]*Double notch n/a n/a 64.9 ± 1.8 [64.9 ± 1.8]V-notched beam 4.12 ± 0.14 [4.12 ± 0.14] 68.4 ± 0.9 [68.4 ± 0.9]

Discontinuous glass-fibre/nylon 66Short beam n/a n/a 18.6 ± 0.4* [18.6 ± 0.4]*Double notch n/a n/a 66.4 ± 4.8 [66.4 ± 4.8]V-notched beam 1.68 ± 0.06 unavailable 56.9 ± 3.6 unavailable

Random glass-fibremat/polypropyleneShort beam n/a n/a 14.2 ± 1.5* [14.2 ± 1.5]*Double notch n/a n/a 18.1 ± 3.3 [18.1 ± 3.3]V-notched beam 1.04 ± 0.04 [1.04 ± 0.04] 22.7 ± 0.8 [22.7 ± 0.8]

[ ] assumed from material symmetry, * non-shear failure mode.

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8.5.4 Comparison of shear data

A comparison of typical T-T shear modulus and shear strength dataobtained from a wide range of composites is shown in Table 8.3. Defaultvalues are bracketed, where it is assumed the material is symmetric in theX-Z and Y-Z planes.

8.6 Concluding remarks

Table 8.4 summarises the suitability of each test method for measuring T-T properties. The differences between tensile and compressive elastic prop-erty measurements are minimal, in view of the problems associated withcorrect alignment, stress non-uniformity and heterogeneity of the materi-als, the results are generally consistent (i.e. ±5% for elastic moduli and±10% for strength). Owing to the ease of specimen preparation (i.e. nobonded loading bars) and testing, a user would be justified in conductingcompression tests to produce the required elastic property data.

Acknowledgements

This chapter was written with the support of the Materials MeasurementProgramme, a programme of underpinning research financed by the UnitedKingdom Department of Trade and Industry. The author acknowledges thecontributions of his colleagues Dr Graham Sims and Miss Maria Lodeiro


Table 8.4. Suitability of test methods for measuring T-T properties.

Method Elastic properties Strength

TensionPlain short block Suitable Not suitableCircular profile Not applicable SuitableElliptical profile Suitable Suitable – needs further assessmentDERA Suitable SuitableC-section Not applicable Not suitableI-section Not applicable Suitable – needs further development

CompressionPlain short block Suitable QA onlyCircular profile Not applicable SuitableElliptical profile Suitable Suitable – needs further assessmentDERA Suitable Suitable – thermoset systems only

ShearShort beam Not applicable QA only – continuous aligned laminatesDouble-notch Not applicable SuitableV-notched beam Suitable Suitable – caution on failure mode

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at the National Physical Laboratory, Dr Clive Messenger and Mr MatthewHiley, Defence Evaluation and Research Agency at Farnborough, and MrRobert Ferguson, Defence Evaluation and Research Agency, Fort Halstead.

References

1. W R Broughton and G D Sims, An Overview of Through-thickness Test Methodsfor Polymer Matrix Composites, NPL Report DMM(A)148, October 1994.

2. S Mespoulet, Through-thickness Test Methods for Laminated Composites – AReview, Centre for Composite Materials, Imperial College, London, UK,February 1995.

3. S Mespoulet, J M Hodgkinson, F L Matthews, D Hitchings and P Robinson, ‘Anovel test method to determine the through-thickness tensile properties of longfibre reinforced composites’, Proceedings of Seventh European Conference onComposite Materials (ECCM-7), Institute of Materials London, UK, Volume 2,Woodhead Publishing, Cambridge, May 1996, 131–7.

4. S Mespoulet, Through-thickness Test Methods for Laminated Composite Materials, PhD Thesis, Centre for Composite Materials, Imperial College,London University, UK, January 1998.

5. N C W Judd and W W Wright, ‘Voids and their effects on the mechanical properties of composites – appraisal’, SAMPE Journal, 1978 January/February10–4.

6. M R Wisnom and M I Jones, ‘Size effects in interlaminar tensile and shearstrength of unidirectional glass fibre/epoxy’, Journal of Reinforced Plastics andComposites, 1996 15 January 2–15.

7. C O Horan and J G Simmonds, ‘Saint-Venant end effects in composite struc-tures’, Composites Engineering, 1994 4(3) 279–86.

8. W R Broughton, ‘A critical evaluation of through-thickness test methods’,Proceedings of the Eleventh International Conference on Composite Materials,Australian Composite Structures Society Gold Coast, Queensland,Australia, edM L Scott, Volume 25, Woodhead Publishing, Cambridge, July 1997, 894–904.

9. M Sumich, ‘Manufacture of composite test specimens for delamination studies’,Experimental Techniques, 1989 13 20–2.

10. C C Hiel, M Sumich and D P Chappell, ‘A curved beam test specimen for deter-mining the interlaminar tensile strength of a laminated composite’, Journal ofComposite Materials, 1991 25 854–68.

11. H W Chandler, A J Longmuir, S McRobbie, Y-S Wu and A G Gibson, ‘Tensiledelamination failure of curved laminates of single and double-skinned con-struction’, Proceedings of the 2nd International Conference on Deformation andFracture of Composites, UMIST, Manchester, UK, March 1993, Institute ofMaterials, published by IoM Communications Ltd, 1993, 16.1–10.

12. S Chaterjee, D Adams and D W Oplinger, Test Methods for Composites a StatusReport, Volume II: Compressive Test Methods, US Department of Transport,Federal Aviation Administration, Report DOT/FAA/CT-93/17, II, NationalTechnical Information Service, Springfield, VA 22161, USA, June 1993.

13. ISO 604: Plastics – Determination of Compressive Properties, 1993.14. S Mespoulet, J M Hodgkinson, F L Matthews, P Robinson and D Hitchings, ‘The

development of a through-thickness compression test for laminated CFRP’,


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Proceedings of the 4th International Conference on Deformation and Fractureof Composites, UMIST, Manchester, UK, March 1997, Institute of Materials,published by IoM Communications Ltd, 1997, 371–8.

15. BS EN ISO 14,130: Fibre-reinforced Plastic Composites – Determination ofApparent Interlaminar Shear Strength by Short Beam Method, 1997.

16. ASTM D 3846: ‘Standard test method for in-plane shear of reinforced plastics’,Annual Book of ASTM Standards, 100 Barr Harbor Drive,West Conshohocken,PA 19428, USA, Vol 8.02, 1998, 479–81.

17. ASTM D 5379: ‘Standard test method for shear properties of composite materials by the V-notched beam method’, Annual Book of ASTM Standards,100 Barr Harbor Drive, West Conshohocken, PA 19428, USA, Vol 15.03, 1997,235–47.

18. BS 4994: Design and Construction of Vessels and Tanks in Reinforced Plastics,1987.

19. BS 6464: Reinforced Plastics Pipes, Fittings and Joints for Process Plants, 1984.20. S Chaterjee, D Adams and D W Oplinger, Test Methods for Composites a Status

Report Volume III: Shear Test Methods, US Department of Transport, FederalAviation Administration, Report DOT/FAA/CT-93/17, III, National TechnicalInformation Service, Springfield, VA 22161, USA, June 1993.

21. R B Pipes, R A Blake Jr, J W Gillespie Jr and L A Carlsson, ‘Test methods’,Delaware Composites Design Encyclopedia, Volume 6, eds L A Carlsson and J W Gillespie Jr, Technomic Publishing, Lancaster, PA, USA, 1990.

22. W R Broughton, M Lodeiro and G D Sims, ‘Experimental validation of shear test methods for through-thickness properties’, Proceedings of SeventhEuropean Conference on Composite Materials (ECCM7), Institute of MaterialsLondon, UK, Volume 2, Woodhead Publishing, Cambridge, May, 1996, 125–30.


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9.1 Introduction

Laminated fibre-reinforced composites made of high strength fibres in a rel-atively weak matrix material are susceptible to delamination (i.e. separa-tion of the layers). A typical quasi-isotropic carbon-fibre reinforced epoxylaminate has an in-plane tensile strength of 700–1200 MPa, dependent onprecise layup,1 but the through-thickness tensile strength can be as low as50MPa and the through-thickness shear strength is also relatively low.2,3 Itis clear therefore that through-thickness stresses in a component (see Fig.9.1 for some possible sources) may give rise to the initiation of delam-ination if they exceed the through-thickness strength. The subsequent propagation of a delamination will, however, be controlled not by thethrough-thickness strength but by the interlaminar fracture toughness ofthe composite material. This chapter describes methods for measuring theinterlaminar fracture toughness.

9.2 Terminology and typical values

9.2.1 Critical energy release rate

Interlaminar fracture toughness of laminated composites is normallyexpressed in terms of the critical energy release rate, which is usually rep-resented by the symbol Gc. The critical energy release rate is the energyconsumed by the material as the delamination front advances through aunit area. The units commonly used for Gc are Joules per square metre orNewtons per metre. Interlaminar fracture toughness can be measured ineach of the modes shown in Fig. 9.2 or in a combination of these modes.Typical values of interlaminar fracture toughness in modes I and II (GIc andGIIc, respectively) are given in Table 9.1 for a variety of carbon fibre andmatrix types.

In isotropic materials, toughness values (usually expressed in terms of the

9Interlaminar fracture toughness

P ROBINSON AND J M HODGKINSON

170

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critical stress intensity factor) are usually only quoted for the mode I case.For these materials the toughness is lowest in this mode, so that even if acrack is loaded to drive the growth in mode II, as shown in Fig. 9.3(a), thecrack will deviate and grow in a direction which will be pure mode I, asshown in Fig. 9.3(b). In laminated composites, however, the delaminationcan be constrained to lie between the strong fibre-reinforced layers, so thatit is possible to have delamination growth in all of the three modes shownin Fig. 9.2.

9.2.2 Relationship between energy release rate and stressintensity factor

For metals and polymers, fracture toughness is often expressed in terms of the critical stress intensity factor, Kc. For linear elastic isotropic

Interlaminar fracture toughness 171

free edge notch (hole) ply drop bonded joint

buckling

pressure, pimpact

delamination delamination

bolted joint

9.1 Possible sources of delamination initiation caused by through-thickness stresses.

mode I mode II mode III

9.2 Schematic diagrams of the basic modes of crack loading, mode I(opening), mode II (shear), mode III (tearing).

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materials, KIc and GIc are related by the following expression for the planestrain case:4

[9.1]

where E is the Young’s modulus and n the Poisson’s ratio.For a typical aerospace aluminium alloy with a KIc of 35MPam1/2, Equa-

tion [9.1] gives a GIc of 16kJm-2, which is considerably higher than thefigures quoted in Table 9.1 for composite laminates and confirms their relative propensity to delaminate.

G KEIc Ic=-( )2

21 n


Table 9.1. Typical values of interlaminar fracture toughness for variousmaterials.

Material Fracture toughness (kJm-2)Fibre/matrix

Mode Initiation Propagation

T300/6376 Mode I 0.27 0.27Mode II (ELS) 0.60 —Mode II (ENF) 0.65 —

XAS/913 Mode I 0.28 0.28Mode II (ENF) 0.66 —

T300/914 Mode I 0.14 0.14Mode II (ENF) 0.72 —

T800/924 Mode I 0.22 0.25Mode II (ELS) 0.44 0.60

AS4/PES Mode I 0.80 2.02Mode II (ELS) 1.23 1.84Mode II (ENF) 1.29 —

AS4/PEEK Mode I 1.68 2.42Mode II (ELS) 1.74 3.16Mode II (ENF) 1.82 —

ELS = end-loaded split; ENF = end-notched flexure, * = eqoxy matrix; PES =polyether sulphone; PEEK = polyether ether ketore.

original crackcrack propagates inthe pure mode Idirection

(a) (b)

9.3 Crack propagation in an isotropic material.

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9.2.3 Criteria for delamination growth

To determine the load at which a delamination in a composite componentwill grow, it is necessary to assess the energy available for driving the delam-ination growth. This involves an analysis of the particular component todetermine the energy release rate, represented by the symbol G. For simplecases closed form solutions for G are available,5 but for more complex casesfinite element analysis is required to evaluate G.6 G, usually in its modalcomponents, can be tested in some criterion involving the critical energyrelease rates for the particular material. For example, in a pure mode I casethe delamination will grow if GI ≥ GIc. The equivalent test using the stressintensity factor approach would be KI ≥ KIc for growth.

9.2.4 Effect of increasing critical energy release rate andstress intensity factor

A significant difference between the stress intensity factor and the energyrelease rate lies in their relationship to the applied load. For example, fora given linear elastic component with a given crack size, the load to causemode I crack growth is directly proportional to the KIc value of the mate-rial. So, if a designer chooses a new material for the component which hastwice the KIc of the original material, then the load to cause crack growthwould be doubled, irrespective of whether the new material has differentstiffness properties, these being incorporated within KIc. It follows fromEquation [9.1] that for an isotropic material with the crack growing underplane strain conditions in mode I the critical load, Pc, will be proportionalto:

Thus doubling GIc, but keeping the stiffness characteristics unchanged,will produce a critical load increased by a factor of √2. However, if in choos-ing the new material, the stiffness characterisistcs are also changed, thenthe critical load will be changed according to the above proportionality relationship.

9.3 Overview of test methods and standards

There has been considerable research into the development of suitable testmethods for the measurement of interlaminar toughness. Standards organi-sations such as the American Society for Testing and Materials (ASTM),the European Structural Integrity Society (ESIS) and the Japanese Indus-try Standards (JIS) have been evaluating some of the proposed methods.

G EIc

1 2-( )n


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The test methods for measuring interlaminar fracture toughness generallyinvolve beam-type specimens and have been developed almost exclusivelyfor application to unidirectional laminates, with the delamination growth inthe direction of the fibres. The strategy in all of these tests requires mea-surement of the load and applied displacement at which a delamination ofknown length grows. For some specimens the growth is stable, so that datacan be collected at many points during the delamination growth. In otherspecimens the delamination growth is unstable, and the critical load andapplied displacement can only be measured for the initial delaminationlength. From the load–displacement–crack length data it is then possible todetermine the interlaminar toughness.

For mode I the commonest test uses the double cantilever beam (DCB)specimen shown in Fig. 9.4. Test standards using this specimen have beenproduced by both JIS7 and ASTM8 and are limited to the testing of unidi-rectional laminates. Similarly, ESIS9 have published a protocol for DCBtesting. Other methods for mode I testing include the width-tapered DCB10

and the wedge-driven test.11 For mode II there are two methods which havereceived most attention; these are the three-point loaded end-notched


End-blockLaminate

Crack length scale

h (ASTM)2h (ESIS)

B

(a)

(b)

L

l2

l1

l1

a

a

3 60 1 2 4 5 7 8 9101112

3 60 1 2 4 5 7 8 9101112

9.4 Double cantilever beam (DCB) specimen geometry, (a) end-blocks,(b) piano hinges.

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flexure (ENF) test, standardised by JIS,7 and the end-loaded split (ELS) asshown in Fig. 9.5. Both of these test methods are currently being evaluatedin ‘round-robin’ trials by standards organisations, with ESIS9 having pub-lished a protocol for the ELS test. Other methods have also been proposedfor measuring the mode II interlaminar toughness, and these include thecentre-notched flexure (CNF) specimen12 and a version of the ENF speci-men which is loaded in four-point flexure, the 4ENF.13 The JIS standard formode II testing prefers the use of test machines which can accept feedbackcontrol so as to stabilise the delamination growth.

However, there remains some concern over the variability of measuredmode II toughness data and the dependence on delamination insert thick-


Pencil lead spacer

Clamp on bearing

(a)

(b)

L

L L

a

a

3 60 1 2 4 5 7

30 1 2 4

2h

2h

9.5 (a) End-loaded split (ELS) and (b) end-notched flexure (ENF) modeII test specimens, in their unloaded and loaded conditions.

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ness and the presence of any precracking (i.e. extension of the initialdelamination prior to the test). The variability may be in part due to thenature of failure processes on the microscopic scale, which can include thedevelopment of inclined tension microcracks ahead of the delaminationfront which eventually coalesce by failure of the ligaments between them.Friction between the sliding surfaces may also contribute to the variationin values of GIIc determined by different data reduction methods.14 Testsinvestigating the dependence of measured toughness on insert thicknessand precracking suggest that it may not be possible to establish a singlevalue of GIIc which can be considered as a purely material property. In viewof the difficulties surrounding the measurement of GIIc and observationsthat many failures in composite structures involve mixed mode I/II frac-ture, with the mode I component being dominant, it has been suggested thatmode I and mixed mode I/II toughness data may prove to be most usefulfor the prediction of delamination failure of practical composite struc-tures.15 This is not, however, a universally held view, with some researchersobserving near-pure mode II fractures in realistic structural configura-tions.16,17 The usefulness of the mode II interlaminar toughness test is clearlystill the subject of debate.

The development of methods for measuring the interlaminar toughnessin mode III is not as far advanced as for modes I and II. Although manyproposals have been made,18 none has so far been found to be fully satis-factory. This is partly due to the difficulty of devising a specimen whichachieves a pure mode III fracture and partly because the mode III inter-laminar fracture toughness is believed to be higher than for the other twomodes, so that delamination growth in real laminated components isexpected to be controlled largely by the resistance in modes I and II. A testmethod currently being evaluated by ASTM is the edge cracked torsion(ECT) test19 shown in Fig. 9.6.

In a real laminated component the delamination growth is likely to occurnot in a single pure mode but as a combination of modes. There is there-fore interest in measuring the interlaminar toughness during mixed modecrack growth. The development of mixed mode test methods has focusedon mixed I/II modes, and the methods proposed include the fixed ratiomixed mode (FRMM) test method and the mixed mode bend (MMB) testwhich are illustrated in Figs. 9.7 and 9.8, respectively.


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Edge crack

Lt

a

B

L

W

9.6 Edge cracked torsion specimen. Dimensions in millimetres: L =76.2, LT = 88.9, W = 31.75, B = 38.1.

Clamp on bearing

L

a

2h 0 1 2 3 4 5 6 7 8 9 10

9.7 Fixed ratio mixed mode (FRMM) test method.

c

FulcrumSaddle and yoke

2h

a

L L

0 1 2 3 4 5 6 7 8 9 10

9.8 Mixed mode bend (MMB) test method.

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9.4 Mode I testing

In the following sections the manufacture, test procedure and data reduc-tion schemes for mode I interlaminar toughness are described, includingrecommendations made in the ASTM standard,8 the more recent of the twotest standards for mode I and the ESIS protocol.9

9.4.1 Specimen manufacture and preparation

In this section the manufacture of DCB test specimens for measuring themode I interlaminar toughness is dealt with. Much of the description is also applicable to other beam-type test specimens used for measuring interlaminar toughness in mode II and mixed mode I/II.

9.4.1.1 The laminate and delamination insert

As noted previously, interlaminar toughness test method development hasfocussed on unidirectional laminates. The starting point in the specimenproduction process is therefore the manufacture of a unidirectional lami-nate containing an initial delamination. The thickness of the laminate willnormally be chosen to ensure that large deflection effects are not signifi-cant. To achieve a mid-plane delamination, the laminate will be made up ofan even number of laminae and the typical thickness for a 60% volumefraction carbon-fibre composite is around 3mm, with that of a 60% volumefraction glass-fibre composite being 5mm. However, if the toughness ishigh, or other types of lower flexural modulus material are to be tested, theASTM standard8 recommends that the thickness be chosen to satisfy thecriterion:

[9.2]

where h is the specimen thickness, GIc is the anticipated critical energyrelease rate, ao is the initial delamination length (measured from the loadline) and E11 is the modulus of elasticity in the fibre direction.

Satisfying this criterion effectively limits the opening displacement of thespecimen arms at the onset of growth so as to ensure the initial load–displacement response is linear. However, during subsequent growth of thedelamination the displacement may become large compared to the cracklength, so that large displacement effects would need to be considered andallowance made for them in the data reduction process. Application of theabove criterion requires prior knowledge of values of GIc and E11 for thematerial to be tested. Values of GIc for similar systems can usually be foundin the literature or manufacturer’s data sheets. Alternatively, those given inTable 9.1 may provide a useful first estimate.

hG a

E≥ 8 28

2

11

3. Ic o


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An initial, or starter, delamination is introduced into the laminate duringlayup by including a thin non-stick film.The ASTM standard8 and ESIS pro-tocol9 recommend that the film thickness should be no greater than 13 mmin order to simulate a sharp crack and cause a minimum disturbance to the laminate. Thicker films can give rise to a resin-rich zone at the tip of thefilm which may give a false initial value of the interlaminar toughness. Thefilm should be chosen so as to be compatible with the cure temperature ofthe composite material. Early work made use of thin aluminium foil asinsert material but polymer films are now recommended in an attempt, notentirely successful, however, to avoid problems with folding and crimpingat cut edges and thermal mismatch. For epoxy matrix composites, cured atbelow 180°C, a thin fluoroethylene polymer film is suitable. For compositescured at higher temperatures (e.g. polyimide, bismaleimide and thermo-plastics) a thin polyimide film should be used. When polyimide film is usedit should be painted or sprayed with a mould release agent before insertioninto the laminate. Silicon-based mould release agents may contaminate thelaminate by migration through the individual layers. To prevent this it isadvisable to bake the coated film at 130°C, subsequently handling the filmcarefully so that the layer of release agent is not damaged or removed.

The film is placed at the mid-plane to give an initial delamination in thespecimen of an appropriate length. For the DCB specimen, the ASTM standard8 recommends that the delamination front formed by the film shouldbe 50mm from the load line, with ESIS9 suggesting that the distance fromthe forward edge of the loading block (or piano hinge) to the film frontshould be at least 45 mm. For unidirectional laminates the film needs to beplaced so that the delamination front is perpendicular to the direction ofthe fibres (i.e. the intended direction of delamination growth). It may behelpful to use a starter film which extends beyond the edges of the lami-nate, as this can aid location of the delamination front in the cured panel.

Having laid up the laminate, incorporating the delamination-starter film,the panel is then cured according to the normal procedures for that mate-rial. Any deviations from the normal curing process should be notedbecause these may affect interlaminar toughness, since this is dependent onthe matrix and matrix-to-fibre bond. Similarly checks on the cured lami-nate, including measurement of fibre volume fraction, void volume fractionand thickness, are recommended. A further quality check using a C-scan ofthe panel should also confirm the location of the starter film.

9.4.1.2 Specimen dimensions

To mark out the specimen geometry on the panel, it is first necessary tolocate the delamination front. If the starter film extends beyond the edgesof the laminate, then the protruding strip of film may be used to mark theposition of the delamination front. However, the film is often distorted or


MTA9 11/22/2000 1:24 PM Page 179

damaged at the edge of the laminate, and it is usually best to trim the panelon a diamond saw and then cut narrow strips from the fibre-direction edgesof the panel; these strips can be totally delaminated by pulling apart by handand the position of the delamination front marked on to the panel. Fromthe delamination front line the rest of the panel can be marked out andspecimens cut with the delamination front perpendicular to the specimenlongitudinal direction. For DCB specimens the ASTM standard8 recom-mends that the specimen length, L, should be at least 125mm and the width20–25mm. ESIS9 gives similar advice. At least five specimens should betested. As usual, the geometry of the test specimens should be recorded.

9.4.1.3 Load introduction

For the DCB specimen, and for some of the other test specimens, the nextstep is to provide some means of applying the load. Adhesively bonded endblocks or hinges, as shown in Fig. 9.4, can be used for this purpose. The geometry of these loading attachments is not prescribed in the ASTM standard8 or ESIS,9 except that they must be at least as wide as the test specimen. For the end blocks the distance from the loading pin centre to themid-plane of the arm of the specimen (dimension l1 in Fig. 9.4) should bekept small to limit the change in lever arm caused by rotation of the block.The ASTM standard recommends that the distance l1 be chosen such that:

[9.3]

where h is the full laminate thickness and a0 the delamination length measured from the loadline. If the condition in Equation [9.3] cannot besatisfied, then end block corrections must be incorporated in the data reduc-tion scheme. These end block corrections and data reduction schemes arediscussed later.

It is usually sufficient to lightly abrade (with sandpaper or grit blasting)and degrease the surfaces to be bonded. Bonding should follow immediatelyafter surface preparation, and in most cases a cyanoacrylate adhesive is ade-quate; alternatively a tough room temperature cure adhesive can be used.

The maximium load to be transmitted by the load attachments in theDCB test is relatively low and can be estimated by Equation [9.4]:

[9.4]

where B is the width of the specimen and h is the full laminate thickness.The maximum force will clearly occur for the shortest delamination length(i.e. the starter delamination length) and so, if debonding of the end attach-

PBa

h E Gmax =

311

96Ic

lh h E

Ga1

311

02

40 01

0 0434£ + +.

.

Ic


MTA9 11/22/2000 1:24 PM Page 180

ments does occur, one remedial strategy is to increase the starter delami-nation length.

It is important that these loading attachments should be properly alignedon the specimen, preferably using some form of jig; otherwise the initialdelamination growth may be non-uniform and consequently give a falsevalue for the initial interlaminar toughness. After curing of the adhesive,any excess adhesive preventing opening of the starter delamination shouldbe removed and, if hinges are used, their free action should be ensured.

9.4.1.4 Delamination measurement

It is preferable to be able to take measurements of delamination growthduring the test from both edges of the specimen. The edges are first coatedwith white water-based typewriter correction fluid, to aid in the visual detec-tion of the crack tip, and then marked with a suitable scale. For the DCBspecimen this involves marking a scale in 1 mm increments for the first 5mm (ASTM)8 or 10mm (ESIS)9 of growth from the starter delaminationfront and then in 5 mm increments for a further 20 mm (ASTM), or at least40mm (ESIS), with ESIS requiring that a final 5mm should be marked at1mm intervals. The ESIS requirement for small scale increments at the endof the delamination growth is an attempt to counter the distorting effectthat the close-packed data, obtained at the beginning of the test, can haveon curve fitting conducted as part of the data analysis.20 The delaminationlength associated with each of the scale lines should be as measured fromthe loading line of the hinges, or a line joining the centres of the loadingpins in the unloaded state (i.e. along the beam). In the ASTM standard itis noted that it may be difficult to locate the exact position of the starterdelamination front. If this proves to be the case, the standard suggests thatthe specimen should be marked with sufficient 1mm increments in theregion of the starter delamination front so as to ensure that during the testthe length of the starter delamination can be determined and growth datarecorded at the next five 1mm increment lines and then at the subsequent5mm increments.

9.4.1.5 Conditioning

Specimens should be moisture conditioned in order to obtain baseline dataat a uniform moisture content. One option is the fully dried condition,and this is recommended because the interlaminar fracture toughness ofpolymer matrix composites is sensitive to resin moisture content. The par-ticular drying temperature and duration should be decided based on advicefrom the resin manufacturer, but for epoxies this might be 70°C in a vacuumoven until no weight loss is detectable. Conditioning should take place after


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the load blocks or piano hinges have been bonded to the specimen. Oncefully conditioned, the specimens may be stored in a desiccator for, at most,24 hours before testing. ASTM8 suggests the use of Procedure D in theirTest Method D 5229M for drying laminates.

Other conditioning procedures may be applied for the investigation ofspecific conditioning effects and ASTM suggests the use of their StandardConditioning Procedure, which is Procedure C in ASTM Test Method D5229M. This procedure gives the laminate the conditioning of a standardlaboratory atmosphere (23°C and 50% relative humidity).

9.4.2 Test procedure

The testing machine should be calibrated and be capable of being operatedin displacement control mode with constant displacement rates in the range0.5–5mmmin-1. The load sensing device should have an accuracy over theload range of interest of within ±1% of the indicated value. Crosshead sepa-ration may be used as a measure of opening displacement of the specimenprovided that the deformation of the testing machine, with gripping fixtureattached, is less than 2% of the opening displacement of the specimen. AnX-Y plotter can be used to make a paper record of the load versus openingdisplacement during the test, or the data may be stored electronically forpostprocessing.

A means must also be provided for the load–displacement data to be‘marked’ as the delamination front advances through each of the scalemarkings on the edge of the specimen. This could simply consist of markingthe paper record of the load–displacement trace manually, or an eventmarker can be used to provide a ‘kick’ to the load axis which can later berelated to the scale crack lengths. If the load–displacement data are beingrecorded electronically, then a signal from a hand-held event marker canalso be recorded and again, after the test, these signals need to be inter-preted in terms of the associated delamination lengths.

The specimen is mounted in a fixture of the testing machine. The fixtureeither allows load to be applied to the pins inserted into the loading blocksattached to the specimen, or uses grips to hold the piano hinges. Eitherapproach allows rotation of the specimen ends. Care should be taken toensure that the specimen is aligned and centred and provision made for thefree end of the specimen to be supported initially, in order to keep the beamorthogonal to the direction of the applied load.

There are a number of acceptable ways of monitoring delaminationgrowth. A travelling optical microscope with a magnification of no morethan 70¥ (20–40¥ is generally sufficient) can be positioned on one side ofthe specimen, with a mirror being used to check for discrepancies from one side of the specimen to the other. Crack length gauges, bonded to thespecimen edges, are another option. Perhaps the ideal is to use two charge


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coupled device (CCD) cameras, one on either side of the specimen, withsuitable optics and adjustable mountings to enable the cameras to followthe advancing delamination tip. The cameras can be coupled to separatemonitors, or to a monitor with split screen capability. Such a system allowsfull delamination growth monitoring capability on both sides of the speci-men, without eye strain! Whatever means is used, it should be capable ofpinpointing the delamination front with an accuracy of at least ±0.5mm.

The loads to be recorded during the test are generally rather low, withpeak loads being in the range 100–200 N. It is, therefore, important that theoutput from the load cell be correctly ‘zeroed’ with any mounting fixturealready in place, prior to inserting the specimen. Also, if there is any ‘play’in the end block-to-loading pin-to fixture, or in the hinge, then it may benecessary to determine the displacement associated with the zero load byextrapolation from the linear portion of the load–displacement curve priorto delamination growth.

At the start of the test the specimen is loaded at a constant crossheadspeed of 0.5 mmmin-1 (ASTM)8 or between 1 and 5 mmmin-1 (ESIS),9 withload and displacement being recorded continuously.The delamination front at the end of the insert material should be observed on both sides of thespecimen, and when the delamination initiates, the load–displacementrecord should be ‘marked’. Even in these opening mode I tests, the initia-tion of delamination growth is often difficult to detect, and for this reasonthe standards propose a number of ways, described later, for identifying GIc

associated with initiation. Use of a low crosshead speed obviously helpsidentify initial movement of the delamination, as does appropriate illumi-nation. Sometimes an unstable delamination growth is observed initially,hence the recommendation from ESIS9 that ten 1mm increments bemarked in the region of the insert front. As the delamination continues togrow, now in a stable manner, the load–displacement data are ‘marked’ asthe delamination front passes the remaining 1 mm increment markers.

At this stage the recommendations of ASTM8 and ESIS9 begin to diverge.ASTM suggests that the test continue past the first five 1mm markers,possibly at an increased crosshead speed, with the load–displacement databeing marked at each of the subsequent 5mm increment markers. Checksshould be made periodically on the opposite edge to see if delaminationgrowth is uniform. If it is not, then the average should be recorded. The dif-ference in delamination length between the two edges should not be greaterthan 2mm; although there is no recommendation that the results from suchspecimens be discarded, this is the implication. When the delaminationlength has extended 25mm from the original insert front, the specimenshould be unloaded, with the unloading cycle also being recorded.

ESIS,9 on the other hand, suggest that once data for five 1mm delami-nation growth increments have been recorded (either after the initial stableinitiation or five readings after the arrest of an unstable initiation), the


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specimen should be completely unloaded at a constant crosshead rate,which may be as high as 25mmmin-1. The delamination tip should then be marked on both sides of the specimen. If the difference is greater than2mm, asymmetrical loading of the specimen is likely to be the cause; ideallythe cause should be identified and rectified before proceeding with subsequent tests. The specimen is then reloaded at the same crosshead rate as the initial loading, with the load–displacement data being markedas the delamination advances from what is now a ‘precrack’. The load–displacement data are marked as growth is initiated from the precrack andat each of the remaining 1 mm increment scale marks, then at the 5mmincrement marks and, finally, at the 1mm increments over the last 5mm ofgrowth. The specimen is then unloaded at a constant crosshead rate.

The relative merits of these different approaches to mode I testing arestill being debated. The ASTM approach gives an initiation value from theinsert. This value may be affected by a resin-rich zone at the delaminationfilm front, but this is likely to be small for the recommended starter filmthickness adopted in the standard. Propagation values may be increasedowing to fibres bridging between the crack surfaces (fibre bridging), so thatthe initiation value is likely to be a lower bound. The ESIS approach alsomeasures this insert initiation value but, in addition, gives information con-cerning delamination initiation from a mode I precrack. The initiation ofgrowth from the precrack is also likely to be affected by fibre bridging,offering a degree of specimen stiffening.

9.4.3 Interpretation of test results

The data acquired during the test are: the initial delamination length,ao (this can be confirmed after the test by separating the two arms of thespecimen by hand); the various delamination lengths, a (where a = ao + themeasured delamination length increments); the corresponding loads, P; anddisplacements, d.These, together with dimensions of the specimen (and end-block, if used), allow determination of the mode I fracture toughness of thematerial and the application of corrections where necessary.

There are several ways in which initiation and propagation values of GIc

may be determined from the data acquired, and these values may be usedto generate a resistance curve, or R curve, by plotting the calculated Gversus crack length, a, as shown in Fig. 9.9. GIc may be determined for testingfrom the starter film and from the mode I precrack, where available.

9.4.3.1 Methods for ascertaining delamination initiation

It was mentioned earlier that the precise identification of delamination initiation by visual inspection can be notoriously difficult and, in any case,


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is highly operator dependent. In order to obtain some degree of re-peatability, three ways of relating points on the load–displacement curve to delamination initiation have been proposed:

• Initiation by visual observation (VIS): A visually observed initiationvalue for GIc can be calculated corresponding to the load and displace-ment at which the delamination is seen to grow from the insert on eitheredge of the specimen.

• Initiation determined by deviation from linearity (NL): Here GIc can becalculated using the load and displacement at the point of non-linearityof the load–displacement curve. The calculation assumes that the de-lamination begins to grow from the centre of the insert, within the specimen.21 It is noted in the ASTM standard8 that the NL value for GIc

represents a lower bound and for brittle matrix composites is typicallythe same point at which delamination is observed to initiate at the specimen edges, see Fig. 9.10(a). However, for tough matrices a regionof non-linear behaviour may precede visual observation of the initiationof delamination at the specimen edges, see Fig. 9.10(b).


2500

2000

1500

1000

500

040 50 60 70 80 90 100

Crack length a (mm)

GIc (

J m

-2)

9.9 Typical R curve for mode I fracture. �, propagation values; �, deviation from linearity; �, visual onset; �, 5% offset.

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Force

NL & VIS

MAX

5%Propagationmarkers

Displacement

Force

VISNL

5%MAX

Propagationmarkers

Displacement

Force

NL & VISMAX

Propagationmarkers

5%

Displacement

9.10 Load–displacement curves for DCB tests, (a) brittle matrix, (b) tough matrix, showing stable crack growth, and (c) unstablecrack growth.

(a)

(b)

(c)

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• Initiation from 5% offset/maximum load (5%/MAX): This value of GIc

may be calculated from the intersection values of the load–deflectioncurve with a line drawn from the origin and offset by a 5% increase incompliance from the original linear portion of the load–deflection curve,as shown in Fig. 9.10. If the maximum load occurs before the point ofintersection, then the maximum load and corresponding displacementshould be used to calculate GIc.

9.4.3.2 Identifying test data associated with propagation

In addition to the data associated with initiation, determined as outlinedabove from either the insert or precrack, propagation values of GIc can bedetermined for each delamination length, load and displacement com-bination measured during delamination propagation. Under displacementcontrol delamination growth is often quite stable, if not precisely steady. Infact, if GIc is constant (i.e. independent of crack length), then the growth ina DCB specimen under displacement control is always stable.5 However,growth can be unstable and this is characterised by one or more periods ofno, or very slow, delamination growth followed by a rapid delamination,yielding sharp drops in the load–displacement graphs with virtually infiniteslope, as shown in Fig. 9.10(c). It is usually impossible to record delamina-tion length readings during unstable delamination growth, which is nor-mally followed by arrest (i.e. no delamination growth) and a reloadingphase which results in a local peak load when delamination growth restarts.If such ‘stick–slip’ behaviour is observed, the arrest points should be ex-cluded from the analysis.

9.4.3.3 Data reduction

The ASTM standard8 gives three methods for calculating GIc, and thesehave been evaluated by round-robin testing.22 The methods consideredwere: a modified beam theory (MBT), a compliance calibration (CC) anda modified compliance calibration (MCC). Since in the round robin, GIc

values determined by the different methods differed by only 3%, it is clearthat none is essentially superior. However, the ASTM standard points outthat the MBT method yielded the most conservative values of GIc for 80%of the specimens tested and recommends the use of this method. ESIS9

offers only the MBT and MCC.These data reduction methods are described in the following sections,

assuming that hinges have been used for applying the load and that thereare no significant large displacement effects. Subsequently the correctionswhich should be applied to account for end blocks and large displacementsare presented.


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9.4.3.3.1 Modified beam theory (MBT) method

The energy release rate for a DCB specimen in which the arms are con-sidered to be clamped at the delamination front is given by simple beamtheory to be:

[9.5]

By inserting into Equation [9.5] the values of load, P, and displacement, d,associated with growth at a particular crack length, a, the critical energyrelease rate, GIc, at that crack length can be determined.

However, in practice, the arms are not perfectly built-in and rotation mayoccur at the delamination front.This rotational effect may be accounted forby treating the DCB as if it contained a longer delamination at each length,a + D, and so the mode I fracture toughness using this modified beam theoryis calculated from Equation [9.6]:23

[9.6]

D may be determined experimentally by plotting the cube root of compli-ance, C1/3, as a function of delamination length, a (the compliance is the ratioof displacement to the applied load, d/P). The values which should be usedto generate this plot are the loads and displacements corresponding to the visually observed delamination onset and the propagation values. Theextrapolation of a least squares fit through the data yields D as the nega-tive of the intercept on the delamination length axis, as shown in Fig. 9.11.The intercept will normally be negative and so D will normally be positive.Typical values of D that have been determined5 for a 3mm thick carbon-fibre reinforced plastic (CFRP) specimen lie in the range 2.8–5.1 mm. Insome cases the intercept turns out to be positive, and in these circumstancesESIS9 recommends that D should be set to zero. ASTM8 makes no recom-mendation concerning the sign of D but uses the modulus of D (i.e. |D|)rather than D in Equation [9.6]. However, if D does turn out to be negative,then the cause should be investigated; such a value could be produced, forexample, if the crack lengths have been mistakenly measured from the endof the specimen rather than from the load line. In these circumstances thenegative value of D would be valid and could be used in Equation [9.6] toproduce valid GIc data.

This approach also allows the determination of the flexural elasticmodulus, E1f:

[9.7]Ea PBh

1

3

3

64f =

+( )Dd

GP

B aIc =+( )

32

dD

GPBaI =

32

d


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Here, following the ASTM convention, h is the full laminate thickness. Thevalues of EIf obtained should be delamination length independent; however,fibre bridging may increase the values determined.

9.4.3.3.2 Compliance calibration (CC) method (Berry’s method)24

This method makes use of the visually observed delamination onset andpropagation values of d and P with the corresponding delamination lengths,a. The method assumes that the compliance, C, is proportional to an. A plotis constructed of log (C) versus log (a) and a least squares best fit line isdrawn through the data. The exponent, n, is the slope of the line, as shownin Fig. 9.12. The mode I interlaminar fracture toughness is calculated fromEquation [9.8]:25

[9.8]

Typical values of n for the standard 3 mm thick CFRP specimen lie in therange 2.7–2.9mm. (Note that simple beam theory gives n = 3.)

In contrast to the modified beam theory, this approach is essentially acurve fitting process which does not directly address the mechanisms con-trolling the behaviour of the specimen. The value of n will change if therange of delamination lengths is changed, but for the crack length rangesnormally used, GIc determined by this method is usually within a few per cent of that calculated using the modified beam theory.

GnP

BaIc =d

2


0.08

-10 10

0.06

0.04

0.02

0.0030 50 70 90 110 130 150

D = 4.55 mmCrack length a (mm)

C1/

3 (m

m1/

3 N-1

/3)

9.11 Determination of D for the modified beam theory.

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9.4.3.3.3 Modified compliance calibration method

In this method the cube root of the compliance, C1/3, is assumed to be lin-early proportional to the crack length, a, and the constant of proportional-ity is determined using a compliance calibration plot. By manipulating thealgebra to produce an equation for G which does not explicitly involve theobserved crack lengths, this method effectively includes the crack lengthcorrection achieved by the modified beam theory (MBT) method.

The ASTM standard8 and the ESIS protocol9 differ slightly in the appli-cation of this data reduction method which uses all of the visually observeddelamination onset and propagation data (although ESIS does allow thevisually observed onset data to be omitted from the linear regressiondescribed below).

In the ASTM method a plot is constructed of the delamination lengthnormalised by specimen thickness, a/h, as a function of the cube root of thecompliance, C1/3, as shown in Fig. 9.13.

A least squares fit to the data gives a line of slope A1 and the mode Iinterlaminar fracture toughness is calculated from Equation [9.9]:26

[9.9]

The ESIS9 approach is similar but uses slightly different nomenclature forthe thickness, where h is now the half thickness of the laminate. The ESISprotocol recommends plotting the cube root of the product of the widthand compliance (BC)1/3 versus the thickness-normalised delamination

GP CA BhIc =

32

2 2 3

1


Dx

Dy

DxDy

n =

log a

log

C

9.12 Determination of n for the compliance calibration method.

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length, a/2h. The least squares slope of this line gives the coefficient, m. Themode I interlaminar fracture toughness is then given by Equation [9.10]:

[9.10]

Note that the ESIS protocol9 mistakenly refers to plotting (BC)2/3 in thetext and omits a factor of 2h in the equation for GIc.

9.4.3.3.4 End block and large displacement corrections

If end blocks are used, these will stiffen the end portions of the specimen.Note that with hinges the stiffening effect is of no consequence, becausethis occurs outside the zone between the load line and the delaminationfront. As a test proceeds, the end blocks will rotate as the specimen deflectsand so reduce the lever arm to the delamination front, reducing the dis-placement for a given load. In addition, if large displacements occur, thenthe deflection will be less than that predicted by small displacement theoryowing to the shortening of the lever arm.

For these reasons the measured displacement will be less than that whichwould occur if the loading were applied at the mid-plane of the arms andthe displacement remained in the linear regime.An approximate correctionfactor, N, has been derived25 which can be applied to yield the correctedlinear displacement, such that:

Gmh

PB

BCIc = ÊË

ˆ¯ ( )3

4

22 3


A1

C1/3

a/h

9.13 Modified compliance calibration.

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[9.11]

where d is the measured displacement and N is given by Equation [9.12]:

[9.12]

where the term (l2/a)3 corrects for block rigidity ignoring the effects of

rotation; corrects for the change in lever arm caused by

rotation of the end block including a further correction for end block

rigidity; and corrects for the change in lever arm caused by large

displacements. See Fig. 9.4 for definitions of l1 and l2.The correction factor, N, can also be used to yield the corrected compli-

ance. Recalling that the measured compliance C = d/P, then:

[9.13]

Clearly the second and third correction terms in N in Equation [9.12] couldbe applied when hinges are used, but the ASTM standard and ESIS proto-col both recommend that N should be considered to be 1 for hinges.

By correcting the displacements, or compliances, with the factor N andthen using the corrected values in the data reduction schemes describedearlier, the resulting GIc is that which would occur if the load measured fora given crack length had been applied at the arm mid-thickness positionand the specimen had deflected in accordance with small displacementlinear theory. In reality, when end blocks are used, the load is applied at apoint significantly removed from the arm mid-thickness position and rota-tion at the end of the specimen will cause a shorter lever arm to the delami-nation front. Similarly large displacements will also cause the lever arm tobe shorter than the crack length measured from the scale marked on theedge of the specimen. A factor, F, can be derived to account approximatelyfor both of these effects, so that the actual lever arm (i.e. the corrected cracklength) can be obtained25 from the crack length, a, measured from the scaleon the edge of the specimen multiplied by √F:

[9.14]

and

[9.15]Fa

la

= - ÊË

ˆ¯ - Ê

Ëˆ¯1

310

32

21

2

d d

a a Fcorrected =

CCNcorrected =

935

2da

ÊË

ˆ¯

98

11

2

22dl

ala

- ÊË

ˆ¯

ÏÌÓ

¸˝˛

Nla

la

la a

= - ÊË

ˆ¯ - - Ê

Ëˆ¯

ÏÌÓ

¸˝˛

- ÊË

ˆ¯1

98

1935

23

1

2

22 2d d

dd

corrected =N


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where corrects for large displacements and corrects for

rotation of the end block.It can be shown that the energy release rate is proportional to the square

of the moment at the delamination front,25 so that for a given load the GIc

determined on the basis of small displacement theory and application ofthe load at the specimen arm mid-thickness position can be corrected tothe true value by multiplying by F:

[9.16]

Again it can be noted that both correction terms in F can be applied whenhinges are used for the load application and, in contrast to the recomen-dations for N, both the ASTM standard and ESIS protocol recommend thatthese terms should be used for hinges.

Table 9.2 summarises the use of the N and F correction terms in the threedata reduction schemes described earlier.

G G FIc corrected Ic( ) =

32

1

2

dla

ÊË

ˆ¯

310

2da

ÊË

ˆ¯


Table 9.2. Use of N and F correction factors in mode I data reduction schemes.

Data reduction method Use of N and F factors

Modified beam theory (i) plot (C/N)1/3 versus crack length todetermine the crack length correction, D

(ii) evaluate GIc from

(iii) the flexural elastic modulus can be

determined from

Compliance calibration (i) determine n from a plot of method (Berry’s method) log(C/N) versus log(a)

(ii) calculate GIc from

Modified compliance ASTM:calibration method (i) determine A1 as the slope of a plot of

(a/h) versus (C/N)1/3

(ii) calculate GIc* from

ESIS:(i) determine m as the slope of a plot of

(BC/N)1/3 versus (a/2h)

(ii) calculate GIc from

*Note that the application of the correction factors for GIc is given incorrectlyin the ASTM standard.5

Gmh

PB

BCN

FIc = ÊË

ˆ¯

ÊË

ˆ¯

34

2 2 3

GP C N

A BhFIc =

( )32

2 2 3

1

GnP N

BaFIc =

( )d2

EP a

N Bh1

3

3

64f =

+( )( )

Dd

GP NB a

FIc =( )

+( )32

dD

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The correction factors F and N usually produce only small correctionsfor 3mm thick unidirectional CFRP specimens for the crack length rangesrecommended. However, for longer crack lengths, or for other materialswhere the critical energy release rate is higher and/or the flexural stiffnessis lower, these corrections can be more significant.

9.5 Mode II testing

As noted earlier, there have been many test methods proposed for meas-uring GIIc. These methods include the end-loaded split (ELS) test,5 the end-notched flexure (ENF) test5 and, more recently, the four-point end-notchedflexure (4ENF) test.13 A test standard for a relatively complex stabilisedENF test has been produced by JIS.7 ASTM and ESIS have been conduct-ing round-robin laboratory evaluations of other mode II test methods;27

ASTM have been investigating the ENF test, while ESIS have examinedboth the ENF and ELS methods. The ESIS protocol9 is for an ELS test fora unidirectional laminate. The following sections consider first the ELS testand then a number of variants of the ENF test.

9.5.1 ELS Test

With this specimen, shown in Fig. 9.5(a), a lateral load is applied by thetesting machine through a load block under displacement control at a con-stant rate. Delamination growth from a non-adhesive insert material or amode I or mode II precrack at the laminate mid-plane is monitored so asto obtain delamination initiation and propagation readings at known posi-tions on the load–displacement curves. Appropriate data reduction allowsthe determination of GIIc for initiation and propagation, which can beplotted versus the delamination length, a, as an R-curve. It should beexpected that different initiation values of GIIc will be determined depen-dent on the type of starter crack and it is recommended that tests directlyfrom the delamination film and following precracking should be performed,so as to obtain the most conservative value.

9.5.1.1 Specimens

Laminate preparation is largely similar to that described earlier for themode I DCB test specimens. If a starter film is to be used, it should be placedat the mid-thickness of the laminate prior to moulding. The starter filmlength in the specimen should be at least 50 mm from the load line so thatthe effects of the load block are reduced.

The normal dimensions for the specimen are a width of 20 mm andoverall length of 170 mm.The free length (i.e. the length measured from the


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load line at the loading block to the clamp) should be approximately 100mm. For a 60% fibre volume fraction CFRP the laminate thickness shouldbe 3mm, and 5mm for the same volume fraction glass-fibre reinforcedplastic (GFRP). Although it is possible to use alternative specimen dimen-sions, ideally the width should be between 15mm and 30mm. An increasein length is not critical, but shorter specimens result in a small amount ofdelamination growth for investigation and too few data points for the analy-sis; care must be taken to ensure that the ratio, a/L, between the initialdelamination length, a, and the distance from load line to clamp, L (see Fig.9.5), is at least 0.55 in order to avoid unstable crack growth.5 Reducing thelaminate thickness may result in specimens which are insufficiently stiff, sothat delamination growth may occur only at large displacements, or failureof the specimen arms may occur instead of delamination growth.

The ELS mode II test requires only one loading block, which is bondedto the specimen following the same procedure as that described for modeI DCB specimens.The position of the end of the delamination insert shouldbe marked on both edges of the specimen and a thin layer of typewritercorrection fluid painted onto both edges. Marks should be drawn on bothedges every 1mm from the tip of the delamination film for at least the first5mm and then every 5mm up to 35mm; subsequently marking shouldreturn to 1mm intervals up to at least 40mm.9 As for the mode I test, thecrack lengths associated with each of these marks is as measured from theload line in the unloaded state.

9.5.1.2 Apparatus

A tensile testing machine capable of giving a constant displacement rate ofbetween 1 and 5mmmin-1 and equipped with a load cell accurate to ±1%is required; typical loads are in the 100N–200N range. A means of record-ing the complete load–displacement curve is required.

A fixture is needed to introduce the load to the pin in the load block,allowing free rotation of the specimen end. A loading jig is also needed toclamp the remote end of the specimen, and this must allow for the hori-zontal movement of the specimen as the test proceeds. There are a numberof alternatives: the end of the specimen may be clamped between rollers;the fixed clamp can be mounted on a fixture which allows horizontal move-ment through bearings (as shown in Fig. 9.5); or a fully fixed clampingarrangement can be used, together with a loading fixture which allows horizontal movement of the load point, so that the applied load remainsvertical.

This vertical load is normally applied to the load block by pulling up withthe load block beneath the specimen, but it is also possible to invert thespecimen and apply the load to the end block by pushing down.


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9.5.1.3 Test procedure

9.5.1.3.1 Elastic modulus determination

If the beam theory analysis is to be used to evaluate the data, it is neces-sary to obtain a value for the elastic modulus of the material from a three-point bend test. The modulus value should be determined beforedelamination testing and on part of the specimen which does not containthe delamination film or precrack. Details for carrying out this test proce-dure are given in Chapter 7.

9.5.1.3.2 Mode II fracture test

The test parameters and data recording are basically the same as thosedescribed previously for mode I testing. Because these specimens do notopen during the test, friction between the faces may be a problem, and toreduce this effect a thin film of PTFE, or a pencil lead, should be placedbetween the delamination faces at the load line (see Fig. 9.5), opening themslightly.

The specimen is loaded at a constant crosshead rate in the range 1–5mmmin-1. For normal length specimens the low end of the speed range is suit-able, but longer specimens can be tested at the higher end.

The point of delamination initiation should be recorded on the load–displacement curve. Observation can be aided by optical microscope, or aCCD camera system, as described earlier for the mode I test, but even sothe tip of the crack is difficult to track since there is no crack opening. Sub-sequent crack positions should be noted as the delamination passes eachmark on the edge of the specimen. Normally loading should stop before thedelamination tip reaches a point 10mm from the clamp. The specimen is then unloaded, usually at a higher rate. Once removed from the jig, thespecimen can be opened by hand in mode I. This reveals the final positionsof the mode II delamination front on both edges of the specimen, since thesurface features are generally quite different between mode I and mode II.If the difference between the two positions is greater than 2 mm, the resultsare suspect.

9.5.1.4 Data analysis

As with the mode I test described previously, the data required for theanalysis are the delamination length, a, together with the correspondingloads, P, and displacements, d. The same initiation values can also be deter-mined, that is, deviation from linearity (NL), visual observation (VIS) and5% offset or MAX. Propagation (PROP) values are also normally avail-able, although in some materials the propagation may be unstable.


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9.5.1.3.3 Modified beam theory (MBT)

As with the mode I data reduction described previously, a correction forrotation at the delamination tip, D, must be introduced into the simple beamtheory.The analysis immediately runs into problems: what value should thiscorrection have? A method for determining D by experiment has been pro-posed which is similar to that described earlier for the mode I test. In thiscase (C - C0)1/3 is plotted against the crack length, a, where C0 is the com-pliance of a specimen without a delamination. Unfortunately there is anaccuracy problem with this approach for mode II tests because it is now thedifference between two compliances which is being plotted.28 There is someevidence28 to suggest that multiplying the value of D obtained from mode Itests by 0.42 gives a good approximation to the value of D correspondingto loading of the ELS specimen. In the absence of mode I test results onthe same material the ESIS protocol suggests setting D to zero, although atheoretical estimate is available for D.25

The mode II fracture toughness is given by Equation [9.17]:9

[9.17]

where P is the load, a is the delamination length, DII is the delamination tiprotation correction, B is the specimen width, E1f is the modulus of elastic-ity parallel to the fibre direction from a three-point bend test and h is thehalf-thickness of the specimen.

Other equations are available for GIIc,28 for example excluding E1f butincluding P, a and d, analogous to Equation [9.6] for mode I. However, thesupport at the clamped end will not be absolutely rigid and corrections willneed to be applied to d to allow for the effect of the support flexibility inaddition to the other corrections discussed earlier for the mode I test.

Equation [9.17] is based on small displacement theory and assumes theload to be applied at the specimen arm mid-plane. As for the DCB test, thecorrection factor, F, can be used for large displacements and end-blockeffects:

[9.18]

where GIIc is calculated from Equation [9.17] and:

[9.19]

in which d is the displacement, l1 is the distance from the centre of the loadblock to the mid-plane of the specimen arm to which the end block isattached and L is the free length of the specimen, see Fig. 9.5(a).

The factors q1 and q2 are calculated from Equations [9.20] and [9.21]:

FL

lL

= - ÊË

ˆ¯ - Ê

Ëˆ¯

È

ÎÍ

˘

˚˙1 1

2

21

2q

dq

d

G G FIIc corrected IIc( ) = ◊

GP a

B E hIIc

II

f

=+( )9

4

2 2

21

3

D


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[9.20]

[9.21]

9.5.1.3.4 Experimental compliance method (ECM)

This alternative approach can be used if the loading and unloadingload–displacement curves are both linear. The compliance, C, is plottedversus the cube of delamination length, a3, using only the VIS and PROPvalues. A least squares fit is obtained, the slope, m, of which can be used todetermine GIIc from Equation [9.22]:

[9.22]

A correction factor, N, to account for end-block rigidity and rotation andlarge displacements has been derived25 for the ELS specimen to correct themeasured compliance, as for the DCB specimen, but the ESIS protocol doesnot suggest that this should be used.

9.5.2 ENF test

In its basic form the ENF test involves performing a three-point bend teston a specimen which contains a starter delamination at one end (see Fig.9.5), where the total length of the specimen is some 150mm and the widthis 20 mm. As with the ELS specimen, the initial delamination may beextended from the insert by precracking, either in mode I, using the DCBconfiguration, or in mode II. To precrack the specimen in mode II the specimen can be positioned in the three-point bend fixture so that thedelamination can only grow a few millimetres before reaching the centralloading roller. This test has a relatively small zone of stable growth (simplebeam theory predicts that for constant GIIc the delamination growth will bestable for a > 0.7L), and this growth is likely to be affected by the centralloading roller. The test is normally conducted in the unstable regime (a/Lª 0.5), yielding initiation data only. Equation [9.23] can be used to evaluateGIIc from the test data:5

GP ma

BIIc =3

2

2 2

q 2

2

33

1 3

1 3

= - ÊË

ˆ¯

+ ÊË

ˆ¯

+ ÈÎÍ

˘˚

È

Î

ÍÍÍÍ

˘

˚

˙˙˙˙

La

aL

aL

q1

2 4

3 2

3 15 50 63

20 1 3

=+ Ê

Ëˆ¯ + Ê

Ëˆ¯

È

ÎÍ

˘

˚˙

+ ÊË

ˆ¯

È

ÎÍ

˘

˚˙

aL

aL

aL


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[9.23]

The P values in Equation [9.23] are those associated with the NL, VIS andMAX/5% offset discussed earlier for mode I, although, as noted for theELS test, detecting delamination growth visually can be difficult. It shouldbe noted that the non-linearity due to large displacements in this specimenis of a softening form (rather than the stiffening form observed in the DCB)and can easily be confused with the non-linearity associated with the ini-tiation of delamination growth.

It is also possible to use an experimental compliance calibrationapproach. Compliance data can be determined before the toughness test isconducted by varying the position of the specimen in the bend fixture sothat the compliance can be measured for a range of different delaminationlengths encompassing the delamination length to be used in the toughnesstest. The cube of the compliance is then plotted against the delaminationlength and the slope, m, of the best fit straight line is used in Equation [9.24]to determine GIIc:

[9.24]

It is possible to stabilise the delamination growth in the ENF specimenso that propagation data can be collected. This can be achieved by usingsome form of feedback control rather than performing the test at a fixedcrosshead displacement rate. Two such methods have been proposed forstabilised ENF (SENF) testing29 and form the basis of the JIS test standard.7

In one method, the relative shear displacement between the two arms ofthe specimen is controlled to increase at a constant rate. In the othermethod, a function involving both the crosshead displacement and theapplied load is controlled to increase monotonically during the test. Bothof these approaches require test machines that can accept feedback control,and this is likely to preclude widespread adoption of the SENF test.

To achieve stable growth in an ENF-type test, but without the complex-ity of the SENF, it is possible to load the ENF specimen in a four-point bendtest rig as shown in Fig. 9.14.13,30

With the delamination tip positioned between the inner loading rollers,the 4ENF test has a number of advantages over the more conventional ENFtest. The delamination front will lie in a zone of pure moment, whereas inthe three-point ENF (and in the ELS) there is also a shear force acting. Ithas been suggested13 that this reduces the friction problems associated withthe other mode II tests, although there is still a compressive normal forceacting between the arms of the specimen outside the central pure momentzone. Also, because the delamination front lies in the pure moment region,

GP ma

BIIc =3

2

2 2

GP a

B E hIIc

f

=+( )9

16

211

2

21

3

D


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the data reduction strategy is relatively simple. The compliance can beplotted against delamination length and the slope, m, of the best fit straightline found. If large displacements occur, then corrections similar to thosepresented earlier will be necessary. GIIc is then evaluated from Equation[9.25]:

[9.25]

Note that Equation [9.25] does not involve the crack length, so that thenature of any R-curve will be directly reflected in the form of the load–displacement curve. So, for example, if GIIc is independent of crack length,then the load will reach a critical value and remain constant; if, however,GIIc increases with delamination growth, then so will the critical load. The4ENF method is a relatively new proposal and is currently being inves-tigated further.

9.6 Mixed mode I/II

Delaminations in real composite structures often grow in a combination ofmodes I, II and III, so that there is considerable interest in establishingmixed mode growth criteria.31,32 To support this, measurement of the de-lamination toughness at various mode ratios is required.

Mixed mode I/II delamination behaviour has been under investigationfor some time.27 Whilst there are a number of practical ways which may beused to induce a mixed mode response, there are two which have received

GP m

BIIc =2

2


P, d

Specimen

Machine base

a

L

9.14 4ENF testing arrangement.

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a great deal of attention. These are the fixed ratio mixed mode (FRMM)and the mixed mode bend (MMB) tests.

9.6.1 FRMM test

The basic form of FRMM specimen is essentially identical to the ELS specimen, discussed previously. It is, however, inverted when loaded, so thatthe loading block is above the specimen, with the testing machine acting in tensile mode, as shown in Fig. 9.7. In the FRMM case the ratio of modeI to mode II is very close to 4 :3 throughout the test, which is carried outin the same way as the mode II ELS test, described earlier. The mode I andmode II contributions to the total mixed mode interlaminar critical energyrelease rate GI/IIc can be deduced from Equations [9.26] and [9.27]:5

[9.26]

[9.27]

where

[9.28]

DI and DII are the crack length correction terms discussed in the earliersection on the ELS data analysis. F is the correction factor for large dis-placements and end-block effects, such that:

[9.29]

where

[9.30]

and

[9.31]

By positioning the initial starter delamination away from the specimen mid-plane it is possible to achieve other mode ratios in the FRMM test,25 but

q 2

2

33

7 1

7 1

= ÊË

ˆ¯

ÊË

ˆ¯ +

ÊË

ˆ¯ +

La

aL

aL

q1

4 2

3

3 367 130 15

20 7 1

=

ÊË

ˆ¯ + Ê

Ëˆ¯ +

ÏÌÓ

¸˝˛

ÊË

ˆ¯ +

ÏÌÓ

¸˝˛

aL

aL

aL

FL

lL

= - ÊË

ˆ¯ - Ê

Ëˆ¯1 1

2

21

2q

dq

d

G G Gm mI IIc Ic IIc= +

G FP a

B h Em

IIcII

f

=+( )9

4

2 2

2 31

D

G FP aB h E

mIc

I

f

=+( )3 2 2

2 31

D


MTA9 11/22/2000 1:25 PM Page 201

then the two techniques for determining the mode separation (the local andglobal33 techniques) yield significantly different mode ratios. Evidence hasbeen published which suggests that for some materials the global mode separation method is valid,34 but for others the local mode separation tech-nique is the most suitable.35

9.6.2 MMB test

The jig used for the MMB test method36 is shown in Fig. 9.8. It makes use of a specimen which is essentially identical to the DCB specimendescribed previously, but the jig allows the determination of the delamina-tion fracture toughness at various ratios of mode I to mode II loading, fromalmost pure mode I to pure mode II. Forces to load the specimen areapplied via end blocks (or piano hinges) at the delaminated end of the specimen and through rollers which bear on the specimen in the undelami-nated region.The base of the jig is attached to the bottom specimen loadingblock and also supports the specimen near the opposite end with a roller,whilst a lever, attached to the top end block, also applies a downward forceon the specimen centrally between the supports at either end of the specimen. By applying a downward load on the lever arm, as indicated inFig. 9.8, the upper block is pulled upwards and a downward load is appliedcentrally to the specimen. To vary the mode mixture, the loading point position on the lever can be changed by varying the dimension ‘c’. It is alsopossible to adjust the mode ratio by moving the upper loading roller awayfrom the central position.34

It is necessary to ensure that the load applied to the lever remains verti-cal throughout the test, and this is normally achieved by the use of a saddleand yolk arrangement. In order to reduce geometric nonlinear effects due to lever rotation, the lever should be loaded so that the position of the loading point is slightly above the mid-plane of the test specimen(approximately 15 mm). Load application to the lever and the specimenshould allow sliding with a minimum of friction; this is generally achievedwith roller bearings.

The method of testing is basically the same as that described previouslyfor the DCB and ELS specimens, load and displacement readings beingtaken and correlated with delamination position. It is recommended thatthe load point displacement be measured using a linearly variable dis-placement transducer (LVDT) rather than from the crosshead displace-ment, since this avoids the complexity of having to determine thecompliance of the loading system separately for every lever length settingto be used.

The desired mode mixture can be set by adjusting the relative positions


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of the lever loading roller and the loading saddle/yolk, such that the dis-tance between them, c, from simple beam theory, is given by Equation[9.32]:

[9.32]

in which GI and GII are the mode I and mode II components, respectively,and G is the total energy release rate. This is reasonably accurate for mostmode mixtures but becomes less so in the low mode II range owing to cor-rections that need to be made for crack tip rotation, when Equation [9.32]can be in error by up to 20%.

The mixed mode interlaminar toughnesses GmIc and Gm

IIc can be obtainedusing Equations [9.33] and [9.34]:

[9.33]

[9.34]

where I is the second moment of area for one delaminated half of the specimen (Bh3/12) and L is the half-span length of the MMB test appara-tus. These equations rely on delamination length corrections25,34 for lami-nate rotation at the delamination front. In this case Equation [9.35] is usedto calculate D, the results of which have been shown to agree well with finiteelement predictions.37

[9.35]

in which where E11 is the longitudinal modulus of elas-

ticity measured in tension, E22 is the transverse modulus of elasticity andG13 is the out-of-plane shear modulus which may be assumed to be equalto the in-plane shear modulus G12 for a unidirectional composite.

E1f in the Equations [9.33] and [9.34] is the flexural modulus of the laminate and can be determined from the initial load–displacementresponse but, if the crosshead displacement has been used, then a correc-tion for the loading system compliance must be included.

G = 1 18 11 22

13. ,

E EG

DG

G= -

+ÊË

ˆ¯

ÏÌÓ

¸˝˛

hEG11

13

2

113 2

1

for mIc

mIIc

f

c L G

GP c L a

BL E I

< =

=+( ) +( )

3 0

3 0 4264

2 2 2

21

. D

for mIc

f

c L GP c L a

BL E I> =

-( ) +( )3

316

2 2 2

21

D

c

GG

GG

GG

GG

L=-Ê

Ëˆ¯ + +Ê

Ëˆ¯

-

8 3 1 3 1 3

39 3

II II II

II


MTA9 11/22/2000 1:25 PM Page 203

9.7 Multidirectional laminates

This chapter has so far largely concerned itself with the investigation ofdelamination growth in unidirectional laminates where the delamination isinitiated between two plies of the same fibre orientation and the delami-nation front is constrained to grow in the fibre direction. A typical compo-nent will, however, be composed of a multidirectional laminate, and thereis no reason to suppose that the location and direction of growth of a delam-ination would be constrained in such a manner. Delaminations may, forexample, arise from manufacturing defects occurring between plies of anyorientation, and delaminations from in-service damage, such as impact, nor-mally occur between plies of different orientation. Whilst it is true that theunidirectional values of fracture toughness allow the ranking of differentmaterials in their delamination resistance, if fracture mechanics is to beused to predict the growth of delaminations in multidirectional compositecomponents, then the fracture toughness as a function of fibre orientationin the delaminating plies needs to be investigated.

9.7.1 Mode I

Early published literature38–42 on mode I delamination growth in multi-directional laminates showed that the conventional DCB test producescomplex fracture behaviour when examining interfaces other than thatbetween unidirectional plies orientated parallel to the delamination direc-tion. In laminates where the delaminating interfaces are not 0°/0°, a largedegree of fibre bridging normally develops behind the propagating crack.This arises from the crack ‘jumping’ from the plane in which it was origi-nally located by transverse cracking of an adjacent off-axis ply.43 When thisoccurs the crack tip bifurcates, leading to the development of significantfibre bridging, often of almost complete plies.

One way of suppressing this behaviour is to use a delaminating film alongboth edges of a DCB specimen in addition to the normal starter crack film.44

A plan view of the mid-plane of the specimen used is shown in Fig. 9.15.


Edge delamination

9.15 Mid-plane plan view of side-delaminated specimen.

MTA9 11/22/2000 1:25 PM Page 204

In this work, multidirectional XAS/913 carbon/epoxy specimens wereprepared with layups which were carefully designed to ensure that the lam-inate stiffness characteristics (i.e. the A-B-D matrix) of the two arms wereidentical, that all the laminate coupling effects (e.g. bend-twisting) wereeliminated and that there was no curvature or in-plane shear distortion ofthe laminate (or half-laminate) caused by thermal stresses resulting fromcuring. (The ply-level residual stresses are, of course, still present and theirmagnitude in the delaminating plies may affect the measured interlaminartoughness.)45

Results using the conventional DCB specimen confirmed the observa-tions of other researchers. Unidirectional specimens exhibited continuousstable crack growth at the intended interface and an essentially constantGIc with a crack length of 0.28 kJm-2. Changing the fibre orientation of thedelaminating plies to +45°/+45° and +45°/-45° resulted in fibre pullout,crack jumping, multiple delamination growth and considerable fibre bridg-ing, as indicated on the fracture surface shown in Fig. 9.16(a).

In edge-delaminated specimens with +45°/+45° and +45°/-45° mid-planeinterfaces the crack tended to remain predominantly at the intended inter-face. The suppression of the complex combination of fracture modes isclearly seen in Fig. 9.16(b). The average GIc recorded for these interfaceswas some 30% greater than that for the 0°/0° interface, whereas with noedge delaminations the increase was in excess of 100%.

Despite the success of this edge delamination approach to the mode Itesting of multidirectional laminates in XAS/91344 and T300/924,46 theunwanted fracture modes could not be fully suppressed in mode I tests on+45°/-45° interfaces in T800/924 laminates,47 as shown in Fig. 9.17. Investi-gation of lower angle +q°/-q° interfaces found that although reduction ofthe interface angle had an effect on the degree of fibre bridging, it was not


9.16 Fracture surfaces of (a) a conventional specimen and (b) anedge-delaminated specimen, for mode I DCB tests on a +45°/-45°interface in XAS/913.

(a)

(b)

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eliminated entirely. The characteristics of the material system that dictatethe success or failure of the edge delamination strategy are yet to be identified, but will include the fibre-to-matrix bond and, possibly, the fibrediameter. (T800 fibres are approximately half the diameter of XAS andT300 fibres.)

9.7.2 Mode II and mixed mode I/II

Whilst it may not be possible to employ successfully the edge delaminationapproach to the mode I (or mode II) testing of all multidirectional inter-faces and fibre/matrix combinations, there is evidence46 that it can work satisfactorily for 0°/q° interfaces under certain circumstances. The key is toreduce the tensile stresses in the q° ply caused by bending so that the delam-ination is inhibited from jumping through the q° ply. This condition can besatisfied in mode II (ELS) and mixed mode I/II (FRMM and MMB) byensuring that the q° interface is in the lower arm of the specimen, whenloaded as shown in Fig. 9.7, for the FRMM. It has been shown that for somematerials, specimens can be tested in this manner without edge delamina-tions, provided the mode I component is sufficiently low.47

9.8 Conclusions

There is a degree of test method standardisation in place. At present this isrestricted to national standards for unidirectional laminates. However, workis progressing on international standards to cover both modes I and II,mixed mode I/II test methods and even mode III. It is likely that these standards will be introduced in the next few years.

There are many problems to be resolved, not least those surrounding themeaningful interlaminar toughness testing of multidirectional laminates,but considerable progress has been made in establishing specimen config-urations, test procedures and data reduction schemes for the determination


crack growth direction

9.17 Fracture surface of edge delaminated mode I DCB test on a+45°/-45° interface in T800/924.

MTA9 11/22/2000 1:25 PM Page 206

of the interlaminar toughness of laminated composites.The measured inter-laminar toughness characteristics of a material system will not only enableit to be ranked against competing material systems, but will also allow pre-diction of delamination growth in real structures, which will have a majorrole in both initial design and in assessing the significance of any delami-nation damage occurring during service.

References

1. N R Sottos, J M Hodgkinson and F L Matthews, ‘A practical comparison of stan-dard test methods using carbon fibre reinforced epoxy’, Proceedings of the SixthInternational Conference on Composite Materials and Second European Con-ference on Composite Materials, Centre for Composite Materials, ImperialCollege, London, eds F L Matthews, N C R Buskell, J M Hodgkinson and JMorton, Elsevier Applied Science, 1987, Volume 1, 310–20.

2. S Mespoulet, J M Hodgkinson, F L Matthews, D Hitchings and P Robinson, ‘Anovel test method to determine the through-thickness tensile properties of longfibre reinforced composites’, Proceedings of Seventh European Conference onComposite Materials (ECCM-7), Institute of Materials London, UK, Volume 2,Woodhead Publishing, Cambridge May 1996, 131–7.

3. S Mespoulet, Through-thickness Test Methods for Laminated Composite Mate-rials, PhD Thesis, Centre for Composite Materials, Imperial College, LondonUniversity, UK, January 1998.

4. J G Williams, Fracture Mechanics of Polymers, Ellis Horwood, Chichester, UK,1984.

5. S Hashemi, A J Kinloch and J G Williams, ‘The analysis of interlaminar frac-ture in uniaxial fibre-polymer composites’, Proc Royal Soc A, 1990 427 173–99.

6. D Hitchings, P Robinson and F Javidrad, ‘A finite element model for delami-nation propagation in composites’, Computers and Structures, 1996 60(6)1093–1104.

7. JIS K7086, Testing Methods for Interlaminar Fracture Toughness of CarbonFiber Reinforced Plastics, 1993.

8. ASTM D 5528-94a, ‘Standard test method for mode I interlaminar fracturetoughness of unidirectional fibre-reinforced polymer matrix composites’,Annual Book of ASTM Standards, 100 Barr Harbor Drive,West Conshohocken,PA 19428, USA, Vol 15.03, 1997.

9. European Structural Integrity Society (ESIS), ‘Protocol for interlaminar frac-ture testing of composites (Mode I DCB – ISO CD 15024.2 and Mode II ELS– ESIS TC4 Version 95-11-10)’, Polymers and Composites Task Group, 1998.

10. I M Daniel, I Shareef and A A Aliyu, ‘Rate effects on delamination fracturetoughness of a toughened graphite/epoxy’, in Toughened Composites, ed N JJohnston, ASTM STP937, 1987, 260–74.

11. A L Glessner, M T Takemori, M A Vallance and S K Gifford, ‘Mode I inter-laminar fracture toughness of unidirectional carbon fiber composites using anovel wedge-driven delamination design’, in Composite Materials, Fatigue andFracture, ed P Lagace, ASTM STP1012, 1989, 181–200.


MTA9 11/22/2000 1:25 PM Page 207

12. H Maikuma, J W Gillespie and D J Wilkins, ‘Mode II interlaminar fracture ofthe center notch flexure specimen under impact loading’, J Composite Materi-als, 1990 24 124–49.

13. R H Martin and B D Davidson, ‘Mode II fracture toughness evaluation usinga 4-point bend end notched flexure test’, Proceedings, 4th International Confer-ence on Deformation and Fracture of Composites, Manchester, Institute ofMaterials, published by IoM Communications Ltd, London, March, 1997,243–52.

14. B R K Blackman and J G Williams, ‘On the mode II testing of carbon-fibrepolymer composites’, Proceedings of the Twelfth European Conference on Frac-ture (ECF-12), Sheffield, ESIS, SIRIUS and University of Sheffield, eds M WBrown, E R los Rios and K J Miller, published by EMAS, Cradley Heath, UK1998, 1411–6.

15. T K O’Brien, ‘Composite interlaminar shear fracture toughness, GIIc: shear measurement or sheer myth?’, NASA Technical Memorandum 110280, NASALangley Research Center, Hampton, Virginia, USA.

16. E Greenhalgh and S Singh, ‘Investigation of the failure mechanisms for delam-ination growth from embedded defects’, Proceedings of the Twelfth InternationalConference on Composite Materials (ICCM-12), Paris, 1999, paper 341.

17. E Greenhalgh, B Millson, R Thompson and P Sayers, ‘Testing and fractureanalysis of a CFRP wingbox containing a 150J impact’, Proceedings of theTwelfth International Conference on Composite Materials (ICCM-12), Paris,1999, paper 340.

18. P Robinson and D Q Song, ‘The development of an improved mode III delam-ination test for composites’, Composites Science and Technology, 1994 52217–33.

19. S M Lee, ‘An edge crack torsion method for mode III delamination fracturetesting’, J Composites Technology and Research, 1993 15(3) 193–201. ASTMD30.06 Sub-committee on Interlaminar Properties, Mode III Interlaminar Fracture Task Group, Edge Crack Torsion Method, 1999.

20. A J Brunner, Interlaminar Fracture Testing of Unidirectional Composites, NATOAdvanced Study Institute, Mechanics of Composite Materials, Portugal, July1995.

21. T de Kalbermatten, R Jaggi, P Flueler, H H Kausch and P Davies, ‘Microfocusradiography studies during mode I interlaminar fracture tests on composites’,Journal of Materials Science Letters, 1992 11 543–6.

22. T K O’Brien and R H Martin, ‘Round robin testing for mode I interlaminarfracture toughness of composite materials’, ASTM Journal of Composites Tech-nology and Research, Winter 1993 15(4) 269–81.

23. S Hashemi, A J Kinloch and J G Williams, ‘Corrections needed in double can-tilever beam tests for assessing the interlaminar failure of fibre-composites’,Journal of Materials Science Letters, 1989 8 125–9.

24. J P Berry, ‘Determination of fracture energies by the cleavage technique’,Journal of Applied Physics, 1963 34(1) 62–8.

25. J G Williams, ‘The fracture mechanics of delamination tests’, Journal of StrainAnalysis, 1989 24(4) 207–14.

26. K Kageyama and M Hojo, ‘Proposed methods for interlaminar fracture tough-ness tests of composite laminates, Proceedings of the 5th US/Japan Conferenceon Composite Materials, Tokyo, June 1990, 227–34.


MTA9 11/22/2000 1:25 PM Page 208

27. P Davies, B R K Blackman and A J Brunner, ‘Standard test methods for delam-ination resistance of composite materials: current status’, Applied CompositeMaterials, 1998 5 345–64.

28. Y Wang and J G Williams, ‘Corrections for mode II fracture toughness speci-mens of composite materials’, Composites Science and Technology, 1992 43(3)251–6.

29. K Tanaka, K Kageyama and M Hojo, ‘Standardisation of mode I and mode IIinterlaminar fracture toughness tests for CFRP in Japan’, Proceedings, 2ndEuropean Conference on Composite Materials – Testing and Standardisation,Hamburg, 1994.

30. R H Martin, T Elms and S Bowron, ‘Characterisation of mode II delaminationusing the 4-ENF’, Proceedings, 4th European Conference on Composite Materi-als – Testing and Standardisation, Lisbon, Portugal, Institute of Materials,published by IoM Communications Ltd, London 1998, 161–70.

31. E Greenhalgh, L Asp and S Singh, ‘Delamination resistance, failure criteria and fracture morphology of 0°/0°, 0°/5° and 0°/90° ply interfaces in CFRP’,Proceedings of the 5th International Conference on Deformation and Fractureof Composites, Manchester, Institute of Materials, published by IoM Commu-nications Ltd, London, 1997, 43–52.

32. J R Reeder, Evaluation of Mixed-mode Delamination Failure Criteria, NASATM 104210, 1992.

33. M Charalamides, A J Kinloch, Y Wang and J G Williams, ‘On the analysis ofmixed-mode fracture’, International Journal of Fracture, 1992 54 269–91.

34. A J Kinloch, Y Wang, J G Williams and P Yayla, ‘The mixed mode delamina-tion of fibre composite materials’, Composites Science and Technology, 199347(3) 225–37.

35. F Ducept, D Gamby and P Davies, ‘Mixed-mode failure criteria derived fromtests on symmetric and asymmetric specimens’, Composites Science and Tech-nology, 1999 59(4) 609–19.

36. J R Reeder and J H J Crews, ‘Redesign of the mixed-mode bending delamina-tion test to reduce nonlinear effects’, Journal of Composites Technology andResearch, 1992 14 12–9.

37. S Bhashyan and B D Davidson, ‘Evaluation of data reduction methods for themixed mode bending test’, AIAA Journal, 1997 35 546–52.

38. A J Russell and K N Street, ‘Factors affecting the interlaminar fracture ofgraphite/epoxy laminates’, Proceedings of 4th International Conference on Composite Materials (ICCM-4), eds T Hayashi, K Kawata and S Umekawa,1982, 279–86.

39. D J Nicholls and J P Gallagher, ‘Determination of GIc in angle ply compositesusing a cantilever beam test method’, Journal of Reinforced Plastics and Com-posites, 1983 2 2–17.

40. H Chai, ‘The characterisation of mode I delamination fracture in non-wovenmultidirectional laminates’, Composites, 1984 15 277–90.

41. W L Bradley, C R Corleto and D P Goetz, Fracture Physics of Delamination inComposite Materials, AFOSR-TR-88-0020, 1987.

42. A Laksimi, M L Benzeggagh, G Jing, M Hecini and J M Roelandt, ‘Mode I inter-laminar fracture of symmetrical cross-ply composites’, Composites Science andTechnology, 1991 41(2) 147–64.

43. S Singh and E Greenhalgh, ‘Micromechanisms of interlaminar fracture in


MTA9 11/22/2000 1:25 PM Page 209

carbon-epoxy composites at multidirectional ply interfaces’, Proceedings of the4th International Conference on Deformation and Fracture of Composites,Manchester, Institute of Materials, published by IoM Communications Ltd,London, 1997, 201–10.

44. P Robinson and D Q Song, ‘A modified DCB specimen for mode I testing of multidirectional laminates’, Journal of Composite Materials, 1992 26(11)1554–77.

45. P Robinson, S Foster and J M Hodgkinson, ‘The effects of starter film thickness,residual stresses and layup on GIc of a 0°/0° interface’, Advanced CompositesLetters, 1996 5(6) 159–63.

46. S Foster, P Robinson and J M Hodgkinson, ‘Interlaminar fracture toughnesstesting of 0°/q° interfaces in carbon-epoxy laminates using edge delaminationstrategy’, Plastics, Rubber and Composites Processing and Applications, 1997,26(10) 430–7.

47. M S Hiley, ‘Delamination between multidirectional interfaces in carbon-epoxycomposite under static and fatigue loading’, Proceedings, 2nd ESIS-TC4 Con-ference on Polymers and Composites, Les Diablerets, Switzerland, September1999.


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10.1 Introduction

Fibre-reinforced/plastic matrix composites owe their high specific basicmechanical properties (reduced probability of flaws in a fibre comparedwith the bulk material) to the synergistic behaviour of the fibre and resin.However, testing has shown that these materials are, in practice, sensitiveto many aspects of in-service use for which it is difficult to provide designdata. For example, impact-induced damage has been shown to reduce com-pression strength in continuous fibre systems.

The types of composite material (short/random/continuous fibre withthermoset/thermoplastic matrices) and their applications (aerospace/auto-motive/civil/marine) vary widely, so that no single test can readily quantifythe myriad of potential impact situations and their subsequent effect. Thismay in itself require further post-impact testing to measure the desiredresidual property (e.g. strength, stiffness, etc).

The object here is to discuss the various impact test methods available,their relevance and the significant practical importance this experimentalapproach has contributed to the use of composite materials in industry. Theemphasis is directed toward high performance composite materials, with acritical examination of the fundamental issues thought to be governing frac-ture and the potential for future impact testing to be simulated (virtualtesting).

10.2 Impact testing

It is common to refer to the impact resistance of a material. However, thisis an all-embracing term that can refer to many quite different aspects of amaterials behaviour in a given structure.

The impact ‘resistance’ of a composite may refer to the ability of the composite to withstand a given blow without any damage (i.e. theresilience); the maximum force necessary to rupture or separate a

10Impact and damage tolerance

P J HOGG AND G A BIBO

211

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composite structure, irrespective of the preceding level of damage (theimpact strength); the amount of energy that is absorbed by a given mass ofthe composite (the crush resistance); or perhaps the level of damage that acomposite can sustain during impact loading without suffering unduereduction to some primary structural function after the impact event(damage tolerance).

Impact loading is usually taken to mean the impact of either a projectileor the composite itself at speeds in the range 1–10m s-1. This phenomenonhas received the greatest attention to date, as out-of-plane impacts in thisvelocity range may have catastrophic consequences on the subsequent loadcarrying capability of the structure. Impacts in the speed range >100ms-1

are termed ballistic events, while those at speeds >1000ms-1 would betermed hypervelocity impacts. This chapter is restricted to impacts withinthe 1–10ms-1 range. While testing within this speed range can present somepractical difficulties, with respect to data analysis caused by vibration andnoise, the complications induced by reflecting stress waves during the testare largely absent.1,2

10.2.1 Theoretical aspects

There are many theoretical aspects that must be considered for the correctinterpretation (particularly if a plastics-based standard is being followed,the impact test may be instrumented) of experimental testing. The level ofthe impact blow (i.e. the impact energy or momentum) is varied in mosttest machines by varying the drop height of the striker, see Fig. 10.1.

This has the effect of changing both the impact energy and the impactvelocity simultaneously.An alternative approach would be to vary the massof the striker, while keeping the velocity constant. Applying the physics ofmotion results in Equations [10.1] to [10.4], defining force F, velocity v, dis-placement x and energy E, respectively:

[10.1]

[10.2]

[10.3]

[10.4]E v f t g ft tM

f tt t t

= + -È

ÎÍ

˘

˚˙Ú Ú Ú0

21

2d d d

0 0 0

x v gtM

f ttt

= + - ÚÚ02

0

12

1d

0

v v gtM

f tt

= + - Ú01

d0

F Mg f Mvt

= - =dd


MTA10 11/22/2000 1:34 PM Page 212

where v0 is the velocity at the point of impact.This allows the forces generated during a test, together with energy

absorption and deflection, to be recorded. In cases such as this it is impor-tant that a reliable and accurate method for measuring the velocity atcontact is employed because this parameter is required for the calculationsof displacement and energy and, if incorrect, will generate erroneousresults.3 In other cases where the test is uninstrumented, an alternativeapproach to determining energy absorption is to measure the reboundheight. Where a post-impact property is being measured it is unusual forthe test to be instrumented, although this may be specified in future in theemerging standards in this area.

The signals generated by an instrumented striker may be noisy owing to excessive vibrations (from the machine, specimen or the striker itself) and it is possible with some test machines, and certainly with post-processing of the impact signal, to filter and smooth the curve.This has the effect of producing a force–time or force–displacement curvemore similar to that generated during slow testing. It is generally agreed, however, by workers in the field that this process is extremely risky if the curves are to be inspected subsequently for signs indica-tive of fracture events. The filtering process cannot distinguish be-tween spurious vibrations and genuine features on the curve that resultfrom the fracture process, and much vital information can be lost throughfiltering.

Impact and damage tolerance 213

Release mechanism

Impactor

Guide

Specimen

Impact supportboundary conditions

Measuring scale

Velocity measurement &anti-multiple strike

10.1 Schematic diagram showing the essential elements of an impacttest apparatus.

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10.2.2 Experimental impact test methods

Unidirectional prepreg tape-based structures or components normallyconsist of relatively thin shell-like laminates; thus the majority of possibleservice impacts can be categorised as events involving thin monolithic shellstructures. Added complications arise if the structure has a honeycombcore, as the skin/core interface bond may fail and, unlike the monolithicmaterial, these are more difficult to inspect non-destructively. Damagecaused by ballistic impact typically takes the form of a neat puncture and,whilst it still requires inspection to determine the spread of internal frac-ture, the damage is clearly visible.4 Consequently, the form of impact sce-nario that has attracted most experimental study has been based on lowvelocity/low energy and monolithic composite materials.

The dropped tool on an aircraft wing, stones hitting the undershield of acar, a lifeboat hitting rocks, a fork-lift truck nudging the side of a portablebuilding, can all be cited as possible examples of composite structuresundergoing out-of-plane impact, albeit with a wide range of relative pro-jectile–target masses, shapes and velocities. This class of impact event isusually simulated in tests by some form of falling weight or driven dartbeing impacted onto a simple square or circular plate. This approach willbe discussed in more detail later.

While the initial utilisation of composites was aerospace driven, the gen-eralisation that all structures are thin is now an oversimplification andbecoming increasingly untenable. Many large structures are now con-structed from thick composites, and this has necessitated considerable activ-ity in the testing arena in order to quantify out-of-plane through-thicknessproperties of composites.To date, the corresponding effort in impact testingof thick composites has not materialised. Some limited studies have beenundertaken but, apart from empirical ballistic studies on thick compositearmour, no systematic studies either of properties or test methods havebeen undertaken.

Alternatively, an area that is currently receiving more attention is that ofin-plane impact testing. This area is being recognised as important becauseof the rate sensitivity of the constituents of composite materials and theirhigh specific energy absorbing capabilities (e.g. formula one cars).

10.2.3 In-plane impact testing

Typically, this might be the result of some high strain rate loading takingplace in a remote part of a structure which results in a general transientmembrane tensile stress being generated. This form of impact might be simulated in testing by the use of a Hopkinson bar apparatus to introducea shock wave through a sample, or in some cases by the application of a


MTA10 11/22/2000 1:34 PM Page 214

high strain rate tensile force by servohydraulic machines.5 It is not alwayspossible to generate a high strain rate tensile stress for a sustained periodof time, and in some respects the transient loading and the tensile test athigh strain rates, for practical purposes, are simply two extremes of whatmight be achieved. A body of high strain rate ‘tensile impact’ testing hasbeen undertaken at Oxford in the UK.6–8 These tests do not introduce anynew dimensions into testing by way of test geometry or fixtures; the onlychange relative to conventional tensile tests lies in the apparatus used tointroduce the high strain rate, and the difficulties of recording accuratedeflection (or strain) versus time data for the construction of the high strainrate stress–strain curves. The data generated from these tests may beregarded with the same significance as those used to generate design data,as they are capable of measuring a pseudo-material property.

Another form of high strain rate in-plane loading that is becomingincreasingly important is connected with the progressive crushing of com-posites, as might be engineered in crash conditions in vehicles and otherenergy absorbing structures.9–11 Crush testing involves compressive loadingrather than tension, and the time duration and displacement involved in acrush test may be greater than in some drop weight impacts. The loadingscenario is, however, a genuine impact event, as a crash involves a finitepacket of energy and the collision of bodies at high speed. Although mostresearch work in this field has been based on ad hoc test specimens, origi-nally based on tubes, some progress has been made towards identifyingstandard test components and fixtures.

10.2.4 Out-of-plane impact testing

The application of an out-of-plane impact can be effected in a number ofways. Objects can be propelled towards a target specimen using pendulumstrikers, falling weights, driven darts and fired sabots. Specimens can besimply supported, clamped, allowed to flex or be constrained, mounted oncompliant fixtures or rigid frames. While variations in conditions willinevitably result in different forces, energy dissipation and fracture pro-cesses, it has been found that tests which produce similar stress states generate similar damage states.12

10.2.4.1 Flexed beam tests

The need to perform impact tests on metals and later on plastics was recog-nised before the advent of composites as engineering materials. It is not sur-prising that the first test methods explored for impact testing of compositeswere derived from the methods used successfully for these other materials.These included variations on the theme of Izod and Charpy impact tests,


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which use a swinging pendulum to strike a specimen which is in the formof a beam. The Izod specimen designed for metals consists of a beamclamped and struck as a cantilever, while the Charpy test developed forplastics has the beam simply supported and loaded in flexure by the pen-dulum striker. The Izod and Charpy tests both have provision for notchedsamples for use with tough specimens, see Fig. 10.2.

These tests are very useful for the isotropic materials for which they weredeveloped. In their simplest forms the pendulums are not instrumented andthe datum recorded from each test is the energy absorbed by the specimen.This is measured by the angle through which the striker moves after it hasimpacted and fractured the specimen. The greater the swing of the pendu-lum after impact, the smaller the amount of energy absorbed. Similarly,impact energy supplied can be varied by adjusting the starting position ofthe pendulum, although in order to maintain a relatively constant velocity,it is usual to change the mass of the pendulum and keep everything elseconstant.

The test can be instrumented in order to record force during the test,thereby allowing a record of the strength of the material under impact con-ditions to be obtained and, if the specimen is notched, the test can be usedas a form of high rate fracture toughness test, see Table 10.1.13

In the general context of composite materials this form of test geometryis of limited value. The provision of a beam-type specimen is the firstproblem area. If the impact test is required to simulate the performance ofa thin composite beam, then obviously the test is appropriate. However, itis unlikely that in service many reinforced thin beams will be manufacturedfrom composite materials, unless the fibres are aligned along the beam. Thetest may well be suitable for ranking or providing a relative measure of vari-ables in the construction of the material, such as interply adhesion, the roleof toughening layers, different fibre types or resin types, for example, effec-


Notch

Striker

SpecimenStriker

Notch

(a)(b)

10.2 Schematic representation of the Charpy (a) and Izod (b) impactequipment.

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tively simulating a high speed bend test. This information is, however, pecu-liar to that test configuration. The impact test becomes something akin toa ‘materials’ or ply level property test with all of the complications of highstrain rate testing (including vibrations, transient effects), and the dataobtained cannot easily be used to predict or model the performance ofmore complicated (practical) laminates.

Some useful studies performed using flexed beam tests were conductedby Marom et al.,14 which enabled the role of different fibres in hybrid com-posite structures to be investigated. Similarly, key work undertaken byCantwell and Morton revealed the relationships between thickness anddamage mechanisms for carbon-fibre composites, although this work reliedon relatively thin and wide strips rather than on beams of the dimensionsusually associated with flexed beam tests.15–18

The flexed beam test also imposes a uniaxial loading condition on the specimen. When composite structures, approximating to plates or shells in service, are impacted, the load almost inevitably involves a biaxialloading constraint. Consequently the failure modes exhibited by beam


Table 10.1. Charpy impact data for (a) longitudinally and (b) transverselyreinforced unidirectional prepreg tape laminates (after Adams and Perry13).

Composite Configuration Maximum Absorbed Normaliseda

force (N) energy (J) absorbed energy(kJm-2)

System (a)

Carbon/epoxy unnotched 12900 10.7 109notched 8500 9.2 113

Glass/epoxy unnotched 13390 77 778notched 11210 56 694

Kevlar 49/epoxy unnotched 7920 68 672notched 5690 57 694

Nylon/epoxy unnotched 5600 14.9 145notched 4230 9.4 116

System (b)

Carbon/epoxy unnotched 778 0.5 5.0notched 512 0.3 3.6

Glass/epoxy unnotched 676 1.1 10.9notched 689 0.9 11.3

Kevlar 49/epoxy unnotched 445 1.4 13.0notched 338 0.9 12.6

Nylon/epoxy unnotched 436 0.5 5.5notched 276 0.5 6.7

NB typically an average of 3 specimens.a Normalised by dividing by the specimen cross-sectional area.

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specimens, even if the beams are cut from laminates with a multiaxial fibreorientation, differ markedly from those exhibited by the majority of com-posite structures. Experience has also shown that in some cases multiaxiallaminates in plate form develop damage which is not symmetric and whichcan propagate extensively within a plate before failure. Such behaviourcannot be reliably predicted on the basis of beam tests.

While a place exists for beam-based impact testing in a laboratorycontext for the purpose of materials development, the test cannot be con-sidered suitable for predicting the response of thin composite structures. Itis probable, however, that as the interest in thick composites grows, Charpyor Izod-type tests, as applied to large sections of metal components, will bere-examined for correspondingly large composite beams.

10.2.4.2 Flexed plate impact testing

Flexed plate impact tests typically comprise the impact of a projectile ontoa plate-type specimen as shown schematically in Fig. 10.3. There are,however, no test methods that have been standardised specifically for theimpact testing of long fibre composites. In many cases standards developedfor plastics have been adapted for use with composites, and this often con-stitutes direct usage with no modification of geometry or specimen size.

This configuration is often used to assess the ultimate load resistance ofthe material and its energy absorbing capabilities, or for studying the devel-opment and consequences of subcritical damage. In the first case it is usualto supply an impact with an excess of energy, such that the striker pene-


Impactor

Specimen

Boundary support conditione.g. 40 mm diameter ring

10.3 Schematic diagram of typical flexed plate impact geometry.

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trates the specimen without significant deceleration during the impactevent. Typical force–time curves generated during excess energy impactsare shown in Fig. 10.4.

The data produced in this way can be characterised using a number ofparameters taken from the force–time (or force–displacement) curves. Themost easily identifiable parameters are the peak force and the total energyabsorbed by the plate. Neither of these parameters represents a materialproperty. There is some indication that the peak force is determined by thestrain to failure of the reinforcing fibres, coupled with the initial stiffness ofthe composite plate, and is independent of resin chemistry.19,20

Other features, such as energy to the peak force, or the force and energyat the onset of damage, may be obtained. The latter parameters are notalways easy to identify, and in some cases no clearly defined load drop canbe seen on the curve at deflections when cracking has begun. A reductionin the magnitude of the initial energy of the striker will result in a changein the force–time curves as shown in Fig. 10.5. During this process, theprominence of peaks associated with initial damage increases and, by suf-ficiently lowering the impact energy, it is possible to identify the onset offracture quite clearly.

For low energy impacts, the parameters such as peak force and absorbedenergy are, on their own, not particularly helpful in the characterisation ofthe material behaviour. It is useful to be able to link absorbed energy orpeak force to a damage parameter. The most widespread form of damagecreated during impact testing is delamination. Delaminations are also criti-cal in the subsequent post-impact compression strength of a compositeplate, as discussed in detail later, while the presence of fibre fracture is influ-ential in terms of residual tensile strength.21 The area, or width, of thedelaminations can be measured. For carbon-fibre composites this must bedone using C-scan, or another non-destructive system, to image the delam-inated area, as shown in Fig. 10.6, while for glass-fibre composites this zonecan usually be seen with the naked eye. It may be noted that the force–displacement curves computed from the equations of motion are reason-ably accurate up to the point at which the velocity of the striker falls to zero. Thereafter, significant errors may arise and the computed data areunreliable.22

The scatter generated during high energy testing is quite significant andovershadows most of the variations that may be present between differentcomposite material systems. Table 10.2 presents data obtained for a seriesof test specimens drawn from one material and an equivalent set generatedby individual specimens of many widely differing glass-fibre composites.The coefficient of variation of both data sets is very similar.

A master plot can be constructed illustrating the similarity of most glass-fibre composite systems, as shown in Fig. 10.7. Similar plots can be


MTA10 11/22/2000 1:34 PM Page 219


8800

7040

5280

3520

1760

0.0 2.5 5.1 7.6 10.2 12.7

Time (ms)

For

ce (

N)

(a)

8800

7040

5280

3520

1760

0.0 6.0 12.0 18.0 24.0 30.0

Displacement (mm)

For

ce (

N)

(b)

100.0

80.0

60.0

40.0

20.0

0.02.5 5.1 7.6 10.2 12.7

Time (ms)

Ene

rgy

(J)

(c)

10.4 Typical raw (unfiltered) data generated during a through-penetration impact test on glass-fibre reinforced quasi-isotropicunidirectional prepreg tape. (a) Force–time, (b) force–displacement, (c) energy–time.

constructed for carbon-fibre composites, Fig. 10.8.The relative performanceof carbon- and glass-fibre composites becomes clear on this form of plot. Itshould be noted that the data for the carbon-fibre systems are mean datapoints for different matrix systems (thermoplastic and thermoset).The data

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1850

1480

1110

740

370

0.01.3 2.6 3.9 5.2 6.5

Time (ms)

For

ce (

N)

(a)

1850

1480

1110

740

370

0.00.6 1.2 1.8 2.4 3.0

Displacement (mm)

For

ce (

N)

(b)

3.0

2.4

1.8

1.2

0.6

0.01.3 2.6 3.9 5.2 6.5

Time (ms)

Ene

rgy

(J)

(c)

10.5 Typical raw (unfiltered) data generated during a low energy/lowvelocity impact test on glass-fibre reinforced quasi-isotropicunidirectional prepreg tape. (a) Force–time, (b) force–displacement, (c) energy–time.

for glass-fibre composites consist mainly of individual data points, apartfrom the SMC which is represented by mean data points.

The behaviour of similar composites tested under low energy conditionsis very different and is a function of resin chemistry, for a similar fibre

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Time / µs

% Areas

Y s

cale

/ m

m

X scale / mm

10.6 C-scan showing the internal fractures induced by a lowenergy/low velocity impact on a triaxial [452,-452,06,-452,452]S

carbon/epoxy unidirectional prepreg tape.

200.0

150.0

100.0

50.0

0.0

0.0 150.0100.0 200.0

Thickness (mm) ¥ fibre volume fraction (%)

Ab

sorb

ed e

ner

gy

(J)

50.0

10.7 Relationship between energy absorbed during through-penetration versus thickness multiplied by fibre volume fractionfor glass-fibre composites. �, Random and woven glass-fibre/thermoset resin; �, sheet moulding compound (SMC); �, random glass-fibre thermoplastic (GMT); �, quasi-isotropiccontinuous glass-fibre reinforced polypropylene; �, quasi-isotropic carbon-fibre epoxy unidirectional prepreg tape (afterBabic et al.).19

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type.20,23–25 Considerable difference in behaviour, as measured by damagezones, is evident in Fig. 10.9. This shows the results for damage width versusimpact energy for glass-fibre and carbon-fibre epoxy and carbon-fibrePEEK (polyether ether ketone) and Radel quasi-isotropic laminates.

It should be noted that impact data generated using a particular testgeometry and specimen size are not necessarily representative of the resultsgenerated using alternative test geometries even for identical materials.Changes in the relative size of striker, specimen, span and support condi-tions influence the distribution of tensile, compressive and shear stresses


Table 10.2. Data from through-penetration tests showing the scatter in thecombined population and within a given material sample.

Material Maximum Absorbed Normalised Normalisedforce (N) energy (J) force energy

[F ¥ (t ¥ Vf)] [E ¥ (t ¥ Vf)]

GRP3 S1 9200 85 101 0.93GRP3 S2 15300 136 103 0.91GRP3 S3 14400 115 119 0.95GRP4 S1 800 78.1 87 0.82GRP4 S2 15300 150 98 0.96GRP4 S3 11000 100 99 0.90GRP5 S1 8000 766 91 0.75GRP5 S2 16100 138 92 0.87GRP5 S3 13400 99.3 104 0.77GRP6 S1 8200 66.8 92 0.75GRP6 S2 15300 118 101 0.78GRP6 S3 10400 83.2 86 0.69GRP7 S1 8600 76.1 93 0.82GRP7 S2 16900 174 115 —GRP7 S3 11200 84.3 97 0.73GRP7 S4 4750 42.6 81 0.73GRP8 6700 65.5 92 0.90GRP9 5900 45.9 92 0.72Mean 97 0.82Stand. deviation 9.6 0.09Coefficient of variation (%) 9.9 10.9

GRP7 S4 Results from 6 specimens illustrating the variation within onematerial

Mean 9.4 0.79Stand. deviation 9.5 0.064Coefficient of variation (%) 9.8 8.1

Vf = fibre volume fraction.

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200.0

150.0

100.0

50.0

0.0

0.0 150.0100.0 200.0

Thickness (mm) ¥ fibre volume fraction (%)

Ab

sorb

ed e

ner

gy

(J)

50.0

10.8 Energy absorbed in through-penetration versus thicknessmultiplied by fibre volume fraction for carbon-fibre reinforcedcomposites superimposed on master curve, from Babic et al.19

�, Glass fibre; �, carbon fibre.

50.0

40.0

30.0

20.0

10.0

0.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

Impact energy (J)

Dam

age

wid

th (

mm

)

Ring support diameter

10.9 Extent of impact-induced delamination damage versus incidentenergy (ISO/DIN) in �, quasi-isotropic carbon-fibre reinforced AS-4/PEEK; �, T650-42/Radel (thermoplastics); �, a toughened epoxy(T800/924); and �, glass-fibre reinforced epoxy (E-glass/914).

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throughout the thickness of the specimen and thereby influence the valuesobtained for the various test parameters. Equally, the same material with adifferent layup may result in different levels of damage, even when usedwith the same impact equipment.

In other cases, impact tests have been standardised as part of a more extensive test method designed to study post-impact compressionproperties. According to the requirements of the user, the impact tests may be used to measure the ultimate resistance to rupture of the compositeplate, or to induce some non-critical damage in the composite that may impinge on subsequent properties under a different loading regime(damage tolerance).

There is no simple method for comparing results generated using differ-ent specimen geometries and layups, particularly if the impact event isdesigned to damage but not destroy the material. Specimens that have arelatively low flexural stiffness will tend to absorb a large quantity of anykinetic energy supplied by a projectile by elastic deformation.15,16,26 Thickspecimens with a relatively high flexural stiffness over a short support spanwill, in contrast, suffer from contact deformation due to their stiffness; shearstresses will result in localised fracture before bending stresses become significant, Fig. 10.10.27

10.2.5 Standardisation of impact test techniques

Rationalisation of the various impact test methods currently being used isurgently required, since many researchers are repeating work and generat-ing data that cannot be readily disseminated between groups because thedata are generated by different impact apparatus (material for supports,boundary conditions, striker material and geometry, data acquisition andanalysis).

Dimensions of specimens and test supports for high energy or throughpenetration impact cited in the literature by numerous research groups aregiven in Table 10.3.28 The fibre layups used with these test configurationsare of course variable according to the needs of a particular research orquality assurance programme. It is rare for testing to be performed on unidirectional plates, as this does not simulate any sensible practical application.

Standard tests specified for plastics but commonly used for high energyimpact testing of composites are included in Table 10.4.Again, the fibre con-struction or layup is not specified by the test standard. When an impact testis performed on a composite in order to measure the subsequent in-planeproperties of the damaged composite, mainly in compression, the laminatesare usually required to be quasi-isotropic layups. To some degree, in theabsence of a specific test standard for impact, the test geometry adopted


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tends to be based on what commercial equipment is available. In the USAa preponderance of research groups utilise the test configuration that comesas standard in the instrumented impact test rig marketed by Dynatup, whichconsists of a hemispherical striker of diameter 16 mm and a non-specifiedsupport geometry; the test is usually undertaken with the specimenclamped. In contrast, much testing in Europe is performed to conform tothe ISO/DIN standard for plastics – as many impact machines sold inEurope have been standardised using this geometry.The ISO/DIN standarddoes not require specimens to be clamped, and they are simply supportedon a 40mm steel support ring.

Low energy non-penetrating impact testing is almost always undertakenin conjunction with subsequent post-impact testing which is usually basedon compression tests. The tests are considered together below.


(b)

(a)

4590

-450

4590

-4500

-4590450

-459045

4590

-450

4590

-4500

-4590450

-459045

10.10 Schematic diagram of the damage induced by impact in (a) lowspan to thickness ratio specimens (shear); (b) high span tothickness ratio specimens (bending), after Cantwell andMorton.27

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Table 10.3. Various common drop-weight impact test geometries (from Wyrickand Adams28).

Plate Type of support Shape of impactor Investigatorsa

dimensions and dimensions and diameter (mm)(mm) (mm)

300 ¥ 1000 100 diameter Hemisphere 12.7 Cantwell et al.ring clamped

300 ¥ 840 200 ¥ 800 Hemisphere 15 Levinclamped and 30

25 ¥ 305 152 apart Sphere 12.7 Joshi and Sunclamped

80 ¥ 220 Only 80 sides Hemisphere 20 Caprino et al.clamped

152 ¥ 152 127 ¥ 127 simply Hemisphere 12.7 Wardle and Tokarskysupported Winkel and Adams

150 ¥ 150 140 ¥ 140 Flat cylinder 9.7 Chaturvedi andclamped Sierakowski

102 ¥ 152 76 ¥ 127 Dart 7.9 Hirschbuehlernot specified

102 ¥ 152 76 ¥ 127 simply Sphere 15.9 Boll et al.supported

25 ¥ 150 28 apart simply Hemisphere 5.5 Caprinosupported

75 ¥ 75 50 diameter ring Hemisphere 12.5 Leach and Moorenot specified

100 diameter 100 diameter Cantilever ball 25.4 Lalclamped



a For reference details, see Wyrick and Adams.28

Table 10.4. Common impact test standards adopted for composites.

Method Impact Shape of impactor Support conditions and velocity and diameter (mm) dimensions (mm)(ms-1)

BS 2782 3.46 Hemisphere 12.7 50 I/D, 57 O/D ring,clamped if specimenless than 0.89 thick. 60diameter or squarespecimen

ASTM D 3029-FA 3.6 Hemisphere 15.86 76 I/D clampedASTM D 3029-FB 3.6 Hemisphere 12.7 38.1 I/D clampedISO/DIS 6603/2 4.4 Hemisphere 20 40 I/D ring, clamping

and 10 options optional. 60 diameter orsquare specimen

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10.3 Damage tolerance – compression after impact

(CAI) tests

Damage tolerance, as an aerospace design philosophy, may be summed upby the general requirements of the FAA’s (Federal Aviation Administra-tion) FAR 25.571: ‘evaluation of the strength, detail design and fabricationmust show that catastrophic failure due to fatigue, corrosion or accidentaldamage will be avoided throughout the operational life of the aeroplane’.29

Specific demands require a damaged structure to possess sufficient resid-ual strength or stiffness for a specified set of flight conditions. Consequently,the susceptibility of composite materials to suffer damage from relativelyminor impacts or other forms of in-service abuse is of major concern,particularly as this damage may not be visible on the surface at the site ofimpact on the material. The most deleterious form of internal damage thatoccurs within laminated composites after an impact is delamination. Thepresence of delaminations makes a composite susceptible to premature collapse during compression loading. The mechanisms thought to be thedriving failure are sublaminate/ply buckling in the delaminated regionand/or a mode I dominated crack growth, see Fig. 10.11.30–32 Tensile prop-erties are less affected by this form of damage until higher energy impactscause fibre fracture.21 Hence, a body of testing has evolved which seeks toassess the relative ability of different composite forms to withstand impactdamage and subsequent in-plane compression loading.


10.11 Compression after impact failure in a quasi-isotropic carbon-fibre reinforced unidirectional prepreg tape (T800/924) showingdelamination propagation and ply buckling failure of a ‘thinfilm’ on a parent material.

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A compression test on a damaged specimen, which is usually a flat platefor convenience, measures the load at which a complex failure event takesplace and may depend on ply layup, specimen width and many other factors.The test is clearly a component test and does not measure a material prop-erty, as such. It is accordingly extremely important to ensure that data generated in this field are compared on a sound basis, and the dimensionsof specimens and test conditions must be consistent.

The general philosophy that has been accepted is to perform an impact test at low energies on a flat plate which is then placed in some form of support fixture before being subjected to a compression test. Effec-tively two separate testing modes, the impact and the compression must becontrolled and standardised if valid comparisons are to be made betweenmaterials and/or laboratories. Most test procedures that have evolvedrequire a single plate to be cut to size and used for both the impact andcompression phase of the test. In some cases, notably the CRAG (Com-posites Research Advisory Group)33 test method emanating from the UK,the specimen on which the impact is undertaken is not controlled. A large plate can be used, with multiple impacts being performed at differentlocations. The target plate is then cut to a specific size for the subsequentcompression tests.

Some test protocols and their derivatives have been developed thatfeature differing combinations of plates, impact support conditions, impactsand impact energies, all for the purpose of introducing the initial damageinto a specimen prior to compression. These are listed in Table 10.5.33–37

After the impact has been performed, the damaged plate must be subjectto compression. As it is usual to employ relatively thin plates for this test,it is important to ensure that any failures in the compression test result froma failure triggered by the impact damage. It is probable that undamagedthin sheets simply loaded in compression would buckle before suffering in-plane compression failure. Consequently it is necessary to suppress thisbehaviour by employing antibuckling guides of some sort. In most tests thetest plate is supported in a fixture which contains some guide constraint atthe vertical edge of the plate, along with slots in the loading fixture for theplate at the top and bottom position.34–37 The CRAG test33 is different inthat it allows for an antibuckling guide rail to be attached to the specimen,see Fig. 10.12, which may then be inserted into a conventional set of loadinggrips, or jaws, to hold the plate during compression.

10.4 Boeing test methods and related variants

The de facto standard test used worldwide is now the Boeing test method,which has become adopted as a testing guide by SACMA (SRM 2-888) andby Airbus (AITM 1.0010) with only minor modifications.35–37


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10.4.1 Impact test details

The impact fixture used for the Boeing test consists of a rectangular plateclamped to a loading plate with a rectangular cut-out using four spotclamps. The plate size is 4 in by 6 in (approximately 102mm by 152mm) andappears to have been selected to approximate the unsupported width of acomposite wing skin between stringers. The required plate thickness is 0.2 in (5mm). This is a fairly large specimen which consumes a lot of mate-rial. This is a problem for all testing laboratories, but it is a particular issuefor those involved in materials development where quantities of experi-mental prepreg for testing may be limited. The same test plate is specifiedby SACMA.

The impact is undertaken by dropping a striker onto the test plate. Thestriker does not need to be instrumented, and the method of introducingthe impact is not rigidly controlled in the test specifications. For conve-nience, a Gardner-style impact apparatus (as used for early plastics testing)is suggested, since this rig may be available in many laboratories; a Dynatup8200 series impactor is also suggested. The key feature, however, is that the striker must be equipped with a hemispherical tip of diameter 0.62 in (15.75mm) and have a mass of 10–15 lbs (4.5–6.8kg). The impact drop height is adjusted to provide the required impact kinetic energy.The original Boeing specification does not state a required impact energy


SCALE: 1cm

10.12 Schematic diagram showing a specimen and antibucklingfixture for compression testing (after Cantwell et al.).38

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level, but the SACMA Recommended Method specifies that energies of1500 in-lb in-1 (6.67Jmm-1) thickness should be used.

Airbus have converted the SACMA geometry to a metric equivalent andspecified plates of 100 mm by 150 mm, with the thickness as close to 4 mmas is possible. This test method also differs slightly from the US approachin that a 16 mm diameter striker is used with specific energy levels definedin absolute terms (rather than adjusted for plate thickness) and corre-sponding to a range of impact masses: 1–3kg for 9, 12, 16, 20 and 25 J impactsand 4–6 kg for 30 and 40 J impacts. Additional proposals to the Airbus(AITM 1.0010, Issue 2) specification have been made by British AerospaceAirbus, suggesting the use of instrumented strikers in order to identify athreshold force at which damage is generated in the plate, along with C-scanning of the impacted plate to measure the extent of damage.

Some non-standard variations in the test method have been used in thepast (ironically sometimes by Boeing), where the hemispherical indentorwas rested on the specimen and was itself hit by a falling projectile. Theseeffects were examined in a round-robin exercise undertaken in Japan.39

Energy losses in this arrangement were found to result in a reduction indamage and spurious improvements in the subsequent apparent residualcompression strength on the order of 10–15%.

The supporting frame used for the original Boeing impact test was con-structed from a combination of plywood with a top plate of steel or alu-minium.The SACMA variant specifies an aluminium support frame and theAirbus variant specifies a steel frame. The difference in the compliance ofthe test fixture introduced by these changes can also be considerable, andthe amount of damage introduced into the plate for a given impact blowmay be substantially reduced if the wooden hybrid frame is used.39

The support frame in all cases features a cut-out, which is 3 in by 5 in (75 mm by 125 mm for Airbus), over which the impact specimen issecured.

10.4.2 Compression test details

The impact plate is supported during an in-plane compression test in theBoeing fixture as shown in Fig. 10.13. The vertical sides of the specimen arerestrained by antibuckling rails with knife edge supports.

The plates fit into slots in the bottom of the main fixture and in theloading plate which sits on the top of the assembly. The height of the sidesupports are smaller than the plates such that, when the rig is assembled,a small part of the plate is unsupported (approximately 5mm) by theantibuckling rails. This allows a maximum compressive strain of approxi-mately 3.3% in the material during the test before excessive deflectionsmean the test has to be terminated before plate failure. The only other dif-


MTA10 11/22/2000 1:35 PM Page 232

ficulty emerges when testing undamaged specimens in order to obtain abaseline property measurement. In these cases failure frequently occurs inthe unsupported material, causing the undamaged compression strength tobe of questionable value. The problem is to some extent eliminated in theAirbus variant of the test where the top plate is made to be the same sizeas the lateral gap between support rails. In this way the top loading plate isfree to slide past the side rails, and the entire length of the test specimencan be laterally supported for the duration of the test.

The Boeing and SACMA tests require the test plate to be equipped withfour strain gauges mounted on the plate as shown in Fig. 10.14, two on eachplate face. These are to ensure that the plate is mounted correctly in thefixture and that out-of-plane deformation does not occur before failure istriggered by the impact damage.

10.4.3 Compression after impact test data

The basic test data generated using the Boeing test and related standardscan be presented as impact energy versus residual compression strength.The test can be used successfully to discriminate between laminates with different resins and fibres in order to gain an overall assessment ofdamage tolerance, as shown in Fig. 10.15 for laminates with brittle and toughresins.

The trend in the aerospace industry has been to settle on one impactenergy (per unit thickness of the specimen) and present the number gen-erated as a CAI value for certification purposes. This is an approach that is


Top plate

Test specimen

Support fixture

10.13 Boeing compression after impact jig.35

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Strain gauge locations(both sides)

1.0

1.01.0

6.0

4.0

Specimencentreline

Impactlocation

Specimencentreline

10.14 Schematic diagram showing specimen geometry and positionof strain gauges on the SACMA compression after impactcoupon.36 All dimensions are in inches.

500.0

400.0

300.0

200.0

100.0

0.0

0.0 10.0 20.0 30.0 40.0

Impact energy (J)

Res

idu

al c

om

pre

ssio

n s

tren

gth

(M

Pa)

10.15 Residual compression strength data using the Boeing testplotted versus impact energy, showing the effect of damagesaturation (damage to support boundary ratio of 1.0) and theeffect of different resin systems on relative performance.44

�, Resin A; �, resin B; �, resin C; �, resin D; �, resin E.

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fraught with problems.The test does not provide an absolute property value(design allowable); however, this test currently sets design strain limits. Ifthe material is relatively brittle, cracking due to impact may extend to theedges of the plate, and when loaded in the compression fixture it is alreadyeffectively saturated. It is for this reason that plots of compression strengthversus impact energy frequently indicate a levelling off of compressionstrength, see Fig. 10.15. This would not be the case if the plate size wereincreased or impact ranges were limited to minimise interactions with thesupport conditions. A further cause for concern is that a ranking of mate-rials based on a single impact energy might change if a different referenceimpact energy level were selected.40–42 This is illustrated in Fig. 10.15,which shows some data generated on experimental and commercial resinlaminates over a range of impact energies.

10.4.4 Miniature tests

The high cost of producing specimens for full size Boeing/SACMA/Airbustests has prompted interest from many laboratories in producing a minia-turised version of the test.43 A variant developed by Hogg et al.44 was anattempt at providing a link between compression after impact test speci-mens and those widely used in Europe for excess energy impact testsaccording to ISO/DIN standards.The Hogg test specimen consists of a platespecimen 89mm by 55mm and 2mm thick. Impact on the specimen is produced using an ISO/DIN impactor of diameter 20mm (cf. 16mm in theAirbus test), with the support geometry being a 40mm diameter steel ringwith clamping optional. The normal ISO/DIN test uses a 60 mm wide specimen. The impacted plates are supported during compression using avariable fixture resembling the larger Boeing fixture with the exception thatinstead of knife edge supports, the plates are being supported by slottedside bars.

A similar specimen has been examined in Japan (50mm by 80 mm) and included as part of a round-robin study of the test method. The resultsfrom both studies indicated a high degree of correlation between the miniaturised test specimens and the full scale Boeing tests, as shown in Fig. 10.16.44–46 One practical issue that must be allowed for when using the small fixture is that damage will tend to saturate the specimens at rela-tively low impact energies.

10.5 Data interpretation

The data generated by the compression after impact test, when presentedin the manner of impact energy versus compression strength, link a testparameter from one test (impact energy) to a property measured in another


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500

400

300

200

100

0

0 10 20 30 40

Impact energy (J)

Res

idu

al c

om

pre

ssio

n s

tren

gth

(M

Pa) F-T-J

S-T-JS-T-UK

F-B-JS-B-JS-B-UK

(a)

500

400

300

200

100

0

0 20 40 60 80 100

Damage width (mm)

Res

idu

al c

om

pre

ssio

n s

tren

gth

(M

Pa)

(b)

F-T-J

F-B-J

F-T+B-UK

Boeing data

10.16 Residual compression strength data from Hexcel (Boeing test),Hogg (miniature test) and Ilcewicz (Boeing test) plotted as afunction of (a) impact energy; (b) damage width for full scaletests; (c) damage width for small scale tests.44–46 F (full scale), S (small scale), T (tough), B (brittle), J (Japan) and UK (UnitedKingdom).

(compression strength). This means that it is impossible to determinewhether or not the relative performance of two laminate systems is con-trolled by their resistance to damage during impact, or the resistance topropagation of that damage during compression.

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In order to gain a better insight into the performance of the composite,it has become increasingly common to record the size of damage inducedin the impacted specimen. For carbon-fibre laminates this has required theuse of ultrasonic C-scan measurements, whereas for glass-fibre composites,transmitted light normally reveals the extent of damage. The damage mea-sured in this way is delamination cracking, which is largely responsible forthe reduction in compression strength of the material. Quasi-isotropic laminates, which are usually the material form examined in the test, gener-ally produce damage zones that are globally circular, although these do inreality consist of lobed delaminations at a number of ply–ply interfaces, seeFig. 10.17. Studies of the composite laminates under compression haverevealed that the delaminations propagate in a sideways direction prior tofinal failure of the plate, but never in the vertical direction, see Fig. 10.18.

Based on these observations, Prichard and Hogg argued that a relevantdamage parameter that could be used to assess impact resistance was thewidth of the delaminated area.42 Using this parameter, it was found that theimpact and compression parts of the test could be separated. This has beenapplied to a set of data generated using a toughened epoxy laminate andtwo thermoplastic laminates (PEEK and Radel) based on similar fibres andwith a quasi-isotropic layup.41 The initial data presented in the conventionalfashion of residual compression strength versus impact energy are shownin Fig. 10.19. In Fig. 10.9 the damage width for both materials is shownplotted against impact energy; this reveals that the PEEK and Radel com-posites are much better than the toughened epoxy in resisting impactdamage. Finally, in Fig. 10.20 the compression strength is plotted against


500

400

300

200

100

00 10 20 30 40 50

Damage width (mm)

Res

du

al c

om

pre

ssio

n s

tren

gth

(M

Pa)

(c)

S-T-JS-B-JS-T-UKS-B-UK

10.16 (cont.)

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10.17 Typical shape of an impact-induced delamination in a carbon-fibre reinforced quasi-isotropic unidirectional prepreg tape(T300/914) laminate.

damage width. This is effectively a way of comparing the resistance of twolaminates to damage propagation, irrespective of how difficult it was to gen-erate that damage in the first instance. In this plot it is interesting to notethat the performance of two distinctly different forms of resin chemistry,thermoset and thermoplastic materials, appears to be very similar.

A broader survey comparing large and small specimens on the basis ofboth impact energy and damage width relative to residual compressionstrength shows that the results from both test methods give similar trendsand that residual strength versus damage width results are numericallysimilar for both tests. When this exercise was undertaken, initially in Japan,it was concluded that the level of equivalence between the two sizes of test

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was poor, but when more data were compared (using European as well asthe Japanese generated data), the level of scatter became apparent, and itis clear that the agreement is good, see Fig. 10.16.45

The use of damage width as a damage parameter is extremely useful for quasi-isotropic laminates, but if the fibre layup in a specimen moves progressively away from such an arrangement, then the damage area


10.18 Quasi-isotropic glass-fibre reinforced unidirectional prepregtape (E-glass/913) showing (a) the distribution of impact-induceddelamination damage; (b) the propagation of delaminatedregions.

(a)

(b)

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500

400

300

200

100

0

0

Impact energy (J)

Res

idu

al c

om

pre

ssio

n s

tren

gth

(M

Pa)

3 6 9 12 15

10.19 Residual compression strength data versus impact energy forquasi-isotropic carbon-fibre reinforced (�) AS-4/PEEK, (�) T650-42/Radel (thermoplastic) and (�) toughened epoxy (T800/924)generated using the miniature jig.41

500

400

300

200

100

00 10 20 30 40 50

Damage width (mm)

Res

idu

al c

om

pre

ssio

n s

tren

gth

(M

Pa)

10.20 Residual compression strength data versus damage extent forquasi-isotropic carbon-fibre reinforced (�) AS-4/PEEK, (�) T650-42/Radel (thermoplastic) and (�) toughened epoxy (T800/924)generated using the miniature jig.41

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itself becomes asymmetric and difficult to quantify in this respect.Some angle ply layups result in slanted strips of delaminated material which are not amenable to this treatment. It should, however, be noted that the projected plan area superposition of delaminations, as measuredby conventional C-scan, has been successfully correlated with residualstrength.38

There is also an increasing interest in the aerospace field in compositelaminates constructed from textile forms. Some of these forms, such as non-crimp multiaxial warp-knitted fabrics, can be used to generate laminateswith quasi-isotropic layups and similar in-plane properties to prepreg materials based on unidirectional tape.47 However, when these fabric-basedlaminates are subjected to impact, the nature of the damage createdchanges slightly.48,49 The textile form makes the creation of large discretedelaminations more difficult. The area of damage generated in non-crimpfabrics may look similar to that created in prepreg tape laminates whenviewed using a C-scan as shown in Fig. 10.21. However, if time of flight scan-ning is used, the damage is revealed to be more irregular, with pockets andregions of interply cracking that link up to form an irregular delamination.Consequently, the use of a physical parameter that represents a damagestate becomes more difficult to define as the reinforcement architecturebecomes increasingly complex (e.g. three-dimensional weaves), effectivelysuppressing delamination fractures.50,51 However, this may be compensatedfor by a reduced damage tolerance in tension, where an alternative andmore suitable parameter may be defined.

10.6 Standardisation status

The compression after impact test procedures produces data with a rela-tively large degree of scatter as shown in the sets of experimental results inFigs. 10.7–10.9, 10.15, 10.16, 10.19 and 10.20. It is not clear at this timewhether improving the test specification could result in a reduction in thisscatter. Accepting the scatter inherent in the test has the advantage that theprocedures are tolerant to variations in scale of specimen and minor factorssuch as impactor diameter. The marked effect of factors such as the com-pliance of the impact support frame and the way the specimen is actuallystruck means, however, that standardisation is very important, particularlygiven the role of impact testing in the certification of composites for aero-space applications.

At present the only documented procedures are those developed by theaerospace companies, Boeing and Airbus, and the recommended methodsof SACMA and CRAG. The Japanese standards body, JIS, is planning tointroduce a standard in the near future based on the Boeing method butwith a provision made for using a smaller test coupon for use in materials


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Depth/mm

% Areas

Calibrated depth: 0.5 mm X scale / mm

Y s

cale

/ m

m

X scale / mm

Depth/mm

% Areas

Y s

cale

/ m

m

10.21 Representative time of flight C-scans showing the internalnature of impact (Boeing test) induced damage for (a) triaxial[452,-452,06,-452,452]S carbon-fibre reinforced unidirectionalprepreg tape (T300/914); (b) triaxial [452,-452,06,-452,452]S

carbon-fibre reinforced non-crimp fabric (T300/914) laminates.

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evaluation studies.ASTM has also been attempting to develop its own stan-dard, based again on the Boeing/SACMA tests.

It is also understood that ASTM are involved in the development of aquasi-static indentation test method, which has the intention of providingguidance for the study of impact damage resistance. The test would intro-duce damage in a more controlled manner than falling-weight tests andmake use of a universal testing machine, rather than specialised equipment.Damage events would be associated with a critical force and the test couldbe used to screen materials for durability, or to put damage into a specimenfor subsequent damage tolerance testing. There is, of course, no claim thata test of this type addresses such issues as wave propagation, vibrations inthe specimen, time-dependent behaviour or inertia-dominated impactevents, but the use of quasi-static testing has support in the research community.52,53

10.7 Future trends

The current situation relating to impact and damage tolerance testing of composites is plainly not satisfactory. The tests themselves produce data that can provide a useful and informative guide to the relative per-formance of different material systems. They do not at this time, however,provide any direct input into the design process. The performance of an aircraft structural part, in service after damage has been induced, may beinferred by reference to the compression after impact test, but cannot actually be predicted. The test methods currently used have allowed themechanisms of impact damage and post-impact failure to be assessed,providing the industry with a realistic physical understanding of theprocesses involved. This in turn will allow more realistic modelling to beundertaken. In the long term, the wide variety of composite structures and the impact or damage events that can take place, the range of post-impact loading that can be imposed and the different criteria for failuremean that testing alone is unlikely to provide all the answers for a com-posites industry hoping to design better structures. It is instead inevitablethat modelling will have to develop in such a way that the response of acomposite structure to high strain rate loading with a specified force–timeprofile can be predicted in detail, such that the nature and level of damagesustained can be predicted and the propagation of that damage under sub-sequent loading can also be predicted until a failure point is reached. Thisform of modelling will require from the testing community a wealth of data not currently available. The dynamic properties of the fibre and resin,the various micromechanical strength parameters and their dependence on testing rate, the dependence of cracking on fibre architecture both in tape-based laminates and more complex textile-based materials will all


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be required. Most critically, physically sound failure criteria are needed that can predict local microfracture events under complex loading states,as a function of rate. In addition to a new range of experimental data, thisapproach will require a vast increase in the computing power available,although this is probably the only thing that it is reasonable to predict will actually materialise in the near future if current trends continue. In the short term, the research community is attempting numerous half-waymeasures using damage mechanics which effectively allow structures to bemodelled such that a damaged zone is assigned reduced properties in a con-ventional structural analysis using finite element or other numericalmethods to predict local stress states in damaged materials. Predicting theonset of failure is still problematic unless gross assumptions are made, orthe situation being modelled is very well defined.This means that the designof composite structures to resist impact and to maximise damage tolerancewill be dependent on testing of the type discussed in this chapter for sometime to come.

References

1. W C Jackson and C C Poe, ‘The use of impact force as a scale parameter for the impact response of composite laminates’, Journal of Composites Technology and Research, Winter 1993 15(4) 282–9.

2. D Delfosse, G Pageau, R Bennett and A Poursartip, ‘Instrumented impacttesting at high velocities’, Journal of Composites Technology and Research,Spring 1993 15(1) 38–45.

3. P Sjoblom, J T Hartness and T M Cordell, ‘On low-velocity impact testing ofcomposite materials’, Journal of Composite Materials, 1988 22 30–52.

4. S V Potti and C T Sun, ‘Prediction of impact induced penetration and delamination in thick composite laminates’, International Journal of ImpactEngineering, 1997 19 31–48.

5. G H Staab and A Gilat, ‘High strain rate response of angle-ply glass/epoxy laminates’, Journal of Composite Materials, 1995 29 1308–20.

6. J Harding and L M Welsh, ‘A tensile testing technique for fibre-reinforced composites at impact rates of strain’, Journal of Materials Science, 1983 181810–26.

7. Y Li, C Ruiz and J Harding, Modeling of the Impact Response of Fibre-reinforced Composites, Technomic Publishing, Lancaster, PA, USA, 1991.

8. K Saka and J Harding, Behaviour of Fibre-reinforced Composites underDynamic Tension, Oxford University Engineering Laboratory Report No.1543/84, 1984.

9. D Hull, ‘A unified approach to the progressive crushing of fibre reinforced com-posites tubes’, Composites Science and Technology, 1991 377–422.

10. K E Jackson, J Morton, C M Traffanstedt and R L Boitnott, ‘Scaling of energyabsorbing composite plates’, Proceedings, American Helicopter Society 48thAnnual Forum and Technology Display, Vol 2, Washington, DC, AHS, 1992,1431–40.


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11. J A Lavoie and J Morton, Design and Application of a Quasi-static Crush TestFixture for Investigating Scale Effects in Energy Absorbing Composite Plates,NASA CR 4526, July 1993.

12. S N Kakarala and J L Roche, ‘Experimental comparison of several impact testmethods’, Instrumented Impact Testing of Plastics and Composite Materials,ASTM STP 936, eds S L Kessler, G C Adams, S B Driscoll and D R Ireland,American Society for Testing and Materials, 1987, 144–62.

13. D F Adams and J L Perry, ‘Instrumented Charpy impact tests of several unidirectional composite materials’, Fibre Science and Technology, 1975 8275–302.

14. G Marom, E Drukker, A Weinberg and J Banbaji, ‘Impact behaviour ofcarbon/Kevlar hybrid composites’, Composites, 1986 17 150–3.

15. W J Cantwell and J Morton, ‘Geometrical effects in the low velocity impactresponse of CFRP’, Composite Structures, 1989 12 39–59.

16. W J Cantwell and J Morton, ‘Comparison of the low and high velocity impactresponse of CFRP’, Composites, 1989 20 545–51.

17. J Morton and E W Godwin, ‘Impact response of tough carbon fibre compos-ites’, Composite Structures, 1989 13 1–19.

18. W J Cantwell and J Morton, ‘Impact perforation of carbon fibre reinforcedplastic’, Composites Science and Technology, 1990 38 119–41.

19. L Babic, C Dunn and P J Hogg, ‘Damage development and its significance inGRP subject to impact’, Plastics and Rubber Processing and Applications, 198912 199–207.

20. G A Bibo, D Leicy, P J Hogg and M Kemp, ‘High temperature damage tolerance of carbon fibre reinforced plastics: part I impact characteristics’, Com-posites, 1994 25 414–24.

21. E F Dost, S R Finn, J J Stevens, K Y Lin, and C E Fitch, ‘Experimental investigations into composite fuselage impact damage resistance and postimpact compression behaviour’, Proceedings, 37th International SAMPE Symposium, Anaheim, CA, Vol. 32, SAMPE, Covina, CA, 1992, 1199–1212.

22. P Reed, ‘Mechanical properties and mechanical testing of polymers’,Handbooks of Polymer Science, ed G M Swallowe, Chapman and Hall, 1997.

23. K Srinivasan, W C Jackson and J A Hinkley, ‘Response of composite materials to low velocity impact’, Proceedings, 36th International SAMPE Symposium, San Diego, CA, SAMPE, Covina, CA, 1991, 850–62.

24. S M Bishop,‘The mechanical performance and impact behaviour of carbon-fibrereinforced PEEK’, Composite Structures, 1985 3 295–318.

25. K Srinivasan, W C Jackson, B T Smith and J A Hinkley, ‘Characterisation ofdamage modes in impacted thermoset and thermoplastic composites’, Journalof Reinforced Plastics and Composites, 1992 11 1111–26.

26. W J Cantwell and J Morton, ‘The influence of varying projectile mass on theimpact response of CFRP’, Composite Structures, 1989 13 101–14.

27. W J Cantwell and J Morton, ‘Detection of impact damage in CFRP laminates’,Composite Structures, 1985 3 241–57.

28. D A Wyrick and D F Adams, ‘Residual strength of carbon/epoxy’, Journal ofComposite Materials, 1988 22 749–65.

29. Anon, Federal Aviation Regulations Part 25, U.S. Department of Transportation, Federal Aviation Administration, 1993, Section 25.571, C22–4.


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30. K N Shivakumar and J D Whitcomb, ‘Buckling of a sublaminate in a quasi-isotropic composite laminate’, Journal of Composite Materials, 1985 19 2–18.

31. W-L Yin, ‘The effects of laminated structure on the delamination buckling andgrowth’, Journal of Composite Materials, 1988 22 502–17.

32. H Chai and C D Babcock, ‘Two-dimensional modelling of compressive failurein delaminated laminates’, Journal of Composite Materials, 1985 19 67–98.

33. P T Curtis (ed), CRAG Test Methods for the Measurement of the EngineeringProperties of Fibre-reinforced Plastics, Royal Aircraft Establishment, Farnbor-ough UK, Technical Report 88012, 1988.

34. Standard Tests for Toughened Resin Composites, NASA Reference Publication1092 (revised edition), 1983.

35. Advanced Composite Compression Tests, Boeing Specification Support Standard, BSS 7260, 1986.

36. SACMA Recommended Test Method for Compression after Impact Propertiesof Oriented Fibre-resin Composites, SACMA Recommended Method, SRM2–88.

37. Airbus Industrie Test Method Fibre Reinforced Plastics, Determination of Compression Strength after Impact, AITM 1.0010, Issue 2, 1994, 1–11.

38. W J Cantwell, P T Curtis and J Morton, ‘An assessment of the impact performance of CFRP reinforced with high-strain carbon fibres’, CompositesScience and Technology, 1986 25 133–48.

39. K Tanaka and K Kageyama, Standardisation Study on Compression afterImpact Test for CFRP’s in Japan, Proceedings of 2nd European Conference onComposite Materials – Composites Testing and Standardization, ECCM-CTS 2,Woodhead, Cambridge, 1994, 469–77.

40. J Brandt and J Warnecke, ‘Influence of material parameters on the impact performance of carbon-fibre-reinforced polymers’, High Tech – the Way into the Nineties, eds K Brunsch, H D Golden and C M Herkert, Elsevier SciencePublishers BV, Amsterdam, 1986, 251–60.

41. G A Bibo, P J Hogg and M Kemp, ‘High temperature damage tolerance ofcarbon fibre reinforced plastics. Part II: Post impact compression characteris-tics’, Composites, 1995 26 91–102.

42. JC Prichard and PJ Hogg, ‘The role of impact damage in post-impact compression testing’, Composites, 1990 21 503–11.

43. P Sjoblom and B Hwang, ‘Compression-after-impact: the $50,000 data point’,Proceedings, 34th International SAMPE Symposium, Reno, NV, SAMPE,Covina, CA, 1989, 1411–21.

44. P J Hogg, J C Prichard and D L Stone, ‘A miniaturised post impact compression test’, Proceedings European Conference on Composite Materials-Composites Testing and Standardisation, ECCM-CTS, Amsterdam, eds P JHogg, G D Sims, F L Matthews, A R Bunsell and A Massiah, European Association for Composite Materials, Bordeaux, France, 1992, 357–70.

45. P J Hogg, G A Bibo and K Tanaka ‘A comparison of full-scale and miniaturisedcompression after impact tests’, Proceedings, 4th Japan International SAMPESymposium, Tokyo, eds Z Maekawa, E Nakata and Y Sakatani, Japan SAMPE,Yokohama, 1995, Vol. 2, 907–14.

46. L B Ilcewicz, E F Dost and R L Coggeshall, ‘A model for compression afterimpact strength evaluation’, 21st International SAMPE Technical Conference,Atlantic City, NJ, SAMPE, Covina, CA, 1989, 130–40.


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47. G A Bibo, P J Hogg and M Kemp, ‘Mechanical characterisation of glass andcarbon fibre reinforced non-crimp fabric’, Composites Science and Technology,1997 57(9/10) 1221–41.

48. G A Bibo, P J Hogg, R Backhouse and A Mills, ‘Deformation mechanisms infabric reinforced composites’, Proceedings, 10th International Conference onComposite Material, ICCM 10, Whistler, BC, Canada, eds A Poursartip and KStreet, Cambridge, Woodhead, 1995, Vol 4, 317–24.

49. G A Bibo, P J Hogg, R Backhouse and A Mills, ‘Carbon fibre non-crimp fabriclaminates for cost effective damage tolerant structures’, Composites Science andTechnology, 1998 58(1) 129–43.

50. G A Bibo and P J Hogg, ‘The role of reinforcement architecture on impact damage mechanisms and post impact behaviour – review’, Journal of Materials Science, 1996 31 1115–37.

51. J Brandt, K Drechsler, M Mohamed and P Gu, ‘Manufacture and performanceof carbon/epoxy 3-D woven composites’, 37th International SAMPE Sympo-sium, Anaheim, CA, SAMPE, Covina, CA, 1992, 864–77.

52. R B Bucinell, R J Nuismer and J L Koury, ‘Response of composite plates toquasi-static impact events’, Composite Materials: Fatigue and Fracture (ThirdVolume), ASTM STP 1110, ed T K O’Brien, American Society for Testing andMaterials, Philadelphia, USA, 1991, 528–49.

53. P A Lagace, J E Williamson, P H W Tsang, E Wolf and S Thomas, ‘A prelimi-nary proposition for a test method to measure (impact) resistance’, Journal ofReinforced Plastics and Composites, 1993 12 584–601.


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11.1 Introduction

Since the early 1980s the reduction of strength and the subsequent failureof materials subjected to cyclic loading has been addressed as one of the most fundamental problems of engineering materials. A satisfactorydescription of fatigue of materials, based on first principles, has not yet beenachieved. Metallic materials, for instance, which are ductile in nature under normal operating conditions, are known to fail in a brittle mannerwhen they are subjected to repeated loading. Because composite materialsare regarded as having good fatigue resistance, they are in fact destined tobe used in applications, such as in aircraft or other vehicles, in which thedegradation of strength and life expectancy by fatigue processes is mostlikely.

In general, the number of cycles to failure depends on a number of vari-ables such as stress levels, stress state, mode of cycling, process history,material composition and environmental conditions. However, compositesare, by nature, inhomogeneous and frequently anisotropic. The fatigueprocesses which reduce strength in these materials are generally verycomplex, involving the accumulation of many damage modes.

This chapter explores the philosophy behind the development ofmethods for the fatigue testing of polymer composite materials. Methodsfor performing tests in the major loading regimes will be described,although in many cases there are no formal standards for fatigue testing ofthese materials. This is partly because of the difficulty in performing fatiguetests on polymer composites but also because it is only recently that stan-dards have been developed for static testing, described in the other chap-ters of this book. As well as describing test methodology, consideration is given to the types (and indeed the suitability) of mechanical testingmachines for measuring fatigue properties of polymer composites. In addi-tion, some of the problems and pitfalls associated with fatigue testing are

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described and techniques for avoiding, or minimising, their effects are dis-cussed. Ways in which fatigue data are analysed and presented for polymercomposites are discussed, so that it can be of most benefit.

Finally, no fatigue test is really complete without a careful study of howdamage develops during the fatigue test.The latter part of this chapter dealswith how to apply inspection techniques to polymer composites in order toestablish important information on fatigue damage development.

11.2 Basic test philosophy

Essentially any test method used for static testing has the potential to beused in fatigue; however, the fatigue environment is usually more demand-ing on both material and test technique. Problems which do not occur instatic testing will almost certainly do so in fatigue loading.

The main requirements for a fatigue test coupon are that it should fail ina manner similar to the material of the comparable structural component.Ideally, this should combine with ease of use and economy of preparation.The literature on composite fatigue behaviour contains many papersreporting work carried out on and comparing different coupon configura-tions for fatigue testing, in efforts to meet these requirements.1,2

Figure 11.1 shows a typical applied stress–strain–time diagram in afatigue test.A cyclic stress is applied between predetermined maximum andminimum limits, the ratio of minimum to maximum stress being describedas the R ratio. The mean stress, stress amplitude and cyclic frequency arealso important parameters. The cyclic stress mode can be sinusoidal, trian-gular or whatever the user decides is most appropriate for the end appli-cation in mind.

amplitude

range1 cycle

Time

Str

ess

or s

trai

n

smin

smin

smean

smax

smax

Note: R =

11.1 Typical applied stress–strain–time diagram.

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Most fatigue tests on composite materials have been performed in uni-axial tension–tension cycling. Tension–compression and compression–compression cycling are not commonly used, since failure by com-pressive buckling may occur in thin laminates and antibuckling guides arerequired. However, completely reversed tension–compression cycling can be achieved by flexural fatigue tests, although these are rarely representative of real-life loading regimes. A limited number of interlami-nar shear fatigue and in-plane fatigue tests have also been performed.In the next sections typical test methods for these loading modes will bedescribed.

11.2.1 Tensile tests

Tensile testing is probably the most common form of materials test. It istherefore essential that tensile tests in fatigue can be performed for polymercomposites.

The first requirement is to ensure that failures occur within the gaugelength of the coupons and not be associated with grips, supports, antibuck-ling guides and so on. Coupon profiles have been varied in attempts toencourage such failures, ranging from waisting and cut-outs to simple par-allel-sided coupons. Waisting usually ensures static failures at positionsremote from the grips, but not necessarily in fatigue. Indeed, the plain parallel-sided specimen frequently yields the longest fatigue lives and thebest all-round behaviour, although failures do occasionally occur at thegrips. With care in preparation of the coupons and the use of end tabs,however, the incidence of failure close to the grips can be minimised. Thisis emphasised in Figs. 11.2 and 11.3. Figure 11.2 shows three gauge profilestested statically and in fatigue. The static tests produced acceptable failuresin all three cases, within the gauge section. In fatigue, however, the twowaisted coupons both failed away from the waist and thus gave unaccept-able results. The corresponding stress–life diagrams are shown in Fig. 11.3,where it is clear that the plain parallel-sided coupons gave the longestfatigue lives. It is recommended, therefore, that for most tensile fatiguetesting, plain parallel-sided coupons should be used as the best compromise.

If waisting must be used, then care should be taken to avoid disturbingthe layup. Waisting is, therefore, usually restricted to across the width ofcoupons, as shown in Fig. 11.2. Waisting in the thickness will undoubtedlydisturb the layup of the laminate, except for materials with all the fibres inthe same direction. However, waisting even in such unidirectional material,with the fibres in the test direction, frequently leads to shear stress failureat the waists, resulting in delaminations which propagate in fatigue loadingback to the grips where failure within the grips is triggered at reduced life-times, as depicted in Fig. 11.4.


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(b)(a)

900

800

700

600

500

400

300

Max

imum

str

ess

(MP

a)

10–1 100 101 102 103 104 105 106 107

Number of cycles

11.2 Coupons with different gauge profiles tested: (a) statically, (b) fatigue.

11.3 Stress–life plots for tensile fatigue coupons with different gaugeprofiles. S-N (stress versus number of cycles) curve of 0 ± 45°material in zero-tension loading, type 3 fibre, DX210 resinsystem. �, 20mm wide rectangular; �, waisted specimens; �,notched specimens; +, 10mm wide rectangular. AFRP = aramidfibre-reinforced plastic.

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11.2.2 Compression tests

Compression–compression and tension–compression fatigue testing aremore complex than tensile loading, with the additional problem of stabilis-ing the coupon during the compressive cycle. This requires that either shortand, therefore, self-stable coupons should be used, or antibuckling guidesare necessary to support the coupon. Short stable coupons, which may beparallel-sided or waisted, suffer from the disadvantage that the stress distribution in the free length may be affected by the restraint at the grips.Reduction of the specimen width to allow for this effect renders the edge stresses more critical. Such specimens are typically 10mm wide witha free length of 10mm and minimum thickness3 of 1.5mm, as shown in Fig. 11.5.

Long coupons are to be preferred, but when a compressive excursion isto be included in the fatigue cycle, it is necessary to provide supports toprevent buckling. No standard antibuckling guide exists, each test labora-tory having developed its own devices. The main factor to consider whendesigning guides is that the free unsupported area of the specimen shouldbe a maximum consistent with the requirement of preventing buckling,3

so as not to restrict any anticipated failure process. In addition, frictionbetween the support and the specimen must be minimised, perhaps by theuse of PTFE (polytetrafluoroethylene) tape on the contact surfaces. Atypical device was shown in Fig. 10.12 in Chapter 10.

11.2.3 Flexural tests

Many laboratories use flexural fatigue testing as an alternative to axialfatigue, since it is easier to perform, requiring no supporting guides and gen-erally significantly lower capacity testing machines. Flexural test methodsused for static loading are generally suitable for fatigue, but care must betaken to minimise friction at the loading rollers. It is also necessary to intro-duce backing rollers on the reverse of the coupons if through-zero testingis intended.

11.4 Schematic diagram showing delamination growth back to the grips in a unidirectional layup fatigue coupon.

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11.2.4 Shear tests

Fatigue testing in shear loading is less common, but ought to be consideredmore widely than it is currently. The most commonly used shear techniqueis the interlaminar shear test.3 This can easily be modified for fatigue useby the introduction of backing rollers opposite the main rollers, particularlyif the deflection is to be reversed in fatigue. A typical test arrangement isshown in Fig. 11.6(a).

Alternative shear fatigue test methods used are also based on modifica-tions to methods used for static testing. The tensile test on ±45° laminatesinduces shear along the fibres and has been used extensively as a static testfor the characterisation of shear behaviour, as discussed in Chapter 6. It canalso be used for the generation of shear fatigue data.3 Versions of the railshear test (Fig. 11.6b), again widely used for static shear strength measure-ments, and discussed in Chapter 6, have also been used in fatigue. The railshear specimen requires some modification for it to be suitable for fatiguetests; work with this type of specimen has shown that the fatigue livesobtainable are very dependent on the surface quality of the exposed edgeof the coupon.4 Polishing the edge results in a significant increase in life,potential cracks presumably being removed. However, when small slots are

10

110 10

50

2

End plates0.5–2.0 mmlight alloy

11.5 Short plain parallel-sided compression fatigue test specimen.

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introduced into the coupon ends, even longer lives are obtained. This islikely to be due to the failure zone being shifted from the coupon edge,where constraint and edge effects lead to complex stress fields, to a regionwhere a simple shear stress field exists.

11.2.5 Biaxial fatigue testing

The test methods described above relate to uniaxial loading, where thematerial is stressed in a single direction. There is, however, considerableinterest in loading materials in two independent directions, usually referredto as biaxial loading. Such loading arrangements cause many additionalproblems, usually associated with regions between the loading arms in thetwo directions, where stress concentrations can lead to premature failure.There are no ideal (or indeed standard) test methods for biaxial fatiguetesting, but a method has been described5 which is effective for notchedcoupons. This approach is based on a cruciform testpiece but is not suitedto plain unnotched specimens.

11.3 Machines and control modes

Most fatigue work is performed on servohydraulic test machines, which aregenerally simple to use and flexible in that any combination of test fre-

11.6 Shear test specimens: (a) ILSS interlaminar specimen; (b) railshear specimen.

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quency and loading or straining mode can be used. They are, however,expensive and it is possible to use much cheaper constant displacementmachines using an offset cam to perform fatigue tests. Vibration or reso-nance machines can also be used, although these usually operate at fre-quencies of 30 Hz and above, which may not always be suited to polymercomposites, where these high frequencies can cause excessive heating todevelop.

A further key decision to be made is that of the controlling mode. Fatiguetests can be performed in load, position or strain control, although the testmachine may not permit all modes to be used. Position control is the cheap-est and most tried method, and requires the displacement to be cycledbetween preselected maximum and minimum values, independent of theload developed in the testpiece or, indeed, how the load may change as aresult of damage developed during the test.

In many applications a component will be required to sustain a cyclicload; thus load controlled fatigue may be more appropriate. This requiresmore sophisticated test machines, such as servohydraulic equipment, inwhich there is a feedback loop. This is essential so that, as the material isdamaged in fatigue, greater displacements result, allowing the testpiece tosupport the applied load.

Strain control is really a more controlled version of position control,whicheliminates errors associated with movement within the grips or supports.In this approach a strain or clip gauge extensometer is attached to thecoupon to monitor the strain, which is then used as the controlling para-meter. There are difficulties associated with this method, as bonded straingauges are usually themselves fatigue sensitive and care in selection isrequired. Attaching clip gauges in a fatigue test is also fraught with diffi-culty, since the knife edges tend to fret on the coupon, and cause damage,are damaged themselves or move during the test. A common remedy forthese problems has been to bond grooved blocks onto coupons to locatethe knife edges, but this all adds to the complication of the test. As a result,few laboratories choose to perform fatigue tests in strain control, load orposition control being the most favoured control parameters.

It is interesting to note here that composite materials exhibit a gradualsoftening, or loss of stiffness, under fatigue testing, due to the appearanceof undetected microscopic damage. As a result, the strain in the specimenincreases in load-controlled tests, whereas the stress decreases in strain-controlled tests. This softening effect is portrayed for these loading modesin Fig. 11.7. It follows that the cycles to failure may not always accuratelyrepresent the specimen life.This is the reason why many tests are performeduntil the specimen stiffness, or residual strength, decreases to a predeter-mined level.

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Time

(a)

(b) (c)

Strain Strain

Stress orload

Stress orstrain

Stress orload

11.7 Fatigue cycling under (a) stress or strain; (b) stress or load control; (c) strain control for polymeric composites.

11.4 Presentation of data

Data presented so far in this chapter have been in the form of stress–lifediagrams or S–N curves, with a linear scale on the stress axis and a log scalefor cycles, or life.This is the most widely used form of data presentation andprovides a simple-to-interpret indication of how life is degraded by con-stant amplitude fatigue. Such diagrams show clearly whether a fatigue limitis reached at long lifetimes but does not describe the full behaviour of thematerial. For example, a single plot cannot show the effects of varying the R ratio (minimum to maximum stress). However, a master curve orGoodman diagram can. In this form of presentation the stress amplitude isplotted as the ordinate (y axis) and mean stress as the abscissa (x axis). Lifeinformation is displayed by showing different traces for fixed cycles tofailure, such as 106 cycles. An example is given in Fig. 11.8. Such plots haveproven to be a useful way to represent the full spectrum of fatigue behav-iour and thus have found use as a guide in design. The excellent perfor-mance of polymer composites compared with metallics shows up well onsuch plots.

11.5 Monitoring fatigue damage growth

A key part of any investigative fatigue programme is the determination offatigue damage development and failure processes. This is important inorder to establish whether the test coupons are failing in a manner repre-

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sentative of the material, rather than from some artefact or problem asso-ciated with the test method. Such investigations also lead to a better under-standing of how the material behaves and the likely performance in service.

The monitoring of fatigue damage growth relies heavily on destructiveand non-destructive testing methods, techniques which cannot be coveredfully here. What is discussed, however, is how such techniques can beapplied to the fatigue testing of composites, with some examples of theobtainable results.

The inspection techniques can be destructive, like optical microscopy, ornon-destructive, like ultrasonics. Some techniques are amenable to continu-ous inspection, such as thermography, or require interruption of the test, asis usually the case for X-radiography.

11.5.1 Microscopy

Optical microscopy is a technique available in most laboratories and canbe particularly useful in the examination of damage at the edges of couponsand holes. The usual approach is to polish the edges of the coupon by con-ventional metallographic routes, followed by regular examination duringthe test. Ideally, the observations should be made without removal of thetest coupon from the testing machine, but this is not always feasible. Alter-natively, the technique can be used destructively by sectioning part-testedor failed coupons, mounting and polishing these by conventional routes for

Atternatingstress (MN m–2)

Compression–Tension

Compr

essio

n

Compr

essio

n Tension–Tension

1000

500

1500 –1000 –500 0 500 1000 1500

CF RPAFRPTitanium Alloy

GFRPAluminium Alloy

Mean stress (MN M 2)

Stress

Alt.Alt.

Mean

t

- +

11.8 Typical Goodman or master plot. CFRP is carbon-fibre reinforced plastic, GFRP is glass-fibre reinforced plastic, AFRP is aramid fibre-reinforced plastic.

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optical examination. One compromise is the ‘edge replication technique’,which relies on the application of a polymeric solution to the edge of thecoupon during an interruption to the test. The dried film is removed, per-mitting the test to continue, and can be examined under a microscope toprovide information on surface damage imprinted on the film.

Examination of edges can be particularly valuable for interlaminartoughness tests, where crack length as a function of cycles is required.Double cantilever beam and edge-notched deflection tests are frequentlyused in fatigue and require little or no modification to work successfully.

Another approach is to use a deplying technique. This relies on destroy-ing the test coupon, or part of it, in a furnace at a temperature which is suf-ficiently high to carbonise the polymer matrix, but which leaves the fibresintact. The resulting debris can easily be separated into plies which carryinformation on their surfaces of delaminations and cracks, which can beenhanced by soaking the part in gold chloride solution prior to carbonisa-tion (other volatile liquids can give similar results and are considerablycheaper); broken fibres are clearly identifiable. Although clearly destruc-tive, this technique has proven to be powerful in studying damage in fatiguetested coupons.

At the end of life, fractographic tools can be valuable in the evaluationof damage sequence. Fatigue testing of polymer composites frequentlyleaves characteristic features on the surfaces of failed coupons and com-ponents which can be used to determine the sequence of failure events or


11.9 Striations on the fracture surface of a fatigue-tested polymer composite.

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damage growth. Figure 11.9 shows a scanning electron micrograph of atypical fatigue failure; the striation markings thus revealed are often seenin the matrix of polymer composites, marking fatigue crack growth andarrest.

11.5.2 Ultrasonics

Ultrasonic C-scan is a non-destructive technique widely applied in fatiguetesting programmes. The technique relies on measuring the attenuation ofan ultrasonic beam passed through the specimen and relating this todamage present. The ultrasonic beam requires a transfer (or coupling)medium, which is usually water, and normally requires removal of thecoupon from the fatigue testing machine to allow immersion in a tank ofwater. Techniques relying on water jetted at the specimen (and carrying theultrasonic signal) are available and enable measurements to be made withthe coupon mounted on the fatigue machine; but such an approach is poten-tially very messy to use around complex testing equipment, and is alsoexpensive, probably beyond the budget of most laboratories.

Ultrasonic inspection is particularly useful for the detection of inter-laminar damage, such as edge cracks and delamination, and for the studyof the growth of these types of damage in fatigue loading. Typical damagegrowth in a coupon, initially impacted and subsequently tested in com-pression fatigue loading, is shown in Fig. 11.10.

Relatively new developments in ultrasonic testing techniques includehighly sophisticated systems with computer analysis/enhancement ofimages which are portable enough to be used to inspect coupons in situ inan interrupted test.A typical example of such equipment is the ANDSCANsystem, initially developed at DERA (Defence Evaluation and ResearchAgency), and now marketed by Wells Krautkramer.

11.10 Ultrasonic scans of impact damage and growth during the compressive fatigue of CFRP (carbon-fibre reinforced plastic).

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11.11 X-radiograph of a notched coupon tested in tensile fatigue.

11.5.3 X-radiography

X-ray inspection of composites during fatigue loading is also a very usefultechnique. Since polymer composites are essentially transparent to X-rays,the technique usually relies on the introduction of an X-ray opaque penetrant into the damaged area of the composite as a liquid solution orsuspension which fills cracks and delaminations, making them more clearlyvisible as shadows on X-ray film.

The usual procedure is to remove the fatigue coupon from the testmachine for inspection, but equipment is available which permits inspec-tion within the fatigue machine. The technique is particularly suitable forthe detection of in-plane damage, such as transverse cracks in 90° layers. Itis therefore a complimentary approach to the ultrasonic technique.

One note of caution is appropriate here. There is some evidence that theuse of penetrants actually enhances the subsequent crack growth as well asthe visibility of damage. As a result, attempts to use X-radiography as aninterrupted technique are difficult, because under further loading, crackgrowth rates will be increased. It is recommended, therefore, that this tech-nique be regarded as effectively destructive.Typical damage growth arounda hole in a coupon loaded in tensile fatigue is shown in Fig. 11.11.

11.5.4 Thermography

What might be considered to be a somewhat more exotic technique is in-frared thermography. This technique is, however, particularly well suited tothe study of damage development during the fatigue loading of polymercomposites. It has the advantage over most other methods in that inspection

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Fatigue 261

requires no interruption to the fatigue test. The resolution obtainabledepends on the particular equipment, but is typically similar to that obtain-able with ultrasonics, and rather less than can be achieved with X-radiogra-phy. Infrared thermography detects heat generated from two sources duringa fatigue test: hysteresis, normally emanating from the resin or interface, andfrictional heating as a result of differential movement at cracks.

A typical thermogram is shown in Fig. 11.12 for a ±45° coupon tested in tensile fatigue and close to failure. Areas at elevated temperature areclearly visible close to the upper end-tab and near the centre of the gaugelength. The hot area in the end-tab region indicates why damage, causingpremature failure, often develops in fatigue close to the grips, which aresubjecting the area to additional constraint. Once an area of damage hasbeen detected using thermography, other higher resolution techniques, canbe employed to examine the area in more detail.

11.6 Potential problems

11.6.1 Stress concentrations

So far only plain coupon fatigue testing has been the main subject of dis-cussion. In reality, tests must be performed on structural elements contain-ing stress concentrating features, such as notches, holes, fasteners, impact

11.12 Infrared thermogram of a ±45° CFRP tensile fatigue specimen,close to failure at 87kcycles.

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damage and other imperfections. Fortunately it has been found that, ingeneral, these stress concentrations have less effect on fatigue strength thanthey do statically. Dependent on the laminate configuration, these stressconcentrations can reduce static tensile strength by as much as 50%. Infatigue, however, damage zones develop at stress concentrators, which canserve to reduce their magnitude; studies of damage development should thisbe a key part of any fatigue testing programme. Damage zones usuallyconsist of cracks along the fibres within layers and interlaminar crackingbetween plies. Such mechanisms, as long as they do not damage fibres, canlead to increased strength. Further cycling results in some loss of strength,but typically, fatigue strength calculated on a net stress basis approachesthat of the plain unnotched material after long lifetimes, resulting in fairlyflat S–N curves.6–9 Consequently, it is not usually necessary to modify testprocedures developed for plain coupons, as these are equally suited tocoupons or elements containing stress raisers.

11.6.2 Frequency effects

Having discussed hysteresis heating effects in connection with infraredthermographic techniques, some reference should be made to frequencyeffects during the fatigue of composite materials. As a general rule, the testfrequency should be chosen so as to minimise the hysteresis heating of thematerial. The source of this heating effect is hysteresis in the resin and,possibly, at the fibre/matrix interface. In some cases, where the reinforcingfibres are polymeric, these can also be a source of heating. Generally,laminates dominated by mainly continuous fibres in the test direction showlower strains and little hysteresis heating, and test frequencies of up to 10Hz, or even more, can be suitable. Resin-dominated laminates, on theother hand, and those with few fibres in the test direction, show largerstrains and marked hysteresis heating, and as a guide, frequencies shouldbe limited to 5Hz or less.10

Heating at damage sites, an alternative source of heating, may still occurand could cause local overheating. Ideally, the specimen temperatureshould be monitored during the test so as to ensure that such overheatingdoes not occur.This is difficult without expensive thermography equipment,although the strategic positioning of thermocouples, the use of hand-heldtemperature sensors and the application of temperature-sensitive coatingsare suitable alternatives, particularly when the site of the heating is known,such as when stress concentrators are present.

The effect of frequency on properties, that is the effect of fatigue loading rate, is negligible for most continuous fibre composites when testedin the fibre direction, as long as hysteresis heating is not present. The mainexception is glass-reinforced plastic (GRP), which has a significant rate

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effect; the greater the rate of testing, the greater the strength. It has been found11 that GRP can have a rate sensitivity of over 100MPa perdecade. The reasons for this are not entirely clear, although it has been suggested that it is due to the environmental sensitivity of the glass fibres,rather than any viscoelastic effect.12 Certainly, the effect has been found tochange when the environment surrounding the glass fibres is changed.Testing composites with no fibres in the test direction, where the resinmatrix has a viscoelastic behaviour, often results in significant rate effects.

When collecting fatigue data on composite materials, the best policy is tocarry out all fatigue tests at a constant rate of stressing,13 such that low loadtests are performed at relatively high frequencies, whereas high load testsshould be at low frequencies.

11.6.3 Edge effects

Edge-induced stresses can be a problem in many types of test, but espe-cially so in fatigue. Some tests, such as those investigating interlaminarbehaviour, may aim to maximise edge effects, but in fatigue tests the policyis usually to attempt to minimise edge-induced stresses and hence thedamage that inevitably develops as a result of their presence. Both shearand normal stresses can develop at the coupon edges, these arising from themismatch of properties between the plies, stresses being generated at theedges due to the inhibition of relative layer strains.14–16 The magnitude ofthese stresses changes with temperature, because the layers have different expansion coefficients, and also with moisture content, since the layersexpand to different extents on absorbing moisture.17 The sign of the stressesmay also change with external loading; for example, a laminate, thoughinsensitive to edge effects in tension loading, may develop edge-induceddamage in compressive loading. Layer stacking sequence is a critical vari-able, the magnitude of edge stresses varying greatly with the relative posi-tions of the layers.

Edge-induced damage, apparent in static loading, usually grows withincreasing numbers of fatigue cycles. In the worst case the layers can be-come completely delaminated, leading to potential environmental attack,and certainly serious loss in compressive strength.

The literature contains many theoretical treatments of edge-inducedstresses,14–16 some allowing the approximate magnitude of the stresses to becalculated from elastic properties. Thus, the susceptibility of a laminate toedge effects may be determined before embarking on a fatigue test pro-gramme. Laminates known to be relatively insensitive to edge effects may,therefore, be selected for the work. In general, laminates with thin, evenlydistributed layers lead to the lowest edge stresses for both tensile and com-pressive externally applied loads.

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11.6.4 Environmental effects

These are dealt with in more detail in Chapter 12, but some comments arepertinent here. The first problem to be tackled in this specialist area ofpolymer composite fatigue work is to decide how to perform the test.Fatigue tests are inevitably of a medium to long term nature, frequentlylasting days or weeks. The possibility of coupons drying out during theperiod of the test must be considered. Room temperature tests generallylead to little change in moisture content (unless hysteretic heating ispresent), because the times involved for most materials to absorb or desorbsignificant quantities of moisture are long. The problem of coupon dryingis particularly acute, however, when the fatigue test takes place at elevatedtemperature. Precautions must be taken to preserve the moisture contentof the specimen. One possibility is to carry out the test in an environmen-tal chamber, in which the temperature and humidity are controlled. Thisdoes, however, involve expensive equipment, which might be beyond thebudget of many laboratories. Alternative approaches include enclosing thespecimen in a polythene bag, in which a salt solution maintains the requiredhumidity, or sealing the specimen totally by encapsulation.18,19

11.7 Fatigue life prediction

Since the early 1980s many damage growth models have been proposed.Sendeckyi20 has characterised them into three basic types: empirical fatigue,residual strength and stiffness reduction. Other models do exist, forexample, actual damage mechanism based models. These, however, arebased directly on observable damage and are difficult to apply quantita-tively, owing to the complexity of the mechanisms involved.

11.7.1 Empirical theories

These theories have been developed to correlate particular sets of data. There are many different forms and their merit lies in their ability to predict performance. Typical of this class is the expression used byMandell21 to relate fatigue performance to the ultimate static strength ofthe composite:

sa = suc - b logNf [11.1]

where sa is the applied stress amplitude, suc is the ultimate static strength,Nf is the number of cycles to failure and b is a constant. Typical values of bare 1.0420 for T300 carbon fibre in a ductile epoxy matrix and 1.2103 forthe same fibre in a brittle epoxy matrix.22


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11.7.2 Residual strength degradation

Unfortunately for these theories it is not possible to assess the damage stateof the laminate non-destructively with any degree of accuracy, as there islittle established correlation between the results of non-destructive evalua-tion (NDE) and residual strength. Nevertheless, they have the merit ofbeing based on measurable degradation behaviour, so they have some useas a predictive technique. Failure occurs when the reducing strength of the composite becomes equal to the applied stress. The models are usuallybased on an expression20 of the form:

[11.2]

where sr is the residual strength, sa the applied stress amplitude, Nf thenumber of cycles to failure, with f and s being functions of the applied loadratio, R = smin/smax.

11.7.3 Stiffness degradation

These theories assume that damage in the laminate, whether caused by fibrefracture, matrix cracking or delamination, all cause a reduction in stiffnesswhich can be used as an index of the rate and extent of damage growth.When sufficient damage has accumulated, the laminate fails. In order forlife predictions to be made, a relationship must be established between thedamage, D, its rate of accumulation with cycles, dD/dN, and the resultantlife. Poursatip and co-workers23,24 proposed a model based on carbonfibre/epoxy laminates of layup [45°/90°/-45°/0°]s. They found that:

[11.3]

where Eo is the original stiffness and dE/dN is the rate of stiffness reduc-tion.

11.7.4 Damage accumulation

In variable amplitude stress loading, the total damage can be expressed byMiner’s linear cumulative damage rule:25

[11.4]

where ni is the number of cycles of a given stress range, Nf is the numberof cycles to cause failure at that load and m is the number of stress rangelevels. Miner’s rule is used extensively to predict the fatigue performanceof metals and has been used, with some success, with composites. However,

nNm

ni

f=

=

Â 11

dd

ddo

DN E

EN

= - ÊË

ˆ¯2 857

1.

s sr a f= + -( )[ ]1 1N fs

Fatigue 265

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according to Harris et al.,26 when the direction of stress changes within afatigue test, as in mixed tension/compression cycling, the damage incurredis not predictable by a simple linear summation and actual lives are wellbelow those that would be predicted from Miner’s rule.

11.8 Post-fatigue residual strength

The post-fatigue performance of a fibre-reinforced composite is studied bymeasuring the static strength and modulus after cycling it for various frac-tions of its total life to failure. Both static strength and modulus are reducedwith increasing number of cycles. It has been reported27 that much of thestatic strength of a [0°/90°]s E-glass fibre/epoxy composite was reducedraidly in the first 25% of its fatigue life, which was then followed by a muchslower rate of strength reduction until final failure.

Reifsnider et al.28 observed an initial increase in the static strength of a[0°/±45°/0°]s boron fibre/epoxy laminate containing a central hole. Thisunique post-fatigue behaviour of a composite material was explained bymeans of a ‘wear-in/wear-out’ mechanism in damage development. Thewear-in process takes place in the early stages of fatigue cycling. During thisprocess, the damage developed locally around the central hole reduced thestress concentrations in the vicinity of the hole, resulting in increasedstrength. This beneficial stage of fatigue cycling was followed by the wear-out process, which comprised large scale and widespread damage develop-ment leading to strength reduction. The residual strength of a composite,after a period of fatigue cycling, could be modelled as:

sresidual = su + swear-in + swear-out [11.5]

where su is the ultimate static strength, swear-in is the change in static strengthdue to wear-in and swear-out is the change in static strength due to wear-out.

The effect of wear-in is more pronounced at high fatigue load levels. Sincefatigue life is longer at low load levels, there is a greater possibility of devel-oping large scale damage throughout the material, so that the effect of wear-out is likely to be more pronounced at low load levels.

References

1. J B Sturgeon, Fatigue Testing of Carbon Fibre Reinforced Plastics, Royal Air-craft Establishment, Farnborough, UK, Technical Report 75135, 1975.

2. P T Curtis and B B Moore, A Comparison of Plain and Double Waisted Couponsfor Static and Fatigue Testing of Unidirectional GRP and CFRP, Royal AircraftEstablishment, Farnborough, UK, Technical Report 82031, 1982.

3. P T Curtis (ed), CRAG Test Methods for the Measurement of the Engineer-ing Properties of Fibre Reinforced Plastics, Royal Aircraft Establishment,Farnborough, UK, Technical Report 88012, 1988.


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4. R J Butler, P M Barnard and P T Curtis, ‘The development of a satisfactory,simple, shear fatigue test for unidirectional E-glass epoxy’, ASTM STP 972,Composite Materials: Testing and Design, 1986, 227–40.

5. P A Tutton and K J Pascoe, The Effect of Specimen Geometry and BiaxialLoading on the Strength of Notched Carbon Fibre Composites, Cambridge University Engineering Department, Report under MoD agreement2029/0153XR/MAT, 1982.

6. P T Curtis and B B Moore, ‘A comparison of the fatigue performance of wovenand non-woven CFRP’, Proceedings of the 5th International Conference onComposite Materials, San Diego, CA, eds W C Harrigan, J Strife and A KDhingia, The Metallurgical Society, Warrendale, PA, 1985, 293–314.

7. P T Curtis and B B Moore, A Comparison of the Fatigue Performance of Wovenand Non-woven CFRP, Royal Aircraft Establishment, Farnborough, UK, Tech-nical Report 85059, 1985.

8. D Schultz, J J Gerharz and E Alschweig, ‘Fatigue properties of unnotched,notched and jointed specimens of a graphite/epoxy composite’,ASTM STP 723,Fatigue of Fibrous Composite Materials, 1981, 31–47.

9. G Dorey, P Sigety, K Stellbrink and W G J t’Hart, Impact Damage Tolerance ofa Carbon Fibre Laminate, Royal Aircraft Establishment, Farnborough, UK,Technical Report 84049, 1984.

10. P T Curtis, J Gates and C Margerison, The Selection of Cyclic Load Frequencyfor the Fatigue Testing of Fibre Reinforced Polymeric Composites, DERA, Farn-borough, UK, Technical Report 93017, 1993.

11. C J Jones, R F Dickson, T Adam, H Reiter and B Harris, ‘The environmentalfatigue behaviour of reinforced plastics’, Proceedings of the Royal Society ofLondon A, 1984 396 315–38.

12. A G Metcalfe and G R Schmitz, ‘Mechanism of stress corrosion in E-glass filaments’, Glass Technology, 1972 13 5–16.

13. G D Sims and D C Gladman, A Framework for Specifying the Fatigue Perfor-mance of Glass Fibre Reinforced Plastics, National Physical Laboratory ReportNPL-DMA(A) 59, 1982.

14. N J Pagano and R B Pipes, ‘The influence of stacking sequence on laminatestrength’, Journal of Composite Materials, 1971 5 50–7.

15. P T Curtis, The Effect of Edge Stresses on the Failure of (0°,45°,90°) CFRP Lam-inates’, Royal Aircraft Establishment, Farnborough, UK, Technical Report80054, 1980.

16. P T Curtis, ‘The effect of edge stresses on the failure of (0°,45°,90°) CFRP lam-inates’, Journal of Materials Science, 1984 19 167–82.

17. P T Curtis, Residual Strains and the Effects of Moisture in Fibre Reinforced Laminates, Royal Aircraft Establishment, Farnborough, UK, Technical Report80045, 1980.

18. P T Curtis and B B Moore, The Effect of Environmental Exposure on the FatigueBehaviour of CFRP Laminates, Royal Aircraft Establishment, Farnborough,UK, Technical Report 84027, 1984.

19. P T Curtis and B B Moore, ‘The effect of environmental exposure on the fatiguebehaviour of CFRP laminates’, Composites, 1983 14 294–300.

20. G P Sendeckyi, ‘Life prediction in resin–matrix composite materials’, in Fatigueof Composite Materials, ed K L Reifsnider, Composite Materials Series, Vol. 4,Elsevier Science, Amsterdam, 1991, 431–83.

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21. J F Mandell, ‘Fatigue behaviour of fibre–resin composites’, in Developments inReinforced Plastics 2, Properties of Laminates, ed G Pritchard, Applied Science,London, 1987, 67–108.

22. L L Lorenzo and H T Hahn, ‘Fatigue failure mechanisms in unidirectional composites’, Composite Materials: Fatigue and Fracture, ASTM STP907, 1986.

23. A Poursatip, M F Ashby and P W R Beaumont, ‘The fatigue damage mechanics of a carbon fibre composite laminate: I – Development of the model’,Composites Science and Technology, 1986 25(3) 193–218.

24. A Poursatip and P W R Beaumont, ‘The fatigue damage mechanics of a carbonfibre composite laminate: II – Life prediction’, Composites Science and Technology, 1986 25(4) 283–99.

25. M A Miner, ‘Cumulative damage in fatigue’, Transactions of the AmericanSociety of Mechanical Engineers – Journal of Applied Mechanics, 1945 12(3)A159–64.

26. B Harris, N Gathercole, M H Beheshty, J A Lee, B Grimm, H Reiter and TAdam, Fatigue Damage Growth and Life Prediction for Carbon Fibre Compos-ites, Final Report on Research Agreement Number CB/FRN/9/4/2112097,DERA, 1996.

27. L J Broutman and S Sahu, ‘Progressive damage of a glass reinforced plasticduring fatigue’, Proceedings, 24th Annual Technical Conference, Society of Plas-tics Industry, Washington, DC, Section 11-D, 1969.

28. K L Reifsnider, W W Stinchcomb and T K O’Brien, ‘Frequency effects on a stiffness-based failure criterion in flawed composite specimens’, Fatigue of Filamentary Composite Materials, ASTM STP636, 1977.


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12.1 Introduction

The physical and mechanical properties of organic matrix fibre compositescannot be regarded as constant with time, as the circumstances of use caninduce changes. This chapter is concerned with the nature of changes pro-duced by the environment. The subject of internationally agreed standardtest methods for assessing the environmental stability of composites isplaced in the context of a wider discussion of the subject, designed to high-light the characteristics of useful test methods.

12.2 Why environmental testing?

It would be a mistake to assume that the properties of composite materials remain unchanged for ever. Ambient moisture, chemicals and radiation often cause changes in the microstructure or the chemi-cal composition of materials, and these changes in turn cause a slow drift in such properties as modulus, strength and ultimate elongation.Typical consequences are: matrix swelling, fibre-resin debonding, matrixmicrocracking and chain scission. Chemical and other changes can occur. Sudden changes in properties are sometimes observed and sponta-neous fracture is not unknown. Figure 12.1 illustrates these statements diagrammatically.

A given property, such as strength, can sometimes decline so slowlyduring service life that it is simply not a factor in determining the product’suseful lifetime. Or the property can decline rather more quickly, shorten-ing the useful life, and requiring some cautious checks on the material’sstructural integrity as time progresses. Again, the strength can be fairlystable for a long time, but then fall suddenly, with no warning, before frac-ture occurs. As an illustration, unidirectional glass laminates can withstandimmersion in dilute mineral acids such as sulphuric or hydrochloric acid inthe absence of a tensile stress, but if both stress and acid are experienced

12Environmental testing of organic

matrix composites

G PRITCHARD

269

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together, failure can occur quite suddenly.1 It is difficult to predict thetimescale of environmental stress ruptures.

These observations are obviously relevant to composites used in contactwith liquids. Fibreglass boats have to last between 20 and 50 years, and likeoffshore oil installations, are exposed to salt water, ultraviolet radiation andrepetitive wave action. But environmental degradation also has to be con-sidered in composite parts in aircraft, where the chemicals are fuels, paintstrippers, hydraulic fluids, brake fluids and runway de-icers. Other vehiclesare also exposed to oils and fuels, and environmental degradation appliesto storage tanks, road tankers, sewage pipes and chemical plants. There areimplications for such diverse applications as building panels and printed circuitboard components.

12.3 Environmental threats to composites

Environmental degradation is caused chiefly by chemicals, temperature,microorganisms and radiation. It is sometimes aggravated by mechanicalstress or electrical fields. Chemicals include all reactive substances, whethersynthetic or natural, including water, oxygen, bleach, petrol, lubricants,detergents, cleaning solvents, acids, etching and oxidizing agents, and so on. In the world of glass and of polymers, water ranks as a fairly reactivechemical.

High or fluctuating temperatures pose a threat to composites, and rapid changes in temperature can produce damage through thermal shock.2

Problems arise when a composite which contains absorbed moisture orsome other liquid is suddenly heated quickly enough to drive off the liquidvery rapidly. Similarly the whole electromagnetic spectrum of radiation


Des

ired

prop

erty

Time

Minimum acceptable property level

c

a

b

12.1 Three ways in which material properties can change with time:(a) remaining acceptable throughout; (b) becoming unacceptableeventually; (c) catastrophic failure after time, e.g. throughenvironmental stress cracking.

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must be considered: ultraviolet, visible, infrared, X-rays and gamma rays.For most purposes, ultraviolet and visible light are the most important.Ordinary sunlight has an adverse effect on some polymers, frequentlycausing discoloration and embrittlement. It is possible to protect againstultraviolet radiation (and against microorganisms) with suitable additives,so the performance of one commercial grade of a given generic polymersuch as polyvinyl chloride is not necessarily a very useful guide to thebehaviour of other grades of the same material which may contain differ-ent additives.

We need to consider possible environmental effects before deciding whatthe design strain (or stress) of a structure should be. This means predictingwhat, if any, aggressive environment will be encountered, which in turnimplies being familiar with the circumstances of use. It can be difficultenough for the laboratory-based scientist or engineer to form a reasonableestimate (unaided) of the year-round surface temperatures on a surface shipor an ordinary aircraft, which may serve in various climates. It is much moredifficult to assess the likely stresses, temperatures and radiation levels onan experimental space platform, or the conditions applicable to a chemicalreaction vessel subject to periodic overheating, or an oceanbed assembly ina remote part of the world, with unknown microorganisms present. Often,one agent initiates a degradation process, and another aggravates it, so bothfactors have to be present for anything to happen. Material reliability pre-dictions therefore always have to be made in close consultation with theproposed user.

12.4 Standard tests

Environmental testing involves an assessment of a material’s properties andmicrostructure before and after exposure to some aggressive environment.The important considerations are:

• careful characterisation and conditioning of the virgin composite material

• selection of a realistic environmental exposure regime which incorpo-rates the significant factors operating during the useful life of the article

• control of the reproducibility of the exposure regime• recognition and quantification of the most significant changes occurring

in the composite during exposure• statistical analysis• cautious extrapolation in order to predict longer term behaviour. This

is vital where a product such as a pipe or bridge may be in use for 30or even 130 years. Obviously, laboratory testing cannot be carried outfor even a fraction of that time.

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The chosen test procedure will depend on the motive for having any tests.The aim may be simply to compare the merits of two competing candidatematerials, or to subject a single material to pass/fail criteria. It is these sit-uations which will be discussed in the present chapter. More complicatedprocedures, containing an element of research and development, may beused where the objective is to find out what the principal mode of degra-dation is, or where the intention is primarily to improve the material. Theseprocedures are outside the scope of this discussion.

Composites are used in so many environments that it is not prac-ticable to devise entirely appropriate international standard tests for all conceivable environmental scenarios. Standards can obviously be written in a generalised format to apply to any of a wide range of chemicals,but the prevailing temperature, stresses, test duration and specimen geom-etry, especially thickness, depend on the intended application. The test criterion frequently reduces to the achievement of a given percent-age retention of specified mechanical properties after immersion in a stan-dard environment under controlled conditions. These mechanical property retention tests are performed in accordance with ISO (International Standardization Organization) or ASTM (American Society for Testing and Materials) or similar standard methods. The immersion process itselfraises a number of issues: whether both sides of a test panel should beimmersed, whether specimens should be removed and cooled for periodicweighing, how to apply a stress at the same time as immersion in a liquid,and whether the test liquid or environment is itself stable over a period oftime.

There are a number of important national and international tests relat-ing to the environmental performance of composite materials. There arealso tests for the individual constituents of fibrous composites, such as thematrix resins, the fibre reinforcements and the chemically resistant liningsof pipes, examples of which are given in Table 12.1. Some of these tests willbe mentioned later.

There are also some general recommendations. BS 4618, Recommenda-tions for the Presentation of Plastics Design Data, Part 4: Environmental andChemical Effects, has the following sections which are relevant to organicmatrix composites:

• Section 4.1 Chemical resistance to liquids• Section 4.2 Resistance to natural weathering• Section 4.3 Resistance to colour change produced by exposure to light• Section 4.4 The effect of marine exposure.

Section 4.1 gives guidance about the various chemical reagents. Themethod of immersion is given as total immersion, whereas in practice tanksand pipes are exposed to their liquid contents on only one side. The effects


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are usually similar, but with total immersion they are achieved much morequickly. Changes in dimensions and appearance after immersion are to beobserved, together with changes in tensile, flexural, shear and impactstrength. The stipulations for the impact test method and other mechanicaltests leave scope for considerable variation.

Section 4.2 deals with natural weathering, which is an obvious influenceon all outdoor composites, but not usually much of a threat to functionalviability, only to the aesthetic properties of the composite. The introductionto the standard warns that the results only give an indication of the likelybehaviour of the material, and tests should preferably be long term (i.e. overseveral years), although even then the outcome may depend on the time ofyear at which the test programme was started. The method of exposureinvolves specimens mounted on racks facing south, with the specimen sur-faces at 45° to the horizontal.There are provisions to eliminate interferencefrom obstructions such as high rise buildings. Consideration is also given tospecimen fixing or mounting. No copper should be used, because of theeffect of copper ions on certain autocatalytic processes; aluminium, plasticsor ceramic fixing materials are preferred. Timber backing is considered anundesirable specimen support, because it raises the specimen temperaturetoo much.

After exposure, the specimens are examined for biological attack beforewashing with soap and water, being machined into shape and subjected toany conditioning process required before the tests. Visual observations playa large part in the evaluation, but mechanical tests can be selected from theusual menu (tensile, flexural, shear strength, impact).


Table 12.1. Examples of standard tests and specifications for environmentalstability, relevant to reinforced plastics.

ASTM D 543 Resistance of plastics to chemical reagentsASTM C 581 Determining chemical resistance of thermosetting

resins used in glass-fibre reinforced structures intended for liquid service

BS EN 60068-2-45 Basic environmental testing procedures: immersion in cleaning solvents

ASTM C 582 Contact-molded reinforced thermosetting plastic (RTP) laminates for corrosion-resistant equipment

ASTM G 20 Standard test method for chemical resistance of pipeline coatings

ASTM D 3681 Test method for chemical resistance of reinforced thermosetting resin pipe in a deflected condition

ISO 175 Plastics: determination of the effects of liquid chemicals, including water

ISO 1776 Glass: resistance to attack by hydrochloric acid at 100°C

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Section 4.3 (on colour stability), is less important than the others for composite materials, although external building panels suffer from light-induced changes in their original pigment colour if the wrong pigment ischosen, or if certain flame retardant additives are used.

Section 4.4, the effect of marine exposure, is, perhaps, more relevant here.It does not specify actual tests, rather the general approach to be taken.Thepreamble identifies three types of marine exposure: (a) near the sea, (b)partially immersed and (c) totally immersed. It is pointed out that, unlikemetals, most plastics are more severely affected by (a) than by (b), and leastaffected by total immersion. This is said to be because ultraviolet light iscommonly considered more of a threat than water (a generalization whichat best applies only to specific polymers and can certainly not be taken forgranted with structural composite materials). Eight agents of marine degra-dation are listed: salt, water, sand, ultraviolet light, marine vegetation andmicroorganisms, marine pollutants and wave action. Thermosetting resincomposites are not seriously affected by salt or sand, although in the verydifferent context of aircraft, water erosion under high speed conditions canrepresent a more serious problem for brittle thermosetting resins than forthe semicrystalline thermoplastics.

Consider now ASTM C 581, mentioned already in Table 12.1. It illustratessome of the issues encountered during environmental testing. First, C581 isintended as a low-cost screening procedure and the results are fairly sub-jective. Second, it is not directed at advanced composites such as carbon-epoxy and aramid laminates. Instead, it is a guide to the selection of a matrixmaterial for process plant, effluent pipes and so on.

Note that the term ‘advanced composite’, as used above, assumes thatspecific strength and modulus are the crucial properties that matter mostto every user, whereas in many applications, environmental considerationsare more important.

Despite the title, the tests in C581 are not confined to the matrix resins.They are actually performed on chopped strand glass mat laminates.Testingresin and fibres separately would give no indication of resin–fibre interfacequality and how it survives the environment. C581 deals with the changesinduced by an environment on the Barcol hardness of a laminate and itsappearance, flexural strength and flexural modulus. It also considers anychange in the appearance of the immersion media. An introductory state-ment points out that the liquid medium may be hazardous.

The test procedure specifies two plies of chopped strand mat, with twolayers of a surfacing veil. The normal additives such as thixotropes, fillersor fire retardants are allowed. The control (i.e. the before-test value of theBarcol hardness) has to achieve a certain minimum, otherwise the resinwould be considered undercured and unsuitable for chemical resistancework. Changes in appearance are recorded after visual inspection, without


MTA12 11/22/2000 1:48 PM Page 274

any objective spectroscopic or other instrumental technique. The guidancenotes on the changes in mechanical properties point out that the rate ofchange of strength, modulus and hardness may be more significant than theabsolute values (a typical test duration is about a year).

The test procedures are simple enough, but the skills required to produceconsistent and representative test laminates by hand layup with such con-stituents should not be underestimated. By the same argument, the testoutcome may reflect the quality of the specimen fabricator.

Finally, there are test methods and specifications applicable to finishedor semi-finished articles, such as plastics or composite pipes and so on.Thesedocuments often contain sections dealing with chemical resistance. As anillustration, ASTM D 3262(88) concerns the short-time hydraulic failure ofplastics pipe, tubing and fittings, but takes account of chemical considera-tions; for example, it includes a section 6.3.1: ‘Pipe specimens, when testedin accordance with 8.2.1, shall be capable of being deflected without failureat the 50 year strain level given in Table 4, when exposed to 1.0N sulfuricacid’.

Specifications may, implicitly or explicitly, offer advice on materials selection. In ASTM D 3299(88), Standard Specification for Filament-woundGlass-fiber-reinforced Thermosetting Resin Chemically Resistant Tanks, it issaid that fire-retardant agents may interfere with visual inspection of lam-inate quality, and should not be used on inner surfaces or interior layers,‘unless their functional advantages outweigh the loss of visual inspection’.

12.5 Sample conditioning

Specimens are first conditioned to achieve a standard and repro-ducible initial state. This initial state may simply mean that the specimensare thoroughly dry, or that they have been held in a standard atmospheresuch as 50% RH (relative humidity), or that some other prescribed treat-ment has been applied. One relevant standard is ASTM D 5229, MoistureAbsorption Properties and Equilibrium Conditioning of Polymer MatrixComposite Materials; so also is BS 2782 Part 10, Method 1, 1977, Methodsof Testing Plastics: Method 1004, Standard Atmospheres for Conditioningand Testing.

Drying requires desiccation over a desiccant such as phosphorus pen-toxide until constant weight is reached. The time taken to dry thick speci-mens can be considerable. Rapid drying at high temperatures to circumventthe need for lengthy specimen conditioning can introduce microcracks. Thethermal history of a specimen can alter the crystallinity of a thermoplasticmatrix, and since crystallinity has an enormous effect on solvent resistance,it is clearly necessary to ensure reproducible and standard laminate pro-cessing procedures prior to environmental testing.


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The main requirement of any conditioning operation is for the diffusionsamples to be representative, completely dry and free of defects such asvoids. In practice composites do contain voids, but they should be presentat a reasonably low and consistent level, otherwise the quantity of liquidabsorbed will be a function of void content. Ideally, preliminary materialcharacterisation is advisable using scanning electron microscopy and ultra-sonic C-scanning, if available. A series of papers by Thomason is relevant,discussing the characterisation of composite interfaces in connection withwater resistance.3–5

12.6 Experimental approaches

Common procedures are:

1 Examination of the sample before and after immersion using optical andscanning electron microscopy (SEM) to detect any debonding or micro-cracks. If inspection before immersion is omitted, defects which werefirst noticed in immersed samples may appear significant until they arelater discovered in the virgin material as well.

Figure 12.2(a) shows an example of defects which developed after aperiod of environmental exposure. They are microcracks in glass-epoxyresins, formed after exposure to hot water, and observed under theSEM. Further prolonged exposure caused these fine cracks to becomelarge enough to be visible to the naked eye, as shown in Fig. 12.2(b).Thecracks were caused by residual hardener which dissolved in the water,producing osmotic cells and incidentally generated ammonia, which isharmful to glass fibres. These effects were originally reported by Kas-turiarachchi and Pritchard.6

2 Measurement of the percentage retention of mechanical properties,such as tensile, shear or flexural strength. A reduction in shear strength,measured by the short beam method, the 10° off-axis tension methodor rail shear, is usually attributable to interface breakdown, althoughmatrix degradation is a possibility. Interface failure should also bereflected in a fall in the transverse tensile or flexural strength of unidi-rectional laminates. Changes in flexural properties are convenient tomeasure, because of the simple specimen geometry. Retention of com-pressive strength in the hot, wet state is another well established crite-rion of environmental durability in wet atmospheres.

Usually we consider whether the surrounding environment affects thecomposite. But the opposite can also be a concern. If containers manufac-tured from composite materials are used to store or transport food, drinkor fuels, the testing programme may require an analysis to determinewhether the contents have been contaminated as a result of leaching


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of trace substances from the composite itself. In the case of drink, very tiny quantities can be detected by the sensitive palate. Gas–liquid chro-matography is the first procedure to be considered for organic chemicalconstituents, preferably coupled with another technique such as Fouriertransform infrared (FTIR) spectroscopy. Inductively coupled plasma emis-sion spectrometry is also an appropriate technique, if trace elements arebeing sought.

Tests on the fibre reinforcement can also be important. Glass fibres varya great deal in their behaviour towards acids and alkalis.7

Individual filaments, or entire bundles, are immersed in an environment,and their tensile strength and modulus retention determined after specifiedperiods. Single filament handling procedures require considerable practicein order to avoid damaging the specimens, especially if they are to bemounted in a liquid medium under stress. Glass fibres are attacked more


12.2 (a) Scanning electron micrograph showing fine cracks in asample of glass/epoxy after exposure to hot water. (b) Afterprolonged exposure the cracks are visible to the naked eye.

(a)

(b)

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seriously by acids which form insoluble mineral salts, such as calcium sul-phate or aluminium oxalate, than by acids forming soluble salts.8 Thus oxalicand sulphuric acids are more aggressive media than nitric acid, at leastbelow pH 1. If single carbon fibres are heated in air, they eventually frac-ture due to oxidation.9 This is relevant to the composite, because exposedfibre ends can be attacked at high temperatures. The decline in the averagediameter of high modulus PAN (polyacrylonitrile) carbon fibres on heatingin air at various temperatures is shown in Fig. 12.3. Close examination showsthat the oxidation occurs selectively and locally as a result of the catalyticeffect of trace impurities. The oxidation resistance is therefore dependenton the impurity profile.

12.7 Determination of sorption behaviour

The mass of liquid absorbed when a composite sample is immersed in a laboratory tank of liquid is usually determined by manual weighing, butautomatic devices based on quartz springs, force transducers and electricalproperty measuring devices are sometimes used.

The environment in which the samples are to be immersed needs to be defined. The chemical composition of some liquids (such as sodiumhypochlorite or petrol) will change gradually during a long test, as a result


100

75

50

25

Dia

met

er r

emai

ning

(%

)

20 60 100 140

793K

813K

833K

853K

873K

Time (minutes)

12.3 Reduction in average diameter of a single high modulus carbonfibre, caused by heating in air at different temperatures.Eventually the fibre fractures, having oxidised preferentially atparticular sites.9

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of either decomposition or volatilization. Supplies therefore need to berefreshed frequently.

Samples immersed in laboratory glass tubes can become difficult to identify after a time in an aggressive liquid, which changes their appear-ance and destroys surface markings. It is important to devise effectivemethods to overcome this problem, without scratching the samples.Numbered slots in inert specimen racks are better than using physicallymarked specimens.

Suppose a sample of dry mass M0 increases in mass during immersion ina solvent, to reach Mt at time t. The usual assumption is that the amount ofsolvent absorbed is (Mt - M0). But if the sample is then dried, the new massmay be Md rather than M0. The reason would be that while sorption wasoccurring, some constituents of the sample itself were entering the liquidenvironment by a process of leaching. This is most noticeable with unsatu-rated polyesters and plasticised resins and can often be neglected with amore stable matrix. Where leaching occurs, the true liquid sorption at timet is given by Equation [12.1]:

[12.1]

The original state of the sample will never be recovered, and a second sorp-tion cycle is unlikely to be superimposable on the first.

The sorption behaviour of resins changes rapidly with temperature as theglass transition temperature, Tg, is approached. It is unlikely that organicmatrix composites will deliberately and knowingly be used within 15°C ofthe matrix Tg. However, sorption of a liquid lowers the Tg, so that the tran-sition temperature has to be given a wider berth than 15°C if sorption isanticipated.

12.8 Lowering of Tg by absorbed liquids

The extent of the lowering of the Tg is very difficult to measure experi-mentally because the procedures involve heating a sample and thisinevitably removes some of the absorbed liquid. It is essential to use asample capable of retaining most of the absorbed liquid during heating forlong enough to allow the property measurements to be made; errors aredifficult to avoid. There are predictive equations, such as that of Kelley andBueche,10 which estimate the change in the glass transition temperature asa result of absorbed liquid diluent:

[12.2]TT T

gp p gp d p gd

p p d p=

+ -( )+ -( )

a n a na n a n

11

MM M

Mst d=

-ÊË

ˆ¯100

0


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where Tg, Tgp and Tgd refer to the glass transition temperatures of thesystem, the polymer and the diluent, respectively. np is the volume fractionof polymer, with ap and ad being the volumetric expansion terms for thepolymer and the diluent, respectively.

McKague et al.11 used rapid heating methods to minimise loss of mois-ture during a study of the effect of water on Tg.They refined Equation [12.2]to give:

[12.3]

where ald and agp refer to the liquid and glassy volumetric expansion coef-ficients, respectively.

Several widely differing values for the glass transition temperature ofwater have been used. McKague and co-workers used 4°C because it is thetemperature at which the density is greatest.

Carter and Kibler12 proposed that water absorption in epoxy resins isdivided into bound and non-bound categories, with the proportion of eachbeing temperature dependent. The implication is that below the Tg, manyof the water molecules are more or less firmly held, whereas above the glasstransition, most are free to move.

12.9 How do composites perform in

adverse environments?

12.9.1 The matrix

Few generalizations are completely safe, but the following points provideuseful guidelines:

• All organic matrix materials are permeable to moisture.• Most organic matrix materials are permeable to a whole range of

organic liquids, with a consequent reduction in matrix modulus,although semi-crystalline matrix resins are less permeable than amor-phous ones. This observation means that the rate of cooling during pro-cessing of crystallisable thermoplastics such as PEEK (polyether etherketone) and the degree of regularity of their chemical repeat units arevery important for solvent resistance.13

• All are poor at withstanding high temperatures. It is possible to predictfrom considerations of chemical structure whether one matrix will bemore resistant to heat or radiation than another. This is a vital step inreducing the costs of material evaluation.

• Most resins are resistant to microorganisms, although the same cannot be said about some of the additives in thermoplastic polymers,

TT T

ggp p gp 1d p gd

gp p 1d p=

+ -( )+ -( )

a n a na n a n

11


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such as plasticisers, or about the adhesives and coatings which may beapplied.

• Most matrix resins withstand dilute acids and alkalis better than lightalloys or stainless steels would.

• Anions and cations do not diffuse easily, if at all, through uncrackedresins.14 This is because of the large size of many ions, especially whensolvated.

12.9.2 The reinforcement

Glass fibres are resistant to most chemicals and glass is the favoured mate-rial for containing chemicals during reactions, but it does not withstandstrong alkalis and acids indefinitely. Flaws are initiated which can propa-gate under stress. Even hot water can cause glass fibres to lose theirstrength. Carbon fibres are resistant to almost all chemical reactions,notably to alkalis, non-oxidizing acids and steam below 1000°C, but theyare vulnerable to oxidation and intercalation.15 The higher their heat treat-ment temperature and corresponding graphitic order, the better carbonfibres resist oxidation and the less well they withstand intercalation.Aramidand other thermoplastic fibres absorb moisture, unlike glass and carbon,and are affected by ultraviolet light, but in practice this is largely a surfaceeffect.

12.9.3 The interface

The interface between fibres and resin can sometimes be broken by liquids,or possibly by thermal cycling. Hot water can break the bond between poly-ester resin and glass fibres. The breakdown can be observed under opticalmicroscopy, and the reduced adhesion can sometimes be reflected in thesmooth appearance of the fibre surfaces in a fractured specimen in a scan-ning electron microscope. It is also reflected in reduced transverse tensilestrength and short beam shear strength. Interfacial breakdown is sometimesreversible on careful drying.

Wherever environmental damage to the interface is expected, the bestfibre surface treatment has to be applied. A matrix which has a high pro-cessing temperature will also require heat-resistant coupling agents forbonding to glass fibres.

12.9.4 Chemical reactions between composites and their environment

Some of the dangers are obvious. Carbon fibres undergo oxidation, glass is attacked by alkalis, and most resins are destroyed by alkalis and strong


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oxidizing acids. Having said that, chemical attack is rarely as severe aproblem as might be imagined, simply because the dangers can be predictedand obviated. Even the much-quoted vulnerability of unsaturated polyesterresins to hydrolysis is rarely a problem if the conditions recommended bythe supplier are fulfilled. There can be degradation reactions involving fre-quently overlooked trace substances, such as unreacted hardener.

12.9.5 Physical changes caused by chemicals

Common chemicals such as water and solvents can cause physical effects,quite apart from any chemical reactions. These effects are chiefly dimen-sional changes, which can be undesirable in themselves, and which can leadto cracking or delamination. Solvents can also dissolve or leach out tracesubstances. The swelling process is usually accompanied by a reduction inthe Young’s modulus through plasticisation, and by an initial rise in matrixstrength, caused by relief of internal stresses, followed rapidly by a muchlarger fall. The elongation at break is frequently lowered. Short immersiontimes will usually produce changes only in the surface of the material.

12.9.6 Protective measures

The matrix offers some protection to the fibres against aggressive liquids,unless it becomes microcracked.16 If such protection is inadequate, a specialsurface layer may be used between environment and fibres. A very thicklayer will simply have the effect of distancing the reinforcement from theaggressive medium. Protective layers can consist of tissues or veneers, madeof special chemically resistant glass or polymer, embedded in a gelcoat, orthey can be highly filled resin layers (see Fig. 12.4) or barrier films made ofpolymer, ceramic or metals.

12.9.7 Effects of mechanical stress

It has already been mentioned that stress can cooperate with an envi-ronment to produce sudden catastrophic failure by environmental stresscracking (ESC). This is chiefly a problem with glass fibres; carbon does notseem to be susceptible. Figure 12.5 shows in schematic form a procedurefor the long term strain corrosion testing of buried sewage pipe.17 Thesewage is simulated by using very dilute sulphuric acid. The composition ofsewage in a pipe can, in practice, be altered by the presence of industrialeffluent.

Stress can alter the free volume of the matrix and therefore alter theamount of liquid absorbed.18 There can be substantially increased absorp-tion in the vicinity of stress-induced damage around holes and notches.


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Figure 12.6 combines these effects, showing the effect of a compressivestress (defined here in terms of the strain) on the uptake of methylene chlo-ride by carbon–PEEK. At first there is a reduced uptake with increasingapplied strain, but later there comes a point when damage around holesincreases the uptake dramatically.19

Creep and stress relaxation are very variable in polymers and are rela-tively low for those which are favoured in structural composites, but any


Surface tissueChopped glass roving

Chopped and filamentwound glass in sandaggregate

Chopped glass roving

Surface tissue

A

B

C

12.4 Schematic cross-section of a GRP sewer pipe laminate: (A)protective, resin-rich outer layer, including chemically resistantpolyester resin and special C-glass tissue, or a polymeric tissue,followed by a layer of about 30% w/w chopped glass, i.e. arelatively high resin content; (B) main structural laminateconsisting of chopped roving, filament wound glass and quartzsand aggregate, together with anticorrosion grade polyesterresin; (C) inner lining, similar to (A).

dilute sulphuric acid

12.5 End view of a pipe is shown. The pipe is placed under constantstrain for a long time (typically several years), while filled withdilute sulphuric acid of pH about 1. A pipe joint may be includedin the test section. The acid simulates sewage in its action on thepipe.

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tendency to these viscoelastic responses is accentuated by solvent uptake,because the absorbed molecules plasticise the matrix. Tests focus on eitherthe effect of the environment on the long term deformation of the samplesunder load, or the possibility of creep rupture occurring. Such tests are normally individually designed to meet the requirements of the particularsituation. As with all tests involving the simultaneous application of a sustained load and a potentially corrosive liquid, suitable apparatus ispurpose built from corrosion-resistant materials, and ingenuity is needed tominimise testing costs.

12.10 Diffusion of liquids into composites

12.10.1 Qualitative considerations

Diffusion has great practical significance for composites. We need to knowhow much of a solvent diffuses into a composite material, how rapidly andto what extent. The amount of liquid absorbed is a useful but not an infal-lible indication of the magnitude of the change in mechanical properties.


0.6

0.5

0.4

0 0.2 0.4 0.6 0.8 1.0

0.36%

Log e

(%

wei

ght a

bsor

bed)

0.7

Compressive strain (%)

12.6 Showing the amount of methylene chloride absorbed in 28 daysat 23°C by carbon-fibre reinforced PEEK (quasi-isotropic APC-2,32 plies), under compressive strain. As the strain increases, thefree volume in the matrix decreases and the amount of solventabsorbed declines. After a certain strain level is reached, damageis caused around holes in the material. This causes an increasein solvent absorption.

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Diffusion of liquids into well-bonded composites occurs chiefly by activated diffusion, with very little contribution from wicking along fibres.The rate of diffusion is indicated by the diffusivity or diffusion coefficient.The presence of fibres means that the composite is anisotropic, and we haveto deal with several different diffusion coefficients. The reason why diffu-sion parallel with the fibre direction in unidirectional laminates is usuallyfaster than in other directions is probably simply a question of the simplic-ity of the diffusion path, although internal stresses cannot be entirelyneglected.

12.10.2 Diffusion equations

The general principles of the mathematics of diffusion have been given byprevious authors such as Crank and Park.20 The more recent account byComyn21 also deals with the principles. It is not practicable to summarisethe detailed arguments here, so only a few key equations will be mentioned.Fick’s first and second laws are given in Equations [12.4] and [12.5], and aregenerally considered as the starting point, although they are not obeyed bypolymers unless certain conditions are met, including, the requirement thatthe rate of diffusion of the permeant is slow compared with the polymersegmental mobility. The first law states that:

[12.4]

The second law introduces time as a parameter:

[12.5]

In these expressions Q is the rate of transfer per unit area of section (kgs-1 m-2), D is the diffusion coefficient (m2 s-1), C the concentration of dif-fusing material (kg m-3) and x the distance in the direction normal to theplane, with y and z referring to the other two directions.

When considering the passage of water through a laminate for which thethickness is small in relation to its other two dimensions, it is possible tosimplify Equation [12.5] by considering one direction (the x direction) only.This gives:

[12.6]

From these equations, more directly usable expressions can be obtained.Carter and Kibler12 give an expression for the mass of penetrant, Mt,

∂∂

∂∂

Ct

DC

x=

2

2

∂∂

∂∂

∂∂

∂∂

Ct

DC

xC

yC

z= + +Ê

Ëˆ¯

2

2

2

2

2

2

Q DCx

= -∂∂


MTA12 11/22/2000 1:49 PM Page 285

absorbed as a function of time, in terms of the equilibrium absorption valueM•. A commonly cited version of that expression is:

[12.7]

where Mt is the mass uptake by the material, M• is the mass uptake at equilibrium and h is the sample thickness.

The curve corresponding to this equation can be divided into two parts,see Fig. 12.7(a). It is linear up to a weight gain of 0.6 Mmax, and it is pos-sible to derive a useful expression for the linear section:

[12.8]

where D is the diffusion coefficient, t is time and M1 and M2 are any twomass uptake values corresponding with times t1 and t2, respectively. The dif-fusion coefficient can then be calculated.

A material with classical Fickian behaviour will absorb a liquid as shownin Fig. 12.7(a). The diffusion of a liquid into a polymer matrix frequently,but not invariably, follows the Fickian relationship with time. The diffusiv-ity can be calculated from the initial slope, and the amount of liquid sorbedin a given time can be deduced for different geometries. Fickian behaviourrequires the initial linearity to be sustained until about 60% of the sorptionhas occurred. The sorption and desorption curves are superimposable, forconstant diffusivity. Diffusion coefficients obey an Arrhenius relationshipwith temperature. Some of the many possible deviations from Fickianbehaviour are shown in Fig. 12.7(b).

Diffusion occurs even in the complete absence of microcapillary chan-nels, as a consequence of the ability of sufficiently small molecules to travelthrough the free volume between the atoms of the organic phase by dis-crete jumps. Whether Fickian or anomalous diffusion occurs depends atleast in part on the frequency of these solvent molecular jumps relative tothe frequency of the macromolecular segmental motions of the resin. Bothfrequencies are temperature dependent.

The solvent absorbed into glass- or carbon-fibre composites has to beaccommodated in the matrix free volume, microvoids or debonded inter-faces. Assuming that there is not an excess of voids or debonded interfaces,the majority of the diffusing substance is accommodated either in the pre-existing free volume or in new matrix space created by swelling stresses.The time taken for swelling stresses to increase the available space dependson the nature of the polymer and can be considerable. Sometimes a plot ofmass uptake against time, or the square root of time, shows a second

DhM

M Mt t

= ÊË

ˆ¯

-( )-( )

ÊË

ˆ¯•

p4

22 1

2 1

2

M Mn

eD n t

ht

n

n

= -+( )

- +( )ÊËÁ

ˆ¯

•=

=•

Â18 1

2 1

2 12 2

2 2

20P

P


MTA12 11/22/2000 1:49 PM Page 286

plateau, as additional space for incoming permeant is eventually madeavailable, as is shown in curve C of Fig. 12.7(b). This means that diffusionexperiments which do not allow sufficient time for the second plateau effectto take place can be misleading about the final equilibrium solubility.Laminates which bear some relation to real materials are usually thick,and the diffusion process takes considerable time to complete. In the case of fibre-reinforced resins, where the second plateau also occurs, an alternative explanation has been mentioned by Morii et al.22 They suggestthat glass filament bundles become gradually loosened through inter-face debonding. Another reason could be the progressive formation of


Mmax

M2

M1

Moi

stur

e ab

sorp

tion,

M (

%)

t 11/2 t2

1/2

Square root of time, t 1/2

(a)

Mas

s up

take

, Mt

Square root of time

C

A

B(b)

12.7 (a) Classical Fickian diffusion behaviour. (b) The three curvesshow departures from Fickian behaviour: (A) pseudo-Fickian, witha short linear portion and anomalous dependence on specimenthickness; (B) sigmoid; (C) two-stage, where equilibrium appearsto have been achieved but further sorption occurs later.

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microvoids through damage induced by chemical or physical processes, butthis is uncommon.

The free volume, and hence the diffusion coefficient, is increased by atensile stress, reduced by a compressive stress and hardly changed by a flexural stress, since this involves both tensile and compressive modes inopposition to each other. In general, free volume increases with increasingtemperature, but for polar polymers within certain temperature ranges, it isfound to increase on cooling.23 Thus a lowering of the water temperaturemeans an increase in water absorbed, even though the equilibrium, ormaximum level, has already apparently been reached. This phenomenonoccurs below Tg; the polymer retains its capacity to accommodate water, asa result of polar interactions acting to keep the structure like a rigid cage.The cage concept also explains why solvent uptake tends to be high withmatrix resins of high Tg.

12.11 Classification of absorption categories

A classification of absorption types, together with criteria for Fickian behav-iour, is given by Marom24 and is summarised below.

For Fickian diffusion:

• Both sorption and desorption curves are linear functions of the squareroot of time in the initial stage.

• Beyond the linear portion, both absorption and desorption curves areconcave to the abscissa.

• The sorption behaviour obeys the film thickness scaling law, i.e. reducedsorption curves with an abscissa of t0.5/h are superimposable for films ofdifferent thicknesses.

• When D is constant, the absorption and the desorption curves coincideover the entire range of t.

• The temperature dependence of D can be expressed by the Arrheniusrelation:

[12.9]

where the pre-exponential term, D0, is the permeability index, E is the activation energy of the diffusion process and R is the gas constant.

Some anomalies in diffusion behaviour are:

• Pseudo-Fickian behaviour: the sorption and desorption curves when plotted against t0.5 show anomalously short initial linear portions, and/or the sorption curves depart from the film thicknessscaling law.

D DE

RT=

-ÊË

ˆ¯0

0exp


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• Sigmoid behaviour: the sorption curves are sigmoid in shape, with asingle inflection point at about 50% equilibrium sorption.The initial rateof desorption exceeds that of sorption, but desorption then becomesslower and the curves cross.

• Two-stage sorption behaviour: The initial uptake is rapid and a linearfunction of t0.5. The sorption curve then approaches a quasi-equilibrium,followed by a slow approach to a final true equilibrium.

In general, the mass of permeant absorbed is a function of time raised toa power n, which is 0.5 for Fickian diffusion, less than 0.5 for pseudo-Fickianbehaviour, between 0.5 and 1 for anomalous diffusion, 1 for ‘Case 2’ diffu-sion and more than 1 for ‘super Case 2’ behaviour. (Both the penetrant mol-ecules and the polymer molecules are in constant motion. The polymermolecules are too long to move as a whole; only segments or sections canmove at a time. The mode is called Case 1 if the rate of diffusion of the penetrant molecules, that is, the frequency of the molecular jumps, is muchless than the frequency of oscillation or relaxation of the segments of thepolymer chain molecules. Case 2 is the opposite situation.)

12.12 Edge corrections

In practice, the use of one-dimensional equations for Fickian diffusion intothick samples, such as structural composites, is common, but it can intro-duce significant errors. There are various ways to minimise such errors:

First, use only very thin samples (this is not possible with most laminatedmaterials), so that diffusion through the edges can be neglected by com-parison with diffusion through the major surfaces. If the sample length andwidth are of the same order of magnitude and the thickness is smaller thaneither of the other two by two orders of magnitude, the true diffusion co-efficient will lie within 5% of the measured diffusion coefficient and no cor-rection is required.25

Second, use geometrical correction equations such as that attributed toShen and Springer:26

[12.10]

where Dm is the diffusion coefficient from measured data, Dt is the true dif-fusion coefficient, h is the sample thickness, l is the sample length and w isthe sample width.

The method ignores diffusion through the perpendicular sample facesand treats diffusion through each pair of opposing surfaces additively.However, this assumption will only hold true for exposure times so shortas to be experimentally useless, because there is increasing congestion at

D Dhw

hlt m= + +Ê

Ëˆ¯

-

12


MTA12 11/22/2000 1:49 PM Page 289

the corners of the specimen. Rothwell and Marshall27 have also addressedthe problem. They do not assume that the interaction of the different sides can be neglected, but attempt to treat the three-dimensional diffusioncase:

[12.11]

where

and W1/W0 is the fractional weight gain, below which data are used to fit astraight line.

For short exposure times (when W1/W0 << 1) the edge correction factorreduces to that proposed by Shen and Springer.

Third, follow Blickstad et al.,28 who discussed the correction of gravi-metric data on moisture absorption in carbon-reinforced epoxy resins, andpointed out the need to use the three-dimensional solution to Fick’s equa-tion. A similar method is proposed by Grayson25 in a paper that describeshow a progressive numerical treatment is used to obtain the gravimetricdata for a one-dimensional sample, which is then used to calculate the dif-fusion coefficient. The procedure for applying Grayson’s edge correctionmethod is as follows:

1 Obtain a value of the diffusion coefficient, Dm, from the measured gravi-metric data using Equation [12.8].

2 Use Dm and the sample dimensions to calculate an edge correction ratio,Rc, for each exposure time from the relationship:

[12.12]

where F(h,D,t) is the fractional weight gain as a function of time for the one-dimensional case, calculated from Equation [12.7], andF(h,w,l,D,t) is the three-dimensional fractional weight gain calculatedfrom the three-dimensional equation.

3 Correct the measured gravimetric data by multiplying each measuredfractional weight gain by its corresponding edge ratio.

RF h D t

F h w l D t=

( )( )

, ,, , , ,

Chwl

=2

Bhl

hw

hwl

= + +2

Ahw

hl

= + +1

D D ABWAW

CA

WWt m= - + Ê

Ëˆ¯

È

ÎÍ

˘

˚˙

-34

35

1

02

1

0

2 2


MTA12 11/22/2000 1:49 PM Page 290

4 Obtain a new value of the diffusion coefficient, D1, from the edge cor-rected gravimetric data.

5 Repeat steps 1–3 until the difference between Dn and Dn-1 is as small asdesired. The subscript n is an integer that refers to the number of timesthe correction cycle has been applied.

As this process is repeated, the calculated value of the diffusion coefficient will approach that of a sample of thickness h, and infinite area.The disadvantage of this method is the lengthy iterative calculationsrequired.

References

1. M A French and G Pritchard, ‘Environmental stress corrosion of hybrid fibrecomposites’, Composites Science and Technology, 1992 45 257–63.

2. Zhao Jiaxiang, Din Kunhe and Wei Jinxian, ‘The thermophysical and thermalshock resistance properties of carbon-carbon composites’, Proceedings ofICCM-6, London, eds FL Matthews, NCR Buskell, J M Hodgkinson and J Morton, Elsevier Applied Science, 1987, Volume 4, 394–400.

3. J L Thomason, ‘The interface region in glass fibre-reinforced epoxy resin composites: 1. Sample preparation, void content and interfacial strength’,Composites, 1995 26 467–75.

4. J L Thomason, ‘The interface region in glass fibre-reinforced epoxy resin composites: 2. Water absorption, voids and the interface’, Composites, 1995 26477–85.

5. J L Thomason, ‘The interface region in glass fibre-reinforced epoxy resin composites: 3. Characterization of fibre surface coatings and the interphase’,Composites, 1995 26 487–98.

6. K A Kasturiarachchi and G Pritchard, ‘Scanning electron microscopy of epoxy-glass laminates exposed to humid conditions’, Journal of MaterialsScience, 1985 20 2038–44.

7. D Santrach and R Matzeg, ‘FRP corrosion resistance: the role of the glass fibertype’, Paper 1-A, 46th Annual Conference, Composites Institute, SPI, Washing-ton, DC, 1991.

8. Q Qiu and M Kumosa, ‘Corrosion of E-glass fibers in acidic environments’,Composites Science and Technology, 1997 57 497–507.

9. G L Hart, The Chemical Stability of Carbon Fibres and their Composites, PhDThesis, Kingston Polytechnic (now Kingston University), Surrey, UK, 1975.

10. F N Kelley and F Bueche, ‘Viscosity and glass transition temperature relation-ships for polymer-diluent systems’, Journal of Polymer Science, 1961 50 549–56.

11. E L McKague, J D Reynolds and J E Halkias, ‘Swelling and glass transition rela-tions for epoxy materials in humid environments’, Journal of Applied PolymerScience, 1978 22 1643–54.

12. H G Carter and K G Kibler, ‘Langmuir type model for anomalous moisture dif-fusion in composite resins’, Journal of Composite Materials, 1978 12 118–31.

13. G Pritchard, ‘Anti-corrosion polymers: PEEK, PEKK and other polyaryls’,RAPRA Review, Report Number 80, RAPRA Technology, Shawbury,Shropshire, UK, 1995, Volume 7(8).


MTA12 11/22/2000 1:49 PM Page 291

14. B D Caddock, K E Evans and D Hull, Proceedings of the 2nd Conference on Fibre Reinforced Composites, Paper C25–86, Liverpool University, UK, Insti-tute of Mechanical Engineers, Mechanical Engineering Publications, 1986.

15. G Pritchard, ‘The chemical reactivity of carbon fiber-reinforced compositematerials’, Polymer-Plastics Technology Engineering, 1975 5(1) 55–81.

16. M A French and G Pritchard, ‘The fracture surfaces of hybrid fibre composites’,Composites Science and Technology, 1993 47 217–23.

17. R D Currie, ‘Manufacture, testing and installation of centrifugally cast pipes’,Pipecon: Conference on Large Diameter Glass Reinforced Plastic Pipes, Paper12, Fibreglass Ltd/Amoco Chemicals SA, London, 1980.

18. A Fahmy and J C Hurt, ‘Stress dependence of water diffusion in epoxy resins’,Polymer Composites, 1980 1(2) 77–80.

19. G Pritchard and S J Randles, ‘The combined effect of mechanical stress andchemical environments on carbon-fibre reinforced PEEK laminates containinga circular hole’, Proceedings of ICCM-10, Whistler, BC, Canada, eds A Pour-sartip and K Street, Woodhead Publishers, Cambridge, UK, 1995, Volume 6,265–72.

20. J Crank and G S Park, Diffusion in Polymers, London/New York, AcademicPress, 1968.

21. J Comyn (ed), Polymer Permeability, London, Elsevier Applied Science, 1985.22. T Morii, T Tanimoto, H Hamada, Z-I Maekawa, T Hirano and K Kiyosumi,

‘Relation between weight changes and bending properties of GFRP panelsimmersed in hot water’, Polymers and Polymer Composites, 1993 1(1) 37–44.

23. M J Adamson, ‘Thermal expansion and swelling of cured epoxy resin used ingraphite/epoxy composite materials’, Journal of Materials Science, 1980 151736–45.

24. G Marom, ‘The role of water transport in polymer materials’, in Polymer Permeability, ed J Comyn, London, Elsevier Applied Science, 1985, Chapter 9.

25. M A Grayson, ‘An improved method of correcting diffusion coefficients fromgravimetric data for edge effects’, Journal of Polymer Science, Part B, PolymerPhysics, 1986 24 1747–54.

26. C H Shen and G S Springer, ‘Moisture absorption and desorption of com-posite materials’, Journal of Composite Materials, 1976 10 2–20.

27. W S Rothwell and H P Marshall, Analysis of Experimental Transport Data:Diffusion of Water in EPDM, LMSC-D566642, 1977.

28. M Blikstad, P O W Sjoblom and T R Johannesson, ‘Long term moisture absorp-tion in graphite/epoxy angle ply laminates’, Journal of Composite Materials,1984 18 32–46.


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13.1 Introduction

The implementation of composite materials in structural applications hasinvolved the fabrication of costly prototypes and large scale experimentalverification of certain design concepts. An alternative method of under-standing and predicting the response of composite structures under avariety of loading conditions is through the use of scale model testing.

Scale model testing requires that the relationships between the responsesof the small scale model and full-size component be known so that thebehaviour of the model can be used to predict the response of the full-sizecomponent. The relationships between the responses can be obtainedthrough applied mechanics formulations. However, the presence of physi-cal constraints can prevent the complete reproduction of certain responsesin small scale models. Responses subject to such physical constraints orscaling conflicts include rate-dependent and notch-sensitive behaviours.1,2

Furthermore, the mechanics formulations are still evolving for advancedmaterials and may not provide the scaling relationships at the local mate-rial level necessary to relate all aspects of the response throughout the sizerange.

The problem of designing, building and testing a scale model structureconstructed of fibre-reinforced composite materials is a challenging one.Complications may arise from factors by which standard similitude lawscannot be satisfied. Such factors are fabrication, fibre diameter, fibre/matrixinterface, ply interface and test method. If these limitations are ignored, oneis left with two obvious scaling options for laminated composites:3,4

• ply-level scaling• sublaminate-level scaling.

Ply-level scaling is achieved when a large scale laminate, with a givenstacking sequence, is constructed from thick layers of the same fibre orien-tation, each built from a number of standard thickness plies. On the otherhand, sublaminate-level scaling is achieved by the introduction of basic sub-

13Scaling effects in laminated composites

C SOUTIS

293

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laminates which are stacked together to form thicker laminates. Forexample, (+45/-45/0)S and (+454/-454/04)S are said to be scaled at a ply level,whereas (+45/-45/0)S and (+45/-45/0)4S are said to be scaled at a sublami-nate level, where (+45/-45/0) is the sublaminate.

In the following sections three approaches to scale-up law developmentare outlined, the applicability and limitations of the existing methods aresummarised and practical application examples are presented.

13.2 Background

At least three approaches to a study of scaling are available. The firstinvolves the use of dimensional analysis and similitude principles to definethose non-dimensional groups of geometric and material variables whichgovern the response of scale models. The non-dimensional parameters maybe derived either from the governing equations and boundary conditionsor from the Pi theorem. Both techniques are described and the advantagesand disadvantages of each are discussed by Baker et al.5 The Pi theorem isthe more general method of the two and consists of identifying the impor-tant physical variables relevant to the problem under consideration. Eachvariable is represented dimensionally in terms of a fundamental set of units,typically either the force–length–time (F-L-T) system or the mass–length–time (M-L-T) system. From these parameters, an experimental programmecan be defined using a number of scaled specimens to permit validation ofthe scaling parameters and to identify any scale effects or non-scaled behav-iour. This approach has been successfully employed with composite struc-tures in studies of transverse impact of beams,1 tensile strength4 and thestatic and dynamic responses of eccentrically loaded beam columns.6,7 Asecond approach is more mechanistic in nature; here, a scale effect is iden-tified as a departure of the response from a known mechanics model, whichoccurs systematically with specimen size. In contrast to the similitudeapproach, the mechanistic approach permits selective scaling or the evalu-ation of the response as a subset of the material, and/or geometric para-meters are varied. This approach may be preferred when there are manyvariables involved in characterising the response, and when it is desired todetermine the sensitivity of the response to the change in individual vari-ables.1 An obvious difficulty with this approach is the need to separategenuine scale effects from any inadequacies in the mechanics model beingused. Finally, the scale effect in failure of composite structures can also beanalysed using statistical methods, particularly Weibull distributions.8–10

13.3 Investigation of failure

Scale model testing is a practical and efficient alternative to full-scaletesting for determining the structural response of most composite lami-


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nates. However, if the testing involves damage or failure of the structure,then the absolute size of the specimen will have a tremendous influence onthe failure behaviour and ultimate strength of the structure. Compositematerials are often used to build thin, high stiffness structures which rou-tinely operate under large deflections and high design loads. If tests on sub-scale specimens are used to determine ultimate loads for these types ofdesign, then the strength of prototype structures may be seriously over-estimated owing to the scale effect in failure.

A large difference in failure loads, strains and end-displacement ratioshas been observed2 between scale models of an eccentrically loaded beamcolumn, Fig. 13.1.The size effect in strength which is observed on the macro-scopic level is the result of damage on the microscopic level which initiateswithin the laminate and develops in a particular manner under the appliedload. The accumulation of damage and interaction of failure mechanismseventually result in the ultimate failure of the structure. It was concluded2

that a detailed investigation of the effect of test specimen size on failureneeds to be addressed on a material level before the phenomenon can beunderstood on the macroscopic level.

Results of applying maximum stress, maximum strain and Tsai-Wu tensorpolynomial failure criteria demonstrated that these criteria cannot predicta difference in strength based on the absolute size of the specimen, see Figs.13.2 and 13.3. For the unidirectional layup, Fig. 13.2, the predicted strengthis conservative, while for the cross-ply laminate the predicted load ratio atfailure is higher than the experimentally observed values, Fig. 13.3. In Fig.13.4 the load ratio is plotted as a function of the scale factor for several lay-ups.2 If no scale effect in strength was present, then all of the data wouldfall on the line drawn at 1.0. The plot indicates that a scale effect is evidenteven between the full and 5/6 scale beams. The effect increases as the sizeof the beam decreases. The unidirectional laminates appear to be least sen-sitive to the effect in strength, although the effect is still observed.

Other researchers10–12 have attempted to model the scale effect instrength of fibre-reinforced composites using either a statistical approachor a fracture mechanics model. These methods and their application to theeccentrically loaded beam column and uniaxially stressed laminates are discussed in the following sections.

13.3.1 Statistical approach

The application of statistical techniques for modelling the size effect instrength of brittle materials is based on the observation that these materi-als are flaw sensitive. Since the presence of imperfections can be describedstatistically in nature, it is reasonable to assume that larger specimens willexhibit a lower strength simply because the probability is higher that astrength-critical flaw, such as a void or crack, is present in the greater

Scaling effects in laminated composites 295

MTA13 11/22/2000 1:52 PM Page 295

volume of material. Basically, two approaches are available to model thesize effect. The ‘weakest link’ theory assumes that a structure consists of anumber of individual elements arranged in series. When one of these ele-ments fails, the entire component fails. In contrast, the ‘bundle theory’models a structure as a parallel arrangement of elements. When an element


Top platen

Upper hinge

Scaled beam specimen

Lower hinge

Load platform

Bottom platen

Front view Side view

Gau

ge le

ngth

(G

L)

2/3

GL 1/2

GL 1/4

GL

Longitudinal straingauge (back-to-back)

Strain gauge rosette(back-to-back)

13.1 Schematic of front and side views of the eccentrically loadedbeam column.2

MTA13 11/22/2000 1:53 PM Page 296

fails, the load is redistributed among the remaining elements. Final failureoccurs when all of the elements have failed. Weibull statistical theory hasbeen applied to both the weakest link and bundle theories to develop math-ematical models for predicting the scale effect in strength. The ultimatefailure of individual carbon fibres and fibre bundles has been successfullymodelled using Weibull statistics based on the weakest link theory.13 Sub-


Unidirectional 1/4 and fullscale0.8

0.6

0.4

0.2

0.0

Load

/Eul

er lo

ad

Full

1/4

Analysis (failure location)

0.80.60.40.20.0 1.0

End displacement/length

13.2 Predicted failure location for unidirectional laminates.2

Cross ply 1/4 and full-scale0.8

0.6

0.4

0.2

0.0

Load

/Eul

er lo

ad

Full

1/4

Analysis (failure location)

0.80.60.40.20.0 1.0

End displacement/length

13.3 Predicted failure location for cross-ply laminates.2

MTA13 11/22/2000 1:53 PM Page 297

sequently, this model has been applied by other researchers to investigatethe scale effect in strength of composite test specimens.

Statistical analysis has been used to explain the higher strength seen incomposite specimens tested in flexure over those tested in uniaxialtension.9,10 Using Weibull theory, Bullock10 showed that the probability thata specimen containing a distribution of flaws throughout its volume couldsurvive an applied stress distribution, s(x,y,z), is Equation [13.1]:

[13.1]

where PS is the probability of survival, s0 is the characteristic ultimatestrength of the unit or reference volume and m is the Weibull shape para-meter. s0 and m are material properties; the characteristic strength has aprobability of survival PS = e-1 = 0.37. The risk of failure, l, the exponent ofe, is called the ‘stress–volume integral’. If smax is the maximum value of theapplied stress through the component and v is the total volume, Equation[13.1] may be written in terms of dimensionless ratios14 as:

[13.2]

The ratio, vc = s0/smax, is a safety factor referred to the characteristic strengthof the reference volume and is called the ‘central safety factor’. The dimen-sionless variable s/smax is independent of the volume for an elastic analy-

ln max

max1

0P

Vv

vV

m

v

m

sd

= = ÊË

ˆ¯

ÊË

ˆ¯Úl

ss

ss

P vv

m

s d e= - ÊË

ˆ¯

È

ÎÍ

˘

˚˙ =Ú -exp

ss

l

0


2.0

1.5

1.0

0.5

Nor

mal

ised

failu

re lo

ad

0.0 0.2 0.4 0.6 0.8 1.0

Scale factor

13.4 Normalised failure load ratio versus scale factor.2 +, uni-directional; ¥, angle ply; �, cross ply; �, quasi-isotropic.

MTA13 11/22/2000 1:53 PM Page 298

sis; that is, geometrically similar structures will have the same stress–volumeintegrals for any volume. Equation [13.2] can be written as:

[13.3]

or

[13.4]

Equation [13.3] states that for a specified central safety factor, stress distri-bution and volume, the probability of survival or the probability of failurePf = 1 - PS may be calculated. According to Equation [13.4], for a specifiedsafety level, the required central safety factor, vc may be calculated.

13.3.1.1 Design examples

13.3.1.1.1 Axial tension or compression

If a uniaxial force, F, is applied to a bar with cross-sectional area A, see Fig. 13.5, the stress in the bar is uniform: s = F/A = constant = smax and theprobability of a failure is:

[13.5]Pv

A v

v

m

mfc c

= - -ÊË

ˆ¯

È

ÎÍ

˘

˚˙ = - -

ÈÎÍ

˘˚˙1

1 11

1exp exp

vP

Vv

vV

v

m m

cs

d= Ê

Ëˆ¯

ÏÌÓ

¸˝˛

Ú11

1

ln max

ss

lnmax

11

Pv

Vv

vV

m

v

m

sc

d= Ê

Ëˆ¯

ÊË

ˆ¯Ú

ss


P

A

Vl

P

13.5 Reliability of a bar with a cross-sectional area, A, under tension.14

MTA13 11/22/2000 1:53 PM Page 299

Equation [13.5] can be used to illustrate the size effect. If two differentvolumes, V1 and V2, under uniform stress, have the same reliabilities (Ps1 =Ps2):

[13.6]

then [13.7]

or [13.8]

Assuming that the volume stressed V2 = 8V1 and m = 16, then, according toEquation [13.8], the strength of the bigger specimen will be reduced bymore than 12% (that is, s2 = 0.878s1). Under uniaxial compression both theapplied stress and the compressive strength of a reference volume are neg-ative and the same relations apply.

The ratio of strengths therefore depends on the relative volumes and theWeibull modulus, m, which is a measure of material variability and isapproximately related to the coefficient of variation (CV) of individualspecimen strengths by the relation m = 1.2/CV. A highly variable materialwill have a low value of m, and would be expected to give a high amountof scatter in specimen strengths and a large size effect. The theory there-fore predicts a direct correlation between strength variability and sizeeffect. Weibull theory satisfactorily explains the size effect in brittle mate-rials; however, its application to composite materials is not entirely clearand special care should be taken when it is applied. Composites are notcompletely brittle materials, but are often able to sustain quite significantdamage before final failure.

13.3.1.1.2 Three-point flexure

For the case of three-point bending loading conditions the stress distribu-tion is non-uniform and Equation [13.1] is expressed as:

[13.9]

where the subscript f is used to identify flexural loading. For two geomet-rically similar specimens (a model and a prototype) of volumes Vm and Vp

the ratio of ultimate strengths for a given probability of failure is given by:

[13.10]ss

m

p

p

m= Ê

Ëˆ¯

VV

m1

P Vm

m

sf ff

0= - Ê

Ëˆ¯ +( )

ÊËÁ

ˆ¯

È

ÎÍ

˘

˚˙exp

ss

1

2 12

ss

2

1

1

2

1

= ÊË

ˆ¯

VV

m

- ÊË

ˆ¯ = - Ê

Ëˆ¯V V

m m

11

02

2

0

ss

ss

P V P Vm m

s1 s2and= - ÊË

ˆ¯

È

ÎÍ

˘

˚˙ = - Ê

Ëˆ¯

È

ÎÍ

˘

˚˙exp exp1

1

02

2

0

ss

ss


MTA13 11/22/2000 1:53 PM Page 300

Equation [13.10] is the same as that under uniaxial tension. The ratio ofmedian failure stress in three-point flexure to that in tension is found bysetting Pst equal to Psf in Equations [13.6] and [13.9]:

[13.11]

If two specimens of equal volume are tested in flexure and in tension, thenby Equation [13.11], the flexural strength will be greater than the tensilestrength by a factor:

[13.12]

using m = 16 then sf = 1.45st, the strength of the beam is 45% greater thanthat of the tension component owing to stress non-uniformity.

Bullock10 applied the statistical analysis presented in Equations [13.1] to[13.12] to predict the strength behaviour of carbon-epoxy (T300/5208) com-posite specimens. Tests were conducted on fibre tows and tensile and flex-ural specimens to verify the analysis. An important finding from Bullock’sresearch is that the flaw-density exponent, m, which must be determinedempirically, was found to be a material constant. For the T300/5208 thevalue of flaw-density exponent was found to be 24. Bullock showed goodagreement between experiment and analysis and concluded that less expen-sive flexural specimens which are easier to test can be used to estimate ulti-mate tensile stresses of composite materials.

While Bullock’s results show promise for predicting the ultimate strengthof specimens which are tested under different conditions, the volume termwas found to underestimate the actual volume effect for specimens ofgreatly different sizes. A limitation of the method includes the requirementthat the flaw-density exponent be found empirically for each materialsystem. Also, no data were presented to indicate how well the model wouldperform for laminates containing off-axis plies. The flaw-density exponent,m, would be most likely to be influenced by the laminate stacking sequence,especially for laminates in which failure mechanisms were matrix domi-nated and not governed by fibre fractures.

The volumetric model given by Equation [13.9] was used by Jackson2 topredict the scale effect in strength observed in the failure response of eccen-trically loaded beams, see Fig. 13.1. The flaw-density exponent was foundempirically to be equal to 7.75 and was used in Equation [13.9] to predictthe scale effect in tensile strength of AS4/3502 unidirectional and multidi-rectional laminates. As shown in Fig. 13.6, the volumetric ratio predicts thescale effect fairly well for the unidirectional and quasi-isotropic laminates.However, agreement between the volumetric ratio and the angle-ply andcross-ply laminates is not good. This is not unexpected, since the failure

s sf t= +( )[ ]2 12

1

m m

ss

f

t

t

f= +( )È

ÎÍ˘˚

2 12

1

mVV

m


MTA13 11/22/2000 1:53 PM Page 301

mechanisms for the angle-ply and cross-ply laminates are characterised bytransverse matrix cracking, but the flaw-density exponent was determinedbased on tests of unidirectional laminates which fail by fibre breakage.Obviously, the volumetric ratio is sensitive to the failure mode and shouldonly be applied for laminates which exhibit similar failure mechanisms.

In summary, results indicate that the Weibull statistical model based onthe weakest link theory has been successful in predicting scale effects;however, it relies on empirical data to determine the Weibull shape andscale parameters.Also, the model lacks the sophistication needed to predictthe difference in magnitude of the scale effect in strength for laminateswhich do not fail predominantly by fibre fracture.

13.3.2 Fracture mechanics theories

Elementary approaches to scaling indicate that under scaled loading con-ditions the stress state in the model is identical to that in the prototype, thatis, stress scales as unity. Ideally, failure should occur at the same stress andstrain levels for both the model and the full-scale specimens. However, asseen in the previous sections, deviations from this elementary approach tostrength scaling are observed. Scale models constructed from brittleisotropic materials typically predict higher failure loads than the full-scaleprototypes when the data are scaled up for comparison. Another explana-tion for this size effect in strength is based on the principles of linear elastic


5

4

3

2

1

0

0.0 0.2 0.4 0.6 0.8 1.0

Scale factor

Nor

mal

ised

failu

re s

tres

s

13.6 Comparison of the volumetric ratio prediction of normalisedfailure tensile stress versus scale factor and experimentalresults.2 +, unidirectional; ¥, angle ply; �, cross ply; �, quasi-isotropic; —, volumetric ratio.

MTA13 11/22/2000 1:53 PM Page 302

fracture mechanics (LEFM).A scaling conflict for stress is introduced whenthe critical stress intensity factor, Kc, is introduced in a dimensional analy-sis;11 the stresses in the region near a sharp crack in a body have beenderived by Irwin15 and have the general form:

[13.13]

where K is the crack tip stress intensity factor (SIF), r and q are polar coordinates to locate a point in the stress field beyond the crack tip and fij

is a non-dimensional function of the variable q; this crack tip stress field isindependent of the loading. Thus, all cracks will have the same stress fieldand will only differ by the intensity factor, K, from one problem to the next.

In the fracture mechanics approach, a critical SIF is defined as the pa-rameter that governs the onset of unstable crack growth, rather than amaximum stress or strain at failure. Since composites often exhibit brittlefracture, it is reasonable to include a variable such as the critical SIF tomodel the fracture behaviour. The critical stress intensity factor is gener-ally assumed to be a material property which is independent of loading con-ditions, initial crack geometry and size, or any other parameter. As such, Kc

should have the same value for both the model and the prototype and,therefore, scale as unity. However, a dimensional analysis including the SIFas a variable4,6 requires that Kc be scaled in proportion to l1/2. Since thiscondition is violated when the geometric scale factor is 1, the stress at ini-tiation of unstable crack propagation scales as l-1/2.Thus, the stress requiredto propagate a crack in a linear elastic model, sm,, will be greater by a factorl-1/2 than the stress needed to propagate a crack in a geometrically and con-stitutively (homologous stress–strain behaviour in the model and prototypesystems) similar prototype, sp:

[13.14]

where l is a geometric scaling factor (ratio of model to full scale dimen-sion). According to Equation [13.14], the stress for crack propagation in a1/4 scale structural model will be twice the value required for the full scalestructure. Consequently, the model will appear twice as strong.

Predicted failure stresses using this fracture model are shown in Fig. 13.7,along with tensile strength experimental data for several AS4/3502 carbon-epoxy laminates.2 The fracture ratio tends to overpredict the scale effect instrength for the smaller scale unidirectional and quasi-isotropic laminatesand underpredicts the effect for the angle-ply and cross-ply laminates. Thecross-ply laminate response deviates from the fracture ratio model by thelargest amount, especially for the smaller scale model specimens. In general,

ss

lmp=

sp

qij ijK

rf= ( )

2


MTA13 11/22/2000 1:53 PM Page 303

the fracture ratio is capable of predicting a scale effect in strength; but, likethe volumetric model, the fracture model does not predict any variation in the scale effect owing to differences in laminate stacking sequence.Results presented in Fig. 13.7 show that a model which predicts the scaleeffects in strength, in order to be successful, must incorporate some measureof the failure mechanism of the laminate.

13.4 Practical application examples

The applicability of classical dimensional analysis principles in compositestructural mechanics is assessed by examining two fundamental problems:16

• axial tension loading of a narrow laminate• buckling of a narrow laminated plate

These problems are selected to highlight two important parameters in thescaling of composites layup and stacking sequence. These parameters arenot relevant to the scaling of metallic structures but have significant effectsin scaling of composites. The applicability of classical dimensional analysisis illustrated in the following examples.

13.4.1 Example 1: axial tension loading

Consider a 24-ply baseline laminate of 25 mm width and subjected to ten-sile loading along the 0° direction. The laminate stacking sequence is


5

4

3

2

1

0

0.0 0.2 0.4 0.6 0.8 1.0

Scale factor

Nor

mal

ised

failu

re s

tres

s

13.7 Comparison of the fraction ratio prediction of normalised failuretensile stress versus scale factor and experimental results.2

+, unidirectional; ¥, angle ply; �, cross ply; �, quasi-isotropic; —, fracture ratio.

MTA13 11/22/2000 1:53 PM Page 304

[±45/02/±45/02/±45/90/0]S, which gives a (42/50/8) distribution of plies. Thelamina mechanical properties are: E11 = 129GPa, E22 = 13GPa, G12 =5.9GPa, n12 = 0.3, h = 0.13mm and ef = 1.1%. The calculated Young’smodulus in the loading direction is Exx = 68.8GPa. The strain response ofthe laminate can be approximated by:

[13.15]

where P is the applied load, n the number of plies, with h the ply thicknessand w the laminate width. To scale down the laminate and simulate thestrain response, two assumptions are made. First, it is assumed that sym-metry of the laminate is maintained and second, that the orthotropy of thelaminate is maintained throughout the scaling process. These assumptionsensure that Equation [13.15] holds true for all of the scaled-down laminates.

Now consider the failure load Pf based upon the maximum strain criterion. Equation [13.15] becomes:

Pf = nwhExef [13.16]

The failure load calculated for the baseline laminate is 61.84kN. For casesof constant modulus Ex, such as metals, the failure load would vary linearlywith the cross-sectional area of the specimen.This is shown by the solid linein Fig. 13.8. However, for composite plates the modulus Ex is a function ofthe thickness (number of plies) and the layup. Scaling in thickness by adding or reducing the number of plies gives rise to a nonlinear relation-

e = =P

AEP

nwhEx x


60

40

20

08 16 24

Laminate thickness (number of plies)

Fai

lure

load

(kN

)

13.8 Tensile failure load of a narrow composite plate as a function oflaminate thickness.16 Maximum strain criterion e = 0.011. Scalingdown from 24-ply [(±45/02)2/±45/90/0]N laminate. � denotespossible ply mix and stacking sequence for constant thickness.

MTA13 11/22/2000 1:53 PM Page 305

ship between the failure load and cross-sectional area. To illustrate thispoint, suppose that the laminate width is given a constant value of w =25mm while the number of plies is reduced. The failure loads will dependupon the type of plies (0, 45, 90) removed from the laminate. For example,if the baseline 24-ply laminate is reduced to 22 plies by removing two 0 plies, two 45 plies or two 90 plies, the corresponding failure loads are 79kN, 91.7 kN and 89kN, respectively. As the number of plies is reduced stillfurther, the possible failure loads are found to lie in an envelope centredabout the linear failure load versus cross-sectional area relationship asshown in Fig. 13.8.

13.4.2 Example 2: buckling of a narrow laminate

The second problem involves a narrow laminate under axial compressiveload. The buckling load for an anisotropic plate of this kind with clampedends and free edges is:

[13.17]

where L is the total length of the plate, D11 is bending rigidity in the loadingdirection and k is a constant equal to 1.0306 for the first buckling mode. Forisotropic material:

[13.18]

From Equation [13.17], the scaling parameters to be considered in this caseare L and D11. Because D11 depends on thickness, modulus and stackingsequence, this problem represents one higher level of complexity overExample 1. Consider the same 24-ply baseline laminate as in Example 1,with an unsupported length L = 76mm. The axial bending rigidity of theplate is 204 Nm. If the modulus is constant, as for metals, D11 varies withh3

tot, where htot is the total thickness. When the thickness is reduced to 22plies, the possible combinations of layup and stacking sequence, along withthe associated bending rigidity and buckling load, are given in Table 13.1.Figure 13.9 shows the buckling load as a function of laminate thickness.Thebuckling loads for the composite laminate fall in an envelope centred aboutthe solid curve, which is the buckling load versus thickness relationship fora constant modulus material. Figure 13.9 illustrates that scaling in com-posites, even for the simplest structural mechanics problem, involves morethan dimensional parameters. Because of the multiplicity of possible lami-nate constructions, structural mechanics methods of analysis must be usedto develop similitude rules.

DEh

11

3

212 1=

-( )n

N kL

Dcr = ÊË

ˆ¯

22

11p


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Similar results can be obtained for two-dimensional problems. The thick-ness, ply orientations and stacking sequence effects on bending of a rec-tangular composite plate under uniform lateral pressure is shown in Fig.13.10, which demonstrates how the structural response deviates from theclassical dimensional analysis results. The deviation is caused by the layupand stacking sequence effects on the plate rigidity parameters Dij. In com-paring the results of the two-dimensional (2-D) problem with that of one-dimensional (1-D), Fig. 13.10 shows a narrower band in the structuralresponse. This is because the results of the 1-D problem are affected onlyby the axial bend stiffness D11, whereas the results of the 2-D problem areaffected by all components of the in-plane mechanical properties. Theoverall effect of all four rigidity components (D11, D12, D22, D66) is less significant than that of a single component.


Table 13.1. Possible 22-ply laminates in Example 2.

Layup Stacking sequence Bending rigidity D11 Buckling load Ncr

(Nm) (Nm-1)

[45/02/±45/02/±45/90/0]s 177 800(45.5/45.5/9) [±45/02/45/02/±45/90/0]s 163 738

[±45/02/±45/02/45/90/0]s 156 705[±45/0/±45/02/±45/90/0]s 140 635

(36/55/9) [±45/02/±45/0/±45/90/0]s 151 682[±45/02/±45/02/±45/90]s 156 706

(45/55/0) [±45/02/±45/02/±45/0]s 156 707

40

30

10

08 16 24


Fai

lure

load

(kN

)

20

13.9 Buckling load as a function of laminate thickness.16 Scaling downfrom 24-ply [(±45/02)2/±45/90/0]S laminate. � denotes possible plymix and stacking sequence for constant thickness.

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13.5 Specialised scaling techniques in composites

The previous section discussed the difficulties in direct application of theprinciple of similitude in composites. It was also shown that a scale modelcan be designed with the aid of structural mechanics. In this section, an ana-lytical procedure to design scale models is presented. The procedure issimilar to the one presented by Deo and Kan16 and McCullers and Neberhans17 and is demonstrated below.

Consider an unstiffened composite cylinder of radius Rs, thickness hs andlength Ls.The scaling parameters significant to buckling can be divided intothree categories:

(a) Load parameters (load ratio, model/prototype) such that:

[13.19]

where Ncr is the buckling load per unit length around the cylinder circum-ference.

(b) Geometric parameters:

Length ratio [13.20]

Radius ratio [13.21]

Thickness ratio [13.22]hhhr

m

p=

RRRr

m

p=

LLL

= m

p

PNNr

cr m

cr p

=( )( )


300

200

100

08 16 24


Fai

lure

pre

ssu

re q

f

13.10 Failure pressure of a rectangular plate as a function of platethickness.16 � denotes possible ply mix and stacking sequencefor constant thickness.

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(c) Property parameters:

Modular ratio [13.23]

Rigidity ratio [13.24]

The load parameter Pr is a predetermined design factor for the model.The load requirement for the test model is usually higher than the actualstructure. In the case where the exact buckling load of the structure is tobe simulated, Pr = 1.0.

The geometric and property parameters interact when buckling is con-sidered. For composite structures, the property parameters are usually notunique because of the anisotropy of the materials. These parameters arealso affected by the thickness parameter because of the ply orientations.Therefore, it is not possible to establish a simple scaling law for compositestructures as discussed in the previous section. In this analysis, the scaledmodel is designed using an iterative procedure. The solution for symmetricbuckling of an isotropic cylinder is first used to estimate the key scalingparameters.The buckling load of an isotropic cylinder with R >> h is given18

as:

[13.25]

Based on this expression, the key scaling parameters can be written as:

[13.26]

[13.27]

[13.28]

[13.29]

Assuming that the test model is fabricated from the same material as thefull-scale structure, then the Poisson ratios nm = np, and the stiffness (rigid-ity) ratio becomes:

Dr = Erhr3 [13.30]

Equation [13.25] indicates that the length parameter is an arbitrary numberif only buckling load is to be simulated. The length of the cylinder controlsthe buckling mode, but not the buckling load.

DR PE hr

r r

r r=

( )2

ER Ph Dr

r r

r r=

( )2

hR PE Dr

r r

r r=

( )2

RP

E D hrr

r r r= ( )1 1 2

NR

EDhcr = ( )2 1 2

DDDr

m

p=

EEEr

m

p=


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For composite cylinders, the scale parameters are first estimated usingEquations [13.26] to [13.30]. Then the following procedure is used:

• Define the load requirement (Pr).• Select the radius and length ratio (Rr, Lr). Since length has no signifi-

cant effect on the buckling load, assume Lr = Rr.• Maintain approximately the same axial Young’s modulus (Er = 1.0).• Estimate hr from Equations [13.27] and [13.30]: hr

2 = PrRr.• Based on the estimated hr, determine the practical thickness of the

model, hm; this practical thickness is determined based on the numberof plies.

• Determine the ply orientations; these should be similar to the full-scalestructure in the initial estimate, because Er = 1.0.

• Determine the laminate stacking sequence based on Dr given in Equa-tion [13.29], taking into account the practical rules for laminate stack-ing sequence.

• Conduct orthotropic buckling analysis to confirm Pr.• Perform iterations until the required Pr is obtained.

The following numerical example illustrates this procedure:16

Consider a full-scale cylinder 1140 mm in radius and 640 mm in length.The cylinder is made from AS4/3501, 18-ply [±45/02/±45/90/0]s laminate witha thickness of 2mm. A 1 :5 subscale model with a load requirement of Pr =1.5 is to be designed.

For the full-scale cylinder buckling:

[13.31]

The required buckling load for the subscale model is:

[13.32]

The dimension requirement gives Rm = 228mm, Lm = 127mm and hr =(PrRr)1/2 = 0.548 or hm = 0.548 ¥ 2 ª 1.1mm.

For the material considered, a 9-ply laminate is required, which hasnominal thickness of 1.1mm. For Er = 1.0, the percentage distribution of 0°, 45° and 90° plies for the 9-ply laminate is either (33.3/55.6/11.1) or(44.4/44.5/11.1). A [±45/02/90/02/±45]T is chosen in this example. A 228mmradius cylinder with this laminate results in a buckling load of 108 Nm- orPr = 1.4, which is below the load requirement of 1.5. Hence further itera-tion on the scale parameters is required. If the dimensional requirement (Rr

= 0.2) can be changed, then the load requirement can be met by reducingthe radius to 213mm. With this radius the buckling load increases to 116Nm-1 or Pr = 1.51 > 1.5. The final values for the subscale model are Rm = 213mm, Lm = 106.5mm and hm = 1.1mm.

To further scale down the structure, a cylindrical panel instead of a sub-

N N mcr m( ) = 115

N N mcr p( ) = 77


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scale cylinder can be considered. This requires determining the panel width(or central angle q), with all other parameters unchanged. Parametricstudies indicate that for simply supported cylindrical panels, the panel buck-ling load, Ncr

p is higher than that of a composite cylinder, Ncrc. However, the

panel buckling load approaches the buckling load of a complete cylinder asthe panel width increases. Beyond a minimum panel width, Ncr

p is within5% of Ncr

c as shown in Fig. 13.11.The minimum width depends on the radiusof the cylinder and can be determined analytically. For the example cylin-der discussed here, the minimum panel width is 120 mm or central angle q = 32.4°.

Figure 13.11 shows the effect of panel width on buckling load. It can beseen that the buckling load of the full-scale cylinder can be experimentallydetermined by testing a curved panel with a minimum width of 120mm. Itmay be noted that although the buckling load of a complete cylinder canbe simulated by a portion of a subscale cylinder (panel), the buckling modeis difficult to simulate.

13.6 Concluding remarks

Various analysis techniques have been presented and used to model scal-ing effects in composite laminates under static loading. A scale effect in strength is observed in unidirectional, angle-ply, cross-ply and quasi-isotropic layups. In general, the failure loads and strains increase as the scale factor decreases. This implies that data generated from tests on scale model specimens will overestimate ultimate loads of prototype structures.


B = 12.07 cm 1.05Ncr = 185.4 kMc

B

�

R

tq

010 20 30 40 50

80

160

240

Complete cylinderNcr = 176.6 kNc

NcrCurved panel

p

(�45/02/90/02/�45)T

SS edges

For B ≥ 12.07 cmNcr is within 1.05Ncr

cp

Panel width B (cm)

Pan

el b

uck

ling

load

Ncr

(kN

m-1

)p

13.11 Effect of panel width on buckling load.16

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Analysis of laminate failure using maximum stress, maximum strain andTsai-Wu tensor polynomial criteria shows that these theories cannot predictthe scale effect in strength.

The scale effect cannot be explained by simple statistical models basedon Weibull distributions of flaw densities and the weakest link approach, orby fracture mechanics models based on the critical stress intensity factor.Both of these approaches can predict a scale effect in strength, but do notaccount for variations in the magnitude of the scale effect caused by dif-ferences in laminate stacking sequences.

The advantages and limitations of applying the principles of similitude tocomposite structures are summarised and illustrated by simple examples.An analytical procedure is formulated to design scale models for an axiallycompressed composite cylinder. Although the buckling load of the cylindercan be simulated by a curved panel (subscale cylinder), the buckling modeis difficult to simulate.

The important point is that generalisations should not be made. There isalways likely to be uncertainty over the question of validity of statisticalmethods or LEFM for any given case. Further information on scaling effectscan be found in other recent works.19–24

References

1. J Morton, ‘Scaling of impact loaded fibre composites’, AIAA Journal, 1988 26(8)989–94.

2. K E Jackson, ‘Scaling effects in the static and dynamic response of graphite-epoxy beam-columns’, NASA TM-102697, AVSCOM TR-90-B-006, July 1990.

3. T M Wieland, J Morton and J H Starnes Jr, ‘Scale effects in buckling, post-buckling, and crippling of graphite-epoxy Z-section stiffeners’, AIAA Journal,1992 30(11) 2750–7.

4. S Kellas and J Morton, ‘Strength scaling in fiber composites’, AIAA Journal,1992 30(4) 1074–80.

5. W E Baker, P S Westine and F T Dodge, Similarity Methods in EngineeringDynamics, Hayden Book Company, Rochelle Park, NJ, USA, 1973.

6. K E Jackson and E L Fasanella, ‘Scaling effects in the static large deflectionresponse of graphite-epoxy composite beams’, NASA TM-101619, June 1989.

7. K E Jackson, S Kellas and J Morton, ‘Scale effects in the response and failureof fiber reinforced composite laminates loaded in tension and in flexure’,Journal of Composite Materials, 1992 26(18) 2674–705.

8. W Weibull, ‘A statistical distribution function of wide applicability’, Journal ofApplied Mechanics, 1951 18 293–7.

9. C Zweben, ‘The effect of stress nonuniformity and size on the strength of com-posite materials’, Composites Technology Review, 1981 3(1) 23–6.

10. R E Bullock, ‘Strength ratios of composite materials in tension and flexure’,Journal of Composite Materials, 1974 8 200–6.

11. A G Atkins and R M Caddell, ‘The laws of similitude and crack propagation’,International Journal of Mechanical Sciences, 1974 16 541–8.


MTA13 11/22/2000 1:53 PM Page 312

12. A Carpinteri and P Bocca, ‘Transferability of small specimen data to full sizestructural components’, Composite Materials Response: Constitutive Relationsand Damage Mechanisms, eds C Sih, G F Smith, I M Marshall and J J Wu, Else-vier Applied Science, London, 1988, 111–31.

13. F Lanza and H Burg, ‘Investigation of the volume effect on mechanical prop-erties of various industrial graphites’, Proceedings of the 11th Biennial Confer-ence on Carbon, Gatlinburg, Tennessee, 1973, 223–4.

14. R A Heller, ‘Size effects in brittle materials’, Periodica Polytechnica SeriesMechanical Engineering, 1992 36(2) 135–52.

15. G R Irwin, ‘Analysis of stresses and strains near the end of a crack transversinga plate’, Journal of Applied Mechanics, 1957 54 361–8.

16. R B Deo and H P Kan, ‘Effects of scale in predicting global structural response’,First NASA Advanced Composites Technology Conference, NASA LangleyResearch Centre, Part 2, January 1991, 761–77.

17. L A McCullers and J D Neberhans, ‘Automated structural design and analysisof advanced composite wing models’, Composites and Structures, 1973 13925–35.

18. S P Timoshenko and J M Gere, Theory of Elastic stability, McGraw-Hill BookCo, NewYork, 1961.

19. G Camoneschi, ‘The effects of specimen scale on the compression strength ofcomposite materials’, Workshop on Scaling Effects in Composite Materials andStructures, NASA-CP-3271, ed K E Jackson, 1994, 81–100.

20. E C Edge, ‘Is there a size effect in composites’, Comments on designer’s cornerby Carl Zweben, Composites, 1994 25(10) 956–7.

21. X Dao, L Ye and Y-W Mai, ‘Statistical fatigue life prediction of cross-ply com-posite laminates’, Journal Composite Materials, 1997 31(14) 1442–60.

22. M R Wisnom, J W Atkinson and M I Jones, ‘Reduction in compressive strain tofailure with increasing size in pin-ended buckling tests’, Composites Science &Technology, 1997 57 1303–8.

23. S T Halliday, ‘Review of scaling and geometry effects on qusai-static mechani-cal properties of GRP marine laminates’, DERA/MSS/CR980367/1.0, August1998.

24. J A Lavoie, C Soutis and J Morton, ‘Apparent strength scaling in continuousfibre composite laminates’, Composites Science and Technology, 2000 60(2)283–99.


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14.1 Introduction

Experimental data focus on a quantity of interest, termed the response vari-able. No two sets of data concerning a particular response variable are everlikely to be the same even when apparently collected under identical con-ditions. A certain amount of variation between any number of samplesdrawn from the same population is to be expected. Often, the objective isto identify factors, the explanatory variables, which influence the response,and this involves separating the variability in the data into that which is dueto natural variation and that which may be due to these other factors.

A principle of statistical testing of variability is that, under certain con-ditions, it is possible to put bounds on sample variation, with a certain prob-ability. That is, a given percentage of the samples drawn from the samepopulation will have a sample parameter, such as the sample mean, whichlies between certain limits. The higher the probability, the further apartthese limits will be. If a sample gives a value of the parameter which isoutside this range, we are inclined to believe that the sample is not drawnfrom the specified population, but has responses influenced by some newfactor.

It is up to the experimenter to decide how to react to this information.When unusual variation is detected, it is important that the real reason forthat variation is determined. It may be due to the use of different ma-terials, but temperature, operator and machine are other possible explana-tory variables.

14.2 Importance of looking at data plots

Some exploratory data analysis based on graphical methods is essentialbefore proceeding to generate statistics which summarise the data. Manystatistical tests rely on assumptions about the nature of the random variability in the data and, whilst some formal tests exist for this purpose,

14Statistical modelling and testing of

data variability

L C WOLSTENHOLME

314

MTA14 11/22/2000 2:55 PM Page 314

Statistical modelling and testing of data variability 315

perfectly adequate assessment can often be made by eye using a suitableplot. Statistical computer packages and many spreadsheet packages willperform this task quickly and effectively. There is usually the facility toextract particular portions of the data and to examine them in every waypossible. Plotting procedures are a way of revealing data structure andshould be used before proceeding to formal analysis.

Figure 14.1 shows carbon fibre strengths plotted against the log of fibrediameter. The plot shows a strong inverse linear relationship. If modellingthe response, strength, is the objective, then the factor diameter could bean important element in the specification of the model parameters.

Figure 14.2 shows a set of results from a low cycle fatigue experi-ment where the same material was used in experiments conducted at 14 different laboratories and reported by Thomas and Varma.1 A nominalstrain level of 1.2% was set but the actual level was recorded in each case. Between one and three similar experiments were conducted at eachlaboratory, and each laboratory is indicated by a different symbol on the plot. There is some evidence of a relationship between cycles to fatiguelife and strain level. Of more striking significance, however, is the cluster-ing of results from individual laboratories at similar strain readings.Individual laboratories seem to produce very consistent results, but theresults are markedly different between laboratories. There is a clear indi-cation that a laboratory effect needs to be investigated. It could be thatthere were differences in material used at each site, though in this particu-lar study it was found that similar laboratory effects were observed acrossdifferent materials. So perhaps the experimental procedure or the equip-

5

4

31.9 2.0 2.1 2.2

Log fibre diameter

Str

engt

h

14.1 Carbon fibre data, strength versus log diameter.

MTA14 11/22/2000 2:55 PM Page 315


ment used needs to be investigated. Ideally, possible explanatory variablesshould be identified before the experiment begins, but that may not be aneasy task.

14.3 Basic statistics

The two principal features of any data set are (1) where the data are locatedon the scale of measurement and (2) to what degree the data are spreadout. Common measures are:

• central tendency: (arithmetic) mean, median – some kind of averagevalue

• dispersion: standard deviation (sd), variance (sd)2, interquartile range.

It is important to differentiate between the true values of such param-eters, which refer to the whole population (possibly infinite), and valuesyielded by a certain sample from that population. For example, we can callall the pebbles on a given beach, the population, and a bag of pebbles col-lected at random along the beach, a sample.

Let a sample of values x1, x2, x3, . . . , xn be a simple random sample drawnfrom a population of x-values with mean, m, and standard deviation, s. Thesample mean is given by Equation [14.1]:

[14.1]xx

n

ii

n

= =Â

1

8.0

7.5

7.0

6.5

1.125 1.150 1.175 1.200 1.225 1.250 1.275

lab1lab2lab4lab5lab6lab7lab9lab13lab14lab15lab16lab18lab19lab20

Strain

Log

cycl

es

14.2 Fatigue data, cycles to fatigue versus strain by laboratory.

MTA14 11/22/2000 2:55 PM Page 316


and the sample standard deviation, s, can be obtained from Equation [14.2]:

[14.2]

Population parameters are frequently unknown and are often estimatedusing the equivalent sample measures. This is written as:(ˆ denotes estimate of ). It should be noted that these are point estimatesand, as such, carry no indication of how close the estimate might be to thetrue value.

14.4 Distribution of sample statistics

The sample measures described above will be different from one sample toanother, owing to the natural variability of data. It is possible to make state-ments about the way in which these measures behave.

If a random variable X has mean mX = m and variance s 2X = s 2,

then , the mean of a sample of size n, has mean m = m and variance s 2 = s 2/n.

The highly important central limit theorem states that for large n, the distribution of is approximately normal, with mean m and variance s 2/n,independent of the distribution of X. It is only possible to define largewithin the observational context, but tens rather than hundreds of obser-vations usually prove adequate.

If X has a normal distribution, then is exactly normal for all n. Thenormal distribution, shown in Fig. 14.3, is a symmetric bell-shaped distribu-tion, centred on the mean m, with 95% of values lying within ±1.96s of m.The distribution may be denoted N(m, s 2).

For testing purposes, all normal variates are converted to standardnormal via the transformation Z = (X - m)/s. The variable Z has a mean 0and variance 1 and 95% of the time -1.96 < Z < 1.96.

14.5 Testing for differences between samples

There are two classes of method:

• Parametric: assumptions are made about the populations from which thedata are drawn, and usually depend on the normal distribution in someway.

• Non-parametric (or distribution free): no assumptions are made aboutunderlying distributions. These methods are more versatile but, ingeneral, slightly less powerful when applied to data for which the para-metric assumptions are valid, and do not extend so easily to morecomplex modelling.

X

X

X

XX

ˆ , ˆm s= =x s

s x x nii

n2 2

1

1= -( ) -( )=Â

MTA14 11/22/2000 2:55 PM Page 317


14.5.1 Parametric methods

14.5.1.1 Testing a single sample against a certain population

In most parametric testing there are three important questions:

(1) Is the sample small or large?(2) Is the population normal?(3) Is the population variance known?

If the answer to (1) is ‘large’, then the answers to (2) and (3) have littlematerial effect on the testing, because the central limit theorem applies and,if s2 is unknown, it can be estimated using Equation [14.2]. If the answerto (1) is ‘small’, then we can only proceed if the population yielding thesample can be assumed to be normally distributed. Further, the answer to(3) also becomes important because the distribution of the test statisticdepends on it. In practice, most data under this heading fall into the smallsample, population variance unknown category.

In testing whether a sample has come from a certain population the nullhypothesis is always that it has, and we look for evidence that it has not.An experiment may, for example, be investigating the effect of a new curingprocess. The statistical test starts by assuming that there is no effect andlooks for evidence that there is, rather than assuming a difference andlooking for evidence of no difference. It is rather like the principle of ‘innocent until proven guilty’ in a court of law.

To test whether a large sample has come from a population with mean,m, we use the fact that:

0.4

0.3

0.2

0.1

0.0

t(5)t(15)N(0,1)

N(0,1)t(15)t(5)

–3 –2 –1 0 1 2 3Number of normal sigma from the mean

Pro

babl

e de

nsity

func

tion

14.3 Normal and t-distributions.

MTA14 11/22/2000 2:55 PM Page 318


[14.3]

and therefore, if

[14.4]

the hypothesis that the sample comes from a population with mean, m, isaccepted with 95% confidence. If the hypothesis were rejected, it would bea 5% level of significance.

When s2 is unknown, it is estimated by s2. In the case of a small sample

from a normal (or approximately normal) population, is only

N(0, 1) if s2 is known. It is far more likely that s 2 is unknown and has to

be estimated, but in that case the sampling distribution of

assumes what is known as the Student or t-distribution. This is a symmetri-cal distribution, centred on zero. It takes a different shape for each value ofits parameter n (known as the degrees of freedom) and tends to the standardnormal distribution as n Æ • (see Fig.14.3). In the single sample test,n wouldtake the value n - 1 and 1.96 is replaced by a value in excess of 1.96.A set ofstatistical tables, such as those prepared by Neave,2 will provide all the critical values required in standard test procedures, but a few useful valuesfrom the standard normal and t-distributions are shown in Table 14.1.

14.5.1.2 A test involving two samples – do they come from the same population?

Consider two independent samples size n1 and n2, with sample means 1

and 2. Suppose the null hypothesis is that both samples come from a population with mean, m, and variance, s2. The test is based on the randomvariable 1 - 2 which has mean mX1 - mX2. Under the null hypothesis thismean is zero and has variance:

[14.5]

For large samples

[14.6]X X

n n

N1 2

1 2

1 10 1

-

+ª ( )

s,

s s ss s2 2 2

2

1

2

21 2 1 2X X X X

n n- = + = +

XX

xx

X n

S-( )m

X n-( )ms

X n-( )<

ms

1 96.

XNX

X

-ª ( )m

s0 1,

MTA14 11/22/2000 2:55 PM Page 319


but is only so for small samples if the populations are normal and the population variance is known.

If s2 is unknown, then it is estimated using a pooled estimate based onboth samples:

[14.7]

and for small normal samples the test is based on the t-distribution, usingn = n1 + n2 - 2.

Example 1: Samples of carbon fibres were collected from different parts of a 1000-fibre tow and gave the following data for their diametersmeasured in microns:

• batch 1: n1 = 15 1 = 7.641 s21 = 0.0718

• batch 2: n2 = 13 2 = 7.371 s22 = 0.0751

Is there evidence of a significant difference in fibre diameter in differentparts of the tow? We will assume that the populations are normal with equalvariance, assumptions which will be examined later.

The t-statistic is

xx

sn s n s

n n2 1 1

22 2

2

1 2

1 12

=-( ) + -( )

+ -

Table 14.1. Critical constants in tests based on the t and normal distributions.

Confidence level (%) 95 99Level of significance (%) 5 1Degrees of freedom t-distribution values

1 12.71 63.662 4.30 9.923 3.18 5.844 2.78 4.605 2.57 4.036 2.45 3.717 2.36 3.508 2.31 3.369 2.26 3.25

10 2.23 3.1715 2.13 2.9520 2.09 2.8525 2.06 2.7930 2.04 2.7540 2.02 2.7050 2.01 2.68Normal distribution values 1.96 2.58

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[14.8]

where giving t = 2.63.

The t-distribution with 26 degrees of freedom has 95% of values between±2.056 and 99% of values between ±2.78. So, at a 5% level of significance,the null hypothesis that the samples come from the same population isrejected, but at a 1% level of significance the null hypothesis is not rejected.This would generally be regarded as a little inconclusive but depends onthe practical consequences of such judgements.

14.5.1.3 Test for equality of variances

For samples from normal populations, the assumption of equality of variance may be tested using the F-distribution. Under the null hypothesiss 2

1 = s 22, s2

1/s22 ~ F(n1 - 1, n2 - 1). This distribution has two parameters,

both called degrees of freedom, which vary the shape of the distribution.F-values are always greater than zero and, in general, the distribution hasa long right-hand tail (i.e. is positively skew). Because of this asymmetry,the critical constants are not of a simple ±k form. Statistical tables gener-ally only give the right-hand value, and the left-hand value is given byfinding the reciprocal of F(n2 - 1, n1 - 1).

In Example 1, s21/s2

2 = 1.036. This is compared with 1/F(14, 12) and F(12, 14) found in, say, Neave.2 At 95% confidence this yields the interval(0.31, 3.05), so the hypothesis of equality of population variances cannot be rejected.

Where the assumption of equal population variances is in doubt, samplesmay be compared using the standardised difference:

[14.9]

Under the null hypothesis of equal population means, this statistic has anapproximate t-distribution with degrees of freedom given by Equation[14.10]:

[14.10]n = +( ) -( ){ } + -( ){ }[ ]s n s n s n n s n n12

1 22

22

14

12

1 24

22

21 1

x x

sn

sn

1 2

12

1

22

2

-

+

ss s2 1

22214 12

26=

+

x x

sn n

1 2

1 2

1 1-

+

MTA14 11/22/2000 2:55 PM Page 321


Statistical packages such as Minitab3 include this version of the two-sample test, but it is omitted in many basic statistics texts. An exception isChatfield,4 which is a generally useful reference book.

14.5.1.4 Checking the normality assumption

Graphical inspection of the data should always precede formal analysis.Theobject here is to check whether the normal population assumption is tenableand to look for any unusual features of the data, for example, observationsremote from the bulk of the data set (outliers).The latter might be perfectlyvalid but may, on the other hand, be due to recording error.

Data displaying an approximately symmetrical bell shape are hoped forbut can be fairly difficult to establish where there are only a small numberof observations. The histogram is a popular plot but is of limited value for small samples. The boxplot is in many ways more useful as it highlightsaspects of spread, symmetry and unusual observations. It shows the posi-tions of quartiles (25%, 50%, 75% points), range and outliers and is usefulfor comparing samples.

A plot focused more directly on the normal distribution is the normalplot. For each observation xi, a normal score, zi, is calculated and the {xi} areplotted against the {zi}. A facility to do this quickly and painlessly is avail-able on packages such as Minitab. If the points lie approximately on astraight line, then the data conform well to a normal distribution. Figure14.4(a) shows such plots for the data of Example 1 and have been producedusing Minitab.

More formal tests of normality are available. For example, the Shapiro–Wilk test5 is based on a measure of the linearity of the normal plot. So too is the Anderson–Darling test indicated in Fig. 14.4(b) and (c). The p-valuequoted represents the probability that the data may have arisen by chanceunder the proposition of a normally distributed population. Only when thep-value is low, say <0.1, are we inclined to reject the normality assumption.It is known, however, that the data analysis techniques considered here arefairly robust (i.e. remain valid) to some departure from normality, so someform of visual impression is generally adequate and the most appealing.

14.5.2 Non-parametric methods

These usually involve ranking the data in order and using the rank numbersrather than the original data. This element of information loss explains why these methods are a little less powerful than parametric methods. Thephrase, less powerful, means that slightly more convincing evidence isrequired to reject the null hypothesis. The appropriate measure of centraltendency to test is the median rather than the mean.

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Batch 1

Batch 2

7.0 7.5 8.0Fibre diameter (mm)

(a)

0.999

0.99

0.95

0.80

0.50

0.20

0.05

0.01

0.001

Pro

babi

lity

7.2 7.7 8.2Fibre diameter (mm)

(b)

0.999

0.99

0.95

0.80

0.50

0.20

0.05

0.01

0.001

Pro

babi

lity

7.0 7.4Fibre diameter (mm)

(c)

7.2 7.6 7.8

14.4 Boxplots and normal plots for data from Example 1. (a) Boxplots,batches 1 and 2. (b) Normal plot, batch 1, average 7.64067, sd0.267541, number of data 15, Anderson–Darling normality test A squared 0.241, p-value 0.7. (c) Normal plot, batch 2, average7.37077, sd 0.273875, number of data 13, Anderson–Darlingnormality test A squared 0.185, p-value 0.887.

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14.5.2.1 Mann–Whitney test

This test is the non-parametric equivalent of the two-sample t-test. It teststhe hypothesis that the populations from which two independent samplesare drawn have the same median.

A favoured method of calculating the test-statistic U* is due to Wilcoxon.Both samples are combined and ranked together. Suppose samples 1 and 2 have n1 and n2 observations. The sum of the ranks of the observa-tions in samples 1 and 2 are given by R1 and R2, respectively. As a check,R1 + R2 = 1–2 n(n + 1) where n = n1 + n2. U* is taken to be the smaller of U1 = R1 - 1–2 n1 (n1 + 1) and U2 = R2 - 1–2 n2(n2 + 1). For modest n1 and n2, sta-tistical tables provide critical values of U*, and small values of U* countagainst the null hypothesis.

Example 2: The raw data for this example are shown in Table 14.2, withappropriate ranks assigned to each observation.

• U1 = R1 - 1–2 n1(n1 + 1) = 265 - 1–2 15(16) = 145• U2 = R2 - 1–2 n2(n2 + 1) = 141 - 1–2 13(14) = 50

The value of U* is therefore 50. For sample sizes 15 and 13 the critical valueat 5% significance level is 61. Since 50 < 61, the hypothesis that the samplescome from populations with the same median is rejected.

For large samples, U1 and U2 are approximately normally distributed withmean 1–2 n1n2 and variance 1/12n1n2(n1 + n2 + 1), but there is little point inusing non-parametric methods for large samples because the central limittheorem applies and parametric methods can be used to good effect.

14.5.2.2 Kolmogorov–Smirnov (K-S) test

This can be used for detecting differences of any kind between the popu-lations from which two samples have been drawn. The two sample cumula-tive distribution functions (CDF) are compared:

Table 14.2. Ranking the fibre diameter data.

Sample Observation Rank Sample Observation Rank Sample Observation Rank

2 6.92 1 1 7.41 10 1 7.68 19.52 7.04 2 2 7.42 11 2 7.68 19.52 7.08 3 2 7.43 12 1 7.71 211 7.22 4.5 1 7.44 13 2 7.74 222 7.22 4.5 2 7.47 14 1 7.77 232 7.24 6 2 7.49 15 2 7.81 242 7.28 7 1 7.52 16 1 7.82 251 7.38 8 1 7.58 17 1 7.84 261 7.40 9 1 7.63 18 1 7.93 27

1 8.28 28

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[14.11]

This produces a step function extending from 0 just below the smallestobservation to 1 at the largest observation.The test statistic, D, is the largestvertical distance between the two functions (Fig. 14.5). Values are given instatistical tables which indicate whether D is large enough to reject thehypothesis that the samples come from the same population.

For the data in Table 14.2 the value of D is 0.436 and the critical value at 5% significance is 0.492. At 10% significance the critical value is 0.446.The K-S test just fails to pick up a difference between the samples becausethe potential difference is specified so generally. The t-test and Mann–Whitney are better for detecting differences in average values, but K-Swould be useful for detecting say, a difference in variance between non-normal samples.

14.6 Comparing several samples simultaneously

Tests such as the t-test and Mann–Whitney can be extended to cover morethan two samples.

• Parametric: analysis of variance (ANOVA)• Non-parametric: Kruskal–Wallis, Freidman

Here the discussion will be confined to parametric methods.

Sample CDFnumber of observations

number of observations in the sample= ( ) =

£p x

x

Fibre diameter

1.0

0.5

0.0

Sam

ple

CD

F

7.0 7.5 8.0

14.5 Cumulative frequency distributions for data of Example 1.

MTA14 11/22/2000 2:55 PM Page 325


14.6.1 Confidence intervals

An interval estimate of a parameter associated with a given level of confi-dence is called a confidence interval. The end-points of such intervals areconfidence limits. A confidence interval for m in simple random samplingtakes the form , where the value of c is a percentage point from

the appropriate sampling distribution of .

Given m samples, the usual approach is to assume that the m populationshave equal variances and that these populations are normal. An estimateof the common variance may be constructed as:

[14.12]

where ni, s2i are the sample size and variance, respectively, for the ith sample.

This is a generalisation of Equation (14.7); s2 is a weighted average of theindividual sample variances and is thus a more reliable estimate of s 2. Thisestimate may be used to derive confidence intervals for the means of thepopulations, as above, and for other purposes.

Example 3: The data in Table 14.3 concern the yield from a chemicalreaction using three different catalysts, C1, C2, C3. It is of interest to know whether there is any difference in the performance of the catalysts.

If the samples come from populations with approximately equal means,then the confidence intervals for the three population means will overlapto some degree. If some intervals do not overlap, then there is evidence, atsome level of uncertainty, that the populations do not all have the samemean. Table 14.4 shows, for the data of Table 14.3, confidence intervals foreach sample based on (1) the sample standard deviation and (2) the pooledstandard deviation.

sn s n s n s

n n nm m

m

2 1 12

2 22 2

1 2

1 1 11 1 1

=-( ) + -( ) + -( )

-( ) + -( ) + + -( ). . .

. . .

X n

S-( )m

x cs n± ( )

Table 14.3. Yield of a chemical reaction using threedifferent catalysts.

C1 C2 C3

2.5 2.6 2.43.6 3.1 2.93.2 3.0 2.82.7 2.5 2.3

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14.6.2 One-way analysis of variance (ANOVA)

This process combines the degree to which the confidence intervals overlapinto a single measure which, under the null hypothesis of equal populationmeans, has an F-distribution. The level of uncertainty is often expressed asa p-value, equivalent to the level of significance at which the null hypothe-sis would be rejected. It represents the probability that the degree ofoverlap, or rather lack of it, could have arisen by chance in samples fromthe same population. If the p-value is very small, say <0.05, then the hypoth-esis of equal means looks very unlikely. In this case, to discover where thedifferences might lie in particular, we have to go back to the confidenceintervals. One-way ANOVA on just two samples is exactly equivalent to thetwo-sample t-test.

Whichever set of confidence intervals is examined in Table 14.4, it is clearthat there is insufficient evidence to suggest significant between-samplevariation. The ANOVA calculation is based on taking the total variationamong all observations and dividing it into within and between sample com-ponents. It is how large a proportion of the whole, taking into account thenumber of samples and the sample sizes, that is attributed to the between-sample variation which determines the conclusion.

Table 14.5 is the ANOVA table for Example 3, and the p-value at 0.361indicates no significant evidence that the mean yields differ amongst cata-lysts.This reflects the overlap of the confidence intervals. It should be notedthat the same assumptions as for the t-test apply, namely normal popula-tions and equal population variances, and whilst the sample standard de-viations differ, they are not different enough for the latter assumption tobe in serious doubt.

Table 14.4. 95% confidence intervals for the population mean of Example 3.

Sample n Sample Samplemean sd

C1 4 3.0 0.497C2 4 2.8 0.294C3 4 2.6 0.294

Sample Confidence interval(1) C1 (2.210, 3.790)

C2 (2.332, 3.268)C3 (2.132, 3.068)

(2) C1 (2.577, 3.423)C2 (2.377, 3.223) pooled sd = 0.3742C3 (2.177, 3.023)

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14.6.3 Multiway analysis of variance

Inherent in the basic approach outlined above is the assumption that alldata in any given sample have been collected under the same conditions.In practice this is not often the case. Identifying the conditions which arelikely to influence results (i.e. the explanatory variables) is not easy, andunfortunately may be alighted upon after the experiment has been con-cluded. It may be discovered too late that potentially critical informationhas not been recorded. It is always better to acquire information whichturns out to be redundant than to miss data which could be vital.

For example, it may be thought that the measurement of a material prop-erty varies between testing laboratories, so an experiment is set up wherebyseveral pieces from a large batch of a certain material are sent to each lab-oratory. Prior to the experiment it may have been assumed that all piecesof material have the same properties, but suppose this is not the case. Aone-way ANOVA will not be able to separate material differences fromlaboratory differences. If, however, the sample material is ‘matched’ acrosslaboratories, then the different effects may be separated, using two-wayANOVA.

Example 3 continued: Suppose the experiments were in fact conductedat four different laboratories, the first measurement for each catalystcoming from laboratory 1, and so on. We will equate ‘catalyst’ here with‘material’ and again test for differences between materials, but in the lightof new knowledge about the testing environment.

If there are l laboratories and m materials, and each laboratory makes asingle measurement on each material, there will be n = ml measurementsin total. Let yij denote the measurement made at laboratory i on materialj, and y the mean of all n observations. A measure of the total variation

among all observations is the total sum of squares, .

ANOVA divides this total variation into ‘between samples’, ‘within samples’and ‘residual’ variation. In the present context these contributions representvariation between laboratories, ssB, variation between materials, ssW, and

ssT y yijij

= -( )Â 2

Table 14.5. Analysis of variance (ANOVA) table.

Source of Degrees of Sum of Mean F pvariation freedom squares squares =

(DF) (SS) SS/DF

Between samples 2 0.32 0.16 1.14 0.361Within samples 9 1.26 0.14

Total 11 1.58

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‘left-over’ variation, ssR, which cannot be attributed to either of the mainsources. Table 14.6 shows the breakdown for the data of Example 3.

As before, if we assume that the responses have constant variance andare normally distributed, then, under the null hypothesis that there are nosignificant material or laboratory effects, the ratios (l - 1)ssW/ssR and (m - 1)ssB/ssR may be compared with the F-distribution and p-values cal-culated. For the results in Table 14.6 these F-ratios are respectively 19.0 and 8.0, indicating that there is a significant difference both between labo-ratories ( p-value <0.01) and between catalysts ( p-value <0.025).The earlierone-way ANOVA failed to detect these differences because laboratory differences were masking material differences.

In Table 14.4 we noted that the estimate of the underlying variability wasgiven by the pooled standard deviation, √ssR/(n - m - 1) = 0.3742. Here,the estimated variance ssR/[(l - 1)(m - 1)] = ssR/(n - m - l - 1). Taking thesquare root yields a standard deviation of 0.02. This much reduced value isthe result of material and laboratory differences accounting for 92% of thevariation in the results. The ‘left-over’ or unexplained variation, ssR, is nowonly 8% of the total, ssT.

14.6.4 The model

The model underlying the analysis is one where the expected response,E(yij) (e.g. material property measurement), is the sum of effects consistingof an overall mean value and departures from this average caused by thedifferent effects:

[14.13]

where ai is the effect due to the ith laboratory and bj is the effect due tothe jth material. By definition, Sai = 0 and Sbj = 0.

E yij i j( ) = + +m a b

Table 14.6. Two-way analysis of variance.

Source of Degrees of freedom (DF) Sum of squares (SS)variation

Laboratories l - 1 = 3

Materials m - 1 = 2

Residual (l - 1)(m - 1) = 6

Total n - 1 = 11

= overall mean, = mean for laboratory i, = mean for material j.y jyiy

ssT y yijij

= -( ) =Â 21 58.

ssR y y y yij i jij

= - - +( ) =Â 20 12.

ssW l y yjj

= -( ) =Â 20 32.

ssB m y yii

= -( ) =Â 21 14.

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The measured responses yij are assumed to vary around the expectedvalue by some quantity eij:

yij = m + ai + bj + eij [14.14]

It is perhaps potentially misleading that eij is often referred to as the ‘error’.The term ‘random departure’ is a better description for this natural varia-tion around the expected response. Fundamental to the model is theassumption that the {eij} are independent, with zero mean; and for the analy-sis using the F-distribution, a normal distribution with constant variancemust also apply.

Possible interaction effects between laboratories and materials may alsobe built into the model and assessed via replication of measurements, sayeach laboratory/material combination observed r times. The resultingANOVA is given in Table 14.7, and it can be seen that for the case r = 1 itreduces to the form of Table 14.6.

14.6.5 Checking the model

Residual plots are an important complement to the calculations. Estimatedresponses are calculated from the fitted model. The residuals, the differ-ences between the fitted and observed responses, may be plotted againstthe fitted values to provide a visual check on the model assumptions. Figure14.6 shows the residuals for the two-way analysis of Example 3 against thefitted responses. The plot should show points scattered at random. If thereis some form of pattern to the plot, then the model assumptions may be indoubt, and some rethink of the approach to the analysis is necessary.

Table 14.7. Two-way analysis of variance with interaction.

Source of DF SS MS F-ratiovariation

Laboratories l - 1 SS/(l - 1)

Materials m - 1 SS/(m - 1)

Laboratory (l - 1)(m - 1) SS/[(l - 1)(m - 1)]material

Residual n - lm SS/(n - lm)

Total n - 1

yijk = kth observation for laboratory i and material j, = mean of r replicationsfor laboratory i and material j, n = lmr (and other terms as for Table 14.6).

yij

y yijijk

-( )Â

y yijk ijijk

-( )Â

r y y y yij i jij

- - +( )Â

lr y yjj

-( )Âmr y yi

i

-( )Â

MTA14 11/22/2000 2:55 PM Page 330


14.6.6 Incomplete data

As we all know, real life does not always work out as planned. Standardmultiway ANOVA assumes a perfectly balanced set of results; that is, thesame number of results for each set of conditions. What if one experimentgoes wrong? It may be possible to repeat it; but suppose the right kind ofexperimental material is not available, or the experiment is too long torepeat. One-way ANOVA is unaffected by this event, but multiway analy-sis of unbalanced data must be carried out by multiple regression usingbinary variables. This approach is not in essence different to ANOVA.Multiple regression on balanced data yields exactly the same results asANOVA, but ANOVA is easier to use.

14.7 General linear model (GLM)

A regression model may be given by Equation [14.15]:

yi = m + a1x1 + a2x2 . . . + alxl + b1z1 + b2z2 + . . . bmzm + ei [14.15]

where yi is the ith observation, {xj} and {zk} are binary or indicator variables taking the value 0 or 1 dependent on whether or not the jth treat-ment (e.g. laboratory) or kth block (e.g. material) is present. The regressioncoefficients {aj} and {bk} are the treatment and block effects, respectively,where, as for Equation [14.14], Saj and Sbk are both zero. Differencesbetween treatments will be determined by values of some aj which are different from zero and, similarly, differences between blocks will be

0.25

0.15

0.05

–0.05

–0.15

–0.252.2 2.4 2.6 2.8 3.0 3.2 3.4

Fitted responses

Res

idua

ls

14.6 Residual plot for analysis in Table 14.6.

MTA14 11/22/2000 2:55 PM Page 331

determined by values of some bk which are different from zero. The judgement as to whether a coefficient is significantly different from zero depends on the assumptions made about the structure of the depar-tures {ei}. We will assume that the {ei} have zero mean, constant varianceand are normally distributed. Under these criteria, the estimated regressioncoefficients are normally distributed and p-values for testing zero effectsmay be assigned via an estimate of the residual variance and use of the t-distribution. Very small p-values suggest that the corresponding effects arenon-zero.

Wolstenholme and Crowder6 examined data from a study by Gould andLoveday7 concerning creep rate measurements made by different labora-tories on samples from a number of different bars of the same batch ofmaterial. A one-way ANOVA was envisaged on the basis that differenceswould be related to laboratories only. However, it was apparent that therewere also differences between bars. The experiment was unbalanced, sotheir analysis is based on Equation [14.15], with differences between labo-ratories and between bars indicated by the small p-values associated withsome of the estimated regression coefficients.

It is possible to have a combination of quantitative and binary variables.For example, Figure 14.2 shows that a model for cycles to fatigue failuremight include a variable for strain as well as binary variables for laborato-ries. This can be represented by Equation [14.16]:

y = m + q1w1 + q2w2 + . . . + a1x1 + a2x2 + . . . + ei [14.16]

where the {xj} are binary variables associated with treatment effects, and wk

are measurements of explanatory variables, such as strain, temperature, sizeor some function of such characteristics.

Example 4: This is an interlaminar short beam shear test experiment. Anexperiment conducted at Imperial College8 investigated the effect of curingconditions on interlaminar shear stress. Six laminated carbon-fibre reinforced/epoxy panels were manufactured. Five were cured in a singleautoclave cycle and placed at different stations on the autoclave table. Twowere near the door of the autoclave, two were at the other end of the tablenear the internal fan and one was placed in the centre of the table.The sixthpanel was cured separately using a pressclave. Ten samples, nominally ofsize ten, were cut from different areas of the panels. One panel had part ofits surface abraded and one sample was drawn from this area. All speci-mens were nominally of the same dimensions but the width, w, and thick-ness, h, of each specimen was measured. The test was carried out inthree-point flexure and the Zwick testing machine recorded the load (Pcrit)at which a delamination initiated. The apparent interlaminar shear strength(ILSS) is then calculated via the expression:


MTA14 11/22/2000 2:55 PM Page 332

[14.17]

The ILSS values were measured according to the CRAG9 recommendation.A summary of the structure of the experiment is shown in Table 14.8.

It has to be said at the outset that there are ways in which the design ofthe experiment could have been improved, using the same number of specimens. There is, for example, no means of assessing surface abrasionwith reference to the heated press.

The first step is to identify the response and explanatory variables.The obvious choice for the response variable is ILSS, but it is worth investigating whether Pcrit is more suitable. Factors to consider are whetherthese variables are approximately normally distributed, and the nature ofthe correlation with the explanatory variables. Quantitative explana-tory variables might be width and thickness of specimen; qualitativeexplanatory variables might be type of curing process and situation withinthe curing process, and the existence of surface abrasion on the specimen.Another question to leave open is whether there is any benefit in keepingsamples from the same panel separate. Clearly in the case of panel 1, surfaceabrasion is a separate factor but if, in general, there is little difference insamples from the same panel, more accurate assessment of influentialfactors will be achieved by an interpanel analysis, rather than an inter-sample analysis.

Figure 14.7 shows boxplots for the sample ILSS and Pcrit values. The exis-tence of some function of specimen size as a possible explanatory variableis responsible for the difference in these pictures. This will be exploredpresently. In the ILSS picture there is a clear indication that surface abra-sion increases response. Further, there is some evidence that response in

ILSSPwh

= 0 75. crit


Table 14.8. Data from interlaminar short beam shear test experiment.

Sample Number of Panel Position in Surface finishspecimens number autoclave

1 9 2 Fan end None2 10 2 Fan end None3 10 3 Fan end None4 10 4 Door end None5 10 4 Door end None6 10 5 Centre None7 10 6 — None8 10 1 Door end None9 10 1 Door end Abraded

10 10 1 Door end None

MTA14 11/22/2000 2:55 PM Page 333

the autoclave is highest in the centre, where it is similar to the result for theheated press. The sample sizes are all fairly small and whilst there is some skewness in the sample distributions, there is little evidence of non-normality in either Pcrit or ILSS. Neither do F-tests reject the hypothesis ofequal variances, so for the purposes of the modelling described here, we canchoose either Pcrit or ILSS as the response variable.

The influence of variables other than the qualitative sample characteris-tics discussed so far needs to be examined.The data show considerable vari-ation in specimen width and non-significant variation in specimen thickness,but it is thickness which is correlated with Pcrit. ILSS is not significantlyrelated to either width or thickness. Figure 14.8 shows a series of plots inves-tigating these potential relationships. The form of Equation [14.17] makesthe cross-sectional area, wh, an obvious additional candidate for an explana-tory variable. From the modelling point of view, any relationships need tobe linear in nature. If ILSS is the response variable, it is clear that none ofthese size considerations need be included in the model, but if there werestrong distributional arguments for choosing Pcrit, then either h or wh shouldbe put into the model.

Following from Equation [14.15], with ILSS as response variable, an appropriate model is one with {xj} representing curing position and zrepresenting surface treatment. We cannot use a simple two-way ANOVAbecause the experiment is unbalanced, that is, there are unequal numbersof observations for each curing/surface combination. Using the samplenumber as curing level proves to be over-detailed for these data. There islittle evidence of any real difference between samples cut from the samepanel. Further, panels in similar positions in the autoclave perform in


10

9

8

7

6

5

4

3

2

1

10

9

8

7

6

5

4

3

2

1

Sam

ple

Sam

ple

90 95 100 105Interlaminar shear stress (MPa)

2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9

Critical load (kN)

14.7 Boxplots for interlaminar short beam shear test data.

MTA14 11/22/2000 2:55 PM Page 334

similar fashion. Supporting statistical tests for the latter statements are notshown here. In the following model, the {xj} indicate the different positionsunder the column headed ‘Position in autoclave’ in Table 14.8.

ILSS = m + a1x1 + a2x2 + a3x3 + a4x4 + b1z1 + b2z2 + e [14.18]

A summary of a GLM analysis performed by Minitab is shown in Table 14.9. [Computation note: the difference between SeqSS and AdjSS is


2.9

2.8

2.7

2.6

2.5

2.4

2.3

2.2

Crit

ical

load

(kN

)

2.9

2.8

2.7

2.6

2.5

2.4

2.3

2.2

Crit

ical

load

(kN

)

2.9

2.8

2.7

2.6

2.5

2.4

2.3

2.2

Crit

ical

load

(kN

)105

100

95

90

ILS

S (

MP

a)105

100

95

90

ILS

S (

MP

a)

105

100

95

90

ILS

S (

MP

a)

9.0 9.5 10.0 10.5

Width (mm)

9.0 9.5 10.0 10.5

Width (mm)

1.85 1.95 2.05 2.15Thickness (mm)

1.85 1.95 2.05 2.15Thickness (mm)

18 19 20 21 22Width ¥ thickness

18 19 20 21 22Width ¥ thickness

14.8 Scatterplots for ILSS data: Pcrit and ILSS versus specimen width,thickness and width ¥ thickness.

MTA14 11/22/2000 2:55 PM Page 335


Table 14.9. General linear model fitted to ILSS data.

Factor Levels Values

Position 4 1 (pressclave) 2 (door) 3 (fan) 4 (centre)Surface 2 1 (not abraded) 2 (abraded)

Analysis of variance for ILSSSource DF Seq SS Adj SS Adj MS F P

Position 3 193.70 161.62 53.87 6.53 0.000Surface 1 292.19 292.19 292.19 35.39 0.000Error 94 776.03 776.03 8.26Total 98 1261.92

Term Coeff sd t-value P

Constant m 98.6790 0.5833 169.16 0.000Position1 a1 1.0838 0.7394 1.47 0.1462 a2 -0.7697 0.4869 -1.56 0.1223 a3 -2.1858 0.5256 -4.16 0.0004 a4 1.8628 0.7394 2.52 0.013Surface1 b1 -3.0218 0.5079 -5.95 0.0002 b2 3.0218 0.5079 5.95 0.000

9

8

7

6

5

Log

cycl

es

–0.5 0.0 0.5

Log strain

14.9 Interlaboratory low cycle fatigue data.

MTA14 11/22/2000 2:55 PM Page 336

explained in the Minitab Reference Manual and is not important for thediscussion here.]

The very low p-values in the analysis of variance table indicate very sig-nificant effects in varying the curing condition and in the presence of surface abrasion. The p-values associated with the coefficients {aj} show that resultsare markedly lower for samples near the fan and highest in the centre ofthe autoclave. There is some evidence that response is higher than averagein the heated press but not significantly so. Surface abrasion increases theresponse markedly and is the most significant result regardless of whetherthe model is based on ILSS or Pcrit.

Example 5: This is a low cycle fatigue test. The data illustrated in Fig. 14.2are part of a larger data set involving tests at 0.6%, 1.2% and 2.0% strainlevels, covering 15 laboratories. The complete data set is shown in Fig. 14.9.Log of cycles to failure and log strain are shown to be linearly related and


2.5

1.5

0.5

–0.5

–1.5

–2.5

–3.5

Sta

ndar

dise

d re

sidu

als

5 6 7 8 9

Fitted responses

2.5

1.5

0.5

–0.5

–1.5

–2.5

–3.5

Sta

ndar

dise

d re

sidu

als

Laboratory

1 5 10 15 20 26

14.10 Residual plots for GLM fitted to low cycle fatigue data.

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are therefore suitable choices for response and quantitative explanatoryvariables. Further, from Fig. 14.2, binary variables {xj} for laboratory effectsshould be included. So, following from Equation [14.16], the model to befitted is:

[14.19]

Table 14.10 shows the results of fitting Equation [14.19] to the data ofFig. 14.9.The analysis of variance table shows a highly significant linear rela-tionship between log(cycles) and log(strain) and significant differencesbetween laboratories. The t-values for the laboratory coefficients show thatlaboratories 1, 2, 7, 15, 26 give markedly higher measurements than average,and laboratories 9, 18, 19, 20 give markedly lower measurements. Figure14.10 shows residual plots for this analysis where the residuals have beenstandardised. This converts the distribution of the residuals to one which

log log . . .cycles strain( ) = + ( ) + + + +m q a a a1 1 2 2 15 15x x x e


Table 14.10. General linear model fitted to low cycle fatigue data.

Factor Levels Values

Lab 15 1 2 4 5 6 7 9 13 14 1516 18 19 20 26

Analysis of variance for log cycles

Source DF Seq SS Adj SS Adj MS F P

lg strain 1 85.7069 78.5126 78.5126 2560.14 0.00Lab 14 12.8781 12.8781 0.9199 30.00 0.00Error 92 2.8214 2.8214 0.0307Total 107 101.4065

Term Coeff. sd t-value P

Constant 7.481 0.01992 375.48 0.000lg strain -1.871 0.03697 -50.60 0.000

Lab1 0.371 0.07510 4.94 0.0002 0.379 0.06460 5.86 0.0004 -0.130 0.06054 -2.14 0.0355 0.198 0.06078 3.26 0.0026 0.271 0.07556 3.59 0.0017 0.271 0.05741 4.73 0.0009 -1.033 0.08421 -12.27 0.000

13 -0.114 0.05740 -1.99 0.05014 0.017 0.05732 0.29 0.77215 0.310 0.07533 4.12 0.00016 0.047 0.06911 0.68 0.50018 -0.469 0.05099 -9.20 0.00019 -0.359 0.05740 -6.25 0.00020 -0.236 0.05740 -4.10 0.00026 0.477 0.09711 4.91 0.000

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not only has zero mean, but a standard deviation, one. Under the normal-ity assumption there should be approximately 5% of residuals outside theinterval [-1.96, 1.96]. In this example, some 10% of observations have largeresiduals, but the plot against fitted responses does not show any particu-lar pattern.When we plot the residuals against individual laboratories, somequite sharp differences in variability show up, for example between labo-ratories 19 and 20. However, although some model deficiencies may exist,the essence of the conclusion is preserved, namely that laboratories dodiffer quite substantially.

As with multiway ANOVA, interaction terms may be built into a regression model, but in the examples considered here there are too few replications to estimate these effects. Or, to put it another way, thereare too few residual degrees of freedom available to spread over the pos-sible laboratory/material interactions. Care is needed in constructing aregression model to ensure that the model is not overburdened with vari-ables, and to avoid the presence of correlated variables. Both features leadto poorly estimated regression coefficients. Further reading may be foundin, for example, the classic reference for regression analysis by Draper and Smith.10

References

1. G B Thomas and R K Varma, in Harmonisation of Testing Practice for HighTemperature Materials, eds M S Loveday and T B Gibbons, Elsevier, London,1992.

2. H R Neave, Elementary Statistics Tables, Routledge, London, 1994.3. Minitab Release 10 Xtra, Minitab Inc., USA, 1995.4. C Chatfield, Statistics for Technology, 3rd edition, Chapman and Hall, London,

1983.5. S S Shapiro and M B Wilk, ‘An analysis of variance test for normality (complete

samples)’, Biometrika, 1965 52 591–611.6. L C Wolstenholme and M J Crowder, ‘Materials metrology: statistical analysis

of data’, in Materials Metrology and Standards for Structural Performance, edsB F Dyson, M S Loveday and M G Gee, Chapman and Hall, London, 1995.

7. D Gould and M S Loveday, The Certification of Nimonic 75 Alloy as a Creep Reference Material, CRM 425, Commission of the European Communities,Luxembourg, 1990.

8. J M Hodgkinson and A Talby, Influence of Autoclave and C-Scan Position onthe Performance of Composites, Final year project report, Department of Aero-nautics, Imperial College, London University, UK, 1992.

9. P T Curtis (ed), CRAG Test Methods for the Measurement of the EngineeringProperties of Fibre-reinforced Plastics, Royal Aircraft Establishment, Farnbor-ough, UK, Technical Report 88012, 1988.

10. N R Draper and H Smith, Applied Regression Analysis, 3rd edition, Wiley,New York, 1998.


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15.1 Introduction

This chapter reviews the development and validation of new standard testmethods and documents the current initiatives related to the mechanicaltesting of advanced composite materials – in particular, the standards andtest methods being developed for international use by the InternationalStandards Organisation (ISO) and the provision of EN standards in supportof the Single European Market (EU) by the Comité Européen de Nor-malisation (CEN) are covered.

ISO standards are not mandatory, and alternative national standardswere previously published related to national conditions. However, forCEN member countries, mainly EU and EFTA (European Free TradeArea) countries, it is mandatory to publish any approved EN standard astheir national standard and withdraw any existing national or internationalstandard of the same scope. It is agreed that where ISO has published, orhas work in progress on a standard of the required scope, the ISO docu-ment will be considered for reballoting as a CEN document. In general,CEN looks towards ISO for the basic test methods, while CEN is more con-cerned to provide product and technical specifications (e.g. as covered byEU directives) in support of the Single European Market.

The main concern in this book is the mechanical testing of compositematerials (i.e. consolidated material), but it should be noted that testmethods and specifications are also needed to characterise fibres, matricesand unconsolidated preimpregnates. Test methods are also required forelectrical and thermal properties, for environmental, chemical and ageingresistance and for toxicity and processing properties (e.g. tack). Thermaland electrical properties can be anisotropic, in a manner similar to themechanical properties.

This chapter mainly covers composite materials containing continuousfibres in an organised or oriented layup. These materials include unidirec-

15Development and use of standard

test methods*

G D SIMS

340

* Crown copyright

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tionally oriented preimpregnates, multidirectional preimpregnates andfabric reinforcement. Although balanced fabric materials (equal warp andweft fibres) can be tested using conventional methods, oriented fabrics orhybrid combinations of unidirectional fibre plus fabric materials need testmethods appropriate to their higher anisotropy. Most of these materials arepressed at elevated temperatures from prepregs to achieve consolidationand cure for thermoset matrices, but similar types of properties can befound through the wet fabrication process of thermoset filament windingand pultruded rods, or from equivalent thermoformed systems with ther-moplastic matrices.

Other groups of composite materials may contain mat reinforcement ineither a thermoset matrix (i.e. conventional hand or sprayed lay-up GRP,or glass reinforced plastic), or the normally filled resin-based sheet mould-ing compounds (SMC), or a thermoplastic matrix, such as the more recentlyintroduced glass mat thermoplastics (GMT). As these materials are gener-ally (unless they include aligned fibres) almost isotropic in-the-plane, stan-dard ‘plastics’ type dumb-bell or wide strip specimens can be used.The maincharacterisation problem is the assessment of the point-to-point variationsin properties that can occur in these materials.

15.2 Development of test methods

Most test methods originate in industrial companies as a means of controlling and measuring specification parameters and material performance. Academic and government research establishments alsodevelop new test methods and are frequently involved in research toimprove them. A method recommended by a trade body, a group of companies or a government body may result from these in-house devel-oped methods. These recommended methods will be offered to nationalstandards bodies to be considered for submission to ISO or CEN, or morerarely now for publication as a national standard. Standards publishedinternationally by ISO or CEN require the support of the national delegatesof the appropriate member countries. More details of these bodies are givenlater.

The measured materials properties are used for several purposes,including:

• materials specification• materials development• materials selection• design data• product development• quality assurance

Development and use of standard test methods 341

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• non-destructive evaluation• research.

Once a method has been prepared from whatever source, the normalroute for a standard to be developed is that it is tabled in a national com-mittee, which will consider whether its submission should be supported forpublication as an international standard. Within the ISO system the draftwill then pass through the stages outlined below (slightly different stagesfor CEN or parallel CEN/ISO votes).

15.2.1 New work item (NWI)

The drafted test method and the proposal justifying the ‘industrial’ need forthe standardisation of the method are circulated by the relevant nationalstandard technical committee to its members for comment. If approved forsubmission to ISO, the draft with the completed case for the new work item(NWI) is prepared. ISO then undertakes a ballot of all voting countries inthat work area to determine, first, if there is support for the proposed topicand, second, if the attached draft is acceptable at either committee draft(CD) or draft international standard (DIS) ballot stage. A good qualitydraft obtaining wide support can be advanced by this latter assessment. Ifthe new topic is approved, then it will be assigned to a working group (WG).

15.2.2 Committee draft (CD)

Normally, the draft proposed initially will form a working draft not circu-lated outside the committee. Either a project leader will be appointed tolead the work or a small task force will be formed that will work on thedraft until it has consensus or majority support for submission to publicballot and comment at the CD level. As this is the primary vote for tech-nical changes, it would be preferable to undertake a five or six months’ longballot as in the CEN system rather than the current three-month ballot inISO.

15.2.3 Draft international standard (DIS)

Providing the CD ballot receives more than 75% approval from countrieswith voting rights for the subject area (i.e. ‘p’ members) and not more than25% negatives from all countries (includes also observer ‘o’ counties), thedraft can be progressed to DIS status. Normally, the CD ballot commentswill be discussed at the working group level and responses agreed with theproject leader.The project leader then prepares ‘a disposition of comments’showing each country’s comments, the response and any intended modifi-


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cations to the text. This information is then presented with the revised textfor the DIS five-month ballot.

15.2.4 Formal draft international standard (FDIS)

The review of ballot voting and comments is repeated so that a final two-month ballot can be undertaken. At this stage and at the DIS stage onlyeditorial changes are expected. If technical changes are required followingvoting, a CD-2 or DIS-2 draft would be prepared at an earlier stage forreballot. If there are no negative votes at the DIS ballot and the ballot isnot in parallel with CEN, then there is no requirement to undertake the FDIS ballot.

In order to speed up the standards making process to meet industrialtimescales and requirements, it is now necessary in proposing a NWI tosubmit a good working draft and a proposed project leader. Other coun-tries voting in support must also nominate their technical expert to workon the standard. In addition, NWIs are only allowed to exist on the workprogramme for five years and an optimum development time is 44 months.This timescale does not really allow repeat ballots (e.g. CD-2 or DIS-2) andhighlights the need for well developed documents at each stage.

The CEN approval system is similar but uses prEN to designate a draftEuropean standard. CEN timescales are also a little different, as are thejoint parallel processing voting schedules.

Progress of an NWI is accelerated if validation has been undertaken priorto submission, so that the precision clause can be completed as discussedbelow.

15.3 Validation of test methods

15.3.1 Procedures

As noted above, standard test methods are used at several stages of theproduct development, certification, manufacturing and supply process,which places increased legal importance on the reliability of the testmethod. Typical occasions when data obtained for a material or productproperties could be used in a legal manner are:

• a dispute regarding material supply• a dispute regarding free trade• a product liability case• a major failure investigation.

Consequently, standard bodies, such as ISO, require that new or revisedmethods are experimentally validated and their precision is determined.


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Although this requirement has been given increased prominence with thearrival of EN standards, it was previously a requirement that a ‘precision’clause be included in standards.1,2

The validation data are normally obtained by a responsible body (e.g. astandards committee) planning a series of tests to be conducted accordingto a draft standard by various establishments, normally ten or more. Thisround, robin (RR) testing involves the supply of nominally identical ma-terial to all the participants who carry out the tests according to the laid-down procedure. The measured data and required test report are sent tothe organiser of the RR, who analyses all the reported data according tothe procedure set out in, for example, ISO 57251 and ASTM E691.2

ISO 57251 provides detailed guidance on the running of an interlabora-tory (round-robin) trial to determine the precision statement for inclusionin the published standard. The number of participants in an experimentalround-robin exercise depends on the number of ‘levels’ (e.g. materials)used. Normally, for four to six materials, eight to ten participants would beappropriate. The difficulty for composites is the wide and endless range ofmaterials that can be, and are, produced. The need is to select ‘generic’ ma-terials that are covered by the standard, represent different primary varia-tions and represent the major volume, commercial or legal interests. Careshould then be used when applying the precision data to materials with sig-nificant differences, and additional checks should be undertaken by the userof the standard in these cases by, for example, back-to-back comparisonusing one of the ‘generic’ materials.

ASTM E691-792 is similar to ISO 5725 except that it requires explana-tions for the occurrence of outlier data prior to elimination, in addition todata being identified as outliers by statistical procedures. In ASTM stan-dards there is reference to ‘bias’ in addition to ‘precision’. However, in mostcases there is no reference value for comparison in order to determine bias.

The precision of a test method is determined from an assessment of boththe repeatability (r) and reproducibility (R) of the method. Repeatabilityis defined in the standard as ‘the value below which the absolute differencebetween two single test results obtained under repeatability conditions maybe expected to lie within a probability of 95%’.

• Repeatability conditions refer to measurements made by the samemethod, by the same laboratory, by the same operator, on the sameequipment, within a short period using identical test material.

• The reproducibility is similarly defined using the same methods but dif-ferent laboratories, different operators, different equipment and identi-cal test material.

For a destructive test the requirement for identical material to be usedin the evaluation cannot be met; consequently the repeatability and repro-


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ducibility values determined also include the material variability, whichreinforces the need to use representative materials with low intrinsic vari-ability. The repeatability and reproducibility standard deviations are thestandard deviations giving the dispersion of test results obtained under therespective conditions.

Although these standards define the procedure to be used to measurethe precision, the actual values that are acceptable are decided by the expertcommittee responsible for drafting the standard in question. Essentially, theprecision of the test method should be commensurate with its intendedpurpose (i.e. it should meet a fitness for purpose criterion). Some standardsalready include such data (e.g.ASTM D790).3 However, standards normallyindicate that data are not available through the wording:

Clause 11 PrecisionThe precision of this test method is not known because inter-laboratory dataare not available. When inter-laboratory data are obtained, a precision state-ment will be added with the next revision.

Clauses indicating the existence of data are less common. An unusualexample is given above in Table 15.1.4 The expression that data from onetest in 20 tests will lie outside the precision range is a more easily under-stood and practical interpretation of the 95% confidence limits.

15.3.2 Validation data

Some examples of recent round-robin validations are available.5 The dataprovided in Table 15.2 are from a round-robin on the manufacture of a testpanel for specimen preparation. The procedure used now forms an inputinto the revision of ISO 1268, a multipart standard at CD ballot in 1998

Table 15.1. Reasonably understandable definition of repeatability andreproducibility.

Repeatability Reproducibility

The difference between two single The difference between two single test results found on identical test and independent results found by material by one operator using the two operators in different same apparatus within a short time laboratories on identical test interval will exceed the repeatability material will exceed the on average not more than on in repeatability on average not more twenty instances of the norma and than one in twenty instances of the correct operation of the method. normal and correct operation of

the method.

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Tab

le 1

5.2.

Pre

cisi

on

dat

a fo

r sp

ecim

ens

take

n f

rom

pla

tes

man

ufa

ctu

red

usi

ng

au

tocl

aves

at

eig

ht

site

s.5

Pro

per

ty a

nd

pan

el

Mea

nR

epea

tab

ility

sdo

f r

Rep

rod

uci

bili

ty

sdo

f R

thic

knes

sr

/Mea

n (

%)

R/M

ean

(%

)

Fib

re1

mm

69.3

%2.

44%

1.4

8.44

%4.

4W

eig

ht

2m

m67

.1%

5.43

%2.

56.

54%

3.5

Frac

tio

n5

mm

69.2

%3.

41%

1.5

4.35

%2.

2In

ter-

lam

inar

sh

ear

2m

m10

4M

Pa

10.0

MP

a3.

422

.4M

Pa

7.6

stre

ng

thFl

exu

re p

rop

erti

es2

mm

E11

122

GP

a6.

81G

Pa

2.0

31.3

GP

a9.

1E

227.

96G

Pa

0.58

GP

a2.

61.

89G

Pa

8.5

S11

1780

MP

a24

6M

Pa

4.9

321

MP

a6.

4S

2215

1M

Pa

39.9

MP

a9.

456

.0M

Pa

13.2

(NB

E =

flex

ure

dm

od

ula

r in

11

or

22 d

irec

tio

n,

S =

flex

ura

l st

ren

gth

sim

ilarl

y).

MTA15 11/22/2000 3:02 PM Page 346

covering all composites process routes. Part 4 deals with the aerospacepreimpregnates materials most relevant to this text. The validation data arefor a single batch of low-bleed carbon-fibre/epoxy preimpregnate, delivereddirectly to eight sites, manufactured at three thicknesses using autoclavesunder the time/pressure conditions specified by the manufacturer and thentested using a range of mainly quality assurance (QA) test methods at asingle site. The results of this validation exercise are given in Table 15.2. Asexpected, the R values are greater than the r values.

15.4 Sources of standards and test methods

The principal sources of standards and recommended methods are briefly reviewed below, together with their main characteristics and output.

15.4.1 International Standards Organisation (ISO)

• There are 167 member countries worldwide.• Composites are principally covered by the Technical Committee (TC)

61(Plastics)/ Sub-Committee (SC) 13(Composites) within six workinggroups (WG) (TC61/SC13/WG 14, 16, 20).

• Some tests for all plastics that are prepared in other SCs within TC61apply to composites.

• A comprehensive series is available for glass fibres and their secondaryproducts (mats, fabrics, woven roving and yarns).

• Set of standards for carbon fibres has been published.• Test panel manufacture is being prepared in ten parts to cover all

current process routes (new methods can be added).• Laminate test methods were published in 1997–2000 to cover all present

and future fibres and matrices that meet the requirements of the standard.

15.4.2 Comité Européen de Normalisation (CEN)

It is mandatory to publish in all European countries, including Iceland.

15.4.2.1 General series

• The plastics work area CEN TC249 with composites sub-committee(SC2) was established in 1990.

• The same convenor and secretariat (AFNOR) as ISO TC61/SC13 com-mittee provide excellent liaison and cooperative working as envisagedunder the Vienna agreement.


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• A similar structure to ISO has been established to aid joint drafting/validation exercises for composites.

• There are working groups on all fibres (specification and test), twoactive on composites materials, one each at the sub-component productlevel (pultrusions) and composite material test methods.

• The main interest is the development of specification standards, whichis complemented by the support and adoption by CEN of ISO testmethods.

• 150 plus ISO test methods for plastics being balloted as CEN standardson a straight yes/no acceptance require German language versions toadd to existing English and French versions.

15.4.2.2 Aerospace

• European aerospace series is prepared by the trade federation Association Européen des Constructeurs de Material Aerospatiale(AECMA).

• Initially, there were fibre specific mechanical and physical test methodsleading to duplicate methods with unwarranted differences in the samemethod for similar fibres (e.g. carbon, glass and aramid).

• Scope is limited to aerospace.• Test methods are normally not experimentally validated but accepted

on a consensus basis.• Some standards are not in agreement with current practice owing to a

long gestation period.• Modulus is measured at set load levels (cf. strain levels in all other series

of standards).• The Airbus Industries Test Methods (AITM) proposed 6000 series has

special drafting and voting arrangements.

15.4.3 EN-ISO Vienna agreement

The Vienna Agreement on sharing of the work load between ISO and CENallows either organisation to lead work items, with agreed responsibilitiesfor consultation and timescales. A parallel voting procedure is used, so thatthe approved document becomes both a CEN and an ISO standard, or oneor other if not agreed by both ISO and CEN. Depending on the lead organ-isation, different responsibilities apply.

For CEN led work, the project leader must take care to consult fully withnon-CEN countries. For ISO led items, ISO must work quickly to match thefast development of standards required in Europe. However, faster devel-opment of standards is also an increasing requirement in ISO. For com-posites, liaison is easily accomplished in the field of composite materials, as


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the ISO and CEN Sub-Committee Chairman and Secretariat (AFNOR) arethe same and many of the leading ISO WG members and convenors arealso CEN convenors.

15.4.4 International prestandardisation research – VAMAS

One aim of the VAMAS (Versailles Project on Advanced Materials andStandards) is to avoid the need for protracted harmonisation on existingstandards, through collaborative international prenormalisation research.The programme is chaired alternately by the UK (NPL) and the USA(NIST). The overall objective is to promote trade in high technology products through international collaboration in prestandards research. Thisgenerates the technical basis from which common accepted standards andspecifications for advanced materials can be developed.The initiative is sup-ported by the G7 countries (i.e. Canada, France, Germany, Italy, Japan, UK,USA and the EU, with Russia becoming the eighth member). Other coun-tries can apply to participate in individual projects.

It is the intention of this initiative that the technical work conductedshould result in a recommended procedure that would be supported by allthe VAMAS member countries to produce an agreed international stan-dard test method and that the VAMAS work should provide the necessaryvalidation evidence. Examples of current activities in 2000 included:

• Fatigue (ISO 13,003) – data obtained in a VAMAS fatigue round-robin5

have been used to support a French proposal dealing with tensile andflexural fatigue testing.

• Fracture toughness – VAMAS has run an intercomparison of four com-peting Mode II methods from Japan, USA and Europe in order to rec-ommend to ISO the preferred method(s) to be standardised.

• Compression-after-impact (CAI) – It was agreed that the programmewould look fundamentally at the general design requirements for meas-uring material impact resistance related to damage tolerance in struc-tures before, if appropriate, working on standardisation of the currentlydeveloped CAI test.

• Interfaces – A round-robin on measurement of ‘interface’ mechanicalstrength is being run by NIST. This work area anticipates future needs,since interfaces are particularly important to the behaviour and perfor-mance of composite materials, but there are no established test methodsor standards.

15.4.5 National standards

The principal national committees contributing to composite test methodsstandardisation are given below. Increasingly national standards in Euro-


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pean countries will be replaced as a consequence of the mandatory publi-cation of EN standards.

(a) UK – British Standards Institution (BSI)• PRM/42 committee provides UK vote on the general engineering

series for fibres and composites at CEN and ISO and produces BSIstandards in this area.

• ACE/64 committee provides UK vote on AECMA/CEN aero-space series.

• PRM/21 provides UK vote on general plastics test methods includ-ing ISO revisions

• A comprehensive series of plastics test methods are available (BS2782), which are being replaced dual numbered by ISO or CENstandards.

(b) Japan – Japanese Industrial Standards (JIS)• An early series of glass-fibre/resin standards was provided, with a

later series of carbon-fibre test methods.• Initially related to ASTM methods, followed by Japanese devel-

opments but now implementing ISO standards.• English translations are available for at least four standards for

carbon-fibre reinforced plastics.(c) USA – American National Standards Institute/American Society for

Testing and Materials (ANSI/ASTM )• ANSI provides the secreteriat for TC61 and provides the official

USA vote, while ASTM provides the specialist composites inputbased on the D30 committee activities.

• ASTM has published many fibre and laminate test methods; they are not fibre-type specific, but a fibre modulus greater than 20GPais required.

• Some carbon-fibre specific standards are provided for tensileproperties, resin flow, gel time and for basic fibre and yarns.

• Use of standards is not limited to the aerospace industry.(d) Germany – Deutsches Instut for Normung (DIN)

• Laminate tests are available in the aerospace series, with somefibre specific methods.

• Fibre property methods are available, especially for textiles andglass fibres.

• There is a full range of general plastics test methods.(e) France – Association Français de Normalisation (AFNOR)

• There are comprehensive series of methods and specifications forglass fibres and glass-fibre based systems.

• Drafting has concentrated on glass-fibre resin prepreg properties.(f) Italy – Ente Nazionale Italiano di Unificazione (UNI)


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• Glass-fibre standards are available; carbon-fibre versions are beingdrafted.

• There is an extensive series of methods for glass-fibre reinforcedthermoplastics pipes.

• No laminate test methods are available.

15.4.6 Trade and other groupings

(a) Suppliers of Advanced Composite Materials Association (SACMA) recommended methods (USA)6

• Well prepared, fibre non-specific set of laminate test methods isavailable.

• Methods are based on ASTM standards where possible but somerevisions (e.g. reduced range of specimen sizes) undertaken.

• New methods have been proposed for preparation as ASTM stan-dards.

(b) Composites Research Advisory Group (CRAG) recommended methods (UK)7

• Methods are recommended by UK grouping of defence establish-ments and aerospace industry companies.

• There are three reports following work started in 1982 and com-pleted in 1988.

• A coherent and consistent set of test methods for all fibre (textilefibre diameter) types and continuous formats (unidirectional, mul-tidirectional and fabric) is recommended.

• There are individual test requirements sensitive to fibre type, ori-entation and so on, where technically required.

• These methods were adopted by the Advanced Composites Groupof the British Plastics Federation (now the Composites Group) andproposed to BSI as the basis for national and international stan-dards, but delayed by lack of experimental evidence for validation.

(c) European Structural Integrity Society (ESIS)ESIS has been active in many areas and in particular on fracturetoughness studies for polymers and composites, with several roundrobins aimed at validation of the draft test methods produced. Itsubmitted the drafts for both Mode I fracture toughness tests forpolymers and for delamination in composites and provided one ofthe Mode II methods currently being compared in the VAMASproject on behalf of ISO.

In addition, many other groups and bodies exist, such as the EuropeanSpace Agency (ESA), USA National Aeronauticals and Space Adminis-tration (NASA), USA Department of Defense (DoD) and the Military


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Engineering Society for Advancing Mobility, Land, Sea, Air and SpaceHandbooks, and so on, that publish or have interests in test methods forcomposites.

15.5 Harmonisation of composite test methods

Several factors have prompted the drive for international harmonisation ofcomposite test methods over the last few years. Principally, these are:

• The internationalisation or globalisation of supply, manufacturing anduser industries

• The need to reduce the cost of all testing, particularly when expensivejigs are required

• earlier availability of a comprehensive and validated database• The need for increased traceability of test methods and data.

As noted in the previous section, a large number of initiatives on com-posite materials test methods were being pursued worldwide, in responseto the strong demand for test methods for advanced composites. The testmethods have been found through experience to be generally reliable andrepeatable, but a detailed review showed that there was an absence of fullvalidation to show the site-to-site reproducibility.8 A detailed assessment ofthe test method specifications9 in these initiatives showed that most hadsimilar philosophies and a large degree of technical similarity. This similar-ity, together with the increasing international aspect of the advanced com-posites industry, highlighted below, supported the harmonisation of thesetest methods.

Several of the initiating bodies were cooperating informally in the har-monisation of test methods, so that it was likely that their validation exer-cises could be used to support the new or revised international (ISO)standards. ASTM had an international task force, with overseas members,working on the comparison of test specifications following the lead takenon behalf of the Advanced Composites Group of the British Plastics Federation.10

The international aspects are illustrated by the following factors:

• Many of the major supply companies are international, with plants andassociated companies in Europe, Japan and the USA, a trend aided byrecent mergers and acquisitions.

• Subcontracted work crosses most boundaries, including the Atlantic andPacific Oceans, in both directions.

• Major products such as aeroplanes are sold and operated worldwide,with a specialist task force entitled the Commercial Aircraft Com-posite Repair Committee (CACRC) involving worldwide representa-


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tion from all sectors of the supply, aircraft manufacture and user interests.

• Other products, such as automobiles, process plant, access engineering(ladders, walkways, handrails), are also produced and sold on a world-wide basis.

The aerospace industry dominates the advanced composite market andthus the material specifications and test methods. However, it is agreed ingeneral that the material properties themselves define the data and testmethod requirements for critical applications and that these will be similarfor both aerospace and non-aerospace use. Hence, it is likely that a commonseries of test methods can be developed (cf. BS 18 Method for tensile testingof metals, which includes aerospace materials11) acceptable to both groupsof users.

A further coincident incentive to harmonisation of standards was theincreasing demand from users and designers for extensive data for design


Table 15.3. Recommended international test methods equivalent to CRAGmethods.

Property and method Recommended method CRAG number

Tensile properties – unidirectional BS EN ISO 527-5 and -1 300, 301– fabric/multidirectional BS EN ISO 527-4 and -1Compression properties BS EN ISO 14126 400, 401Flexural properties BS EN ISO 14125 200Interlaminar shear strength BS EN ISO 14130 100In-plane shear properties BS EN ISO 14129 101Notched (hole) tensile strength ISO NWI (UK draft)/ASTM D 303

5766Notched (hole) compressive ISO NWI (UK draft)/ASTM D 403

strength 6484Bearing properties – pin ISO NWI (UK draft) prEN 700

6037– bolt ASTM D 5961

Fracture toughness – Mode I ISO 15024 600– Mode II ISO NWI proposal from

VAMAS (see text)Fatigue properties ISO/CD 13003 500Fibre, resin and void fractions 1000

– glass fibre ISO 1172/ISO 7822– carbon fibre ISO 14127

Density of plastics ISO 1183 800Hot/wet conditioning prEN 2823 902Out-gassing ESA-PSS-01-722 802Coefficient of linear expansion ISO 11359-3 801

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Table 15.4. Standards organisations and other bodies.

Acronym Title

ACE/64 Aerospace series – Reinforced Plastics Committee at BSI (UK)ACG Advanced Composites Group of BPF (UK)AECMA Association Européen des Constructeurs de Material Aerospatiale AFNOR Association Français de Normalisation (France)ASTM American Society for Testing and Materials (USA)BPF British Plastics Federation (UK)BSI British Standards Institution (UK)CEN Comité Européen de NormalisationCEC Commission of the European CommunitiesCFMA Carbon Fibres Manufacturers Association (Japan)CRAG Composites Research Advisory Group (UK – Ministry of Defence)DIN Deutsches Instut fur Normung (Germany)DoD ESA Department of Defense (USA) European Space AgencyESIS European Structural Integrity Society (was EGF)ETAC European Trade Association of Advanced Composite Materials

SuppliersEFTA European Free Trade AssociationISO International Standards OrganisationJIS Japanese Industrial Standards (Japan)MoD Ministry of Defence (UK)PRM/42 Fibres for reinforcements and test methods for composites, BSI

CommitteePRM/21/-/3 Plastics – mechanical properties, BSI CommitteeSACMA Suppliers of Advanced Composite Materials Association (USA)VAMAS Versailles Project on Advanced Materials and Standards

calculations (e.g. in finite element analysis packages), together with anincreasing concern over the cost of testing and qualifying materials.Although there is a great similarity between different versions of the sametest, there are detailed differences which have poorly, if at all, understoodinfluences on the data recorded.

For example, while most compression test methods for unidirectionallyreinforced material use a plain strip specimen (normally tabbed), there area multitude of loading/support jigs and associated specimen aspect ratioswhich yield different results.12 At the same time basic questions remainabout the compression failure mode, how it should be measured, the influ-ence of macro- and microbuckling, and so on, so that it still needs to beestablished if any individual method is appropriate to the prediction ofservice performance under compression loads. The new BS EN ISO 14,126standard, and its equivalent ASTM method D3410, concentrate on thequality of the test by limiting the specimen bending regardless of the testjig.

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15.6 Recommended mechanical test methods

As noted previously, the specifications for the most commonly used testmethods for advanced composites have been found to be similar and har-monised standards have been published. It is informative to consider theoriginal list of CRAG recommendations, as being the most complete andintegrated series to assess the progress over the last few years. Table 15.3shows the test methods from CRAG7 with the current equivalent recom-mendation from the ISO, CEN or ASTM series.

Some methods do not have equivalents in the official standards system.For example, there is no official standard for the measurement of porosityusing ultrasonics (CRAG number 1001), although work at NPL (NationalPhysical Laboratory) supported by DERA (Defence Evaluation andResearch Agency) has led to procedures aimed at establishing the tech-nique itself on a firmer and traceable basis.13 The data requirement sup-porting ‘background information on environmental effects’ (CRAGnumber 900) is covered by several ISO and EN test methods.

It is clear from the information presented in this chapter that the require-ments for a comprehensive and consistent series of standard test methodsfor advanced composites are being developed from the available recom-mended methods by cooperative action within the international bodies suchas ISO, CEN and, for supporting research, VAMAS and ESIS. Thisapproach is drastically reducing (1) the number of standards to be pro-duced, (2) the chances of confusion and (3) the costs of qualification testingand the cost of introducing new materials. A coherent set of test methodswill also increase the designer’s confidence in these materials by providinga larger and more reliable source of property data.

Table 15.4 identifies standards organisations and other bodies interestedin test methods, and Appendix A gives their contact points.

References

1. ISO 5725, 1986; BS 5497: Precision of Test Methods, BSI (London), 1987.2. ASTM E 691-92: ‘Standard practice for conducting an interlaboratory study to

determine the precision of a test method’, Annual Book of ASTM Standards,Section 14, General Methods and Instrumentation, Vol 14.02, 1992.

3. ASTM D 790M-93: ‘Standard test methods for flexural properties of unrein-forced and reinforced plastics and electrical insulating materials’, Annual Bookof ASTM Standards, Section 8, Plastics, Vol 8.01, 1994.

4. ISO 1924-2: ‘Paper and board – Determination of tensile properties – Part 2:Constant rate of elongation method’, 1995.

5. G D Sims, ‘Validation results from VAMAS and ISO round robin exercises’,Tenth International Conference on Composite Materials, Whistler, Vancouver,BC, Canada, eds A Poursartip and K Street, Woodhead, Cambridge, UK, Vol 4,1995, 195–202.

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6. SACMA Recommended Methods, SACMA, 1600 Wilson Boulevard, Suite 1008,Arlington, VA 22209, USA.

7. P T Curtis, CRAG Test Methods for the Measurement of the Engineering Prop-erties of Fibre Reinforced Plastics, Royal Aircraft Establishment, FarnboroughUK, Technical Report Technical Report 88012, 1988.

8. G D Sims, Standards for Polymer Matrix Composites. Part I – Assessment ofCRAG Test Data, NPL Report DMM(A)6, 1990.

9. G D Sims, Standards for Polymer Matrix Composites, Part II – Assessment andComparison of CRAG Test Methods, NPL Report DMM(A)7, 1990.

10. G D Sims, Development of Standards for Advanced Polymer Matrix Compos-ites – a BPF/ACG Overview, NPL Report DMM(A)8, 1990.

11. BS 18: Method for Tensile Testing of Metals (Including Aerospace Materials),1987.

12. F L Matthews, E W Godwin and G Rueda, ‘Mechanical testing and relevanceof standards’, Institute of Mechanical E Conference on Designing with Com-posites, London, 1989.

13. W R Broughton, M J Lodeiro and G D Sims, Validation of Procedures for Ultra-sonic Inspection of PMCs: UK Round Robin, NPL Report CMMT(A)179.

Bibliography – selected ISO standards

BS EN ISO 527 – Part 1 Plastics – Determination of tensile properties – Generalprinciples.

BS EN ISO 527 – Part 4 Determination of tensile properties – Test conditions for isotropic and orthotropic fibre-reinforced plasticcomposites.

BS EN ISO 527 – Part 5 Plastics – Determination of tensile properties – Test conditions for unidirectional fibre-reinforced plasticcomposites.

BS EN ISO 14125 Fibre-reinforced plastic composites – Determination offlexural properties.

BS EN ISO 14126 Fibre-reinforced plastic composites – Determination ofthe in-plane compression strength.

BS EN ISO 14129 Fibre-reinforced plastic composites – Determination ofthe in-plane shear stress/shear strain, including the in-plane shear modulus and strength, by the ±45° tensiontest method.

BS EN ISO 14130 Fibre-reinforced plastic composites – Determination ofthe apparent interlaminar shear strength by the short-beam method.

ISO 13003 Fibre-reinforced plastics – Determination of fatigueproperties under cyclic conditions.

ISO 15024 Standard test method for mode I interlaminar fracturetoughness Gic of unidirectional fibre-reinforced polymermatrix composites.

ISO 15310 Fibre-reinforced plastic composites – Determination ofin-plane shear modulus by the plate twist method.

ISO 1268 Fibre-reinforced plastics – Test plates manufacturingmethods. Part 1: General conditions.


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ISO 1172 Textile glass-reinforced plastics – Determination of losson ignition.

ISO 10352 Fibre-reinforced plastics – Moulding compounds andprepregs. Determination of mass per unit area.

ISO 7822 Textile glass-reinforced plastics – Determination of voidcontent.

ISO 14127 Determination of the resin, fibre and void content forcomposites reinforced with carbon fibres.

ISO 10350-2 Plastics – Acquisition and presentation of comparablesingle point data. Part 2: Long fibre-reinforced plastics.

ISO 11359-2 Plastics – Thermomechanical analysis (TMA). Part 2:Determination of coefficient of linear thermal expansionand glass transistion temperature.

Appendix A – Contact details for

standards organisations

1. International Standards Organisation (ISO) – standards available from nationalbodies.

2. Comité Européen de Normalisation (EN) – standards available from Europeannational bodies.

3. British Standards Organisation (BSI), 2 Park Street, London WIA 2BS, UK.4. Association Français de Normalisation (AFNOR), Tour Europe, La Défense,

Cedex 7, 92080-Paris, France.5. Deutsches Institut fur Normung e.V (DIN), Postfact 1107 D-1000, Berlin 30,

Germany.6. American Society for Testing and Materials (ASTM), 100 Barr Harbor Drive,

West Conshohocken, PA 19428, USA; [Plastics (Vol. 8.01, 8.02, 8.03) Composites(Vol. 15.3)].

7. Japanese Industrial Standards (JIS), Standards Department,Agency of IndustrialScience and Technology, Ministry of International Trade and Industry, 1-3-1Kasumigaseki, Chiyoda-ku, Tokyo, Japan.

8. Ente Nazionale Italiano di Unificazione (UNI), Piazza Armando Diaz 2, 1 20123,Milano, Italy.

Latest information and hot-links on standards available from Composite GroupWeb Pages at NP (www.npl.co.uk/cog/index.html)


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analysis of variance, 22anti-buckling guide, 87, 229, 231–2, 250, 252Arrhenius, 286, 288autoclave, 37–9, 41, 90, 332–4, 337, 347

Barcol hardness, 274barely visible damage, 32beam, 17, 26–7, 29, 31, 116, 124, 127–8, 130

short, 17, 27, 29, 161–3, 166–7v-notched, 101, 110–11, 113, 118, 120–1,

161, 164–7Bending moment diagram, 125–6bias, 344buckling, 157, 159–60, 163, 250, 304, 306–12

macro-, 85, 96, 354micro-, 76, 156, 354ply, 228sublaminate, 228

Celanese (fixture) jig, 77, 79–83, 85–6, 93central

limit theorem, 317–18, 324tendency, 316, 322

chain scission, 269charge coupled devices, 182, 196committee draft, 342–5compliance calibration, 187, 189–90, 193,

198–9compression, 8, 16–17, 21, 24–5, 29, 33, 40,

51, 75, 78, 87–92, 94–6, 109, 116, 124after impact, 228, 230, 349post-impact, 225

confidence, 319, 320–1, 326–7limits, 21, 23, 326

controlload, 255–6position, 255strain, 255–6

creep, 7, 13, 33, 63, 283, 332rupture, 7, 22, 30, 33, 284

criticalenergy release rate, 170, 173, 178, 188,

193–4, 201–2

stress intensity factor, 171, 173, 303cyclic, 2, 119–20, 150, 248–9, 255

damageaccumulation, 265mechanics, 244parameter, 219, 237, 239subcritical, 218tolerance, 32–3, 212, 225, 228, 233, 241,

243–4, 349data

acquisition, 50, 62, 152, 225analysis, 196, 212, 225interpretation, 235reduction, 64, 101, 117, 119–21, 144, 148,

150, 152, 156, 162, 176, 178, 180, 187,190, 192–3, 197, 200, 206

delamination, 15, 59, 104, 109, 144, 154,170–207, 219, 228, 237–8, 241, 250–1,258–9, 282, 332, 351

deply, 258design allowables, 145, 235diffusion, 276, 284–9

coefficient, 285–91equations, 285

direct loading, 76, 78dispersion, 316draft international standard, 342–3drilling, 39dry cutting, 39, 69ductility, 6, 7, 24

edge delamination, 205–6end block, 174, 180, 183, 187, 191–2, 197–8,

201–2end-tab, 27, 40–1, 44, 51, 57–60, 62, 65–6,

71–3, 76, 84–6, 89, 91–2, 94, 102, 107, 261environment(al), 2, 30, 34, 62, 106, 119–20,

151–2, 155, 263–4, 269–72, 276–9, 282,284, 340, 355

conditioning, 181–2hot/wet, 29, 276, 353stress cracking, 270, 282

Index

359

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360 Index

testing, 269, 274–5threats, 270

explanatory variable, 314, 316, 333–4, 338extensometer, 53–5, 63, 71, 103, 119, 148,

158, 160, 255

failure mode, 67, 71, 89–90, 112–14, 121,133–4, 217, 354

fatigue, 7, 22, 30, 152, 184, 228, 248, 315,336–8, 349, 353

biaxial, 254compression-compression, 250, 252damage development, 249, 256flexure, 250, 252, 349limit, 256resistance, 248shear, 253tension-compression, 250, 252, 266tension-tension, 250test coupon, 249

fibrebridging, 184, 188, 204–5buckling, 76, 96, 144

Fick(ian), 285–90finite element analysis, 106, 111, 143, 160,

162, 173, 203, 244, 353flexure, 8, 24, 26–7, 124

four point, 87, 125, 127, 130, 133, 163, 199three point, 17, 26, 125–6, 130, 132, 136,

161–2, 198, 300–1fracture mechanics, 302–3, 312fracture toughness, 6, 18, 25, 29, 33, 124, 188,

204, 216, 349, 351, 353

gauge length (section), 25, 56–7, 63, 67, 71–2,85, 87, 89, 91–2, 102, 107, 111, 113,116–17, 145, 147, 150–1, 153, 158–9, 250

glass transition temperature, 279–80Goodman diagram, 256–7

honeycomb, 87, 124, 214Hopkinson bar, 214

ICSTM jig, 79, 82, 85, 93–4, 96, 97impact, 7, 31, 32, 273

ballistic, 212, 214boeing, 229–36, 241–3charpy, 215–18compression after, 228, 230, 233–5, 241,

243damage, 211, 228–9, 233, 237, 243dynatup, 226, 231energy, 212, 223–4, 229–40flexed beam, 215–17flexed plate, 218gardner, 231hypervelocity, 212in-plane, 214instrumented, 212

izod, 215–18out-of-plane, 212, 214–15post-, 211, 213, 219, 225–6, 243resistance, 7, 33, 211, 237, 243, 349strength, 212test(ing), 211–18, 227–31test methods, 225through penetration, 222–3, 225velocity, 212, 217

interface, 8–9, 15, 17, 204–5, 262, 276, 281,293, 349

interlaminarfailure, 156, 162fatigue, 250fracture toughness, 170–81, 258stresses, 143, 145, 155, 162tensile strength, 146, 150, 155

interquartile range, 316ITRII jig, 79–81, 85–7, 94

laminate production, 36, 84, 90

mean, 314, 316–19, 322, 324, 326–7, 329,346

stress, 249, 256value, 20–2

median, 20, 316, 322, 324microcrack(ing), 176, 269, 275–6, 282mixed mode, 29, 104, 112, 118–19, 156, 164,

176, 178, 200–1, 206mode i, 170–85, 188–9, 194, 196–8, 200–6,

228, 351, 353mode ii, 170–8, 194–203, 206, 351, 353mode iii, 171, 176, 200, 206mode separation, 202modified beam theory, 187–90, 193, 197modulus, 7–8, 16–17, 47, 49, 53, 67, 75, 90, 92,

95–7, 102, 112, 116, 269, 305, 310, 348,350

compression, 25, 92–3, 124elastic, 6–7, 24, 51, 64–5, 71, 167, 196–7,

203flexural, 25–6, 131, 134–5, 138, 178, 188,

203, 274secant, 64–5shear, 13–16, 25–6, 100–24, 166–7tangent, 65tensile, 15–16, 25–8, 33, 43, 47, 124, 277

multi-directional, 58–9, 73, 87–8, 91–2, 114,145, 204–6, 341, 351, 353

new work item, 342–3non-crimp fabrics, 241–2non-destructive, 116, 118, 214, 219, 265, 342normal distribution, 317, 319–20, 322, 330

open hole, 29out-of-plane, 100, 111–12, 114, 141, 143, 164,

166, 233

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Index 361

parallel-sided, 44, 72, 250–3parametric, 317, 322, 324–5pattern, 41permeability index, 288plane strain, 173Poisson’s ratio, 13, 25, 47, 54–5, 65, 110, 115,

146, 148, 172, 309pooled distribution, 320population, 20, 314, 316–21, 324–7precision, 343–6precrack(ing), 176, 184, 194, 198press-clave, 37–8, 90, 332, 336probability, 21, 298, 300, 314, 322–3, 327

qualityassurance, 4, 225, 341, 347control, 4, 30, 39, 125, 161

quasi-isotropic, 67, 93, 170, 220–8, 237–41,298, 301–4, 311

radiation, 270–1repeatability, 88, 121, 344–6reproducibility, 88, 101, 344–6, 352residual

strength, 219, 228, 232–7, 240–1, 255,264–6

stresses, 58, 106, 144, 148, 205resistance curve, 184–5, 200response variable, 314, 333–4, 338round robin, 76–7, 110, 116, 175, 187, 232,

235, 344–5, 349, 351

Saint Venant’s Principle, 13, 25, 57, 145sandwich, 85, 87, 124, 157–8scale

effect(s), 294–7, 301–4, 311–12model, 293–5, 302, 308–10

scaling, 293–4, 305scrim cloth, 41shear, 2, 13, 15, 17, 24, 26–7, 33, 76–8, 81, 87,

90, 93, 100–1, 108, 110–13, 116–18, 121,159

buckling, 116coupling, 103failure, 160–1force diagram, 125–6interlaminar, 6, 9, 16–17, 25, 29, 33, 87,

124, 128, 133–4, 145, 161, 163, 353pure, 100–1, 103, 109, 111, 114, 116, 160rail test, 101, 107–10, 118, 121, 253–4wyoming fixture, 110

significance, 319–21span/thickness (depth) ratio, 17, 27, 128–30,

133, 136, 141, 162specimen (sample)

bow-tie, 44–5configuration, 206c-section, 146, 153, 167design, 2, 46, 73, 107

dog-bone, 44–5double cantilever beam, 174, 178–81, 186,

188, 194, 195, 197–9, 202, 204, 205double-notch, 161, 166dumbbell, 116, 341edge cracked torsion, 176–7edge delaminated, 204–6end-loaded split, 172, 175 194–5, 198–9,

201–2, 206end-notched flexure, 172, 174–5, 194,

198–9, 253–4, 258fabrication, 101, 117, 120, 144, 148, 160,

161fixed ratio mixed mode, 176–7, 201, 206geometry, 15, 164, 272i-section, 146, 152, 167manufacture, 39, 178mixed mode bend, 176–7, 201–2, 206±45° tensile, 101–6, 118–19, 253plate-twist, 114–16, 118, 120, 121preparation, 36, 67, 76, 83, 109, 119, 161,

164, 178, 345production, 89–9010° off-axis, 101, 104–7, 119

stacking sequence, 15–16, 19, 26, 62, 100,263, 304–8, 310, 312

standard deviation, 20–1, 71, 316–17, 326,329, 339, 345

statisticalanalysis, 271, 298approach, 295

strain-gauge, 25, 36, 41, 52–3, 55–6, 62, 84–5,90, 95, 97, 103, 105–9, 111, 117, 119–20,126, 148, 151–2, 158–60, 233–4, 255

strain measurement, 53, 62strength, 6–7, 21, 24, 28, 33, 45, 68–9, 73,

75–6, 92–3, 95, 97, 102, 110, 119–20, 269compression(ive), 25, 75–6, 78, 87, 90, 93,

97, 159, 211, 300flexural, 25, 128, 135, 138, 273–4, 276, 301shear, 15, 44, 59, 95, 100–1, 103–4, 107–8,

112–14, 118–21, 124, 164, 166–7, 273, 276tensile, 15, 25, 27, 29, 43–4, 47, 59, 69–70,

75, 145, 273, 276–7, 353through-thickness, 147, 153, 158, 161

stressamplitude, 249, 256relaxation, 7, 283

stress-life diagram, 250–1stress-strain curve, 64, 89, 91, 103–4, 106,

108, 112stress-strain-time, 249Student’s t, 21–2, 319–21

tension, 8, 13, 15, 17, 26–7, 40, 43test(ing)

apparatus, 144equipment, 50, 101, 117, 119, 161jig, 2

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362 Index

machine, 2, 25, 32, 50–4, 59, 62–3, 68, 90–1,117, 182, 194–5, 199, 212–13, 248, 254,332

thermal shock, 270thermography, 257, 260, 262through-thickness, 7, 52, 57–9, 62, 72, 81,

100–1, 106, 109, 114, 118–20, 214compression, 156flexure, 140shear, 160–1, 163–4, 170tensile, 146, 170testing, 143

time dependent, 7, 13, 243thoughness, 7, 171transverse

sensitivity, 41, 55strength, 138

tube (cylinder)filament wound, 18–19

hoop wound, 116–18thin-walled, 101, 116, 120

ultrasonic, 39, 84, 257, 259–60, 276, 355

VAMAS, 349, 351, 354–5variance, 20–1, 316–21, 324–7, 330, 332, 334Vienna agreement, 347–8viscoelastic, 7, 13, 63, 263, 284volume fraction, 8–9, 14, 16–18, 34, 62, 179,

195

waisted(ing), 44, 57, 72, 85, 87, 145, 153,156

block, 149, 151, 156, 158Weibull, 294, 297–8, 300, 302, 312Wheatstone bridge, 55

x-radiography, 257, 260

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Documents

Mechanical testing of advanced ﬁbre composites · 10.6 Standardisation status 241 10.7 Future trends 243 References 244 11 Fatigue 248 p t curtis 11.1 Introduction 248 11.2 Basic