Biaxial Testing of Sheet Metal: An Experimental-Numerical Analysis

Biaxial Testing of Sheet Metal:An Experimental-Numerical

Analysis

Gerard QuaakMT 08.10

TU/e Master ThesisMay, 2008

Engineering thesis committeeprof.dr.ir. M.G.D. Geers (Chairman)dr.ir. J.P.M. Hoefnagels (Coach)ir. C. Tasan (Coach)dr.ir. P.J.G. Schreursdr.ir. H. Vegter

Eindhoven University of TechnologyDepartment of Mechanical EngineeringComputational and Experimental Mechanics

Abstract

With the recent increase in the popularity of advanced high strength steels(e.g. dual phase, TRIP) in automotive industry, new challenges have arisen.Conventional continuum models are found not to capture the reported pre-mature ductile failures in such steels, which are governed by damage evolution.Another challenge is understanding and predicting metal behaviour under com-plex strain paths. The ability to precisely capture these e�ects in continuummodels is important for the sheet metal forming industry, in order to carry outthese processes as e�cient as possible. However, improvements of the numericaltools highly depend on the development of accurate and practical experimentaltechniques. A testing device for biaxial deformation of sheet metal is such anexperimental tool that has been studied by many researchers before. Althoughseveral experimental set-ups have been proposed in the literature, most of thesedesigns are not capable of providing information up to the point of fracture.Additionally, these set-ups are not usable for real-time, in-situ examination ofthe deforming structure with advanced microscopic techniques such as SEM,AFM, surface pro�lometry, or digital image correlation, because a miniaturizedform is not available or was never investigated.The main goal of this project therefore is to �nd a practical and accurate set-up that can deform sheet metal specimens under varying complex strain paths,while allowing for real-time, in-situ microscopic examination. For this pur-pose, several experimental set-ups (e.g. bulge, punch, Marciniak and cruciformtests) have been studied and compared both experimentally and numerically.For testing cruciform samples a simpli�ed in-plane biaxial-loading set-up wasdesigned and build, while Marciniak tests were carried out at Corus RD&T.The corresponding experimental results were used to verify and compare thesetests in terms of practical aspects (e.g. specimen preparation). The computa-tional results are used to analyze stress and strain distributions and for betterunderstanding of the e�ects of miniaturization.Combining literature, numerical and experimental test results, it was concludedthat the cruciform and Marciniak test are the most promising set-ups for minia-turized biaxial testing of sheet metal with in-situ microscopic examination.Both test have their limits, but when taken these into account can providevaluable data.

i

Samenvatting

Met de recente populariteit van 'advanced high strength' staalsoorten (dualphase, TRIP) in de automotive industrie, zijn nieuwe vraagstukken ontstaan.Conventionele continuum modellen blijken niet in staat om de aanwezige taaiebreuk te beschrijven, waardoor het voorspellen van het materiaal gedrag tijdensomvormen van deze metalen niet mogelijk blijkt. Wanner niet lineaire rek padeneen rol spelen blijken de huidige continuum modellen zelfs nog minder accuraat.Voor het verbeteren van de numerieke gereedschappen zijn echter betrouwbareexperimentele technieken nodig, zodat het materiaal gedrag voor deze groepmetalen is te bepalen. Een voorbeeld van zo een opstelling, is er een om biaxialedeformatie van plaat staal te bestuderen. Hiernaar is reeds veel onderzoek aanbesteed, maar hoewel verschillende gereedschappen onderzocht zijn, bestaater tot op heden geen opstelling om tot breuk te deformeren zonder externeinvloeden. Daar komt nog bij dat om de micro structuur van het materiaalte onderzoeken geavanceerde technieken als SEM en AFM of digital imagecorrelation gebruikt moeten worden, wat inhoudt dat een miniatuur opstellingnodig is. Mogelijkheden voor een dergelijke opstelling zijn nog niet eerderonderzocht.Het belangrijkste doel van dit project is dan ook het vinden van een praktischemanier om plaat staal onder veranderende rek paden, met de mogelijkheid real-time metingen te doen. Hiervoor zijn verschillende experimentele opstellingen(bulge, punch, Marciniak en cruciform test) numeriek en experimenteel onder-zocht en vergeleken. De numerieke resultaten geven o.a. inzicht in spannings-en rek velden en de e�ecten van miniaturisatie, de experimentele resultatenworden gebruikt voor veri�catie en vergelijk op praktische gebied, zoals hetmaken van test samples. Voor het testem van kruisvormige trekstaven is eenopstelling ontworpen en gebouwd, als onderdeel van dit onderzoek. Voor deMarciniak testen is gebruik gemaakt van een opstelling beschikbaar gestelddoor Corus RD&T.De literatuur studie, numerieke en experimentele resultaten laten zien dat zowelde kruisvormige trekstaven als de Marciniak test bruikbaar zijn in een geminia-turiseerde vorm. Beide tests hebben beperkingen, maar wanneer hier rekeningmee wordt gehouden kunnen zij waardevolle informatie opleveren.

ii

Acknowledgement

This Master project was mainly carried out at Eindhoven University of Tech-nology, in the group of professor Marc Geers. Experimental work has beendone at Corus RD&T in IJmuiden and in the University Multi-scale Labora-tory. Special thanks goes to Sjef Garenfeld for his time and patience in thedesign process of the biaxial testing set-up and specimens. I also want to thankMarc van Maris, supervisor of the Multi-scale Laboratory, for his guidance andadvice during experimental work and Tom Engels for his help with the tensiletesting machine. From I want to thank Corus RD&T Menno de Bruine, oper-ator of the Marciniak test set-up, Carel ten Horn and Louisa Carless for theirtime and e�ort with the experimental work on the Marciniak test. At PhilipsDrachten a lot of insight was provided in possible material removal techniques,for which I want to express my gratitude to Gerrit Klaseboer, Harmen Altenaand Willem Hoogsteen for receiving us and a good discussion of the materialremoval problem. I also want to thank Johan Hoefnagels and Cem Tasan fortheir input in the project, the many evenings discussing and the help with the�nal report.Gerard QuaakEindhoven, May 2008

iii

Contents

Abstract i

Samenvatting ii

1 Introduction 11.1 Formability and strain path dependency . . . . . . . . . . . . . 21.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Literature Survey 52.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Bulge test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Punch test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4 Marciniak test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5 In-plane loading with cruciform geometry . . . . . . . . . . . . 172.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3 Numerical methodology 233.1 Material model . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 Bulge test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3 Punch test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.4 Marciniak test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.5 In-plane loading with cruciform geometry . . . . . . . . . . . . 28

4 Experimental methodology 294.1 Marciniak test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.1.1 In-plane testing with the Marciniak set-up . . . . . . . . 294.1.2 Specimen manufacturing . . . . . . . . . . . . . . . . . . 30

4.2 In-plane loading with cruciform geometry . . . . . . . . . . . . 304.2.1 Design of a test set-up . . . . . . . . . . . . . . . . . . . 304.2.2 Tests with in-plane cruciform geometry . . . . . . . . . 344.2.3 Specimen manufacturing and characterization . . . . . . 36

5 Results 395.1 Bulge test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.1.1 Miniaturization . . . . . . . . . . . . . . . . . . . . . . . 405.1.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.2 Punch test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

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CONTENTS

5.2.1 Miniaturization . . . . . . . . . . . . . . . . . . . . . . . 445.2.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.3 Marciniak test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.3.1 Working principle of the Marciniak test . . . . . . . . . 475.3.2 Numerical - experimental study of the Marciniak test . . 495.3.3 Minaturization . . . . . . . . . . . . . . . . . . . . . . . 535.3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.4 In-plane loading with cruciform geometry . . . . . . . . . . . . 565.4.1 Optimization of the cruciform design . . . . . . . . . . . 565.4.2 Proof of principle . . . . . . . . . . . . . . . . . . . . . . 575.4.3 Specimen manufacturing and characterization . . . . . . 605.4.4 Miniaturization . . . . . . . . . . . . . . . . . . . . . . . 665.4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.5 Comparative evaluation of the set-ups . . . . . . . . . . . . . . 68

6 Conclusions and recommendations 726.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726.2 Recommendations for future work . . . . . . . . . . . . . . . . . 73

Bibliography 75

A Electrical Discharge Machining 79

B Electrical Chemical Machining (ECM) 83

C Specimen Preparation: TegraPol or Target System 86

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Chapter 1

Introduction

Metals, and in particular sheet metals, are used in a wide variety of appli-cations in industry, with the main �elds of application being packaging (foodcontainers, beverage cans), automotive and aerospace industry. As materialcosts are a substantial part of the costs of manufactured products and mostof the products are produced in large numbers, large cost reductions can beachieved by lowering the amount of material used. Moreover, several otherreasons that can be thought of for lowering the amount of used material, e.g.lowering weight and lowering impact on the environment by polluting. All ofthese reasons result in e�orts to achieve material use reduction without qualityloss in the product.

Figure 1.1: Advantages and disadvantages of using aluminium instead of steel for astandard medium size car [44]

In the automobile industry a �rst attempt to achieve weight reduction wasdone by using low density materials like aluminium, magnesium and plastics,but recent studies show a promising future for steels instead. The InternationalIron and Steel Institute (IISI) computed how the use of aluminium makes thecar body lighter, but does not have a signi�cant e�ect on the total weight ofthe car and causing more environmental impact because of higher equivalentCO2-emissions (see �gure 1.1). The development of Advanced High StrengthSteels that can replace the existing steels is therefore closely followed by theautomotive industry. [16, 44]

1

CHAPTER 1. INTRODUCTION

Figure 1.2: Overview of steel grades as used in the automotive industry [44]

Figure 1.2 shows an overview of regularly used types of steel for automotiveapplications. In this �gure the materials furthest to the left are most suitablefor forming virtually any desired shape, while consuming relative low amountsof energy. The steels on the right, however, can withstand much larger forces,which makes manufacturing more di�cult. An ideal material would have prop-erties of both steel types, being highly formable, yet very strong. Under certaincircumstances, a good combination of these properties can be achieved e.g. bysuitable phase transformations.[44]

Advanced High Strength Steels (AHSS) have such properties, e.g. a relativelyhigh yield strength and high hardening rate compared to conventional steels. Inthe past decades signi�cant amounts of e�orts are put in setting up strategies forimproving FE models to capture these failures. However, to make optimal use ofFE-modelling, a good description of the materials behaviour is necessary, whichrelies on the accuracy of the used constitutive laws for describing the materialbehaviour. The deformation-induced evolution of metal micro structure forwhich, as will be explained in more detailed later, new experimental tools arenecessary. [44]

1.1 Formability and strain path dependency

In the previous section the problems with AHSS were shown, which will beexplained in more detail with the help of the Forming Limit Diagram (FLD)that will be introduced now. The FLD is based on the assumption that forforming purposes, the maximum deformation is limited by the initiation ofunstable deformation, e.g. necking. When forming metal sheets the material issubjected to di�erent strains and strain paths, which have been found to havedi�erent maximum allowable deformations. Therefore in industry the FLD, asshown in �gure 1.3 (a), is used to show these limiting deformations.

On the axes are the strains in the two principle directions in the plane, withthe line giving the point of necking for the combination of strains at that point.The numbers in the �gure show the strain paths pure shear (1), simple tension

2


Figure 1.3: a) Schematic forming limit diagram; b) Stress limit diagram (From Ba-nabic [3])

(2), plane strain tension (3) and biaxial tension (4). These maxima are onlytrue for linear strain paths to that point, and are therefore not a simple to useas it seems.

The limits of the FLD are becoming clear when testing a sheet metal under achanging strain path. The �rst �gure, 1.4(a), shows the strain paths up to neck-ing for linear strain paths on an undeformed sheet of metal. The second �gure,1.4(b), shows where necking starts for a sheet metal that is �rst deformed underuniaxial tension, and then by biaxial tension. A large increase in formability isfound, that was not predicted by the original FLD. When starting with biaxialtension followed by uniaxial tension, a large decrease in formability is found, asshown in �gure 1.4(c). This e�ect is stronger for AHSS then for conventionalsteels, which makes the need for understanding what happens necessary to beable to use the new steels up to full potential. [3, 24]

Figure 1.4: a) Linear strain paths on an undeformed sheet; b) Forming with uniaxialtensile state followed by biaxial; c) Forming with biaxial tensile stagefollowed by uniaxial (From Banabic [3])

A quite similar concept, but not less sensitive to strain path changes and thusthe strain history of the material, is the stress forming limit diagram, as shownin �gure 1.3(b). A disadvantage of the stress based forming limit is uncer-tainty of the computed stresses, which in practice can only be determined frommeasured or computed strain �elds. A FE model could be used to determinethese forming stresses, but therefore the used material model should accuratelydescribe the material behaviour.[24]

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1.2 Objective

The challenges that have grown due to the increased use of AHSS in new de-signs, lead to the goal of this project. This is the development of an experimen-tal methodology to deform a sheet metal specimen under biaxial tension. Theneed for such a methodology to analyze microstructural changes under biaxialloading is obvious, as no such set-up exists. The data obtained with such a testmethod can then be used to predict damage evolution and thus in the futuremake better FE-modelling possible for (re)designing products.

An experimental set-up that can be used to study the microstructural changeswill have to �t in or under standard microscope systems and has to be usablewith digital image correlation systems for in-situ examination of the deformingmaterial. Such a set-up can then be used in future to study and characterizenew materials, as developed by the industry.

The most important properties that will be considered are:

• The existence of a homogeneous stress- and strain distribution in thestudied area of the specimen, which is not in�uenced by contact, frictionor other e�ects introduced by the test equipment.

• The possibility to deform under complex strain paths, preferably with theoption to change the strain path during a test.

• The initial point of fracture and the crack itself should be free to form.In�uences from specimen or set-up must be minimized so the obtainedmaterial data is as undistorted as possible.

1.3 Strategy

Working towards a suitable test method, various known methods for testingunder biaxial loading are studied. The literature survey in chapter 2 is meantto provide better understanding of the problem and di�erent set-ups, so a choicecan be made which testing methods will be used.

The validation and further studying of the most promising set-ups was doneboth numerically and experimentally. The models and the assumptions madeto simplify the computations are being discussed in the �rst part of chapter 3.The second part of chapter 3 contains the experimental set-ups used to validatethe numerical work.

The results of both numerical and experimental work are discussed in chapter4. The numerical and experimental results are compared in order to �nd lim-itations and possible future improvements for both, resulting in an extensiveoverview of all the studied set-ups.

4

Chapter 2

Literature Survey

In the last decades several scientists have studied methods to deform sheet metalunder complex strain paths, including punch tests [3, 36, 39], bulge pressuretests [49, 50], viscous pressure forming tests [37], biaxial compression tests [30]or cruciform tests [11, 19, 32].

Currently the most used method for determining FLCs in the industry is byusing punch tests, which are known to overestimate the maximum allowablestrains [3]. As the exact amount of the overestimation of can not be exactlydetermined, an unknown error in the resulting FLD makes a relatively largesafety margin (up to 10 %) is applied to the maximum allowable strains whenusing the material in a forming process. This means more material will be usedto make a safe structure or product, leading to higher costs. [3, 45, 47]

This chapter will �rst describe several properties of the biaxial testing set-ups,that will be used in the following sections to compare the di�erent set-ups.A de�nition of biaxial stress is giving, followed by de�nitions for the workingplane, geometrical constraining and properties to measure. The set-ups to bediscussed are the punch test, the bulge test, the cruciform tensile test andthe Marciniak test, with a study of the workings of each set-up and recentdevelopments. The last section gives an overview of the studied set-ups, foreasy comparing of each set-up.

2.1 Introduction

Biaxial loading

In the biaxial stress state forces are working in two directions on an in�nitesimalsmall volume, the third direction is the out of plane direction that is related tothe two in plane directions, just like an uniaxial stress state as shown in �gure2.1 on the left. The stresses working on the volume under biaxial stress canbe visualized, as shown in �gure 2.1 on the right: forces are acting on the fourareas perpendicular on the plane, from which the stresses can be computed

5

CHAPTER 2. LITERATURE SURVEY

dividing the force by the area it is acting on.

Strains in a biaxial deformation can than be computed via equations 2.1 to 2.3.Often it is more convenient to measure strains, equations 2.4 and 2.5 are givenfor calculating stresses from known strains. σ3 = 0 as there is no force actingon the plane. These equations are only valid in the elastic regime, whereas inthe plastic regime pure biaxial loading only takes place up to localization. [13]

Figure 2.1: Uniaxial and biaxial stress states [13]

ε1 =1E

(σ1 − νσ2) (2.1)

ε2 =1E

(σ2 − νσ1) (2.2)

ε3 = − ν

E(σ1 + σ2) (2.3)

σ1 =E

(1− ν2)(ε1 + νε2) (2.4)

σ2 =E

(1− ν2)(ε2 + νε1) (2.5)

A complicating factor in the biaxial case is to determine the area that the forcesare acting on, which makes determining stresses σ1 and σ2 more di�cult thanfor the uniaxial case. Furthermore, during an actual manufacturing process thebiggest problem is determining the plastic response. This cannot be describedwith a set of equations as given above.

An important observation is that real biaxial loading only occurs up to lo-calization. Due to damage, necking and failure in a material, asymmetry isintroduced and the simpli�ed approaches as used in the elasticity regime arenot correct anymore. Still the elastic behaviour is important, as this is wherethe �nal failure mode might be determined.

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Working plane

Some experimental set-ups test a material in-plane, others out-of-plane, de-pending mostly on tooling. As out-of-plane testing gives rise to bending, it ispreferred to test in-plane. This means stresses and strains are constant over thethickness of the sheet, which makes computing of the stresses and measuringthe strains less complicated.

Some studies also show an in�uence to the forming limit while comparing in-plan and out-of-plane testing. Forming limits up to 6 % higher where foundwith out-of-plane testing of the same material. [47]

Geometrical constraints

The geometry of a tested specimen or the set-up itself can in�uence the datameasured during an experiment. Possible in�uences are areas of contact wherefriction plays a role or a geometry that is sensitive to a certain mode of failure.These so-called geometrical constraints can be introduced by contact or frictionwith the used tool set in the region of interest, by asymmetry of the toolset, by non-isotropic material behaviour or by a geometry that leads to stressconcentrations. A well known example is anisotropy in sheet metals, whichgives rise to the need to test a material in more then one orientation relativeto the rolling direction of the sheet. When deforming biaxially, the anisotropywill introduce a weaker direction, which is more likely to fail. [47]

Measuring stresses, strains or forces

Not every experiment has the same possibilities for measuring stresses, strainsor forces. As stated before, directly measuring stresses would be the most idealsolution in most cases, but this is hardly ever possible. Stresses are normallycalculated from either a strain �eld or forces and the area they are working on.Measuring strain �elds can be done with a digital image correlation set-up thatfor sheet metal can measure strains on top or bottom surface. Stresses can becalculated with the use of a FE-model, but therefore depends on an accuratematerial model.

The other solution is measuring forces and the area they work on, as is donefor uniaxial tensile tests. This is only possible when both the force on an areaand the area itself can be measured. This works �ne for a simple tension test,but for more complex stress states this is often not possible.

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2.2 Bulge test

The bulge test is a well described experimental set-up for biaxial loading, wherepressure is used to deform a specimen. The set-up consists only of a pressurechamber and clamping mechanism. The bulge test is mostly used for testingthin �lms, as bending stresses can be neglected for that case. The pressure canbe build up by a gas, a �uid or even a �owing polymer [21, 37].

Figure 2.2: Pure biaxial bulge test with rounded die [21]

In �gure 2.2 a simple bulge test set-up is shown, with the most importantproperties visualized being t0 and td, the initial and �nal thickness of the sheet,dsheet the diameter of the sheet, dc the diameter of the die cavity, hd the heightof the dome and RC the radius of the die edge. Rd is the radius of the bulge ina circular set-up. Rd is divided in two values R1 and R2 for an elliptic bulge,with the two radii relating to the bulge radius in the principle directions. Forlarge apertures, the membrane theory can be used to compute stresses, strainsand pressures, as will be discussed in the next section.

Membrane theory

σ1

R1+

σ2

R2=

p

t(2.6)

where σ1 and σ2 are the principle stresses on the sheet surface, R1 and R2 theradii, perpendicular to each other, p the pressure applied to the sheet and tthe thickness of the sheet. In the pure biaxial case where the bulge is a perfectbowl, R1 = R2 = Rd and σ = σ1 = σ2, so the equations can be simpli�ed to

σ =pRd

2td(2.7)

with td the thickness at the top of the dome. The e�ective stress can be writtenas

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σ =p

2

(Rd

td+ 1

)(2.8)

In the above relations the dome radius Rd is de�ned as

Rd =((dc/2) + Rc)2 + h2

d − 2Rchd

2hd(2.9)

and the thickness at the top of the dome as

td = t0

(1

1 + (2hd/dc)2

)2

(2.10)

with dc, Rc and hd de�ned as shown in �gure 2.2. This model includes theplastic deformations by using a correction for hardening, although in a simpli-�ed way. The hardening component can be adjusted by replacing the exponent2 in equation 2.10 by (2−m), where m is the hardening power law exponent.[21]

Slota et al [51] state that a die aperture of at least one hundred times the thick-ness of the sheet is needed to be able to neglect bending in�uences. Especiallyfor determining reliable strain �elds this is important, because the strains varywith the thickness of the sheet due to bending.

Advantages and Disadvantages

An advantage of the bulge test is the absence of contact (and therefore fric-tion) in the area of interest, which makes the analytical solution less complex.There are no geometrical constraints due to the tooling or the geometry of thespecimen.1

Some disadvantages of the bulge test include the large height di�erence be-tween the deformed and undeformed specimen, making it di�cult to use lenssystems for online and in-situ measurements (e.g. imaging correlation analy-sis). Moreover, only strains in the ε1 > 0 and ε2 > 0 region can be determined,as the sheet needs to be clamped over the whole outer region to prevent thepressurizing air or �uid from escaping.

The high pressure also leads to uncontrollable neck and crack propagation, be-cause of the force controlled nature of the experiment. Necking and fracturemight occur in a split second, with no tools available to measure the phe-nomenon. The high pressure needed in a miniature set-up might even proveto be a problem to reach in a conventional set-up without the use of a largehydraulic system or polymer as pressure body. [37]

1In a bulge test the thickness of the sheet varies, with the thinnest part of the sheetforming in the centre. This can be considered a geometrical constraint, as it forces fractureat this point.

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Further literature

The most important properties described extensively in literature includingout-of-plane bending, especially for small apertures [15, 51], uncertainty of theexact shape and thickness of the bulge [15, 49] and uncertainty of the momentof fracture [50]. A big disadvantage is found when changing strain distributions,as this leads to building new die shapes for every wanted distribution [3, 9, 50].

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2.3 Punch test

A second, somewhat similar approach, is the use of a punch to deform sheetmetal under many strain paths, including biaxial tension. Several standardizedtests are available (e.g Keeler, Nakazima and Hasek tests) as described byBanabic [3]. Although all these tests are used to determine the same materialproperties, there are several di�erences. The biggest disadvantage of the punchtest is the presence of contact, as this both gives rise to geometrical constraintsand adds friction to the problem.

An advantage of the punch test is its ability to undergo various strain paths,all of them up to necking and fracture. Many ideas to achieve di�erent strainpaths have been proposed and will be brie�y discussed. Changing the strainpath during a test is practically impossible for a punch test, as tooling geometryand specimen are �xed in most cases.

Punch set-ups

The Keeler test uses punches of di�erent radii to vary the strain path of thetested sheet metal specimen, introducing di�erent strain paths due to geome-try and friction variations. The specimens are the same for every test, whichmakes the test easy to prepare. The di�erent punch shapes, as shown in �gure2.3, make the test more time consuming if a larger part of the FLC is to bedetermined. The test can only determine the positive part of the FLC, ε1 > 0and ε2 > 0.

An alternative where the same specimen, but only one type of punch are used,is the Hecker test. In this case the amount or type of lubricant is varied, whichgives di�erent strain paths. For this test again only the positive part of theFLC can be found. [3]

Figure 2.3: Punch shapes as used in the Keeler test [3]

In the industry the Nakazima test (or sometimes the similar Hasek test) ismost often used to determine material properties. For both tests a simplehemispherical punch and a circular die are used, while the shape of the specimendetermines the strain path. Especially for the Nakazima test both tooling andspecimen are relatively simple. The Nakazima specimen, as shown in �gure2.4 on the left side, only di�er in width W . Strain paths for ε1 > 0 can be

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found with this test. The main disadvantages apart from those due to frictionare possible wrinkling and measurement errors caused by the curvature of thepunch. Specimens proposed by Hasek (�gure 2.4) can be used if wrinkling is aproblem. The advantages and disadvantages are the same as for the Nakazimatest. The advantage of avoiding wrinkling is countered by the extra work neededto manufacture the specimen.

Figure 2.4: Specimen geometries for Nakazima and Hasek punch tests [3]

Tooling in�uence

The test methods as shown up to here have di�erent regimes they can be usedfor, as shown in �gure 2.5. This clearly shows the limits of the uniaxial tensiontest, the bulge test and Keelers test. It also shows how di�erent tests can leadto di�erent results, mainly because of di�erences in tooling and deformationsbecause of that.

Figure 2.5: FLCs established using di�erent testing methods: 1. Hasek; 2. Nakaz-ima; 3. Uniaxial tension; 4. Keeler; 5. Hydraulic bulge [3]

12


Sheet thickness

Another observation is sheet thickness in�uencing the results in all set-ups,caused by di�erences in bending stresses. Both Raghavan and Banabic show arising FLC for thicker sheets, showing how a thicker sheet, with more materialto �ow, is leading to higher forming limits. This is observed for both in-planeand out-of-plane testing and can therefore not be described as a pure bendinge�ect. More likely is the presence of an edge e�ect, leading to sti�ening of thesurface of the sheet and leading to earlier fracture in thin sheets as there isless material in the centre to distribute the stresses introduced by deformation.[3, 47]

Overestimation of fracture strains

A second disadvantage of the punch test is the overestimation of acceptablestrains, mainly because of tooling introduced geometrical constraints on neckingbehaviour. [3, 45, 47]

An e�ect found in punch tests, mainly due to friction, is localizing of the neckaway from the centre of the specimen. A second problem is that the punch testdoes not allow di�use necking of the material, leading to larger formability [38].This happens as the material on top of the punch sticks to the punch, resultingin lower strains. Depending on the shape of the punch, the test method andthe lubrication this determines where the material fails and under what strainpath. For most punch tests this behaviour is unwanted, but tests like Keelersare partly based on this principle. A test with a hemispherical punch andvarying lubrication states can be used to determine failure from pure biaxialstrain paths (in the centre) to almost pure stretching. [3, 8]

Measuring

The punch test can be used with an image correlation system, as the top areais free from obstacles, but the strain �eld can only be measured at the outerlayer of the sheet. As the strain �eld will not be homogeneous through thethickness of the sheet and therefore the measured strains might not representthe actual strain �eld. The e�ect of friction on the surface of the punch mightalso introduce an error that has to be compensated for when wanting to measurethe real material properties instead of the properties under the given set ofrestrictions.

13


2.4 Marciniak test

An alternative punch test was proposed by Marciniak and Kuczy«ski [39], re-sulting from their theory on loss of material stability under biaxial tension,which manifests itself by a groove running perpendicular to the largest princi-ple stress. They showed how their hypothesis about local strains concentratingin this groove could experimentally be veri�ed with a set-up as shown in �gure2.6.

The idea behind the Marciniak test is it simply converting a vertical force intoa biaxial force in the horizontal plane. This is done by a �at punch deforminga test specimen indirectly via a washer sheet with a central hole. The holeexpands radially as the punch moves in and because of friction the tested sheetof metal expands with the washer. The radial friction forces in the contactregion between washer and sheet also prevent the sheet from fracturing nearthe rounded edge of the punch, with the largest strains found in the �at centralpart of the specimen. The central part is now uniformly balanced, biaxiallyloaded, with no contact in the area, allowing failure to occur anywhere in thisregion.

History

In 1977 Tadros and Mellor [53] expanded the theory of Marciniak and Kucz«skiby adding di�erent tooling shapes. They proposed using elliptical shaped tool-ing, resulting in various biaxial loads from pure biaxial to aspect ratios of 1:7.They give results for several materials, for some the test set-up works, for oth-ers like brass 70/30 it does not. Further research by Mellor showed di�erentdamage behaviour up to fracture for brass. [46, 47]

Figure 2.6: Schematic diagram of the Marciniak test tooling set-up for in-plane test-ing of sheet metal [47]

As di�erent punch geometries are a costly method for testing, other options toachieve di�erent strain paths have been investigated. One method in particularseems to have potential and is described by Raghavan [47] as a simple techniqueto generate in-plane forming limits. His proposal, based on earlier work byGronostajski and Dolny [20], di�ers from the others by the use of di�erent

14


specimen and washer geometries. With this combination, compared to earliermethods, a wide range of strain paths can be prescribed.

Strain paths

The Marciniak set-up has been used to study the role of material defects underbalanced biaxial stretching conditions, but the Raghavan proposal makes ituseable for failure under di�erent strain paths. Any strain path from uniaxialto balanced biaxial can be achieved with the right washer and sheet geometry.The used sheet and washer geometries are shown in �gure 2.7 and divided inseveral types, depending on strainpaths that can be generated with them. [47]

Figure 2.7: Typical specimen (top) and washer (bottom) con�gurations used fordrawing and stretching strain states in the in-plane Marciniak test fol-lowing from the Raghavan proposal [47]

In tests with di�erent types of steel and aluminium both the elliptical tool-ing suggested by Tadros and Mellor, and the the varying washer geometriessuggested by Raghavan were capable of reaching strains of up to 40 %. Thelargest di�erence is the fact that Raghavans method can go into negative minorstrain paths, i.e. in his tests he spans a range from -25 % to 40 %, while theelliptical punch only reaches positive strains. The type I Raghavan geometryspans minor strains from -25 % to -10 % for determining forming limits inthe draw region, the type II geometry can be used for determining the planestrain region, with minor strains from -10 % to 10 %. Geometries III and IVgive strain paths in the stretching region, with the latter equal to the classicbiaxial balanced Marciniak test. Both Tadros and Mellor, and Raghavan foundpositive minor strains from 15% to 40% with these geometries. [47, 53]

15


Tooling geometry constraints

The mentioned articles not only show high strains can be reached, they evendeform up to fracture and succeed in that. In the classic Marciniak biaxialbalanced case, the type IV geometry, the central part of the specimen is underuniformly biaxial tension and failure can therefore initiate anywhere in thecentral region. This results in several nearly biaxially loaded necking areas.With all other geometries, both for Raghavan and the elliptical tooling, thestrain distribution is not perfectly uniform, resulting in failure near the centreof the specimen. This again is considered a geometrical constraint, although theobserved fracture paths suggest at least some defect sensitivity, as the fracturepaths vary between similar tests. [47]

Further literature

Some other properties of the Marciniak test discussed in literature include theability to see the in�uence of anisotropy (r-value) [2, 47] and the in�uence ofsheet thickness [47, 53]. Also the simple set-up that can be build on a conven-tional tensile tester with only the specimen geometry to vary for di�erent strainpaths [14, 47]. set-ups in several sizes have been used ranging from diameter of75mm [53] to large enough plates to cut out tensile specimen for uniaxial test-ing [14]. Strain measurements can be done with an image correlation system,which is easy because of the �at nature of the area of interest [14].

16


2.5 In-plane loading with cruciform geometry

The set-ups shown earlier mostly test the sheet metal out-of-plane, introducingbending stresses. As this is undesired when producing "clean" material data todetermine the properties of a material, in-plane alternatives have been studiedfor a long time to replace the out-of-plane set-ups.

Figure 2.8: Flat cruciform shape with necking widths for the arms (1) and the centre(2) shown

A lot of research is focusing on cruciform shaped specimen to overcome theout-of-plane problem. The basic idea of a cruciform specimen is based on astandard tensile test, but with a second direction of loading added. The fourarms of a cruciform specimen can be given a displacement, thus introducingtensile forces in two directions perpendicular to each other in the centre of thespecimen, as shown in �gure 2.8.

History

The idea of using �at, cruciform shaped specimen has been researched sincethe sixties, by Shiratori and Ikegami (1967), Hayhurst (1973), Kelly (1976),Makinde (1989) and several others [11, 30]. The methods described by themful�l the requirements as mentioned in the introduction, by generating an ho-mogeneous strain distribution in the thickness direction, yielding in the centralpart of the specimen and being capable of describing di�erent strain paths. Notall methods are useful for reaching necking or fracture conditions though, fordi�erent reasons.

Several authors studied the possibilities of cruciform specimen for determiningyield loci or hardening, which has the advantage of only going into the yieldregion and no further. Promising results for determining yield-locus wherefound by Müller and Pöhlandt [42] by using a specimen as shown in �gure2.9(a). For this geometry, high stress localization is found near the notches,but for deformation up to yield the geometry is useable.

A similar goal, but with a di�erent geometry, was achieved by Hoferlin et al.

17


[26], who used a square sheet with multiple small clamps to prevent introducingan in-plane bending moment. The method was used to experimentally deter-mine the yield locus of �ve di�erent materials and comparing it with �niteelement simulations.

Several authors used cruciforms related to the geometry as shown in �gure2.9(b). [19, 31, 32, 57] These all have slits in the direction parallel to the tensileforces in common, with the idea behind it being the avoidance of bending forcesin the plane of interest. Kuwabara et al. [31] claims the slits to make the straindistribution in the biaxially loaded zone almost uniform. Some of these studiesuse curved arms, others use straight arms, some even use both to compare.

Kuwabara [31, 32] tested low-carbon sheet metal and determined experimen-tally the plastic work for a strain range up to ε < 0.03 in the biaxially loadedzone under load ratios of 4:2 and 4:4. In a second work they determine theyield surface, with the use of an abrupt strain path change. A similar specimenis used by Wu et al. [57] for testing a biaxial tensile set-up capable of realiz-ing complex loading paths. No local strain measurements where done for thisset-up though, making it di�cult to compare the useability.

An optimization of the Kuwabara specimen was performed by Gozzi et al. [19],in order to study the mechanical behaviour of extra high strength steel. Theyhad a problem with reaching the desired amount stress, as failure occurredbefore reaching that stress in the biaxially loaded region. A geometry as shownin �gure 2.9 b) was used and optimized, where the notches where changed tokeep the stress in the corners low enough to prevent failure there. Di�erentlengths of slits where found to be preferable in some situations.

A di�erent geometry is proposed by Yu et al. [58] in a study on forming limitsfor sheets under complex strain paths. Using a �nite element model to optimize,they come up with a cruciform shape as shown in �gure 2.9(c). The centre ofthe cruciform has been thinned, with a cross-shape thinned area surroundinga bowl shaped area that is even further thinned. The general idea behind thisshape is obtaining the most uniform stress distribution in the central region.According to the authors, complex strain paths can be achieved by adjustingthe velocity ratios imposed on the specimen arms.

Demmerle and Boehler [11] describe several cruciform geometries in their arti-cle, ranging from uniform thickness specimen with trapezoidal arms to platesclamped by three or more limbs from each side. The geometry they investigatemost is the one proposed by Kelly, as shown in �gure 2.9(d). From their theylook into two alternatives based on the original specimen of Kelly, namely 2.9(e)and 2.9(f) where the centre area is thinned in a square form or round form re-spectively. They �nd a uniform stress distribution in the centre, but with stresslocalizations in the corners. A last design proposed by them is shown in �gure2.10 and is found the best as it has the lowest stress localization out of thecentre. The design was found to expensive to realize though and never tried.

A problem described by Demmerle and Boehler [11] is loading of anisotropicmaterials, which will result in a distortion of the loading axes. Some solutions

18


Figure 2.9: Several cruciform geometries as used in di�erent studies; a) Müller andPöhlandt [42]; b) Kuwabara and Gozzi et al. [19, 32] ; c) Yu et al. [58]; d) Kelly [27] ; e) Square modi�ed Kelly [11]; f) Round modi�ed Kelly[11]

19


Figure 2.10: Optimal design of a biaxial specimen by Demmerle [11]

for this problem that are proposed in literature are making slots in the arms[19, 31, 57] or giving the tensile set-up that is used more degrees of freedom[7, 11]. No studies where found on using the cruciform geometry up to fractureunder biaxial loading, other then for composites [52].

Alternative approaches

An alternative to weakening the centre part of the cruciform is strengtheningthe arms. This method is used in composite testing Smits et al. [52], whereit is relatively easy to shape the test specimen in the desired form. For sheetmetals no literature was found on strengthening the arms, although some al-ternative solutions to be though of are to glue extra material to the arms orto change material properties in the arms, for instance by changing the mate-rials microstructure by case- or surface hardening (e.g. carburizing, nitriding,boriding or titanium-carbon di�usion).

Manufacturing

The main problem mentioned for a thickness reduced cruciform specimen is thechange in material properties due to manufacturing and the change in sheetproperties due the removal of the outer layer. The former problem can only beminimized, by studying removal methods that introduce only minimal damageto the original material, including Electro Discharge Machining as is used inother studies and said to have little impact on the tested material. [56]

Test set-ups

The set-up as proposed by Kuwabara et al. [31] and also by Smits et al. [52]uses hydraulics to drive the tensile tests. This has the advantage of beingable to directly connect the two opposing hydraulic cylinders via to a commonhydraulic reservoir and thus keeping the pressures (and therefore forces) exactlythe same. With a servo controlled system it is possible to change the strainpath.

20


A second approach found in literature is the use of a mechanism, �xed in aconventional tensile testing machine [26, 43]. set-ups like this can be divided intwo main groups - vertical and horizontal loading - as is shown in �gure 2.11.All mechanisms need to be adjusted for di�ering strain paths, which make apath change during an experiment impossible.

Figure 2.11: Possible mechanisms in conventional tensile stage. Top pictures: verti-cal under stage; Bottom pictures: horizontal under compression [43]

21


2.6 Summary

The four methods discussed in this chapter, the bulge test, the hemisphericalpunch test, the in-plane cruciform tensile test and the Marcianiak test are themost practical tests for creating biaxial stress �elds. Each of them has itsadvantages and disadvantages that will be analyzed in this report with moredetails using both numerical and experimental tools.

For the bulge test, the biggest advantage is its simplicity and the existence ofan analytical model. The useability of the analytical model and the typicaldimensions for a miniaturized set-up is analyzed. In the punch test, the mostimportant property in�uencing the results is friction. Therefore the in�uenceof friction when miniaturizing is analyzed. The Marciniak test, advertised ashaving perfect in-plane, biaxial loading will be both numerically and experi-mentally veri�ed. The main properties that will be investigated are friction,tooling geometry and tooling forces, for �nding the possibilities for a miniatur-ized set-up. The last set-up to be analyzed is the in-plane cruciform set-up,for which the main challenge will be designing and building the set-up andproducing the specimens. Combining the results of the four methods, the mostsuitable method for biaxial testing of sheet metal to fracture will be suggested,with recommendations for possible further investigation.

22

Chapter 3

Numerical methodology

The literature survey describes several experimental set-ups that are used forbiaxial testing of sheet metal in the industry. Each of these set-ups has itsadvantages and disadvantages, some of which can be investigated with the helpof a numerical model. The models used in this study are presented here, afterin the �rst section the used material model is described, as this is the same forall numerical models.

3.1 Material model

All numerical and experimental work is done with IF-steel, which is providedby Corus RD&T. In MSC.Marc the elasto-plastic material model is used todescribe the IF-steel, which is an isotropic model, using Young's Modulus (E),Poisson's Ratio (ν) and a plasticity criterium as input parameters.

Table 3.1: Material properties for MSC.Marc isotropic elasto-plastic material model

Property ValueYoung's Modulus [GPa] 45Poisson's Ratio [-] 0.29Initial Von Mises Yield Stress [MPa] 130

Plasticity is modelled with the piecewise linear method, using a table of equiv-alent plastic strain and Von Mises stress. The used values for these propertiesare given in table 3.1, with the plasticity curve that is given in �gure 3.1. Thestress in this �gure is determined in a standard tensile test, which per de�-nition is equal to σV M (the Von Mises stress) as used by MSC. Marc. Fromthe obtained stress-strain distribution only the part up to necking is loaded inMSC. Marc, as the elastic-plastic material model is de�ned as such.

23

CHAPTER 3. NUMERICAL METHODOLOGY

Figure 3.1: Plasticity curve as used in the MSC.Marc material model

Necking, damage and localization

When interpreting the numerical results, it is important to understand howplasticity is implemented, as this can otherwise lead to wrong assumptions. Theplasticity curve as used here only describes the stress evolution up to neckingof the material. The reason for this is that local strains become much higherand result in necking, which is not described by the elasto-plastic materialmodel. Furthermore the numerical model cannot accurately describe localiza-tion, which is found when the material starts to neck and fail. To avoid thisproblem a failure criterium or local damage model is needed, which is beyondthe scope of this project as such a damage model can only be determined withthe obtained experimental data from the biaxial set-ups.

3.2 Bulge test

The model for the bulge test is based on the analytical model given by Gutscher[21] as shown in �gure 2.2 in the literature survey. The most important prop-erties to study are the resulting stress- and strain �elds and possibilities tominiaturize.

The FE model

The model was build using straight axisymmetric thick shell elements of type1, which are suitable for large displacements and large deformations. Shellelements are chosen for their suitable computational behaviour and bendingincorporation. The degrees of freedom (axial, radial and right hand rotation)are su�cient to describe the problem, and a pressure boundary condition canbe used as well.

24


Figure 3.2: FE Model of the bulge test (expanded view is used for the shell elements)(MSC.MARC Mentat)

The element only has one integration point for sti�ness and two integrationpoints for mass and pressure determination, which means small time stepsare necessary when describing large plastic deformations. Stresses over thethickness of the element are integrated with Simpson's rule, over 5 layers and11 integration points (default settings that are suitable for complex plasticdeformation).

To take into account the thickness variation during the bulge test, the updatedlagrange method is used.

Table 3.2: Properties of the bulge test model

Property ValueSheet thickness t0 [mm] 0.7Cavity diameter dc [mm] 20 to 150Clamp rounding Rd [mm] 5.25

To determine the needed pressure and maximum dome height at the point ofnecking, it is assumed that failure occurs when the Von Mises strains reach themaximum of 380MPa as determined in a uniaxial tensile test.

3.3 Punch test

The punch test set-up that will be studied is the hemispherical punch, as this isthe most commonly used punch type in industry, e.g. in Nakazima tests. Themain goal of the analysis will be to study the e�ect of friction on deformation, as

25


friction is believed to in�uence the measured material parameters. The modelis build up from solid elements, as they are more suitable for visualizing stress-and strain gradients. The set-up is modelled axisymmetric to keep the numberof elements as low as possible.

Figure 3.3: FE Model of the punch test (MSC.MARC Mentat)

FE model

The axisymmetric model has four bodies in it, namely the sheet that is modelledusing solid axisymmetric elements of type 10, a four node quadrilateral elementwith bilinear interpolation1, the punch and the two clamps that are modelledas rigid body curves, see �gure 3.3.

Table 3.3: Properties of the computational punch model

Property ValuePunch diameter [mm] 50

Inner diameter die [mm] 56Radius die edge [mm] 2Clamp force [kN] 200

Number of elements 2000Element Type Axisymmetric solid (quad), bilinear (Type 10)

To study the e�ect of friction the coulomb model is used, which is used inMSC.Marc to describe any friction except for shear friction. The coe�cient offriction, Mps will be varied between 0 and 1. (For more information on frictionand friction coe�cients, see Giancoli [18]). To investigate the miniaturizationproblem the same model is used with the geometry scaled down to the di�erentpunch sizes.

1Higher order elements can not be e�ectively used, as in contact MSC.MARC only usesthe bilinear approximation

26


3.4 Marciniak test

Similar to the bulge and punch models, the Marciniak FE model is describedhere, followed by the most important properties that will be studied. Themodel can be used to gain more insight in the general workings of the set-upand e�ects of several design parameters, including punch edge geometry, punchsize and washer geometry.

FE model

The model was build using element type 10, axisymmetric solids, which werealso used in the punch test analysis2. Tests showed 3D shell element can be usedas an alternative, but for faster computation the axisymmetric solids approachwas chosen. In table 3.4 the used set-up and geometries are described. Themodel describes the experimental set-up that is available at Corus RD&T andwill also be used for experimental work.

Figure 3.4: FE Model of the Marciniak test (MSC.MARC Mentat)

The simulations to investigate the in�uence of changing parameters are per-formed with dimensions of the experimental set-up that is available at CorusRD&T. The in�uence of friction is studied by varying friction coe�cients be-tween the washer and sheet (Mws), and between washer and punch (Mwp) are

22D axisymmetric shell elements are available and can be used to describe the modelgeometry. These shell elements do not work well in contact though when using more thenone deformable body

27


Table 3.4: Dimensions of the Marciniak test set-up for the FE Model

Property ValuePunch diameter [mm] 50Punch edge radius [mm] 10Inner diameter die [mm] 53.78Radius die edge [mm] 3Clamp force [kN] 200Number of elements 2000Element Type Axisymm. solid (quad), bilinear (Type 10)

varied between 0 and 1. The friction is modelled using the Coulomb Frictionmodel in MSC. Marc.


The cruciform model is computed with 3D elements to describe the thicknessreduced geometry, with only one-eight of the cruciform being modelled whenpossible.

Table 3.5: Dimensions and properties of the cruciform model [54]

Property ValueWidth (w) [mm] 10.0Radius of rounding (Rw) [mm] 3.0Radius of bowl (Rreduced) [mm] 6.5Thickness sheet [mm] 0.7Number of elements (one-eight) 5000Element Type 3D solid (hex), trilinear (Type 7)

Boundary conditions in the cruciform test are symmetry planes and displace-ments of the arms only, as they are there is no contact in the set-up outside ofthe clamping area. To compare the numerical results with the experimental re-sults, the numerical strain �elds have been calculated for the same strain typesas can be found experimentally. This is total strain, major strain and minorstrain.

The resulting stress �eld is used to �nd where the maximum tensile stress isreached, which is assumed to be the starting point for necking. Parameters thathave been varied to optimize the numerical model are the thickness reductionand the radius between the arms. All models have a bowl shaped thicknessreduction, where the radius in the plane of the sheet is kept equal at all times.

28

Chapter 4

Experimental methodology

To verify the numerical results from the tests as mentioned in the previoussection, several experiments have been carried out. The experimental work canbe divided in two main parts, the Marciniak test and the cruciform geometry.

4.1 Marciniak test

To compare the numerical results with experimental results, IF steel specimenswere tested on a set-up that was made available by Corus RD&T. The set-upused is an existing tooling set, normally used for testing deep drawing prop-erties. This means the used geometry is mostly pre-determined by the toolingavailable. The properties that were varied were washer hole size and the amountof friction between washer and sheet.

4.1.1 In-plane testing with the Marciniak set-up

The test set-up is a hydraulic punch with a 100mm die attached. The punchmeasures 50mm in diameter and has a rounding of 10mm. The die used toclamp the specimen has an outer diameter of 100mm and an inner diameterof 53.78mm. The edge of the die is rounded with a radius of 4.5mm, whichis considered large enough not to cause fracture on the die. The clampingforce used in the tests is set to 300kN , so no material can �ow out of the die.The speed of the punch can be adjusted for each test, but is normally set to10mm/min.

To make clear photos for strain measurements, some of the tests are carried outwith stops and the last test is carried out at a slow punch speed without stopsto make photos. Both a simple digital photo camera and an advanced photocamera set-up as used by Corus RD&T where used. Several specimen havebeen painted with a high contrast pattern for use with the Aramis system, usingstandard black and white paint. This system works by following the distortionof a pattern that is sprayed on top of the specimen of interest, comparing each

29

CHAPTER 4. EXPERIMENTAL METHODOLOGY

picture that is taken to the previous. Lightening for the test was providedby ambient light and a clip-on di�use LED light. Furthermore a pattern ofregular dots was applied to each of the specimens for use with the Argus strainmeasurement system.

4.1.2 Specimen manufacturing

Manufacturing of specimen for the Marciniak test is done by stamping and wireEDM. The 100mm sheets to be tested are stamped from a steel strip at theCorus workshop. The 100mm washer sheets are cut by wire EDM, after whichthe hole in the centre is removed with the same process. As the width of thespecimen is much larger then the EDM or stamping a�ected zone, no in�uenceof the manufacturing process is found in the test specimen.

A set of washer was produced with holes of 5mm, 7.5mm, 10mm, 10.5mm,11mm, 11.5mm and 12mm, as 11mm was numerically found to be the bestchoice.


The cruciform geometry will be experimentally tested, to verify the numericalresults and to study possible di�culties that occur in an experimental environ-ment. The experimental set-up that was used to carry out the biaxial tests wasdesigned �rst, and therefore the design of this set-up is explained �rst.

4.2.1 Design of a test set-up

A set-up to test the cruciform specimen at the Eindhoven University of Technol-ogy was designed keeping several guidelines in mind. First of all the set-up hadto go all the way to fracture, resulting in a total elongation of approximately4mm. The maximum forces to be expected are under 2kN in two directions.The set-up has to pull the cruciform with equal force from all sides, with allthe forces acting in one plane. The possible use of the Aramis strain measuringequipment is preferred, and so is the possibility to change the strain path for atest.

Table 4.1: Properties for the experimental set-up

Property SizeDisplacement [mm] 4-6Force [kN] 2-5Other Strain path changeable

Strains measurable

Several designs have been discussed, including the use of a Kammrath undWeiss tensile stage with additional parts to pull in the perpendicular direction.

30


The compactness of such a set-up makes this impossible to achieve in the planeof the force acting on the cruciform though. Other designs ended up withthe similar problems, leaving a mechanism to be placed in a standard tensilemachine as the best option.

Several of these mechanisms have been analyzed, with the cruciform eitherhorizontal or vertical position in relation to the mechanism. The vertical solu-tion has the obvious advantage that the deformation of the cruciform is easilyfollowed, as it is clearly visible from the sides, with no obstructions by eitherthe mechanism itself of the tensile machine. Practical design of a set-up withthe cruciform clamped vertically was found to be a big challenge, as a simplemechanism cannot elongate the cruciform in four directions at the same time.Slider mechanisms or double hinges would be necessary, which lead to frictionproblems that can make the test rig instable. [17]

Figure 4.1: Principle of the biaxial tester and non-linear movement of the joint

The �nal design was therefore made with the cruciform in a horizontal position,where a compression movement of the Zwick 1474 tensile machine is used topush four arms outwards and thus stretching the cruciform biaxially. The set-upwas build at the university workshop, with the use of standard parts mostly. Asa result of the use of ball joints in the mechanism, the vertical movement of thetensile testing equipment is not perfectly transferred in horizontal direction. Asshown in �gure 4.1, the joint directly responsible for the horizontal movementof the test specimen is following an arch-like path. For small displacements thedisplacement is approximately linear, which means linear displacements can beaccurately described.

The photo of the set-up (�gure 4.2) shows the total set-up. This set-up can beplaced in a conventional tensile testing machine, placing the bottom cylinder(2) in a centre ring on the tensile testing machine and screwing a standardcylindrical connector to the top cylinder (3) to attach the set-up to the movingpart of the machinery. When the tensile tester then moves in the direction ofthe blue arrows, the joints of the arms move out in the direction of the redarrows. In the set-up available at the Technical University of Eindhoven thebottom cylinder is �xed, with the top cylinder being pressed down by the tensiletester.

31


Figure 4.2: Experimental set-up for testing cruciform specimen

32


The eight 125mm arms form four mechanisms, with three joints each to convertthe vertical displacement into a horizontal displacement. To change the loaddistribution, the arm length can be changed by using longer or shorter arms,so di�erent strain paths can be tested. Small adjustments can be made byelongating the arms itself. The arms have ball joints as shown in �gure 4.2(5), that can freely rotate in all directions to prevent a clamped cruciform frombeing suppressed in more directions then there are degrees of freedom.

The clamping mechanism has been made by pressing a clamp onto the clampingarea of the cruciform, as shown in �gure 4.2 (6) and (7). The four clampscan move in vertical direction and have a thread that is used to pre-stressthe clamped cruciform. This makes it possible to adjust the position of thecruciform and get it aligned.

The test set-up is used in a standard tensile machine as stated, which gives twoproblems. The �rst is the fact that the clamped specimen, although loadedin-plane, will move in vertical direction as the joints that are connected to theclamps move in vertical direction. The second problem is the fact that thecruciform is clamped horizontally, with the tensile machine present above andbeneath, which makes it more di�cult to have a clear view of the cruciform.

The �rst problem is easily solved, as preliminary tests showed the camera isable to keep focus over the distance the cruciform moves. The other problemwas solved by adding a cavity in the lower cylinder of the biaxial test set-up(3) where a mirror is placed under 45◦. This mirror gives a clear view (4) onthe deformed specimen, with the possibility to add a camera set-up for onlinestrain measurements in front of the tensile tester. The camera can be pointedat the mirror in the bottom cylinder through a hole in the cylinder, as shownin �gure 4.2.

Misalignment

Misalignment of the forces in a cruciform set-up can be introduced by clampingthe specimen in under an angle in one of the clamps. In �gure 4.3 stressdistributions are shown in cruciform specimen under di�erent misalignments,to analyze the resulting behaviour. The four test are all exactly the same, withthe cruciform being pulled 2mm in each direction, so not reaching the maximaltensile stress. In all three misaligned cases, a movement of 1mm away from theprinciple direction is added.

Each of these possible misalignments results in a highest stress in the centreof the cruciform, with hardly any distortion of the stress and strain �elds.This observation is an important one, as it shows how the test is insensitiveto misalignment due to faulty or skew clamping. The biggest in�uence ofmisalignment as predicted by the simulations is the development of a preferrednecking direction, as bands of higher stress develop. These bands develop inplaces where the material is likely to fail without this extra high stress as well,which makes the impact less signi�cant.

33


Figure 4.3: Stress distribution in a cruciform specimen and the in�uence of mis-alignment in the cruciform set-up; a) Symmetric tensile test; b) Onearm misaligned; c) Two arms with opposite misalignment displacement;d) Two arms with equal misalignment

4.2.2 Tests with in-plane cruciform geometry

To run a biaxial tensile test, the following steps need to be carried out. Firstthe tensile set-up is fastened in the specially designed holder, in which the armscan be positioned in a 45◦angle. For the current set-up, the holder is �xed inthe exact position to achieve this. The mechanism needs to be position in theholder in the right direction, which can be checked by aligning the black markson the holder and mechanism for both the top and bottom cylinder.

With the mechanism in the holder a cruciform specimen can be fastened inthe set-up. It is important to make sure the clamps are on the device beforeattaching the cruciform, as the cylindrical part of the clamps cannot be addedwith a cruciform in place.

It is recommended to �x the cruciform in two opposite clamps �rst, whilemaking sure the clamps are aligned. With the �rst two clamps tightened, theother two clamps can be fastened, where it is important again to align theclamps before tightening. When the four clamps are fastened and checked, theset-up is ready to be placed in the tensile testing machine.

To move the mechanism without deforming the clamped specimen, two steelbars are screwed to the mechanism. While attaching the bars, it is importantthat the bottom cylinder is kept in contact with the holder. The alignmentmarkers have to stay in touch as well. If the bars are �xed, the mechanism can

34


be taken from the holder and placed in the tensile machine.

To attach the mechanism to the Zwick tensile machine, a metal connector isscrewed to the top cylinder. The hole in this connector has to be alignedwith the mirror hole in the bottom cylinder. If the connector is in place, themechanism can be placed on the metal centre pad in the tensile machine and thecompression rig can be lowered into the connector. Positioning the compressionrig low enough for the steel �xation bar to be put in place requires some caution,the rig may not exert any force yet.

With the mechanism fastened, the compression rig can be directed to the zeroposition by balancing the force to zero. To start the test, the Zwick softwareis used and set-up for a standard compression test.

Force displacement measurements

As the experimental set-up as mentioned above does not measure forces ordisplacements on the specimen itself, these have to be computed from dataobtained from the Zwick tensile testing equipment. The force-displacementcurves from the tensile testing equipment can be converted are obtained viathe controlling software and give time, displacement and force.

As the angle of the arms of the test rig are approximately 45◦, the force anddisplacement of the tensile tester are simple to determine. The movement ofthe joint to which the clamps are �xed is approximately equal for the horizontaland vertical displacement. The force on the cruciform in one direction is ap-proximately half the force measured by the tensile machine. This does not takeinto account any losses in the testing rig though, which cannot be determinedwithout adding load cells on the separate arms.

Aramis strain measurements

Using the mirror set-up as described above, strain measurements are made withthe Aramis system. When the biaxial tensile set-up is placed and fastened inthe tensile tester, the Aramis system can be installed. The camera is pointed atthe 45◦mirror and adjusted so it shows the cruciform specimen in the Aramissoftware. A (di�use) light source is then installed, after which the shutter timeof the camera can be set. If needed the needed shutter time can be changedby adjusting the diaphragm of the camera1. After the camera is set-up andfocused, the Aramis software is set-up to take a photo every second, which isthe minimum time step. For slower tests this might be adjusted, a number of50 to 100 photos are needed for the strain �eld calculations.

1For shutter times close to 50Hz the background lighting in�uences the photos, whichmakes using the diaphragm needed to be able to increase or decrease the shutter time withoutover- or underlightening

35


4.2.3 Specimen manufacturing and characterization

During the manufacturing process of the cruciform specimen several manufac-turing steps are used, of which some might lead to damage or errors in thegeometry. The steps will therefore be explained here, and several test to inves-tigate the in�uence of the main production step, EDM, are introduced.

3

Figure 4.4: Shape and size of the cruciform specimen

The �rst step in manufacturing the cruciform specimen is cutting the cruciformshape, with dimensions as given in �gure 4.4. The cutting is done by wireEDM, this will not have a huge in�uence on the material, as the thicknessof the a�ected material is small compared to the thickness and width of thespecimen. The second step for manufacturing the cruciform specimen is diesink EDM, to thin the centre of the cruciform. EDM is used as it can achievethe wanted precision and can cut the wanted geometry, without a big distortionof the original material, according to several studies (see Appendix A).

The in�uence of the EDM process is characterized by several experimentaltests. These include height pro�lometry, SEM, grain size measurements, nanoindentation and tensile tests, which are brie�y discussed.

Surface pro�lometry

The EDM process copies the geometry of the electrode into the workpiecematerial, removing material from both the workpiece and the electrode. The�nal product should be a perfect copy, which will be veri�ed using the SensofarOptical microscope. The microscope is used to make a height pro�le.

36


The settings used for the height pro�le are a resolution of 4 with the 5x mag-ni�cation. A height of 1000µm is scanned to capture the cruciform and theremoved bowl shape.

Scanning Electron Microscopy

SEM images of the cross-section of the as received steel sheet and the thicknessreduced specimen are prepared by grinding and polishing with the Struers tar-get machine. The specimen where cut mechanically from the sheet and grindedfor more then 2 mm to remove any deformed material. The results are com-pared with the results for the as received material. To make the grains visible,the cross-section was etched with the same method as the microscopy samples.

Grain size measurements

Using the Zeiss Axioplan 2 grain size measurements of thickness reduced spec-imen are compared to specimen from as received material. The preparationof the specimen is the same as for the tests with as received material. Thesamples are cut from as received material and then a cross-section is grindedand polished to make the surface �at enough for microscopy. After the �nestpolishing step, the surface is etched using a 30 second nittal bath (5 % solution)and a 20 second step with Marshall's Reagent. The combination of these twoattacks all the grain boundaries and makes the grains clearly visible.

The recipe of the Marshall´s reagent is as follows, constituted by two parts.Part A consists of 5 ml sulfuric acid (concentrated), 8 g oxalic acid and 100ml of water. Part B is a 30% solution hydrogen peroxide solution. Before use,mix part A and B in equal parts and use the mixed solution fresh. For betterresults, 1ml of hydro�uoric acid per 100ml of solution can be added. Part Acan be stored, the mixture cannot.

Nano indentation

Nano indentation test are carried out on thickness reduced specimen and spec-imen of the as received material. For each position 21 indentations where doneover the thickness of the specimen with a Berkovitch tip, with a 50 µm spacingover the thickness and a �nal displacement of 500µm into the material. Thesets of measurements perpendicular to the thickness have been made 100 µmfrom each other. The location of the indents is shown in �gure 4.5. The hard-ness that is used to compare the microstructure over the thickness of the sheetand to compare the original material with the thickness reduced material iscomputed by the indentor software. Preparation of the specimen was carriedout with the Struers Target System.

37


Figure 4.5: Positions where nano indentation was done to determine local hardness.

Tensile tests

The tensile tests as done to characterize the e�ect of EDM are carried out withthe same specimens as the earlier mentioned tests. The specimens for this testhave been thickness reduced using EDM or wire EDM though, to study thee�ect of these processes.

Thickness treduced is 200µm, the transition from the clamping area is a smoothone due to rounding by the EDM process.

6,5

10

31

12

4

ttreduced

Figure 4.6: Tensile bar specimen with thickness reduction for tensile testing

38

Chapter 5

Results

For the out-of-plane set-ups, the most important challenge about the threestudied set-ups is the possibility to build a miniaturized version for use withmicroscopy. This is analyzed for the di�erent set-ups, and it will play animportant role in the end to give an answer to the question which test is the bestchoice for biaxial testing with microscopy tools. For the cruciform specimenhowever, miniaturization is not the most important property to analyze, asthe biggest challenge here lies not in miniaturization but in deformation up tofracture with as little distortions as possible.

39

CHAPTER 5. RESULTS

5.1 Bulge test

The advantage of the bulge test is the availability of an analytical model, aswas shown in the literature review. This model is valid for large set-ups, butfor smaller set-ups it might not be as usable as bending will become morein�uencing. For the bulge test the stress distribution in a specimen near fractureis shown in �gure 5.1, as predicted by the FE model. The distribution showsonly a small gradient over the thickness of the sheet in the top of the dome. Forsmaller set-ups however, the role of bending stresses increases, as is analyzedin the next section.

Figure 5.1: Computed Von Mises stress �eld for the bulge test with an aperturediameter of 50mm close to fracture

A second disadvantage of the bulge test originating in the concept itself, is tokeep top of the bulge, where fracture occurs, in focus for use with microscopetechniques. This means the distance between microscope and specimen has tobe kept constant by moving the microscope along with the growing bulge. Alast problem is the explosive burst that is to be expected when the materialfractures, resulting in both dangerous situations and deformation of the fracturezone.

5.1.1 Miniaturization

Miniaturization of a bulge set-up means the aperture which allows the sheetto deform, will be decreased in diameter. For apertures of 20 to 200mm theresults are given in table 5.1.

The decreasing height for a miniaturized set-up is a good sign, as for microscopyonly limited height is available in most set-ups. The rising pressures on theother hand are a big challenge, as this means the set-up needs to be reinforced tocope with the forces acting on it. High pressure is dangerous under microscopesas well, especially in a SEM vacuum chamber where an sudden increase of theinternal pressure will damage the microscope.

The numerical computations made with MSC.Marc have been compared with

40

CHAPTER 5. RESULTS

Table 5.1: Numerical results at fracture of bulge test simulations with MSC.Marcfor varying cavity diameters for stresses close to σfracture

Cavity diameter Height Pressure Normalized height1dc [mm] hdmax [mm] Pmax [MPa] hd/dc [-]

20 6.60 30.00 0.33025 7.85 25.00 0.31430 9.05 21.10 0.30240 11.60 16.40 0.29050 13.95 13.25 0.27960 16.55 11.25 0.27680 21.30 8.50 0.266100 26.30 6.90 0.263150 38.65 4.65 0.258200 50.75 3.50 0.254

the analytical solution, as shown in �gure 5.2. The analytically determinedpressure at the point of necking can be calculated by rearranging equation 2.8:

Pmax =2σ

(Rdtd

+ 1)(5.1)

Figure 5.2: Comparison of numerical and analytical solution for bulge pressure ex-periment near fracture

The analytical model follows the numerical model for large apertures, but forsmall set-ups the analytical model predicts a lower pressure then is found nu-merically. The reason for this change originates from the neglection of bendingstresses in the analytical model, which makes the analytical model overestimatethe thickness reduction. The advantage of the bulge test having an analyticalmodel to determine stresses therefore does not hold for a miniaturized set-up,which means numerical computing is still needed.

41

CHAPTER 5. RESULTS

For the results as shown above a miniaturized version of the bulge test smallenough to �t under a microscope would need to have cavity diameter with amaximum of 50mm, considering the total set-up with clamps will then easilymeasure 100mm in diameter. The height di�erence of approximately 15mm isrelatively large, especially for use with microscopes.

5.1.2 Summary

• Pressure for testing up to fracture is predicted to reach 12MPa or more,which can lead to dangerous situations in case of fracture. The explosivecharacter of the test also can lead to alteration of the fracture surface,which is unwanted.

• The increasing pressure results in a second disadvantage, being the needfor a robust set-up. Miniaturizing now leads to the need for a stronger set-up, to cope with the higher pressures, and for very small bulge diametersthis results in an increased size of the test apparatus.

• For use with microscopes the area where fracture will occur has to bekept in the same plane, which is di�cult with a bulge test.

• One of the biggest advantages of the bulge test normally found, is thegood description of the forces and stresses by the analytical model, butfor a miniaturized set-up the analytical model is found not to be correctanymore.

42

CHAPTER 5. RESULTS

5.2 Punch test

The punch test, in several forms, is the most used material characterizationtest in industry. The reason for this is simple, as the test can be used over alarge range of strain paths and test specimens are easy to make. A disadvantagethat is taken for granted though is that friction in�uences the measured materialdata.

When looking at the stress distribution as shown in �gure 5.3, the punch testand the bulge test look to behave similar, but this is not entirely true. Thisoriginates in the fact that for a sheet on a punch, localization is postponed dueto restriction of material �ow. This is not the case in the bulge test, where themaximum allowed strains thus are found to be larger.

Figure 5.3: Numerically found stress �eld for a 50mm spherical punch test at fracture

Data obtained from the punch test simulations is given in �gures 5.4 where thein�uence of friction is shown. In table 5.2 the location of necking relative to thecentre is given in relation to friction, where higher friction results in fractureaway from the centre. Experimental work con�rms this problem, e.g. at CorusRD&T punch tests frequently have to be repeated several times before fractureat the centre of the contact area of punch and specimen is found. [40]

This in�uence of friction leads to a fundamental problem of the punch test:Friction is known to in�uence the measured material data, but the frictioncoe�cient itself is often unknown. This results in measured material data thatdoes not represent the actual material behaviour, but material behaviour in acertain set-up. This e�ect was also found in literature, as was shown in �gure2.5.

43

CHAPTER 5. RESULTS

Table 5.2: Properties of the miniaturization study FE model

Friction coe�cient Necking Distance Sheet Thickness[-] from centre [mm] in centre [mm]0 0 0.490

0.01 0.05 0.4920.025 0.1 0.4950.05 0.4 0.4990.10 1.0 0.5040.20 3.5 0.5070.30 5.0 0.5110.40 8.6 0.5250.50 10.7 0.5460.75 15.4 0.5811.00 16.5 0.616

Figure 5.4: The in�uence of friction between punch and sheet on the stress distribu-tion in a 50mm punch near fracture


A logical result for miniaturizing a punch set-up is the growth of the in�uenceof bending stresses. Therefore a normal industrial set-up with a punch diameterof 100mm is compared with a miniaturized version with a punch diameter of30mm. In the standard set-up, as shown in �gure 5.5 b), the gradient of thestresses and strains over the thickness of the element is small. The stresses onthe outer layer are only 1.5 % higher then on the inner layer. The strains varyeven more, measuring approximately 7 % increase from outer to inner layer.For the same region in a miniaturized set-up we �nd much steeper gradients,as shown in �gure 5.5 a), with variations up to 20 % for the plastic strain.Figure 5.5 clearly shows how a miniaturized punch set-up gives di�culties indetermining material properties, as the assumption that neglecting bending

44

CHAPTER 5. RESULTS

Figure 5.5: Comparison of large punch (D = 100mm) (a) and small punch (D =30mm) (b) stress- and strain distributions (Von Mises) in a radius of2.5mm round the centre at fracture; Note that the e�ect is exaggerateddue to scaling.

stresses is not in�uencing the results, does not hold anymore. A useable punchsize of 50mm gives strain gradients of 8 % in the failure region, which is stillunwanted.

Table 5.3: Maximum punch forces at necking, obtained via FE-modelling inMSC.MARC for di�erent set-up sizes

Punch diameter [mm] Punch Force [kN]10 3.820 8.330 12.740 17.350 21.860 26.380 35.1100 43.9

A last property determined via the FE-modelling of the punch test is the nec-essary force for a given size of the set-up. Table 5.3 shows the punch forcesobtained from the MSC.MARC model. Punch forces are directly related tothe size of the set-up, decreasing with miniaturization. For a set-up of 50mmforces of approximately 22kN are needed, which is still a very high force to beachieved by a small set-up. Smaller set-ups are not desirable, as bending startsplaying a larger role, in�uencing the results even more.

45

CHAPTER 5. RESULTS

5.2.2 Summary

• Fracture in the punch test is not similar to fracture in a free surface underbiaxial tension, due to friction and bending. This results in an error inthe material behaviour that is measured.

• An increase or decrease in friction results in a change in the measureddata. As the in�uence of friction cannot be measured, the e�ect of it onthe measured material data is unknown.

• Miniaturizing results in an increased bending stress, due to the decrease inthe punch radius. Therefore the material data measured in a miniaturizedset-up is even more in�uenced by external factors then in a large set-up.

• Forces needed for a miniaturized set-up with a diameter of 50mm arefound to be around 22kN .

46

CHAPTER 5. RESULTS

5.3 Marciniak test

The Marciniak test makes it possible to transfer a vertical displacement in to ahorizontal load, which can be used to deform a sheet biaxially in the horizontalplane. The modi�cation proposed by Raghavan enables a sample to be loadednot only biaxially, but in multiple strain paths, as has been described in theliterature study. This makes the Marciniak test an interesting set-up to use, ifit can be miniaturized for use with microscope equipment.

5.3.1 Working principle of the Marciniak test

Figure 5.6: Overview of the stress-�eld in the Marciniak test under loading up tonecking

The numerical model is �rst used to verify the claims that no stress gradient isto be found in the biaxially loaded region of the specimen, which can be seen in�gure 5.6. The stress �eld is found to be similar as found in literature. Whenlook at the stress distribution away from the centre, a problem occurs. Thestress (σcentre) is found to be lower then the stress on the outer radius of thepunch (σedge) and for all numerically tested set-ups it was found that:

σedge

σcentre≥ 1 (5.2)

This indicates failure is expected to always occur away from the centre of thesheet. However, when looking at the test results of the set-up that was madeavailable by Corus RD&T (see 4.1.1) three modes of failure are found. An oftenobserved failure mode is cutting behaviour, where the edge of the washer holecuts into the tested sheet, thereby initiating a crack and guiding it in a circulardirection. A second failure mode is a typical deep drawing failure, where thesheet and washer fracture in the sidewall after stretching. The wanted failuremode is fracture in the centre under biaxial loading, which is found in someof the tests. In �gure 5.7 (a) cutting, (b) deep drawing and (c) random crackmode are shown.

47

CHAPTER 5. RESULTS

Figure 5.7: Three modes of failure found when testing sheet metal with theMarciniak test; a) Cutting; b) Deep drawing; c) Random crack

The experimental results show that the set-up does result in fracture in thecentre, under the right circumstances. The numerical computations and exper-imental results are found to do show similarities, as both seem to be critical forreaching fracture in the centre. Therefore the experimental results have beenanalyzed in more detail to �nd a possible explanation. To determine whetherthe stresses occurring in the experimental Marciniak test reach higher valuesoutside of the biaxially loaded region as well, the local strains were measuredusing a regular pattern on the undeformed sheet and comparing this to the re-sulting pattern on the tested sheet. This system, known as Argus, needs everydot to be visible in at least 3 and preferably 5 photos taken from di�erent an-gles, but this was found to be an impossible task with the small test specimen.A photo and a set of microscope pictures of the sample as shown in 5.8 havebeen used instead to approximate the strains manually instead.

Figure 5.8: Marciniak test with regular pattern on top to determine the strain �eld

By comparing the increase in distance between the undeformed pattern and thepattern after the test, local strains even can be computed as ε = (L− L0)/L0.For several fractured specimen, this results in strains of (28 +/- 2%) and (29+/- 2%) for the respectively the centre and edge of the test specimen. Thisresults in a measured value of approximately 1.04 for σedge/σcentre, again largerthen one. The numerical model is veri�ed with another geometry as well, asused in the article by Raghavan [47].

It seems that with the quotient of σedge/σcentre is larger then one experimentally

48

CHAPTER 5. RESULTS

as well,but the specimen can still fracture in the centre. An explanation forthis is that interaction between washer and sheet restricts the tested sheet fromlocalizing in the contact area. This result is in agrement with experimentalresults, where necking is only found in the free centre of the specimen and noton the washer. The critical balance that is observed is likely to originate fromthis phenomenon as well, as σedge can not be a lot larger then σcentre to stillget fracture in the centre.

Figure 5.9: Close-up of the random fractured sheet with necks stopping at thewasher-sheet interface for the 7.5mm washer hole

An interesting observation is made on the randomly fractured sheets and shownin �gure 5.9). It can be seen that several necks have formed, that all stop atthe point where the washer is in contact with the sheet. This leads to thehypothesis that the deformation away from the centre can indeed be largerthen in the centre, but due to restriction of localization the sheet cannot fail inthe edge and therefore eventually fails in the centre.

From the above it can be concluded that the restriction of localization is akey factor in the Marciniak test. It is therefore important to get a betterunderstanding how several design parameters in�uence the stresses. This infor-mation can then be used when miniaturizing. The numerical model is found tobe useable for this, as the simulations seem to predict the (absolute) very well.The point where localization starts can not be predicted yet, and therefore thelocation of the �nal crack can not be predicted.

5.3.2 Numerical - experimental study of the Marciniak test

For better understanding of possibilities to optimize the Marciniak test forminiaturizing, the important design parameters will be analyzed numerically.The parameters that are studied are the friction between punch and washer(Mpw), the friction between washer and sheet (Mws), the punch edge radius,the washer hole radius, inner die radius and die edge radius. These numericalcomputations will be complemented with a set of experimental tests, to verifythe numerical results. These test have been carried out with a set-up availableat the Corus RD&T. The results are shown in table 5.4.

In table 5.4 the washer hole radius is the size of the hole in the washer, punch

49

CHAPTER 5. RESULTS

Table 5.4: Marciak Tests at Corus - Results

Nr. Washer hole Punchspeed Stops Roughened Load Displ. Failure moderadius [mm] [kN] [mm]

1 11 10 mm/min No No 65.0 14.9 Cutting2 11 20 mm/min No No 64.0 14.4 Cutting3 11 2 mm/min No No 63.4 14.0 Cutting4 10 10 mm/min No No 65.3 15.8 Cutting5 7.5 10 mm/min No No 73.0 16.8 Random6 5 10 mm/min No No 78.1 12.1 Deepdraw7 10 10 mm/min No Yes 67.4 14.8 Random8 10 10 mm/min No Yes 66.1 15.7 Random9 10 10 mm/min Yes Yes − − Cutting 2

10 10 1 mm/min Yes Yes 70.0 14.7 Random11 7.5 1 mm/min No Yes 85.2 15.7 Deepdraw12 10.5 1 mm/min No Yes 72.7 14.6 Random13 7.5 10 mm/min No Yes 79.4 14.7 Deepdraw

speed is the speed of the punch moving up. Stops were used in some testto take photos during the test, for use with the Aramis strain measurementsystem. Roughening was done by grinding of the washer, to increase the amountof friction between washer and sheet. All tests but the �rst one were donewith lubrication of the punch, as it was not possible to vary the lubricationconditions.

Friction

The e�ect of friction was studied by varying the friction coe�cient in the sheet-washer (Msw( and punch-washer contact (Mpw). It is important to know thatfriction coe�cients for unlubricated steel on steel contact go as high as 0.65,while lubricated contact friction coe�cients can be as low as 0.04, in the caseof perfect lubrication with te�on for instance [18].

Figure 5.10 shows the in�uence of (Msw). The results show a rather small butclear in�uence, where low friction between the sheets results in higher stresseson the outside of the tested sheet as the washer can not transfer its deformationon to the tested sheet. For high friction coe�cients the stresses in washer andsheet grow to become of the same size, resulting a relatively higher stress inthe centre.

Figure 5.10: In�uence of friction between the washer and the sheet; Dpunch =50mm; Rpunchedge = 10mm; Rwasherhole = 11mm; Mwp = 0.05;

50

CHAPTER 5. RESULTS

Experimentally the e�ect of increasing friction between washer and sheet canclearly be seen that for a washer with a hole radius of 10mm. This results ina cutting mode type of failure for low friction (test nr. 4), while for increasedfriction a random crack forms in the biaxially loaded region (tests nr. 7, 8 and10). The increased friction is does not result in a huge improvement of theσedge/σcentre value, but due to high sensitivity to this value a small change infriction can be of in�uence. This delicate balance is also found when comparingtests nr. 5 and 11, where a 7.5mm washer hole was used.

The second set of models shows the in�uence Mpw, as shown in �gure 5.11. Thefriction coe�cient in the washer-sheet contact is set to 0.8, as this high valuewas found to be needed. As is expected, a low friction results in a better stressdistribution, but again the in�uence seems to be small when only checking thestress quotient. From �gure 5.11 it can not be seen how the stress distributionchanges for friction coe�cients higher then approximately 0.5, where the biaxialloaded region never reaches the maximum tensile stress due to failure in a deepdrawing mode.

Figure 5.11: In�uence of friction between the washer and the punch; Dpunch =50mm; Rpunchedge = 10mm; Rwasherhole = 11mm; Msw = 0.8;

The experimental results have not been used to verify the in�uence of Mwp, aschanging lubrication conditions in a controlled manner was not possible.

Washer hole size

The radius of the washer hole is a simple property to adjust, so for an experi-mental set-up it is important to know its in�uence to take advantage of it. In�gure 5.12 it can be seen how the washer hole diameter has an optimum ataround 10mm. The in�nitesimal small washer hole equals a deep drawing testof a sheet that is twice the thickness of the tested material.

Figure 5.12: In�uence of the washer hole radius; Dpunch = 50mm; Rpunchedge =10mm; Mwp = 0.05; Msw = 0.8;

51

CHAPTER 5. RESULTS

The experiments con�rmed that for small washer holes the failure mode indeedbecomes similar to a deep drawing test (e.g. test nr. 6). Tests nr. 11 and 13show failure in a deep drawing mode as well for the 7.5mm washer hole size.This shows both friction and washer geometry can cause this failure mode, asthe 7.5mm washer hole of test nr. 5 fails in a random fracture due to lowerfriction between washer and sheet.

A larger washer hole can result in the washer sliding of the punch and therebyinitiating a cutting type of failure. This is found with the 11mm washer hole intests nr. 1, 2 and 3. The fact that for 10mm and 10.5mm washer holes randomfailure is possible shows once more the sensitivity of the Marciniak test.

Punch edge radius

The radius of the punch edge is important when miniaturizing, as it in�uencesthe stress �eld and can thus be used to lower the value of σedge/σcentre. Toanalyze the in�uence, di�erent radii edge radii have been numerically tested.The washer hole size was adjusted to be approximately Rpunch−Rpunchedge ·0.9,so the washer sheet stays on top of the punch during the test.

Figure 5.13: In�uence of the punch edge radius; Dpunch = 50mm; Rwasherhole =11mm; Mwp = 0.05; Msw = 0.8;

As is shown in �gure 5.13 the maximum stress in the central region of the testedsheet cannot reach its maximum for small radii of the punch edge. This caneasily be explained, as for an in�nitesimal small radius the punch has becomea cutting tool, where the tested sheet will fail due to shear.

Other design parameters

Numerical computations have been done to study the in�uence of the inner dieradius and die edge radius as well, showing no in�uence on the stress distribu-tion.

Conclusions

The numerical and experimental results show similar trends, which means themodel can be used for a qualitative analysis. The small di�erences between the

52

CHAPTER 5. RESULTS

centre and edge stresses show that it is not easy to lower the stress quotient,which means optimizing the set-up for miniaturization will not be easy.

5.3.3 Minaturization

All the earlier studied properties work together in a miniaturized set-up. Whenscaling down the set-up in total, the curve in �gure 5.14 is the result. Thisshows how the quotient of the stresses raises when miniaturizing, which isto be expected due to increasing bending stresses. Also it can not predict aminimum size that will still work, but it does show a clear trend.

Figure 5.14: In�uence of miniaturizing the Marciniak set-up; Rwasherhole = 11mm;Mwp = 0.05; Msw = 0.8;

To �nd the best set-up, several design parameters have been analyzed and fromthe results obtained it is possible to construct a numerical model of a miniatureMarciniak test choosing all the best values. This perfect set-up has large frictionon the sheet-washer interface and low friction on the punch interface and awasher with a hole scaled to the optimal size found for a 50mm punch.

Table 5.5: Geometry for the miniaturized Marciniak set-up

Property ValuePunch diameter [mm] 40

Punch edge diameter [mm] 8Washer hole size [mm] 15Inner die radius [mm] 42Die edge radius [mm] 3.5

The result for this optimized set-up was found to be marginally worse (σedge/σcentre =1.015) then for the simply scaled set-up as shown in �gure 5.14 (σedge/σcentre =1.012). This again shows how optimizing the Marciniak test set-up is not astrivial as for other set-ups. With a more extensive optimization it is thoughtto be possible to �nd a better geometry, and several other design parameterscan be considered as well.

Additional washer on top

The use of an additional washer on top of the standard set-up is thought toresult in better restriction of localization, and more force transferring betweenthe washers and sheet. The expected decrease of σedge/σcentre is not foundthough, as the computational model results in worse behaviour then the originaltest. Experimentally adding an extra washer might still work due due to an

53

CHAPTER 5. RESULTS

increase in restriction of localization that the washer and additional washerhave on the tested sheet, but at the expense of increased forces.

Washer material

An alternative approach for changing the stress �eld is to change the materialof which the washer is made. Finding a suitable material might prove di�cultthough, as the following requirements have to be met:

• The material needs to have high friction with the sheet material.

• The material needs to have low friction in the contact with the punch.

• The material must be roughly as formable as the tested sheet, so thewasher can drag the sheet outward.

• The material must be capable of reaching stresses comparable to thestresses in the tested sheet so it can transfer forces and restrict localiza-tion.

Some materials that come to mind are polymers, rubbers and other metals.The last group will result in higher forces, as another metal has to be as strongor stronger then the tested material. Polymers and rubbers can easily undergothe large deformations, but due to their generally lower strength might notable to transfer enough stress to and from the tested sheet. As friction andthe area of contact play an important role in the transfer of stresses as well,optimization of a set-up with another material proves to be a complicated task,but there is room for improvement.

Other design restrictions

When the miniaturizing both the needed forces and maximum height of theset-up are important, therefore these values where computed for �ve di�erentsizes of the punch. When comparing the values in 5.6 with those found for thepunch test, it immediately becomes clear that the forces in the Marciniak testare a lot higher. The maximum height is found to be relatively low, as 11mmis not expected to cause problems with microscopy set-ups. The forces canprove to be a problem though, as a set-up strong enough to cope with forcesof approximately 70kN might be impossible to be build on a small scale. Forhigh strength steel or thicker sheets the forces will even be higher.

The computed punch forces as shown in table 5.6 were compared with the forcesfound in the experimental set-up. For a washer with a 11mm hole radius itwas found that the computed maximum force equals 62kN , the measured forcelays between 63 and 65kN . For a smaller washer of 7.5mm the computed forceis 70kN , which is again a little lower then the measured punch force of 73kN .

54

CHAPTER 5. RESULTS

Table 5.6: Maximum punch forces at necking for a Marciniak test set-up;Rwasherhole = 11mm; Mwp = 0.05; Msw = 0.8;

Punch diameter [mm] Force [kN] Maximum height [mm]25 28 6.235 41 8.250 62 11.175 92 15.6100 125 20.3

An idea to decrease the needed force for the Marciniak set-up is to use a thinnerwasher sheet. It was numerically veri�ed that reducing the thickness of thewasher up to 50% is possible without a signi�cant in�uence on the stress �eld.This results in a force that is approximately 20% lower, depending on washerhole radius as well.

Conclusion

The results for miniaturization show that a challenge lies ahead when wantingto miniaturize the Marciniak set-up. There are several possibilities to improvethe used set-up though, which leaad to opportunities to miniaturize.

5.3.4 Summary

The experimental results clearly show the Marciniak test works, although anexact prediction of the failure mode is di�cult. Friction between washer andsheet is found to be important, as is the washer size.

The numerical results obtained with the FE model showed lower stresses in thecentre of the cup then on the edge. This is con�rmed experimentally and leadsto the hypothesis that necking or localization is restricted on the washer-sheetinterface.

• The Marciniak test is found to experimentally work and can be qualita-tively described with a numerical model up to necking.

• The Marciniak test shows a high sensitivity to friction and tool geometry,resulting in failure modes other then fracture under biaxial tension. Forminiaturization purposes optimization is needed to �nd the best toolinggeometry, which probably varies with material properties of the testedspecimen.

• Building a Marciniak test of dimensions small enough to �t under a mi-croscope is found to be possible. However, a disadvantage is the needfor high forces up to 50kN or more, which ask for a clever design whenminiaturizing.

55

CHAPTER 5. RESULTS


Many researches studied the use of cruciform specimen over the last decades,with most of the studies focussing on yielding properties. One step further isstudying necking and fracture with cruciform test specimen, which leads to thenew challenge of having to raise the stresses in the centre of the cruciform sofailure occurs there.

A study performed by Roel Vos [54] showed the cruciform specimen can beused up to fracture, but a thickness reduction is needed in the central part tomake it fail before one of the arms does. After analyzing several geometriesa bowl shaped thickness reduction was suggested, which will be the geometryused for further numerical and experimental work. The study by Vos predicts areduced thickness of 0.2mm should be su�cient to reach fracture in the centreof a cruciform with 10mm width arms.

5.4.1 Optimization of the cruciform design

To verify the earlier results and analyze the resulting stress and strain �elds,new simulations have been run. The resulting strain distributions for VonMises, major and minor strains are shown in �gure 5.15. The two importantproperties that are found from the numerical analysis are the biaxial strainingof the centre and the strain band developing from the centre outwards. The �rstindicates failure can occur in the centre, the shows geometrical constraining.The diagonal strain band shows how a crack can only develop in this direction,which means the orientation of the crack is not de�ned by the material but bythe geometry. This results in the need for testing with specimen of di�erentorientation to fully characterize a material that is anisotropic.

Figure 5.15: Strain �elds as determined numerically showing Von Mises strains, ma-jor strains and minor strains

For an experimental set-up the clamping area of the specimen is important toprevent slip in the arms. As the width of the clamps in the biaxial testingset-up is 12mm, this is the maximum width the specimen can have. To reducethe forces on the set-up and reduce the change of clamp slip, the width of thearms for experimental testing has been reduced to 6mm. This results in thedimensions as shown in table 5.7. The thickness of the centre is adjusted to180µm to increase the chance of fracture in the centre.

56

CHAPTER 5. RESULTS

Table 5.7: Dimensions of the cruciform specimen as shown in �gure 4.4

Property ValueWidth (w) [mm] 6.0Radius of rounding (Rw) [mm] 3.0Radius of bowl (Rreduced) [mm] 4.75Thickness sheet [mm] 0.7Thickness of centre [µ m] 180

5.4.2 Proof of principle

Using the experimental set-up as described in section 4.2.1, a set of cruciformspecimen with dimensions as given in table 5.7 was biaxially loaded up tofailure. From six specimen tested, only one fractured in the centre, showingeither the thickness reduction predicted by the numerical analysis is not enoughor the material behaviour in the thickness reduction is not exactly the same asthe global material behaviour of the IF-steel.

A new set of specimen with a thickness reduced area of 160µm was manufac-tured and tested, resulting in �ve successful tests out of �ve tested specimen.Fracture in all specimen occurred as predicted numerically, as is shown in �gure5.16. The crack clearly develops diagonal, and video footage show the crackstarts in the exact centre of the specimen.

Figure 5.16: Cruciform specimen fractured under biaxial deformation, with andwithout an Aramis pattern on the surface

For comparison of the experimental results with the numerical results, theAramis system is used to measure the local strains on the tested specimen. All�ve experiments show similar strain distributions, and similar strain values atfracture, as is shown in �gure 5.17. These measured strains are similar to thecomputed strains as shown in �gure 5.15.

The reason for the di�erence between measured and computed strains, espe-cially in the centre of the specimens, is the fact that local strains are measured,which are not numerically computed. The problem can also be originating inthe manufacturing of the cruciform specimens, which could lead to damageor alteration of the material properties. This will be investigated in the nextsection of this chapter.

With the computed and measured strain �elds being so similar, the next step isto analyze the displacements and forces acting on the cruciform. This is done by

57

CHAPTER 5. RESULTS

Figure 5.17: Strain �elds measured with Aramis for three di�erent cruciform speci-mens, showing Von Mises strains, major strains and minor strains

measuring the displacement and force at the tensile machine, the Zwick 1474,as no load cells are present in the biaxial tester. As the set-up is only for smalldisplacements, the displacements at the clamps can easily be determined fromthis as 1/2 of the total displacement. The total elongation of the cruciform inone direction therefore is equal to the displacement of the tensile machine. Forthe forces a similar computation can be made, as due to the 45◦angles the totalvertical force is equal to the total horizontal force, which means 1/4th of thetotal force is acting on each clamp.

Figure 5.18: Elongation-Force diagrams for the cruciform specimens deformed up tofracture (Total elongation of the cruciform in one direction)

The stress acting on the arms of the cruciform can now be calculated from theseresults, by dividing the force acting on the arms by the area of the cross-section.

58

CHAPTER 5. RESULTS

This results in a stress of σ = F/A = 1200/(6 · 10−3 ∗ 0.7 · 10−3 = 286MPa,which is clearly under the maximal value of 325MPa as was found as themaximum allowed (engineering) stress for IF-steel. To determine the stresses inthe biaxially loaded centre of the cruciform numerical computations are neededfor which the material model has to be used. A problem that arises here is tochoose the right parameters for the material model, as the material behaviourof the cruciform is not the same as the material behaviour of the sheet metal.This originates from the fact that sheet metals are not homogenous over thethickness of the sheet, as is assumed in simple material models.

An e�ect that cannot be numerically modelled and was not experimentallystudied is the in�uence of size e�ects. As the grains in the used IF steel areapproximately 10− 15µm, a thickness of 150µm is expected to not be sensibleto size e�ects, but for material with larger grains this might become an issuethat has to be dealt with.

59

CHAPTER 5. RESULTS

5.4.3 Specimen manufacturing and characterization

As was mentioned earlier for the punch test, material data as measured in a testis not always due to deformation of the material. In case of the punch a cleare�ect is introduced by friction, in the case of the cruciform an e�ect might befound due to specimen preparation. In this section the e�ects of manufacturingcruciform specimen with EDM will be analyzed, while more information aboutEDM in general can be found in Appendix A.

It is known from literature that the EDM process alters the surface of a metal,as vaporized material falls back on the surface en solidi�es. This so-called whitelayer, or recast zone, exists as a hard layer on top of the original material, withmicro cracks in it due to thermal expansion.

To get a better understanding of the in�uences of manufacturing the cruciformspecimen, several characterization techniques including surface pro�lometry,microscopy, grain size measurement, tensile testing and nano indentation havebeen used.

Surface pro�lometry

To get a better idea of the in�uence of EDM on the surface of the materialand on the microstructure, the �rst step in characterizing the EDM processfor manufacturing of cruciform specimen is to analyze both the surface andcross-section of the specimen.

Using the Sensofar confocal microscope, height pro�les where made of the cru-ciform specimen, as shown in �gure 5.19. This image shows the surface textureof the thickness reduced area to di�er from the original material, as it looksmore bumpy. A second observation is asymmetry found in the specimen, mean-ing the top and bottom sides of the cruciform are not exactly similar. This wasfound for all the tested cruciform specimen.

Figure 5.19: Height pro�le as measured with the Sensofar confocal microscope,showing top and bottom side of a cruciform specimen with measure-ments on the same scale

A last observation is the existence of variation in the thickness, although thisis found to be less then 15µm for the measured specimen. This is an increaseof more then 9% for a 160µm thick specimen.

60

CHAPTER 5. RESULTS

Microscopy analysis

A �rst hint that reveals the EDM process might alter the material behaviour, isfound by examining the surface of the thickness reduced specimen. Figure 5.20shows how a layer of resolidi�ed material is left behind by the process. Whencomparing with the as received material, it is clear that EDM does change thesurface of the sheet, even though the measured global roughness is the same asfor the as received material.

Figure 5.20: Microscope pictures of IF and by EDM thickness reduced IF showingresolidi�ed material from the EDM process

Grain size measurements

In �gure 5.21 the small grains on the edge and larger grains in the centre of theoriginal sheet are visible. This shows that the assumption of a homogeneousmaterial is not correct a representation of reality.

Figure 5.21: Cross-section of IF-steel sample after etching with Nittal / MarshallReagent

A similar study of the cruciform sample shows slightly larger grains near theedge of the cross-section, in the same order as the grains that where originally

61

CHAPTER 5. RESULTS

originated at those positions before the outer layer was removed. Due to therandom distribution in the grain size and the limited resources to compute theaverage grain size over a large area of the cross-section, no qualitative compar-ison can be made, but comparing several smaller areas show no indication ofgrain size increasing or decreasing due to the EDM process.

Figure 5.22: Microscopic pictures comparing the thickness reduced area with theoriginal sheet

Scanning Electron Microscopy

When analyzing the cross-section of a sheet metal with a SEM, the originalmaterial shows a clean surface with no irregularities while the cross-sectionthat was subjected to the EDM process shows deposited foreign material on theoutside of the sheet, as can be seen in �gure 5.23. The size of these resolidi�eddroplets range from 10 to 30 µm in width and 3 to 6 µm in height. This so-called white layer (or recast layer) has been investigated more, to �nd out thein�uence on the biaxial tensile tests.

Figure 5.23: Close-ups of the cross-section the edge of both the unaltered sheetand the edge after EDM processing, showing an irregular edge withresolidi�ed material attached to the surface

62

CHAPTER 5. RESULTS

A �rst observation when analyzing the cruciform specimen in SEM after frac-ture, is the existence of micro cracks in the mentioned recast layer. In �gure5.24 an example of such a crack in the recast layer is shown, resulting in a notchin the under lying steel. The existence of a micro crack on the surface can leadto fracture starting at the surface instead of failure from the middle of thesheet, as is found normally in ductile fracture. To verify fracture did not startat the surface, the crack tip of the cruciform specimen is compared to the cracktip of the Marciniak test specimen. The reason to use the Marciniak specimenas a reference is that for this specimen no external in�uences are present thatalter the biaxial fracture mode.

Figure 5.24: SEM image of the fractured recast layer in a biaxially tested cruciformspecimen

When comparing the two crack tips, a similar type of fracture is observed. In�gure 5.25 the crack tips for the Marciniak specimen and the cruciform speci-men are shown, which do not show a di�erence that can lead to the conclusionthat the fracture mechanisms di�er. Both the Marciniak and cruciform speci-men are found to have no visual evidence of a crack starting from the surfaceof the sheet.

Figure 5.25: SEM images of the crack tip of biaxially fractured material in theMarciniak test and the cruciform test showing many similarities

63

CHAPTER 5. RESULTS

Tensile tests

Microscopy showed possible e�ects of the EDM process are to be found in thealtering of the surface roughness, as the microstructure of the material is notchanged. To analyze the in�uence of this change on the biaxial measurements,the following section shows the results of mechanical testing of the material.

The results of the tensile tests (�gure 5.26) show a clear in�uence of the EDMand wire EDM processes, especially for the fracture strain and hardening showsa minor decrease as well. The huge decrease of the fracture strain can beexplained by the micro cracks that have formed. For biaxial loading these donot show a clear in�uence, as the measured maximum stresses are found to beroughly the same for all tests. For the uniaxial tensile tests the cracks are ofmore in�uence though, due to easier localization at the notch that was formed.This is the result of the equal thickness of the tensile bar.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

50

100

150

200

250

300

350

400

450

True Strain [−]

Tru

e S

tres

s [M

Pa]

Uniform Thickness SpecimenWire EDM Thickness ReducedSink EDM Thickness Reduced

Figure 5.26: Results of the tensile tests for thickness reduced IF-steel

The di�erences between die sinking EDM and wire EDM shown in the stress-strain curves, showing an increase of the fracture strain for wire EDM. Thisshows that wire EDM and die sinking EDM can not considered as resulting inthe exact same damage to the material, as was suggested by the EDMworkshop.[10]

For hardening it is more logical to increases, due to the addition of the recastlayer, but the response of the total specimen shows a decrease. This can beexplained by the heterogeneity of the sheet through the thickness, of whichonly the centre part is tested due to the thickness reduction. From the nanoindentation results it can be found that the centre of the sheet has a lowerhardness, resulting in less hardening of the thickness reduced specimen.

64

CHAPTER 5. RESULTS

Nano indentation

The hardness as determined by nano indention is visually represented in �gure5.27, where the results for both an unaltered sheet (in red) and a thicknessreduced sheet (in black) are given. The results show an increase in hardnessfrom the centre of the material outwards, which for the unaltered materialincreases approximately 20%, from a hardness of around 1.4 GPa to almost 1.7GPa near the edges. The measurements on the thickness reduced sample showa similar result, with the hardness increasing outwards from the centre. Theaverage hardness of the thickness reduced samples increases slightly faster thenthe hardness of the original material, but in the centre part of the cross-sectionno in�uences are found at all. The measured lower hardening in the tensiletests is thus found to originate from the fact that the part of the sheet that ismeasured has a lower hardness, due to the removal of the harder outer layer.

Figure 5.27: Hardness distribution determined by nano indentation

In the �gure the error bars show an uncertainty of up to 5% for most of thedata, which is caused by the in�uences of the microstructure of the material,like grain boundaries. A larger uncertainty is usually found near the edges,mainly due to specimen preparation. In appendix C an example of increaseduncertainty is given, caused by the polishing step used.

E�ects of thickness reduction on measured material behaviour

An e�ect of material removal is an in�uence on the global behaviour of the sheetmetal, e.g. hardening, as was shown in �gure 5.27. This change of measuredsheet properties originates in the heterogenous structure of a typical metal sheetas shown in �gure 5.28. For sheets containing di�erent phases like dual phasesteels, this e�ect is even stronger as the microstructure vary greatly over thethickness then for the tested IF-steel.

This e�ect introduces opportunities when determining material properties. Re-moving a part of the sheet by thinning may be carried out in such a way that in-stead of testing the sheet, testing a small part of the material or microstructurein the sheet becomes possible by removing the other layers. Some possibilitiesinclude material removal from one side only, as shown in 5.28 in the bottompicture. This approach would test the material near the surface, instead of the

65

CHAPTER 5. RESULTS

Figure 5.28: In�uence of microstructural inhomogeneities over the thickness of asheet metal

material in the centre of the sheet, and might provide insight in the layeredstructure of some sheet metals.

Combining material properties found through the thickness of the sheet canthen give more insight in the deformation behaviour of the sheet as a whole.This combined material model should give the same result as the a modeldetermined for the sheet metal itself, as both average the materials behaviourover the thickness.

A challenge that remains is to remove the material without in�uencing themeasured material data. For the removal of the in�uencing recast layer, theuse of ECM to polish or using ECM as only step instead are to be considered.Research into optimizing the manufacturing process has been started, but hasnot been �nished during this project. There are strong indications though thatthe recast layer can be fully removed, as was con�rmed during a meeting withPhilips. [41]


With the earlier mentioned set-ups, the possibility for building a miniatureversion of an existing set-up is the main problem. For cruciform specimens thisis not the case, as the designed set-up already is build at small scale.

The current set-up for 60x60mm specimen can be decreased in size by shorten-ing the arms. From the numerical computations it can be found that the strain�eld is only showing a gradient up to 12mm from the centre of the specimen.This means a specimen of 24mm, not including the clamping area, should bepossible. When reducing the width of the arms, an even smaller specimen canbe used. The limiting factor is only the material used, as large grains or othermicrostructural properties can lead to size e�ects when miniaturizing into asmall length scale.

Tensile forces and displacements

For a cruciform with arms of 6mm width, the needed forces were found to beless then 3kN . By decreasing the width of the arms this force can be loweredeven more. For building a set-up, the low forces are not expected to be aproblem.

Experimental and numerical results show the cruciform specimens have a max-

66

CHAPTER 5. RESULTS

Table 5.8: Numerical results for force and displacement for a cruciform with a centrethickness of 160µm

Property ValueMaximum Elongation [mm] 4.5 (2 x 2.25)

Maximum Force [kN] 2.95 (2 x 1.47)

imum displacement of 4− 6mm. This value can be lowered by shortening thearms, which gives more space for clamping as well.

Table 5.9: Comparing numerical and experimental results for the strain �eld in acruciform with a centre thickness of 160µm

Property Numerical ExperimentalMaximum Strain in the Arms [-] 0.11 0.15-0.20Maximum Strain in the centre [-] 0.41 0.46-0.65

When combining the results, no reason can be found that makes building abiaxial testing device for cruciform specimen that can be used with SEM andother microscopes.

5.4.5 Summary

The cruciform specimen is found to be an excellent method for testing underbiaxial loads. Both size and forces can be kept small for this set-up, making itrelatively easy to build as a miniature set-up.

• The cruciform test is found to be experimentally usable to deform metalsheets up to fracture under biaxial loading.

• The numerical and experimental data up to necking is found to be remark-ably similar for the used simple numerical model. This makes designingand optimizing the cruciform geometry a relatively easy task.

• Miniaturization is not an issue with the cruciform specimen, unless scalingdown into the domain where size e�ects become important. Forces anddisplacements are small in comparison to other techniques.

• The manufacturing of cruciform specimen is the biggest challenge, al-though promising processes have been discovered and are currently beinginvestigated.

67

CHAPTER 5. RESULTS

5.5 Comparative evaluation of the set-ups

The four tested set-ups have all got their advantages, which will be discussedin this section. The result of this is summarized in table 5.10.

Limitations of set-up and specimen

As is shown in literature, some set-ups provide better material data then others.This is mainly in�uenced by in-plane or out-of-plane testing, contact in the areaof the measurement and constraints that lead to force failure modes:

• The bulge test is an out-of-plane test, resulting in bending in�uences,which make the measured data deviate signi�cantly from the actual ma-terial data.

• The punch test is an out-of-plane test, like the bulge test, making bendingalso a problem. Contact in the area of interest makes the measured datadeviate even more for describing the material.

• The Marciniak test is an in-plane test, with no contact in the area ofinterest. The Marciniak test deforms the sheet under pure biaxial load,without any distortions from contact or bending.

• The in-plane cruciform test also has no contact or bending in�uencingthe measured data, but due to the specimen geometry a forced failuredirection exists.

Specimen preparation

• The specimen for a bulge test is cut out of the original plate, to �t in theclamping die. No special manufacturing steps are needed and becauseof that all materials, as long as they are impenetrable for �uids, can betested with the bulge test.

• The punch test specimen is exactly the same as for the bulge test. Alsofor the punch test there are no real limitations on what materials can betested.

• For the Marciniak test a specimen like the one for the bulge and punchtest is needed. A washer sheet is needed as well, which is a copy of thetest sheet, with a hole cut out in the centre. Determining the exact shapeof washer is a challenge, as the test is sensitive to small changes in theshape. For testing di�erent materials, it is likely that the set-up needsto be optimized again, resulting in di�erent set-ups or washer geometriesfor di�erent materials. Strong heterogeneity over the thickness can resultin early fracture at the punch edge due to bending stresses.

68

CHAPTER 5. RESULTS

• The in-plane cruciform test has the most challenging specimen design.Manufacturing of a thickness reduced test specimen involves EDM orECM, which is both time consuming and can alter the material. In the-ory any material can be tested with the cruciform loading test, but thee�ect of EDM or ECM might not be equal for every material. Stronglyheterogenous sheets can prove to be di�cult to characterize, as the dif-ferent layers have to be taken into account.

Measuring opportunities

• With the bulge test image correlation or microscopy can be used, butthe lens will have to move with the growing bulge. This results in achallenging set-up, that involves constant measuring of the bulge height.The measurements at the surface are not representative for the wholesheet, as the stress- and strain �elds are not uniform.

• The punch test has the same problem with non uniform stress- and strain�elds as the bulge test. Keeping the top of the bulge at the same distancefrom the lens is easier though, as the movement of the punch dictates themovement of the sheet.

• In the Marciniak test the area of interest stays in the same plane, whichmakes digital image correlation or microscopy easy. The stress �eld canbe computed, if the material model is known, which can be a challengeas it is the material model that needs to be determined.

• For the in-plane cruciform test a digital image correlation system or mi-croscope can be used as well, as the area of interest stays in-plane. Theuncertainty in the exact geometry of the specimen makes determining thestress �eld more di�cult, and involves numerical computing again for thethickness reduced centre.

Strain paths and strain path changes

• The bulge test can only be used for strain paths with ε1 > 0 and ε2 > 0.To achieve di�erent strain paths, elliptical dies with di�erent aspect ratiosare needed. There is no possibility to change the strain path during atest

• The punch test can be used for strain paths with ε1 ≥ 0, while ε2 can beboth positive and negative. This can be achieved easiest by changing thegeometry of the test specimen, for instance with a Nakazima test. Strainpath changes can not be made during a test

• The Marciniak test has the same strain path range as the punch test,ε1 ≥ 0 while ε2 can be both positive and negative. This is done withdi�erent specimen and washer geometries [47]. Varying the strain pathduring the test is not possible

69

CHAPTER 5. RESULTS

• The in-plane cruciform test is the only test where the strain path can bechanged during a tensile test. All strain paths under tensile loading canbe achieved by changing the load on the di�erent arms

Miniaturizing

• Miniaturizing the bulge test results in two problems that make it unde-sired to do so. The �rst is the increased bending in�uence for a smallbulge test. Even more problematic is the pressure of over 10MPa thatis needed to go up to fracture in a bulge test with 50mm diameter. Thisresults in uncontrollable and dangerous situations at fracture.

• The punch test shows the same problems with bending as the bulge test,but decreasing the size of this set-up results in a lower force needed togo to fracture, but an increase in friction in�uence due to the decreaseof the area the forces are working. The needed forces still go as high as20kN and to be able to neglect bending a large set-up is preferred.

• In the Marciniak test the bending problem is not found, which makesminiaturizing easier. The critical balance between the di�erent parame-ters makes a miniature set-up di�cult to optimize and to get it working.Also high forces are needed to deform up to fracture, as forces go as highas 60kN for a punch diameter of 50mm

• To deform a cruciform specimen up to fracture, forces as low as 2.5kNare su�cient. The only fundamental limitation for miniaturizing is thethickness reduction, that still has to be large enough to not feel size e�ects

70

CHAPTER 5. RESULTS

Table5.10

:Co

mpa

rison

ofthedi�e

rent

biax

ialtestm

etho

ds

Prop

erty

BulgeTe

stPu

nchTe

stMarcin

iakTe

stCr

ucifo

rmIn-plane

No

No

Yes

Yes

Contactin

region

ofinterest

No

Yes

No

No

Geometric

alcon-

straints

inregion

ofinterest

No

Yes,frictiondictates

the

fracturestartin

gpo

int

No,

fracture

isfre

eto

startan

ywhe

reforthe

biax

ialc

ase

Yes,

direction

offra

c-ture

isdictated

Specim

enprep

a-ratio

nUna

lteredsheet

Una

lteredsheet

Una

ltered

sheetan

da

simplewa

sher

geom

etry

Thinne

dsheet,

preci-

sion

job

alterin

gspeci-

men

geom

etry

Measurin

gop

-tio

nsStrain�e

ld,p

ressure

Strain�e

ld,p

unch

force

Strain�e

ld,p

unch

force

Strain

�eld,t

ensileload

inarms

Strain

�elds

Ellip

tical

dies,o

nlypo

s-itive

ε 1an

dε 2

Punchshap

es,spe

cimen

shap

es,fric

tion,

posit

ive

ε 1,po

sitive

and

nega

-tiv

eε 2

Specim

enan

dwa

sher

shap

es,

,po

sitive

ε 1,

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71

Chapter 6

Conclusions andrecommendations

6.1 Conclusions

From the result it can be concluded that the best options for a miniature set-upto study biaxial deformation and strain path changes are in-plane loading usinga cruciform geometry (ILCG) and the Marciniak test. Which of these is betteris dictated by the results that are wanted, as each has its own advantages anddisadvantages.

For the cruciform set-up, the following can be concluded:

• The cruciform test set-up is best a better option to be used under amicroscope, as it can be miniaturized relatively easily. Necessary forcesand the specimen size are both small enough to make a miniaturized set-up possible. Forces as low as 2kN are found to deform IF steel up tofracture.

• A disadvantage of the cruciform set-up is the challenge that lies in manu-facturing test specimen. Manufacturing induced e�ects can lead to datanot representative of the tested sheet, due to either damage introducedin the tested material or altered material properties over the thicknessof the specimen. To obtain reliable data these e�ects need to be kept assmall as possible.

• A second disadvantage of the thickness reduction is the need to deter-mine the needed thickness reduction to reach fracture. The ideal thick-ness therefore depends on material behaviour and therefore the optimalcruciform geometry changes with every material.

• A concurring advantage associated with the need for precise specimenpreparation in order to achieve thickness reduction in the cruciform spec-imen, is the possibility to test di�erent layers in a sheet metal. As most

72

CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS

sheet metals are heterogeneous over their thickness, this can prove to bea welcome addition to standard sheet tests.

• A huge advantage of the cruciform test set-up, that is not found in anyother test, is the possibility to change strain paths during a test. Com-plex strain paths can be described relatively easily, by prescribing thedisplacements of the clamps. The other set-ups that have been analyzedhave no possibilities for doing this.

• The Marciniak test is an interesting alternative, as it undistorted biaxialloading results due to the nature of the test and no distortion of themeasured data by specimen preparation is found. A miniaturized testset-up needs punch forces as high as 50kN for IF-steel, which might bechallenging when designing a small set-up.

• When miniaturizing the Marciniak set-up many design parameters arein�uencing a critical balance between the biaxial fracture mode and otherfailure modes. This results in a complex optimization problem, whichcannot easily be solved. It is likely that a miniaturized set-up can beoptimized to work, but no proof can be given at this moment. Also,optimizations are needed for di�erent materials so a set-up can be usedto test more then one material.

• If there is need for changing strain paths, the Marciniak test cannot beused. The only strain path changes that can be carried out involve usingpre-strained material to cut test specimen from. This gives severe limi-tations to the variety of strain paths that can be assessed, and leads toa more lengthy test procedure. Also when testing under di�erent strainpaths di�erent washer and specimen shapes are needed. This involvesmore optimizations, just as the original test set-up.

6.2 Recommendations for future work

The challenges that need to be solved to develop an ideal set-up that is useableunder all circumstances are the following:

• The in-plane cruciform specimen has not been optimized yet, only theearlier found geometry of Vos has been used and reduced in thickness toachieve fracture. To make the cruciform test smaller, an optimization ofthe cruciform size, the thickness reduction and geometry of the thicknessreduction is recommended.

• A study into EDM, ECM or another advanced method for material re-moval is recommended, in order to make the cruciform specimen witha less distorted microstructure. A method useable in a laboratory en-vironment is desirable, to make the specimen design cycle shorter. Astudy into optimizing the EDM process or using ECM has been started,in cooperation with Philips DAP [41], but results are pending.

73

CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS

• To understand the Marciniak test, studying of the local necking be-haviour is necessary, so numerical results can be improved to describethe Marciniak test with the localizations that were found. The improvednumerical model can then be used to analyze miniaturization further.

74

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[10] de Laat, H. (2007). Personal communication.

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[20] Gronostajski, J. and Dolny, A. (1980). Determination of forming limitcurves by means of marciniak punch. Mem. Sci. Rev. Metall., 77(4):570�578.

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[22] Guu, Y. (2005). AFM surface imaging of AISI D2 tool steel machined bythe EDM process. Appl. Surf. Sc., 242:245�250.

[23] Guu, Y., Hocheng, H., Chou, C., and Deng, C. (2003). E�ect of electricaldischarge machining on surface characeristics and machining damage of AISID2 tool steel. Mat. Sc. and Eng., 358:37�43.

[24] Hannon, A. and Tiernan, P. (2008). A review of planar biaxial tensile testsystems for sheet metal. J. Mat. Proc. Techn., 198:1�13.

[25] Ho, K. and Newman, S. (2003). State of the art electrical discharge ma-chining (EDM). J. Mach. Tools & Manufacture, 43:1287�1300.

[26] Hoferlin, E., van Bael, A., van Houtte, P., Steyaert, G., and de Mar, C.(1998). Biaxial tests on cruciform specimens for the validation of crystallo-graphic yield loci. Mat. Proc. Techn., 80-1:545�550.

[27] Kelly, D. (1976). Problems in creep testing under biaxial stress systems.J. Strain Anal., 1:11.

[28] Keskin, Y., Halkac�, H., and Kizil, M. (2006). An experimental study fordetermination of the e�ects of machining parameters on surface roughness inelectrical discharge machining (EDM). Int J. Adv. Manuf. Techn., 28:1118�1121.

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[30] Kuwabara, T. (2007). Advances in experiments on metal sheets and tubesin support of constitutive modeling and forming simulations. Plasticity,23:385�419.

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[56] Wierzbicki, T. (2006). Fracture of advanced high strenght steels (AHSS).Technical report, Massachusetts Institute of Technology.

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78

APPENDIX A. ELECTRICAL DISCHARGE MACHINING

Appendix A

Electrical Discharge Machining

Theory

The EDM process is basically a cathode-anode set-up of two electrodes, sepa-rated by a liquid dielectric, with a tool and workpiece. During the machiningprocess, a voltage is applied over the gap between anode and cathode, causingthe dielectric to break down. During the 'on-time' of the electrode a plasmachannel grows, surrounded by a vapour bubble. The dense liquid dielectricrestricts the growth of the plasma channel width, which results in the energybeing concentrated in a small volume. Local temperatures can reach as highas 20 000 to 40 000 K, with plasma pressures as high as 3 kbar. The shape ofthis plasma channel as seen in �gure A.1.

Plasma

Compressed

Liquid

Shockwave

Front

Ambient

Liquid

Dielectric

Cathode Melt

Cavity

Anode (+)

Cathode (-)

Anode Melt

Cavity

Ero

sio

n r

ate

Anode

Cathode

‘On-time’

Figure A.1: Schematic diagram of the EDM process showing the circle heat sources,plasma con�guration and melt cavities (left);The di�erence between anode and cathode material removal rates inrespect to 'on-times' (right) [12]

High energy levels in the plasma cause both electrodes to melt, but due to thehigh plasma pressures, vaporization is limited. When the pulse is turned on,the anode will be the �rst to rapidly melt because of fast moving electrons, andmelting of the cathode starts later during the process, due the lower mobility ofthe positive ions. This results in di�erent material removal rates for the anode

79


and cathode side, as is shown in �gure A.1.

For die sinking machines the cathode is usually the workpiece, resulting inrelatively large 'on-times' in the order of 10-100 µs to make sure material isremoved from the workpiece, instead of the tool. For most wire machines, thecathode is the wire, cutting into the anodic workpiece. The pulse time for wiremachines therefore is generally much shorter, in the order of less then 10 µs.

At the end of the 'on-time', the current is terminated and a violent collapseof the plasma channel follows. This causes the superheated, molten liquid onthe surface of the electrodes to explode into the dielectric �uid. Part of thematerial is then carried away, the remainder resolidi�es on the surface. [12, 25]

White layer and Heat A�ected Zone (HAZ)

Bleys et al [6] saw several di�erent layers in the thermally in�uenced zonein EDM. They report formation and thickness of these layers depends on theprocess conditions and work piece properties.

The 'white layer', a molten and resolidi�ed layer, also known as the recast layeris a result of EDM. In this layer micro cracks are found, that seldom go deeperthen the layer itself. Also present are micro-holes and droplets of resolidi�edmaterial. Below the recast layer, the heat a�ected zone (HAZ) is found. Thematerial in this zone has not been melted, but did undergo thermal in�uence.Several layers are present, although they are not easily distinguished. It isshown that it is possible to reduce the recast layer to a thickness in the orderof micrometres, by �nishing in several steps with decreasing pulse current.

Hardness test on an EDM machined surface show an increase in hardness inthe HAZ, because of either di�used carbon or a �ner grain structure due torapid cooling after the EDM process. The study shows residual stresses up to500 MPa, present from several µm to almost 10 µm into the material.

EDM parameters and their in�uence

Four parameters determine the material removal rate and thickness of the heata�ected zone and recast layer. These parameters are pulsed current, pulsedvoltage, pulse 'on-time' and pulse 'o�-time'. The �rst three determine the en-ergy put into the process, the latter determines the cooling time in betweenpulses. According to di�erent sources, pulsed current and pulse 'on-time' in-�uence the surface roughness, recast layer thickness and induced stresses most[22, 23, 48].

Varying pulse 'on-time' and pulse current has shown similar results for severalresearches. Kiyak and Çak�r [29] show a relation for pulse time and currenton AISI P20 tool steel, where pulse time clearly has more in�uence then pulsecurrent. They conclude a better �nish is obtained for low currents and shortpulse 'on-time', in combination with a relatively high pulse 'o�-time'. Guu et al

80


[23] give an empirical model that describes how the surface roughness changesin relation to pulse current (Ip) and pulse 'on-time' (τon) Ra = A ∗ (Ip)a(τ)b

that can be �tted to experimental data.

Lee et al [34] investigated the in�uence of pulse 'on-times' of 25 µs up to600 µs, showing surface roughness, tool wear and material removal rate isalmost constant for pulse 'on-times' higher then 50 µs. Keskin et al [28] showa similar result, but for pulse 'on-times' of 100 µs and higher, with di�erentpower settings and materials.

Lee and Li [35] studied the e�ect of pulse current and pulse 'on-time' on thethickness and composition of the recast layer. They conclude the recast layergrows with higher pulse current or pulse 'on-time'. Denser materials wherefound up to 15 µs into the material for pulse 'on-times' of 12.5 µs. The compo-sition of the top layer was studied with energy dispersive X-ray method (EDX),showing higher levels of carbon in the layer. The study of Guu et al [23] givesa similar result, and gives an empirical model for the recast layer thickness, tt = A ∗ (Ip)a(τon)b. The experimentally found thickness varies from 7 to 31µm, for relatively long pulse 'on-times' of 20 to 180 µs.

A study of Guu et al [23] shows correlation between tensile strength and machin-ing parameters, where a lower tensile strength was found for EDM machinedmaterials. In a later article, Guu [22] shows the depth of micro-cracks growswith increasing pulse current and pulse 'on-time' as well, measuring 1272 to1873 nm in depth for currents up to 1.5 A and 'on-times' up to 6.4 µs. Re-moving the recast layer is named as a possible solution to remove this e�ect.

Figure A.2: Surface roughness for positive (left) and negative (right) polarity on tool[1]

A study by Amorim and Weingaertner [1] shows clear di�erences for usingpositive or negative electrodes as tooling. The large di�erence in removal ratesis due to the plasma channel shape as explained earlier. An optimal 'on-time'of around 50 µs is found for a positively charged tool, while an 'on-time' ofaround 8-12 µs is found optimal for a negatively loaded tool. This e�ect wasalso predicted by [12]. Amorim and Weingaertner also studied the in�uence ofpolarity on the surface roughness, as shown in �gure A.2. This �gure clearlyshows how a negatively charged tool (tool as cathode) gives a smoother �nish,

81


at the cost of a much lower material removal rate and greater tool wear. Astudy by Bleys et al [6] into surface roughness shows very low roughness valuescan only be obtained by using low currents and inverse polarity, so-called 'EDMpolishing'. A surface roughness Ra of 0.09 to 0.26 µm is shown to be possibleby EDM polishing.

Tool wear

A side e�ect that should not be forgotten, is tool wear, as wearing of thetool cannot be prevented. Wang et al [55] show increased tool wear for highand short pulse currents. For extremely long pulse times, the di�erence inwear becomes less and eventually virtually negligible. As for a �ne surfaceroughness it was found that the pulse current should be low, this will not causeany problems for EDM where a �ne surface roughness is required.

82

APPENDIX B. ELECTRICAL CHEMICAL MACHINING (ECM)

Appendix B

Electrical Chemical Machining(ECM)

Theory

The concept of using chemical solutions for material dissipation has alreadybeen patented in 1929, but was not improved much till the late 50s and 60s,when aircraft industry started to using ECM. In the last decade the microma-chining step has evolved, allowing surfaces to be machined with micrometreresolution and polished with the same machine. This specialized use in theform of Electrochemical Micro Machining (EMM) show great potential as notool wear exists and high removal rates are possible. Alternatives like lasercutting, EDM and other non conventional machining tools are mostly thermaloriented, therefore making high precision more di�cult due to heating of theworkpiece. [4, 5]

The ECM EMM process physical background lies in anodic dissolution ofworkpiece material, where the workpiece and tool act as anode and cathode,separated by an electrolyte. By applying an electric current, the anode work-piece dissolves locally, so shaping it to become the mirrored image of the tool.The electrolyte, often a salt solution, is then used to bind the free ions fromthe dissolved material and removes it by �owing through the machining gap.[4]

The standard ECM process makes precise machining of vertical walls nearlyimpossible, but with a clever tooling geometry as shown in �gure B.1 it canbe done. A more complex dual pole set-up can be used to achieve even betterresults. [33]

The ECM EMM process is still under development and likely to be moreenhanced over the coming years, but is being used in several commercial man-ufacturing processes. Manufacturing steps like cutting slots in sheet metal,machining MEMS components and shaping of surgical equipment can all bedone with ECM. [4, 33]

83


Figure B.1: Comparison of di�erent anode-cathode set-ups for EMM. a) uninsulated,b) insulated, and c) dual pole tools [33]

ECM parameters and their in�uences

The most important parameters in the ECM process are again pulse 'on-time', pulse 'o�-time', pulsed current and pulsed voltage, like for the EDMprocess. The combination of these parameters determines the width of theinter-electrode gap, by resulting in equilibrium. As the material is not evapo-rated during the ECM process, heating up of the workpiece can be controlleda lot better, which results in a cleaner surface. [5]

For high precision material removal low currents are preferred, so the removedmaterial contaminating the die-electric can �ow away before in�uencing thelocal material removal rates. The inter-electrode gap can be as small as afew micrometre, but this limits the maximum material removal rate. Otherproperties in�uencing the accuracy of the ECM process are the choice of theelectrolyte and the tool, where the latter should be thermally and electricallyconductive, corrosion resistant and sti� enough to withstand the electrolytepressure without vibrating. [5]

The electrolyte used is a last process parameter that can be used to enhancethe ECM process, as di�erent materials may need di�erent electrolytes. Adi�erent electrolyte can also be used to favour certain chemical reactions andthereby change the material removal process. Electrolytes can be divided in

84


two main types: passivating electrolytes, that contain oxidizing anions, likesodium nitrate or sodium chlorate, and non-passivating electrolytes containingmore aggressive anions such as sodium chloride. The �rst are used for bettermachining precision, the latter for higher removal rates. [33]

Surface roughness

Surface �nishing by ECM is better then for most other processes, but as �gureB.2 shows this does depend on the length scale being considered. The reason forthe worsening for larger length scales is the development of wave-like patternson the surface because of hydrodynamic vortex phenomena (di�erences in �owspeed). Choosing the right ECM tooling helps to reduces this surface roughnessproblem. [5, 33]

Figure B.2: Comparison of surface roughness for conventional polishing and ECM[33]

Tool wear

The problem of EDM where the electrode shape changes is not found in ECM,as only hydrogen gas is evolving at the cathode, thus no material is removedfrom the electrode during the process.

85

Appendix C

Specimen Preparation: TegraPolor Target System

An important aspect to take into account when interpreting data, is the amountof scatter found. For data sets where the scatter is large, there might be aproblem with the acquisition of the data. This might be due to a problem withthe set-up or a problem with the used specimen.

Figure C.1: Maximum load in an indentor test over the cross-section of a metal sheeton a specimen prepared with the TegraPol system

While using the nano indentor to determine the hardness gradient of the IFsteel sheet, a large scatter was found on specimen prepared with the TegraPolpolishing system as can be seen in �gure C.1. It was found that this was relatedto the �atness of the specimen.

86

APPENDIX C. SPECIMEN PREPARATION: TEGRAPOL OR TARGETSYSTEM

Figure C.2: Maximum load in an indentor test over the cross-section of a metal sheeton a specimen prepared with the Target system, showing lower scatterthen for the TegraPol prepared specimen

The data obtained from specimen prepared with the Struers Target system,where the surface was found to be better then for conventional polishing, showeda lot less scatter. Even though one side of the specimen still showed roundingof the edges, as can be seen in �gure C.2 the scatter for the same measurementwas decreasing.

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Biaxial Testing of Sheet Metal: An Experimental-Numerical Analysis