EFFECT OF GEOMETRICAL AND PROCESS PARAMETERS ON THE QUALITY

OF OPEN MOULDED COMPOSITE PARTS WITH SHARP CORNERS:

A DECISION-BASED APPROACH

by

Juan David Torres

B.A. Sc., La Universidad del Zulia, 2008

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF APPLIED SCIENCE

in

THE COLLEGE OF GRADUATE STUDIES

(Mechanical Engineering)

THE UNIVERSITY OF BRITISH COLUMBIA

(Okanagan)

May 2015

© Juan David Torres, 2015

ii

Abstract

The use of autoclaves and ovens in modern composite manufacturing processes has

shown a potential to greatly control the geometry and structural properties of composite

materials. The use of such manufacturing tools has been supported by numerical tools and

optimization/statistical methods, in order to further improve the quality of composite

products. However, the costs associated with these advanced manufacturing techniques are

not always acceptable for all Fiber Reinforced Composite (FRC) manufacturers. In

particular, for large products with low production rates (e.g., marine and automotive

industries), open moulding are preferred as they typically offer the best compromise between

the quality of the part and manufacturing production cost. The quality of open-moulded parts,

however, is highly dependent on the skill of the operator, hence resulting in possible

variations in part properties, particularly for geometrically complex parts. This variation

often causes out-of-specification products, resulting in costly trial and error approaches to

minimize the product defects.

The purpose of this thesis was to study the FRC process conditions that have a

statistically significant effect on the generation of defects in open-moulded parts with sharp

corner (i.e., small radius) features. Samples with different geometrical, material and process

parameters were manufactured. Defects such as void content, corner fiber bridging, fabric

formability, fiber misalignment and bending resistance of the material were evaluated

through different characterization techniques. The statistical analysis of the data has provided

new means to determine the contribution of each parameter to the final quality of the

composite part. The results suggest that the part radius and part thickness both have

iii

significant effects on the bending resistance of the FRC specimens. Also, it was observed that

reinforcement orientation has a significant effect on the formability and surface defects

around the part corners. Finally, a novel Multiple Criteria Decision Making (MCDM)

approach has been developed using “signal to noise” ratios with subjective and objective

weighting, in order to identify the optimum design parameters for both aesthetic and

structural properties of the open moulded FRC parts with sharp corners.

iv

Preface

Portions of this thesis have been published as a part of the Society for the Advancement of

Materials and Process Engineering (SAMPE) 2014 Conference in Seattle, WA as: J. Torres,

B. Crawford, F. Islam, L. Bichler, A.S. Milani (2014) The Effect of Design Parameters on the

Quality of Open Moulded Fiber Reinforced Composites with Sharp Corners. SAMPE Tech

Conference and Exhibition. Seattle, WA. Two journal articles are also under submission from

parts of Chapter 4.

v

Table of Contents

Abstract ..................................................................................................................................... ii

Preface...................................................................................................................................... iv

Table of Contents ...................................................................................................................... v

List of Tables ......................................................................................................................... viii

List of Figures ........................................................................................................................... x

Acknowledgements ................................................................................................................ xiii

Dedication .............................................................................................................................. xiv

Chapter 1: Introduction ....................................................................................................... 1

Thesis Objectives ...................................................................................................... 3 1.1

Chapter 2: Literature Review.............................................................................................. 5

Composite Materials ................................................................................................. 5 2.1

2.1.1 Thermoset Matrix Composites .............................................................................. 6

2.1.1.1 Unsaturated Polyester Resins ........................................................................ 7

2.1.1.1.1 Effects of Processing Parameters on the Curing of UP Resins ................ 8

2.1.2 Manufacturing Methods for Composites ............................................................ 11

2.1.3 Open Moulding Techniques ................................................................................ 13

2.1.3.1 Wet Lay-up ................................................................................................. 13

2.1.3.1.1 Advantages of Wet Lay-up ..................................................................... 14

2.1.3.1.2 Disadvantages of Wet lay-up ................................................................. 14

2.1.4 Mechanical Properties of Angled Composites .................................................... 15

2.1.5 Defects Affecting Quality of Composites ........................................................... 21

2.1.5.1 Void Content ............................................................................................... 21

2.1.5.2 Defects on Angled Laminates ..................................................................... 24

2.1.6 Flexural Rigidity of Fibers .................................................................................. 24

MCDM Methods ..................................................................................................... 25 2.2

2.2.1 TOPSIS ............................................................................................................... 26

2.2.1.1 Weighting Method ...................................................................................... 28

2.2.2 Signal to Noise Ratio (S/N) ................................................................................ 29

Chapter 3: Experimental Methods and MCDM Procedure .............................................. 31

vi

Manufacturing of Test Coupons ............................................................................. 31 3.1

Experiment #1: Evaluation of Geometrical Parameters.......................................... 32 3.2

3.2.1 Quality Evaluation .............................................................................................. 33

3.2.1.1 Void Content Test ....................................................................................... 33

3.2.1.2 Curved Beam Strength (CBS) ..................................................................... 34

3.2.1.2.1 Digital Image Correlation for the CBS Test ........................................... 37

3.2.1.2.2 Finite Element Model (FEM) for the CBS Test ..................................... 39

3.2.1.3 Fiber Misalignment ..................................................................................... 41

3.2.1.4 Thickness Uniformity ................................................................................. 41

3.2.1.5 External Surface Defects............................................................................. 42

3.2.1.6 External Formability of Reinforcement ...................................................... 43

3.2.2 Multiple Criteria Decision Making (MCDM) Procedure ................................... 44

Experiment #2: Effective Flexural Rigidity Evaluation ......................................... 50 3.3

Experiment #3: Process Conditions Evaluation ...................................................... 51 3.4

Chapter 4: Results and Discussion ................................................................................... 53

Experiment #1 Results: Influence of Geometrical Parameters ............................... 53 4.1

4.1.1 DIC for the CBS Test .......................................................................................... 53

4.1.2 Non-linear Response Evaluation via FEM ......................................................... 57

4.1.3 Sensitivity Analysis Results ................................................................................ 60

4.1.3.1 CBS Tests.................................................................................................... 60

4.1.3.2 Void Content ............................................................................................... 64

4.1.3.3 Fiber Misalignment ..................................................................................... 66

4.1.3.4 Thickness Uniformity ................................................................................. 68

4.1.3.5 Corner Bridging .......................................................................................... 70

4.1.3.6 External Formability of Reinforcement ...................................................... 74

4.1.3.7 External Surface Defects............................................................................. 76

4.1.3.8 Summary of Geometrical Parameters Effects ............................................. 77

4.1.4 MCDM Results and Discussions ........................................................................ 81

4.1.4.1 Structural Scenario Ranking ....................................................................... 84

4.1.4.2 Aesthetic Scenario Ranking ........................................................................ 85

Experiment #2 Results: Influence of Flexural Rigidity .......................................... 85 4.2

vii

Experiment #3 Results: Influence of the Cure ........................................................ 88 4.3

Chapter 5: Conclusions and Future Work ............................................................................... 90

Conclusions ............................................................................................................. 90 5.1

Future Work ............................................................................................................ 93 5.2

Bibliography ........................................................................................................................... 94

Appendices .............................................................................................................................. 99

Appendix A: ANOVA Experimental Results for Samples of Group 2 ............................. 99

Appendix B: DIC Qualitative Evaluations on Experimental Group 3 ............................. 101

Appendix C: Experimental Raw Data .............................................................................. 103

viii

List of Tables

Table 3.1 Mechanical properties used for the reference FEM model; properties

extracted from........................................................................................................ 40

Table 3.2 Schematic of MCDM for the experimental methodology ..................................... 45

Table 3.3 Relative importance between criteria based on the MDL method ......................... 47

Table 3.4 Experimental matrix for flexural stiffness evaluation (Experiment #2) ................ 51

Table 3.5 Experimental matrix for Experiment #3 ................................................................ 52

Table 4.1 ANOVA results for the CBS response (α=0.05) ................................................... 61

Table 4.2 ANCOVA results for the CBS response (α=0.05) ................................................. 63

Table 4.3 ANOVA results for the void content response (α=0.05) ....................................... 64

Table 4.4 ANOVA results for the misalignment response (α=0.05) ..................................... 66

Table 4.5 ANOVA results for the thickness uniformity response (α=0.05) .......................... 68

Table 4.6 ANOVA results for the bridging response (α=0.05) ............................................. 70

Table 4.7 ANOVA results for the external formability response (α=0.05) ........................... 74

Table 4.8 ANOVA results for the surface defects response (α=0.05) ................................... 76

Table 4.9 Comparison between DIC results and optical imaging for samples

with 70° angle ........................................................................................................ 78

Table 4.10 Comparison between DIC results and optical imaging for select

samples with 40° angle ......................................................................................... 79

Table 4.11 Trends of the influence of significant design inputs on the quality

metrics; ranking of input variables are given in brackets in each

column; ‘No’ refers to statistical insignificance .................................................. 81

Table 4.12 Images corresponding to the best quality designs under different

quality metric criteria ........................................................................................... 81

Table 4.13 Relative importances between criteria based on the MDL method;

structural scenario ................................................................................................ 82

Table 4.14 Relative importances between criteria based on the MDL method;

aesthetic scenario ................................................................................................. 82

Table 4.15 Pearson's correlation results for criteria pairs; Rjk ............................................... 83

ix

Table 4.16 Summary of weighting results under the combinative method

for each design scenario ....................................................................................... 83

Table 4.17 TOPSIS results using four design alternatives for a structural application ......... 84

Table 4.18 TOPSIS results using four design alternatives for an aesthetic application ........ 85

Table 4.19 Flexural rigidity values for the reinforcement material at different

orientations ........................................................................................................... 85

Table 4.20 Comparison for all quality metrics between -45 o/45

o and 0

o/90

o specimens

(green marks indicate a statistically preferred condition) .................................... 86

Table 4.21 ANOVA results for the CBS response as a function of process conditions

(α=0.05) ................................................................................................................ 88

Table A.1 ANOVA results for the CBS response (group 2) (α=0.05)................................... 99

Table A.2 ANOVA results for the void content response (group 2) (α=0.05) ...................... 99

Table A.3 ANOVA results for the formability response (group 2) (α=0.05) ........................ 99

Table A.4 ANOVA results for the thickness ratio response (group 2) (α=0.05) ................. 100

Table A.5 ANOVA results for the bridging response (group 2) (α=0.05) .......................... 100

Table A.6 Comparison between DIC results and optical imaging for samples

with 5 layers (group 3) ....................................................................................... 101

Table A.7 Comparison between DIC results and optical imaging for samples

with 3 layers (group 3) ....................................................................................... 102

Table A.8 Raw data for experiment #1 (geometry effect) ................................................... 103

Table A.9 Raw data for experiment #1 (geometry effect) (continued) ................................ 104

Table A.10 Experimental design alternatives for the MCDM (experiment #2) .................. 105

Table A.11 Raw data for experiment #2 (reinforcement orientation effect) ....................... 106

Table A.12 Raw data for experiment #3 (degree of cure effect) ......................................... 107

x

List of Figures

Figure 2.1 UP polymerization reaction (Strong, 2008) ............................................................ 7

Figure 2.2 Conversion (cure) profile as a function of time under different temperatures. ...... 9

Figure 2.3 Gel time as a function of temperature for a UP resin under three

different initiator concentrations. ......................................................................... 10

Figure 2.4 Schematic of the change on the storage modulus based on the degree

of cure of an UP resin. ......................................................................................... 11

Figure 2.5 Schematic of hand lay-up process ........................................................................ 14

Figure 2.6 Composite diagram indicating transverse direction in flat and curved parts ....... 15

Figure 2.7 Schematic of geometrical parameters used for the radial stress calculation

in a curved composite beam ................................................................................. 16

Figure 2.8 Theoretical radial stress versus different curvature radii .................................... 19

Figure 2.9 CBS versus: a) Thickness (mm), b) R/t and maximum radial stress versus:

c) Thickness, d) R/t of the composite laminated beams ....................................... 20

Figure 2.10 Void content vs. shear, flexural, and tensile strengths ....................................... 22

Figure 2.11 Visual reference for void content in unidirectional samples .............................. 23

Figure 2.12 Euclidean distances from an ideal positive and negative solutions) .................. 27

Figure 3.1 Schematic of the master mould ............................................................................ 31

Figure 3.2 Sample geometry and input parameters used ....................................................... 32

Figure 3.3 The CBS test fixture used ..................................................................................... 35

Figure 3.4 CBS test geometrical considerations (ASTM D6415, 2007). .............................. 36

Figure 3.5 Typical response for multidirectional composite specimens ................................ 36

Figure 3.6 Fixture and calibration plate for DIC imaging ..................................................... 38

Figure 3.7 Speckle pattern used for DIC measurements on CBS test ................................... 39

Figure 3.8 Schematic of FEM model of CBS 4-point bending test for 40° sample ............... 40

Figure 3.9 Curved part with non-uniform surface geometry, as modified in the model ....... 41

Figure 3.10 Misalignment angle measurement on the curved specimens ............................. 41

Figure 3.11 Measurements of the total (white arrows) thickness on: a ) the corner

(Tc) and b) the flat region (Tf). ........................................................................... 42

Figure 3.12 (a) Top and (b) lateral views of a typical corner surface defect ......................... 43

xi

Figure 3.13 (a) Design curvature, and (b) the actual reinforcement curvature at

the outer surface ................................................................................................. 43

Figure 3.14 Reference of ply orientation for a) 0o /90

o degrees and b)-45

o /+45

o degrees .... 50

Figure 3.15 Cantilever bending tester used of the stiffness characterization of the

reinforcement ..................................................................................................... 50

Figure 4.1 Load vs. extension plot with DIC results, indicating: a) stage without failure,

b) first delamination on the upper region, and c) second delamination; specimen

with a radius of 1/8”, part angle of 70° and 3 layers. ........................................... 54

Figure 4.2 Load vs. extension plot with DIC results, indicating: (a) stage without

failure, (b) first delamination on the lower region, (c) extension of the

first delamination and (d) second delamination on multiple regions;

specimen with a radius of 5/16”, part angle of 40° and 3 layers. ......................... 55

Figure 4.3 Load vs. extension plot: Three different runs under with variable maximum

loads to evaluate repeatability on the curve for evaluation of the elastic

region in a specimen with a radius of 1/4”, part angle of 40° and 3 layers .......... 56

Figure 4.4 Stress distribution of the sample on the y. direction ............................................ 57

Figure 4.5 Force vs. displacement response from the FEM simulation ................................. 58

Figure 4.6 Cross-section of a sample manufactured with manual wet lay-up ....................... 58

Figure 4.7 Comparison of force vs. extension plot between an ideal (plain) inner

surface and an internal surface with rough geometry .......................................... 59

Figure 4.8 Comparison of experimental force vs. extension plots for a specimen with a

modified (plain) internal surface and the one with the original (rough) inner

surface .................................................................................................................. 60

Figure 4.9 Main effect plots of CBS vs. (a) part angle in degrees, (b) corner radii

in inch and (c) number of layers .......................................................................... 62

Figure 4.10 Main effect plot of a) void content vs. corner radius in inch and

b) void content vs. corner angle ......................................................................... 65

Figure 4.11 Main effect plots of misalignment vs. (a) part angle in degrees, and

(b) corner radii in inch ....................................................................................... 66

Figure 4.12 Draping comparison between a) mould with 40° and b) mould

with 70° angle .................................................................................................... 67

xii

Figure 4.13 Main effect plots of thickness uniformity vs. (a) part angle in degrees,

(b) corner radii in inch and (c) number of layers ............................................... 69

Figure 4.14 Main effect plots of bridging vs. (a) part angle in degrees,

(b) corner radii in inch and (c) number of layers ............................................... 71

Figure 4.15 Bridging effect plot for AB interaction; bridging values are in [mm] ............... 72

Figure 4.16 Comparison between bridging for (a) sample with 40°, 1/8” (b) sample with

70°, 1/8” (c) sample with 5/16”, 40° and (d) sample with 5/16”, 70° .............. 73

Figure 4.17 Main effect plots of external formability vs. (a) part angle in degrees,

(b) corner radii in inch ....................................................................................... 74

Figure 4.18 CBS effects plot for the interaction AB ............................................................. 75

Figure 4.19 Main effect plots of surface defects vs. (a) part angle in degrees,

(b) corner radii in inch and (c) number of layers ............................................... 77

Figure 4.20 Effect plots for interaction between angle and layer orientations for

formability metric .............................................................................................. 87

Figure 4.21 Effect plot for interaction between angle, number of layers and

reinforcement orientation for the surface defects metric ................................... 88

xiii

Acknowledgements

I would like to express my deepest gratitude to my supervisors, Dr. Abbas Milani and Dr.

Lukas Bichler. Thank you for your professional guidance and support during these years.

Also, I would like to thank to the research group of the Composites Laboratory of UBC

Okanagan, especially Mr. Bryn Crawford for all his support and kind help on all the activities

related to this project. Moreover, I would like to thank Mr. Faisal Islam, Mr. Prabhakar Pal

and Mr. Norberto Feito for all their help on the experiments developed during this research.

Last, I would like to recognize the help and support that I have constantly received from my

friends and family over the years. Especially from my parents, sisters, cousins and my wife,

thanks for being there in all difficult moments to offer the right word, advice and

opportunities that let me achieve my goals.

xiv

Dedication

To my wife Karol,

Gracias por estar siempre a mi lado y por tu amor incondicional, te amo.

1

Chapter 1: Introduction

The concept of “composite material” refers to a material that is composed of two or more

constituent materials, with properties different from the individual components. One

important group of composite materials is fiber reinforced composites (FRCs), which are

normally material systems comprised of a polymeric resin and the reinforcing fibers. FRCs

have already demonstrated great advantages over traditional materials such as aluminum and

steel, including higher specific strength, specific stiffness, and fatigue resistance. However,

difficulties on maintaining part quality along with the lack of standard design rules,

especially for parts with complex geometrical features such as sharp corners/curvatures, the

full implementation of FRCs is still limited in a number of industries (Strong, 2008). The use

of autoclaves and ovens in modern FRC manufacturing processes has enhanced the ability

for some manufacturers to greatly control complex geometrical features and structural

properties of curved composite parts. These manufacturing tools are also often supported by

numerical tools and optimization methods to produce more robust products (Liu et al., 2005).

However, the production costs associated with advanced manufacturing techniques are not

suitable for all FRC manufacturers. Therefore, other cost-effective processes are currently

considered in small-to-medium enterprises in the composite sector. In particular, for common

engineering composites (e.g., Glass Fiber Reinforced Plastics (GFRPs)) with large product

sizes and lower production rates, open moulding techniques offer the best compromise

between the part quality and the manufacturing cost (Strong, 2008).

The term ‘quality’ is subjective and highly dependent on the application of the final product.

For example, what is classified as a defect in an “advanced” composite may be acceptable for

an “engineering” composite (e.g., non-aerospace applications). However, defect formation

2

mechanisms and contributing factors in advanced and engineering composite materials and

processes are similar. Regarding open-moulded parts, quality is known to highly depend on

the skill of the operator, hence resulting in a wide variation in product outcomes (Mazumdar,

2002). This variation occasionally results in parts with out-of-specification dimensions.

Accordingly, optimization of the design and manufacturing process is associated with

lengthy and costly trial-and-errors.

Mechanical properties of FRP composites such as shear and flexural strengths are known to

be highly sensitive to the void content in composite materials (Liu et al. 2005). Similarly,

the bending resistance of parts is affected by the void content or dimensional distortions

(Hubert and Poursartip, 2001). Other factors influencing the mechanical behavior of FRP

composites are fiber misalignment and the volume fraction. Both of these factors are more

pronounced in curved sections of parts (Hubert and Poursartip, 2001); (Potter et al. 2008);

(Potter, 2009). The mechanical stress developed on curved parts under bending is highly

dependent on the interlaminar properties (Lekhnitskii, 1968). Several investigations have

been carried out exploring the effect of process parameters and geometrical conditions on the

development of the aforementioned defects on advanced composite parts (Potter, 2009;

Cauberhs and Hubert, 2011; Michel et al. 2013; Wisnom and Jones, 1996). These

investigations have defined admissible thresholds variables for the control of defects in

composites. However, a very limited portion of these previous works has considered the

application of control strategies to statistically reduce the number of defects in open moulded

parts.

3

Thesis Objectives 1.1

This thesis attempts to quantify (via statistical approach) the quality of open moulded parts

with sharp corners. This knowledge could be used by industrial manufacturers in order to

create quality-based guidelines for the design and manufacture of complex parts in open

moulded FRP processes. The specific objectives of this thesis are to:

1. Define a characterization procedure for assessing the quality of hand lay-up open

moulded samples with sharp corners.

2. Quantify the effect of different geometrical and process parameters on the ensuing

quality of the open moulded parts.

3. Propose a new methodology, based on statistical analysis and multiple criteria decision

making, to arrive at desired design solutions for open moulded, sharp-cornered parts

under conflicting quality metrics.

In chapter 2, a general summary of composite materials and their manufacturing processes

relevant to this thesis are provided. The chapter also includes a review of Multiple Criteria

Decision Making (MCDM) methods. Chapter 3 describes the experimental methods and the

samples under different ranges of geometrical parameters. Characterization methods for

common defects such as void content, bridging and fibre misalignment are described.

Mechanical performance of the samples is also evaluated through a modification of the

standard curved beam strength (CBS). A modified MCDM procedure for the evaluation of

geometry influence is described. In Chapter 4, the statistical analysis of the obtained data is

used to provide new means to determine the contribution of each design and process

4

parameter to the final quality of the open-moulded composite parts. Based on the statistical

trends of the quality metrics, the results of the MCDM technique are also presented for the

geometrical design case. In Chapter 5, conclusions and potential future work from the above

experimental and optimization results are summarized.

5

Chapter 2: Literature Review

This chapter is divided into two main sections. First, Section 2.1 provides an overview of

thermoset composites and their common manufacturing methods. A general description of

the typical manufacturing defects that control the quality of curved composite parts is also

discussed. Moreover, a brief discussion of the stress response of angled composite specimens

under bending conditions is presented. Then, in Section 2.2, a general background on the use

of Multiple Criteria Decision Making Techniques is presented.

Composite Materials 2.1

The concept of a “composite material” refers to every material that is composed of more than

one solid element, where each element provides complementary properties (Strong, 2008).

This concept includes a wide variety of different materials including: wood laminates,

reinforced concrete and fiber reinforced plastics. Fiber reinforced composites are defined as a

group of composite materials that are formed by a matrix that holds in place fiber

reinforcements (Strong, 2008).

The properties of a composite material are governed by the constituent elements of the

composite. The matrix provides the shape to the structure and protects the embedded fibers;

the reinforcement fibers provide strength and stiffness to the part and increase the mechanical

properties in the direction coincident with the fibre orientation (Strong, 2008).

Fiber reinforced composites can be divided into two groups based to the nature of the matrix

material. The first group corresponds to thermoplastic composites, which are comprised of

composites with thermoplastic resins as the matrix material. Thermoplastics are usually in

6

solid state at the room temperature, and the resin has to be melted and softened prior to

processing. As a result, the molding process temperatures for thermoplastic materials have to

be above the melting point of the resin, in order for the resin to penetrate between fibers and

form the desired mold shape. After filling the mold, and as the temperature decreases below

the crystallization temperature, the composite part cures and is formed. In general,

thermoplastic resins show better toughness and impact resistance than thermoset resins;

however, the high viscosity and higher cost associated with thermoplastic materials create

unique challenges. As a result, thermoset materials have found a more widespread use in

many engineering applications of composites (Strong, 2008).

2.1.1 Thermoset Matrix Composites

In thermoset composites, the molecules of the polymer develop chemical bonds called

crosslinks during the curing process. The formation of multiple crosslinks generates a

significant increase in the molecular weight of the resin, which causes the melting point of

the resin exceed the decomposition temperature of the matrix. As a result, thermoset resins

cannot be melted or recycled. A key advantage of thermoset resins is their low viscosity,

which allows the resin to penetrate the fibers of the reinforcement, even after the curing

reaction has started. As a result, the time to properly impregnate the reinforcement and adopt

the geometry of the mold is increased. Another advantage of this material is related to its

elevated glass transition temperature, which allows the composite part to operate at

temperatures above the curing temperature (Strong, 2008).

Within thermoset resins, the unsaturated polyester (UP) is one of the most common resin

materials used today due to its low cost when compared with other thermoset resins such as

7

epoxies or vinyl esters (25% less than vinyl esters and up to 50% less than epoxies) (Strong,

2008).

2.1.1.1 Unsaturated Polyester Resins

Unsaturated Polyester (UP) resins are created by polymerization through the combination of

two monomers: 1) a glycol with an alcohol group (OH) and 2) diacids with a COOH group,

as shown in Figure 2.1:

Figure 2.1 UP polymerization reaction (Strong, 2008)

When glycols react with diacids, the reactive groups of both monomers join to form a water

molecule. During this reaction, the remaining oxygen in the glycol molecule bonds with

Carbon of the acid, and creates an ester link. The active ends of the polyester molecule

continue reacting with new glycol and diacid monomers, thus elongating the new molecule

until the concentration of monomers is low enough to enable further reaction of the polyester

8

(Strong 2008). The term “unsaturated” refers to organic molecules, which contain carbon-

carbon double bonds in the polyester from the diacid monomer.

The curing reaction of the composite is achieved via a cross-linking mechanism.

Crosslinking starts with the organic peroxide initiator generating free radicals which reacts

with the double bonds of the UP to create a new free radical in one of the carbon bonds. This

bond subsequently reacts and creates further bonds with other polyester molecules. A

traditional element often used to facilitate the reaction is styrene, an aromatic ring attached to

a carbon-carbon double bond able that work as a reactive diluent on the resin.

2.1.1.1.1 Effects of Processing Parameters on the Curing of UP Resins

There are several factors which influence the reaction of UP resins. These factors include:

curing temperature, amount of initiator and the chemical composition of the resin itself. From

the practical consideration, two main factors that manufacturers readily control during the

composites molding process are the curing temperature and the amount of the initiator. With

the increase of the temperature in a UP curing reaction, the movement of molecules is

increased resulting in a higher level of crosslinking. Several studies were carried out on the

effect of temperature on the curing time of UP resins and the level of conversion of the

double bonds (Huang and Leu 1992), (Delahaye et al., 1998) (Vilas et al., 2000).

The evaluation of the degree of conversion of carbon-carbon double bonds for UP resins with

1% of the initiator Methyl Ethyl Ketone Peroxide (MEKP) was developed by Vilas et al.

(2000). The results from their differential scanning calorimeter tests indicated the different

degrees of conversion under different ambient temperatures for UP resins, as shown in Figure

2.2.

9

Figure 2.2 Conversion (cure) profile as a function of time under different temperatures.

UP resin with 1% MEKP (Vilas et al., 2000)

In Figure 2.2, the maximum degree of conversion was obtained at 80 °C. For average

temperature conditions (typically 30 °C), the conversion rate reached a maximum of only

50%. Also, the higher curing temperature provided shorter curing times. Thus, the results

suggest that the curing conversion rates and the time were sensitive to temperature

conditions. For low temperature curing conditions, a post curing process was necessary to

increase the degree of conversion in UP resins (Delahaye et al., 1998).

The variation of the gel time is also affected by the amount of initiator used on the reaction of

UP resin. This is illustrated in Figure 2.3 for different amounts of initiator (Vilas et al.,

2000).

10

Figure 2.3 Gel time as a function of temperature for a UP resin under three different initiator

concentrations. (Vilas et al., 2000)

Figure 2.3 shows the influence of the amount of initiator on the decrease of the gel time on

the UP resin system. The more MEKP was added, the shorter the gel time was. Also, the

addition of a higher percentage of initiator contributed significantly to the degree of

conversion of the resin.

The degree of cure of UP resins has an influence on its mechanical properties. The work by

Shah Mohammadi et al. (2013) confirmed the effect of the curing temperature on the elastic

modulus of an UP resin. These results are illustrated in Figure 2.4 for parts cured at 20, 30

and 40 ⁰C.

11

Figure 2.4 Schematic of the change on the storage modulus based on the degree of cure of an UP resin.

(Shah Mohammadi et al., 2013)

Figure 2.4 schematically illustrates a difference in the modulus of elasticity of the resin under

different degrees of cure. Thus, the change in the degree of cure of the resin will modify the

properties of the composite material, especially those properties that are strongly influenced

by the matrix conditions (e.g., transverse modulus).

2.1.2 Manufacturing Methods for Composites

The selection of an appropriate manufacturing process for composite materials is a

challenging task. The engineering and business aspects of the material, and part process must

be considered. The most important parameters include:

Production rate: Depending on a given application and customer requirement for

product delivery, the selection of the manufacturing process with respect to the

production rate considers the type of resin, type of molding operation and the part

size.

12

Performance target of the composite material: The general mechanical properties

targeted for composite materials are governed by different principles depending on

whether the parts are used in advanced or general engineering applications.

Parameters such as fiber architecture, length, orientation and content directly

influence the mechanical properties of the composites. These parameters can also

restrict the selection of the optimum manufacturing process.

Size: For small sized products, the use of closed moulds and injection processes is

preferred. For large parts, the use of open moulds offers optimal balance between the

manufacturing costs and the achievable production rates.

Shape: Depending on the geometry of the part, proper manufacturing method must be

selected. For example, for complex geometries hand lay-up is preferred, while for

simple cylindrical parts filament winding is used.

Cost: Depending on the market and the product application, cost may preclude the

use of complex technologies. For example, the use of autoclaves to fabricate high

quality components can be justified only in situations where economic profitability

can be achieved.

Once these parameters are decided upon, the manufacturer needs to select the type of resin

for the composite material. Thermoset resins have advantages such as the low viscosity of the

resin, which helps the fibers to get properly soaked in resin and create a better bonding

between layers. Also, a process where solidification of the resin is associated with a chemical

reaction may reduce the energy costs associated with melting and cooling processes. On the

other hand, the main disadvantage of thermoset resins is their long curing reaction time,

13

which eliminates the possibility of using this kind of materials in applications with high

production rates (e.g., in the automotive industry).

2.1.3 Open Moulding Techniques

Traditional open moulding techniques are performed with a single mould and without the

application of matching tools. Open moulds are commonly used for manufacturing of parts of

diverse sizes and geometries. The deposition of fibers and resin into the mold is a manual

process. Therefore, variations in the fiber orientation of pre-impregnated parts (prepregs),

spray lay-up or wet lay-up are often considered. The experimental part of this thesis focused

on the use of the wet lay-up to create angled composite parts. As a result, the following

section reviews the wet lay-up open moulding process.

2.1.3.1 Wet Lay-up

One of the basic methods used in composite manufacture is the wet lay-up process. This

process consists of a manual placement of the thermoset liquid resin in combination with the

desired reinforcement material. The fibers must be fully wetted by the resin, and subsequent

layers are placed on top of the reinforcement material until the desired thickness is obtained.

Also, pressure is applied to the composite with a roller for better compaction of the fabric

layers, as illustrated in Figure 2.5. The resin is typically left for extensive periods of time at

room temperature to achieve a total consolidation of the material (Mazumdar, 2002).

14

Figure 2.5 Schematic of hand lay-up process (Mazumdar, 2002)

2.1.3.1.1 Advantages of Wet Lay-up

In spite of being one of the earliest composite manufacturing methods, wet lay-up is still

widely used in the engineering composite industries mainly due to the following advantages

(Mazumdar, 2002):

It requires a low capital investment in equipment.

Various geometries, sizes and fiber orientation configurations can be quickly

prepared.

The use of fibers and thermoset liquid resins is less expensive than the use of

advanced materials (e.g., prepregs).

2.1.3.1.2 Disadvantages of Wet lay-up

The use of manual processes provides a limited control of the manufacturing conditions and

thus the main disadvantages of wet lay-up process are:

15

It is a labor intensive process and provides limited control over manufacturing

conditions.

It is economically viable only for large structures with a low requirement on

mechanical properties.

It has a poor consistency in sample quality.

The absence of pressure systems reduces the possibility to obtain ideal fiber/resin

ratios on the parts (between 60 to 70%) (Mazumdar, 2002).

2.1.4 Mechanical Properties of Angled Composites

It is widely known that composite materials have deficiencies in their transverse direction

(Figure 2.6), and frequently fail in this direction. The transversal, or “through the thickness”

properties of composites are mainly governed by the matrix properties, which has just a

fraction of the material properties in coordinates coincident with the orientation of the

reinforcement (Kedward et al. 1989), (Cui et al. 1995).

Figure 2.6 Composite diagram indicating transverse direction in flat and curved parts

Transverse direction.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Curved region

Transverse direction.

16

Equation 2.1

Depending on the part geometry, composite parts can be exposed to transverse loads in real

world applications. In particular, angled composite beams under pure bending experience

such loads. When pure bending is applied on angled composites, radial stresses develop in

the curvature region, leading to a failure due to delamination or matrix cracking.

The theoretical solution for the calculation of the radial stress on a curved beam with

cylindrical anisotropy under flexural loads was developed by Lekhnitskii (1968). The

following expression (Equation 2.1) was obtained for cylindrically anisotropic homogeneous

curved beams under pure bending through classical elasticity theory:

𝝈𝒓 =𝑴

𝑹𝒐∗𝒃∗𝒈[𝟏 −

𝟏−𝒄𝒌+𝟏

𝟏−𝒄𝟐𝒌 (𝒓

𝑹𝒐)

𝒌−𝟏

− 𝟏−𝒄𝒌−𝟏

𝟏−𝒄𝟐𝒌 𝒄𝒌+𝟏 (𝑹𝒐

𝒓)

𝒌+𝟏

]

Where, 𝑀 corresponds to the applied moment, 𝑏 is the width of the specimen and 𝑅𝑖

represents the inner curve radius (Figure 2.7)

Figure 2.7 Schematic of geometrical parameters used for the radial stress calculation in a curved

composite beam (Kedward, 1989)

The radial location 𝑟 corresponding to the maximum stress is given by Equation 2.2:

17

Equation 2.2

𝑟 = [(𝑘+1)(1−𝑐𝑘−1)𝑐(𝑅𝑖𝑅𝑜)𝑘

(𝑘−1)(1−𝑐𝑘+1)]

1

2𝑘

Where,

𝒈 =𝟏−𝒄𝟐

𝟐−

𝒌

𝒌+𝟏

(𝟏−𝒄𝒌+𝟏)𝟐

𝟏−𝒄𝟐𝒌 +𝒌𝒄𝟐

𝒌−𝟏

(𝟏−𝒄𝒌−𝟏)𝟐

𝟏−𝒄𝟐𝒌

The dimensionless parameters k and c can be calculated from Equations 2.4 and 2.5,

respectively:

𝑘 = (𝐸𝜃

𝐸𝑟)

1/2

𝑐 =𝑅𝑖

𝑅𝑜

Where, 𝑅𝑜 and 𝑅𝑖 represent the corresponding outer and inner curvature radii, and 𝐸𝜃 and 𝐸𝑟

are the effective elastic modulus on the tangential and radial directions, respectively.

Other approximate expressions for maximum radial stresses have been reported in the

literature. Kuhn (1956) used Equation 2.6 to calculate radial stresses in curved composite

parts:

𝜎𝑟 =3𝑀

2∗𝑏∗𝑡∗𝑅𝑚

Where Rm is the mean radius, and t is the thickness of the part. This expression was

developed assuming that the location of the maximum load was coincident with the mean

Equation 2.5

Equation 2.6

Equation 2.3

Equation 2.4

18

radius Rm. An approximation for determining the location of the maximum radial stress was

developed by Mabson and Neil (1988):

𝜎𝑟,𝑚𝑎𝑥 =12𝑀

𝑏∗𝑡3 ∗ [𝑅𝑚 − (𝑅𝑖 ∗ 𝑅𝑜)1/2]

Kedward (1989) combined equations 2.6 and 2.7 into Equation 2.8.

𝜎𝑟,𝑚𝑎𝑥 =3𝑀

2∗𝑏∗𝑡∗(𝑅𝑖∗𝑅𝑜)1/2

The error generated when using equations 2.6, 2.7 and 2.8 versus the classical elasticity

method, was minimal for Equation 2.8 (Kedward, 1989) when 𝑅𝑖 and 𝑅𝑜 had similar values.

The current ASTM standard D6415 for the evaluation of stresses in curved parts, suggests the

use of Eq. 2.2 and Eq.2.8 for the calculation of radial stress; however, the use of the

simplified solution (Eq.2.8) provides a more accurate approximation when the ratio 𝐸𝜃/𝐸𝑟

decreases and the ratio 𝑅𝑖/𝑅𝑜 increases.

The above expressions show a dependency of radial stress on the curvature of the part. By

evaluating the stress response using Equation 2.2 for a constant moment and thickness (but

variable curvature radius), Figure 2.8 shows that the radial stress is expected to decrease as

the design radius increases. The observed increase in stress is higher for curvatures with a

radius ≤ 5/16”.

Equation 2.7

Equation 2.8

19

Figure 2.8 Theoretical radial stress versus different curvature radii (the vertical dashed lines show the

region tested experimentally in this research; Chapter 3)

Avalon et al. (2010) evaluated the effect of part radius, part thickness and the use of resins

enhanced with vapor-grown carbon nano-fibers on the failure mode of curved composite

specimens under bending loads. The experimental results from four-point bending tests on

curved beam samples indicated that there was no effect of the number of plies, radius or type

of additives used on the radial stress response. A similar experiment was carried out by Hao

et al. (2012), where carbon/epoxy unidirectional specimens were evaluated and the influence

of the part thickness and radius on parameters such as curved beam strength and radial stress

via Eq. (2.2) was calculated. The results are presented in Figure 2.9.

0

5

10

15

20

25

30

35

40

45

0 1/8 1/4 3/8 1/2 5/8 3/4 7/8 1 1 1/8

Rad

ial S

tres

s (N

/mm

^2)

Design Radius (in)

20

Figure 2.9 CBS versus: a) Thickness (mm), b) R/t and maximum radial stress versus: c) Thickness, d) R/t

of the composite laminated beams (Hao et al., 2012)

The results in Figure 2.9 reveal the influence of the radius and the part thickness on the

curved beam strength (CBS) and stress response of the tested composite. From Figures 2.8a

and 2.8b, it can be observed that the composite CBS increased with every increase in the

radius and part thickness, with the most significant increase resulting from the variation of

the part thickness. On the other hand, Figures 2.9c and 2.8d show the effect of part thickness

and radius on the maximum radial stress. The results indicate that the maximum radial stress

decreased with an increase in the part thickness and radius. This effect was attributed to the

high susceptibility of the material to flaws and process induced defects on specimens with

bigger sizes. Such phenomena are described in the composite manufacturing industry as “size

effects”.

The presence of size effects influencing the quality of composite materials has been explored

by Zweben, (1994), Wisnom and Jones (1996) and Hitchon (1978). All these studies have

21

reported a trend indicating the decrease of the mechanical properties such as tension,

bending, short beam shear and in-plane transverse tension with an increase in the size of the

composite parts. In 1996, an experimental study developed by Wisnom and Jones explored

size effects on curved laminates by developing samples with different numbers of plies. A

drop on the interlaminar tensile stress from 109MPa (in specimens with 16 plies) to 61MPa

(in specimens with 64 plies) was observed. This reduction was associated with the presence

of voids in the specimens with higher number of plies.

2.1.5 Defects Affecting Quality of Composites

Potter (2009) has comprehensively discussed the origin of defects in the composite materials.

His study classified possible sources of variability in the final quality of composite parts.

Defects in composite materials have multiple origins. For example, the mechanical properties

of composite part can be affected by fiber alignment. The tensile properties of the

reinforcement dominate the tensile properties of the composite. Hence, inappropriate

alignment could reduce the tensile strength of the material in a specific direction.

Nevertheless, next to fiber placement/geometrical defects, void content was described as the

most significant quality parameter affecting the mechanical performance of composite parts.

2.1.5.1 Void Content

The presence of voids is often observed in composite parts independently of the

manufacturing process (Guo et al. 2006). Formation of voids in composites is attributed to

several reasons, including entrapped air during the manufacturing process, moisture absorbed

by the reinforcement material and volatiles that are not released from the resin during the

22

cure reaction. If hydrostatic pressure of the resin system is not sufficient to expel the

entrapped air, voids will form (Campbell et al., 1994). The presence of packed fibers

impregnated with high-viscosity resins is also known to limit the resin flow, which enables

further growth of the voids (Guo et al., 2006; Liu et al. 2005; Hagstrand et al., 2003).

The presence of voids critically affects various mechanical properties. Depending on the

specific composite applications, the maximum admissible levels of voids vary from 1% to

5% of the total volume of the part. Most of the characterization works previously developed

have reported reduced flexural, tensile and interlaminar shear strength (ILSS) with an

increase of void content (Olivier et al., 1994; Guo et al., 2006; Liu et al., 2005; Hagstrand et

al., 2003). Since the void content is dependent of the hydrostatic pressure of the resin, the

application of external compacting pressure during the resin consolidation of the part has

demonstrated to effectively reduce the void content in the composite. The relation between

void content, mechanical properties and compaction pressure can be observed in Figure 2.10

from the results reported by Liu et al. (2005).

Figure 2.10 Void content vs. shear, flexural, and tensile strengths (Liu et al., 2005)

23

Figure 2.10, shows a reduction of about 20% in the flexural, shear and tensile strength of the

composite with a variation of voids between 0.5 and 3.3%. At the same time, it is evident that

the applied pressure significantly reduced the porosity levels in the part.

Typically, void content is evaluated by standard methods that measure the void fraction

based the total volume through resin matrix burn-off or chemical digestion. However, the use

of microscopy imaging in the void content analysis provides additional information related to

the size and location of the voids. For instance, Purslow (1984) made the following key

observations:

- Volatiles present in the resin can contribute to ~0.5% of void content. The

resulting voids are circular with a diameter of ~10μm.

- Air pockets may develop between plies. These may contribute to ~1%. These

pockets usually are form near misaligned fibers. The dimension of the void is

equivalent to the fiber diameter and the length is ~100μm.

Purslow (1984) also provided a void content diagram (Figure 2.10) as a qualitative visual

reference for his results.

Figure 2.11 Visual reference for void content in unidirectional samples (Purslow, 1984)

24

2.1.5.2 Defects on Angled Laminates

An experimental research carried out by Hubert and Poursartip (2001) on angled composite

parts identified defects that are likely to occur in hand lay-up products. Thickness variation in

corner regions of concave molds was observed and related to resin flow towards the lower

regions of the mold. Also, difficulties in proper compaction of fabric in the corners, which

created a higher void content in corner regions was reported. Their study also described the

effect of fiber orientation on the final draping capacity of the material. The reinforcement

fiber orientation was difficult to control in regions with sharp curvatures. Similar results were

reported for out of autoclave materials prepared by Cauberghs and Hubert (2011). Most of

the experimental works previously carried out evaluated qualitatively the manufacturing

defects in high value advanced composite materials. However, there is only limited literature

on the defect formation in general ‘engineering composites’.

2.1.6 Flexural Rigidity of Fibers

Pierce (1930) proposed an experimental method to measure the stiffness of textile materials

in order to establish a parameter that could define the capacity of the fibers to drape over a

desired shape. The proposed method consisted of the combined measurements of the fabric

weight and its bending length. The measurement of flexural rigidity was used as a reference

to evaluate the draping capacity of textiles, as well as reinforcement materials used in

composites (Behre, 1961), Dahlberg (1961), (Grosberg, 1966).

Recent experiments have evaluated the relation between the fabric properties and the flexural

rigidity. Parameters such as fabric density, fibers dimensions and modulus of were seen to

25

influence the flexural stiffness of the composite (Yuksekkaya et al. 2008). For angled

composite parts, the flexural rigidity of the fibers could potentially represent a key parameter

to help manufacturers obtain premium quality parts.

MCDM Methods 2.2

The design stage of composite parts often deals with the consideration of multiple conflicting

criteria. This means that the ideal design solution for one evaluation parameter could be in

conflict with the ideal solution of other parameter. For this reason, the decision of the

optimum design solution is not a simple selection process and requires the use of Multiple

Criteria Decision Making (MCDM) techniques to systematically evaluate multiple possible

solutions.

MCDM techniques can be classified into two principal groups: 1) compensatory and 2) non-

compensatory methods. In the case of non-compensatory techniques, each attribute is

considered equally important and there is no trade-off between criteria, meaning that the

higher evaluation of one alternative on a specific criterion is not affected by the evaluation of

different parameters. Some examples of this approach include techniques such as Maximin,

Maximax, Conjunctive, Disjunctive, Lexicographical (Hwang and Yoon, 1995) and

Elimination by aspects (Tversky, 1972). The second group of the MCDM techniques

corresponds to the compensatory techniques, in this case an alternative that is slightly less

favourable under one evaluation criteria might end up being and optimum solution, if it

represents a superior alternative for one or more other attributes. Some of the methods in this

category include the Simple Additive Weighting (Fishburn, 1967), Weighted Product

Method, ELECTRE, PROMETHEE, Analytic Hierarchy Process (AHP) and Technique for

26

Order Preference by Similarity to Ideal Solution (TOPSIS) (Hwang and Yoon, 1981). The

application of non-compensatory techniques generally is more specific and requires proactive

‘attitude-oriented’ decisions by the decision maker, while compensatory techniques have

demonstrated to be fairly simple and effective in achieving valid results in a wide range of

applications (Hwang and Yoon, 1995). In this thesis, the TOPSIS compensatory method was

used for data analysis.

2.2.1 TOPSIS

Proposed by Hwang and Yoon (1981), the application of TOPSIS has been proven to be an

effective tool for the design selection and decision making in diverse engineering fields

(Davoodi et al. 2011; Jee and Kang, 2000). This MCDM technique is based on the principle

that the optimum solution corresponds to an alternative that is the most similar with respect

to an ideally positive solution (an imaginary alternative with the best possible score on each

and every single attribute) and additionally, is more dissimilar to the ideally negative solution

(an imaginary alternative with the worst possible score on each and every single attribute). In

other words, by considering a number of n attributes to evaluate and compare a series of m

alternatives in an n-dimensional space, the optimum solution will correspond to the attribute

that offers the shortest Euclidean distance to the ideal positive scenario and the longest

distance to the worst case scenario (Hwang and Yoon, 1981). This concept is graphically

described in Figure 2.12.

27

Figure 2.12 Euclidean distances from an ideal positive and negative solutions (Yoon and Hwang, 1995)

In Figure 2.12, as an example, the alternatives A1, A2 and A3 are evaluated with respect to

two attributes. Alternative 2 (A2) is the optimum solution based on the TOPSIS principle,

since this alternative has the shortest distance from the ideal positive solution and the longest

distance from the ideally negative solution. An additional detail to observe from this example

is that A2 is the optimum solution even though it is outranked by A1 on attribute 2. This

shows the nature of a compensatory MCDM method such as TOPSIS, where the low

performance of an alternative under one attribute is allowed to be compensated with the

good scores under the rest of attributes, providing an “overall” best solution.

28

2.2.1.1 Weighting Method

The correct application of TOPSIS and many other MCDM techniques depends on the

weighting methodology. The assignment of weights defines the level of importance of each

of the evaluation attributes in the given application. Weighting techniques are divided in

three different groups: subjective, objective and combinative methods. Subjective weighting

methods correspond to the group in which the preference between attributes for a specific

application merely relies on the decision maker (DM). This preference can be based on the

design requirements or previous experience (Jahan et al. 2011). Methods such as weights

from ranks, ratio weighting and Digital Logic are examples of the subjective weighting

techniques (Stillwell et al., 1981; Saaty, 1980; Farag, 1997).

The Digital Logic (DL) approach is a useful method to establish weights based on

comparisons between multiple evaluation criteria. According to the opinion of the expert, the

attributes are compared by pairs assigning a score of 1 to the more favorable attribute and 0

to the less favorable. After all the attributes have been compared, the weights are given by a

number of positive decisions (1) obtained per attribute. A Modified Digital Logic (MDL)

weighting technique was proposed by Dehghan-Manshadi et al. (2005), based on the same

principle of the original DL method, but this time three different scores (1, 2, or 3) on every

pair-wise comparison between attributes were allowed. Namely, the least convenient attribute

receives a value of 1 instead of 0. In this way, no attribute is totally removed from the

weighting considerations. The method also creates the possibility to establish comparisons

with ‘equal’ importance sate (in which case both attributes receive a score of 2), and finally

the preferred attribute gains a score of 3.

29

The subjective methods have a possible degree of uncertainty that arises from the capacity of

judgement of the DM. On the other hand, objective methods evaluate the importance of the

attributes solely based on the nature of the measured data. These methods are important when

there is no decision maker or when it is difficult to obtain reliable subjective weights. Some

examples of such methods include the Mean Weight method, Entropy, and Criteria

Importance Through Inter-criteria Correlation (CRITIC) (Diakoulaki et al., 1995). The

general principle of the CRITIC method is to provide a higher level of importance to the

criteria that have less correlation with the rest of attributes. In 1995, Djakoulaki et al. noticed

that one of the principal sources of errors in data comes from the level of inter-dependency

between parameters. For this reason the use of Pearson’s correlations between parameters

was suggested to determine the weighting value of attributes.

The use of objective methods sometimes presents significantly different results with respect

to the DM’s opinion (Jahan et al. 2011). For that reason, a method that could combine both

objective and subjective approaches is often deemed more effective in order to obtain an

ideal solution. An example of combinative methods was proposed by Jahan et al. (2011), by

combining the use of the DL as a subjective method and the Entropy and CRITIC as

objective methods. This approach enabled more balanced importance for all the previously

obtained weights and clearly overcame the limitations of using just one weighting method.

2.2.2 The Use of Signal to Noise Ratio (S/N) in Optimization

The use of Signal to noise (S/N) in experimental optimization techniques was introduced by

Taguchi (1990). The S/N metric results in a ratio where the signal represents the mean or the

desired value, and the noise corresponds to the standard deviation obtained from repeated

30

measurements. Taguchi recommended using the S/N since it measures the quality

characteristics of the data with respect to a desired target. The calculation of the S/N ratio is

given by Equation 2.9:

𝑆/𝑁 = −10 ∗ 𝐿𝑜𝑔(𝑀𝑆𝐷)

Where MSD is the mean squared deviation, calculated according to the quality nature of the

corresponding attribute; that is, depending of the evaluation parameter there is a specific

expression for criteria with different characteristics: the “higher the better” (benefit

attributes), “the lower the better” (cost attributes) or “the target is best” (for calibration

problems). The use of this concept for data treatment could represent an advantage for

experiments with limited control and high noise in their outcomes. By replacing the average

value by the S/N through test repeats, an outcome with a higher repeatability (robustness)

would receive priority in ranking analyses.

Equation 2.9

31

Chapter 3: Experimental Methods and MCDM Procedure

This chapter provides an overview of the procedures that have been employed during the

manufacture of curved test specimens and their quality evaluations, as well as the

implementation of a new S/N Multiple Criteria Decision Making method. Quality evaluations

for open moulded samples mainly included the use of optical imaging techniques for the

measurement of fiber misalignment at sharp corners, fabric formability, and surface defects.

In addition, the mechanical performance of test specimens was evaluated using the Digital

Image Correlation (CIC) and Curved Beam Strength (CBS) tests.

Manufacturing of Test Coupons 3.1

V-shape composite samples were prepared using unsaturated polyester resin (Envirez™)

with 1% initiator (methyl ethyl ketone peroxide) and E-glass fibers (142oz 3 WEAVE®)

heavy tri-axial fabric; the fibers were laid on the mold in warp direction along part length.

All samples were fabricated using the wet lay-up process using horizontal female molds, as

shown in Figure 3.1. After demolding, the obtained curved beams were trimmed at the edges

to eliminate undesired irregularities, and then sectioned in 2.5cm wide sub-samples using a

conventional band saw (Figure 3.2). The sub samples were used for the destructive and non-

destructive evaluation of the curved beam’s properties.

Figure 3.1 Schematic of the master mould

32

Using the same master mould, the analyses of geometry, lay-up orientation, and process

parameters were classified into three different experimental groups. The procedures for each

experimental group are presented in the following sections.

Experiment #1: Evaluation of Geometrical Parameters 3.2

The first set of experiments was performed with the objective of exploring the influence of

the part geometry on the final quality of the composite part. Thus, samples were fabricated in

four master moulds (one master mould per radius level) using a fiber orientation of 0/90° at

room temperature (25°C) with the following geometrical features.

Corner Radius: 1/8”, 3/16”, 1/4” and 5/16”.

Part angle: 40⁰, 50⁰, 60⁰ and 70⁰.

Number of layers: 3 and 5.

Figure 3.2 Sample geometry and input parameters used

These parameters were chosen based on a literature review of historical design ranges for

open moulded parts. Typically, the mould design recommendations avoid sharp corners with

33

the radii of curvature lower than 0.08” (Mazumdar, 2002). Using the open moulding hand

lay-up technique, 64 sample configurations were manufactured with four corner radii, four

part angles, and two different numbers of layers, and two repeats of each configuration.

3.2.1 Quality Evaluation

The quality of open moulded parts was evaluated through quantitative measurements of: void

content, curved beam strength, fiber misalignment, thickness uniformity, external surface

defects and reinforcement formability. In these evaluations, statistical methods such as

Analysis of Variance (ANOVA) and Analysis of Covariance (ANCOVA) were implemented

as outlined below.

3.2.1.1 Void Content Test

The method for quantifying the void content in the fabricated samples was based on the

ASTM D2734 standard. This standard relates the density of the cured sample to a calculated

theoretical value based on fiber and matrix densities. With the use of a MDS-300 specific

gravity tester, the value of the density of each trimmed specimen and its mass were

measured. Subsequently, in order to determine the corresponding mass of the resin and the

fibers, each sample was placed in a furnace following the ASTM 3171 test for matrix

decomposition at 565 ⁰C. Once the resin was burned off, the mass of the fibers was

determined and the theoretical density was obtained using Equation 3.1:

34

𝑻𝒅 = 𝟏𝟎𝟎 (𝑹

𝑫+

𝒓

𝒅)

Where, 𝑇𝑑 was the theoretical density value, R and r were the weight fractions of the resin

and reinforcement, respectively; the densities of the resin and reinforcement were represented

by D and d, respectively. Finally, the theoretical density of the specimen was compared with

the measured value (𝑀𝑑) to obtain the final void content as expressed in Equation 3.2:

Void content = 100(𝑇𝑑−𝑀𝑑)

𝑇𝑑

3.2.1.2 Curved Beam Strength (CBS)

The bending strength of the samples was evaluated using a modified version of the ASTM

D6415 standard for flexural testing of curved beams. Specifically, the fixture specified in the

original standard was customized (Figure 3.3) to accommodate different dimensions and

geometries of sample configurations based on the previously defined geometrical inputs.

Equation 3.1

Equation 3.2

35

Figure 3.3 The CBS test fixture used

According to ASTM D6415, the distance between upper supports should be 75 mm.

However, the modified fixture had a separation of 22mm. This modification was made to use

the same bar separation for all the geometries examined in this research. Additionally, the

roller bearing system was replaced with two rigid polished bars lubricated with mineral oil

(to reduce error induced by friction).

By definition, the CBS value corresponds to the moment per unit of width of the composite

specimen at the first delamination point. Since one of the parameters to evaluate in the

present work was the number of layers (i.e., variation of thickness), the part resistance to the

moment applied was expected to be highly sensitive to this variable. The CBS value from

each test configuration was calculated using (ASTM D6415, 2007):

𝐂𝐁𝐒 = (𝐏

𝟐𝐰∗𝐜𝐨𝐬 (∅)) ((

𝐝𝐱

𝐜𝐨𝐬(∅)) + (𝐃 + 𝐭)𝐭𝐚𝐧 (∅) )

Where P corresponded to the applied force at the point where the first failure was detected; in

this work, it was identified from the first kink appearing in the force-displacement curve

obtained by an Instron 5969 load frame; t was the part thickness, w was the width, ∅ was the

Equation 3.3

36

specimen’s flat surface angle relative to the horizontal line (Figure 3.4), 𝑑𝑥 was the

horizontal distance between centers of the fixture bars of diameter D.

Figure 3.4 CBS test geometrical considerations (ASTM D6415, 2007).

The expected typical response from the standard test for curved beam samples is presented in

Figure 3.5. The presence of different kinks in such progressive sequence of delamination

events can help to clearly identify the location of the maximum load needed for Equation 3.3

(i.e., at the onset of first delamination).

Figure 3.5 Typical response for multidirectional composite specimens (ASTM D6415, 2007)

37

In the experiments performed in this research, two factors were expected to introduce

inaccuracy during the CBS tests. First, the presence of high void levels in the samples due to

the nature of the wet lay-up manufacturing process. Second, the non-uniform geometry of the

test samples which can randomly vary across different sample surfaces (e.g., random surface

roughness at different locations of the part). Recognizing these limitations, and to gain a

deeper understanding of the underlying composite behavior, a complementary imaging

technology known as Digital Image Correlation (DIC) was employed to relate the macro-

level CBS measurements to the local failure mode of each part with a particular geometry. In

addition, an auxiliary finite element model (FEM) of the test was established to understand

some non-linear behavior (as opposed to Figure 2.5) that was seen for a few geometrical

configurations. The employed DIC and FE modeling methods are described in detail in the

following sub-sections.

3.2.1.2.1 Digital Image Correlation for the CBS Test

DIC has demonstrated to be a useful tool in the characterization of complex deformations of

composites (Dridi et al., 2012; Lomov, et al., 2008; Komeili, 2014), and to arrive at new

levels of understanding of composites behaviour. For instance, a recent application of DIC to

analyze 2D strain fields in composite brackets subjected to four-point bending revealed that

the initial cracks develop in regions where “interlaminar” strain evolves (Hao et al., 2012).

The 3D digital image correlation in the present research was carried out using a Q-400

System®. The principle acting in the DIC is the use of stereoscopic vision camera system

with two or more different perspectives of a single object. Then, a reconstruction of 2D or 3D

38

images was performed (Bhatti, 2008; Pan et al., 2009;”Q-400 DIC and ISTRA4D training,”

2011).

In order to determine the location of the cameras with respect to the specimen, a calibration

process was performed. Calibration plates with pre-established dimensional references

(Figure 3.6) were placed in front of the cameras. Once the calibration plate was focused in

both cameras, the software automatically determined their relative position.

Figure 3.6 Fixture and calibration plate for DIC imaging

Next, a speckle pattern was sprayed on the surface of the test sample to be analyzed, as seen

in Figure 3.7. This pattern provided a unique visual reference on the specimen, and allowed

the software to track the location of specific points on the sample surface.

Calibration Plate

Camera 2

Camera 1

39

Figure 3.7 Speckle pattern used for DIC measurements on CBS test

The DIC strain measurement process started with the collection of images during the CBS

test. For this phase, a PIP counter attached to the Instron® machine was used. The PIP

counter was used during live CBS tests as a reference system for the experimenter to

externally trigger a specific point/event (e.g., matrix cracking) via the observations in camera

images and register it in the load vs displacement curve for further data analysis.

Subsequently, the group of images was post-processed and the area of interest (corner region)

was divided into facets and space regions. The location of these facets was tracked on every

image, and the local positions were captured by the DIC software. Subsequently, mapping

the strain field on the specimens was achieved via the software calculations.

3.2.1.2.2 Finite Element Model (FEM) for the CBS Test

Throughout the CBS experiments, it was observed that specimens with an angle of 40° and

three layers, had a non-linear elastic region on the CBS curves. Therefore, a finite element

model of the four point bending test was created in ABAQUS® for a specimen with 40°

(angle), 5/16” (radius) and 3 layers. The analysis was performed in order to study the origin

of the non-linear behavior. A schematic of the model is shown in Figure 3.8.

40

Figure 3.8 Schematic of FEM model of CBS 4-point bending test for 40° sample

The model was created with the use of a deformable composite solid with three different

layers of 1.67mm thickness. The main assumption considered in this model was a hard

contact on the ‘normal’ direction between master and slave elements. Also, frictionless

‘tangential’ contact between the supports and the part were assumed.

The properties of the material were obtained from the literature (Kachlakev and McCurry,

2000) for similar experiments with fiberglass woven fabrics and UP resin (Table 3.1). In

addition, the internal surface of the part in contact with the fixture bars was modeled to have

a ribbed surface, in order to mimic the internal surface finish of the open moulded composite

samples with rough surface (Figure 3.9).

Table 3.1 Mechanical properties used for the reference FEM model; properties extracted from

(Kachlakev and McCurry, 2000)

Tensile

modulus

(E11,E22)

Tensile

modulus

(E33)

Poisson's

ratio(13,23)

Poisson's

ratio (12)

Shear

Modulus

(13,23)

Shear

Modulus

(12)

Tensile

strength

20.7 GPa 6.89 GPa 0.26 0.3 2.65 GPa 1.52 GPa 600 MPa

41

Figure 3.9 Curved part with non-uniform surface geometry, as modified in the model

3.2.1.3 Fiber Misalignment

With the help of optical imaging and the Omnimet® BUEHLER software, the average

deviation of fibers from the vertical direction was measured for each sample. The

misalignment was defined as the average of inclination angle of the external-layer fibers with

respect to the vertical plane, as shown in Figure 3.8.

Figure 3.10 Misalignment angle measurement on the curved specimens

3.2.1.4 Thickness Uniformity

Due to the shape and orientation of the female molds (Figure 3.2), the resin was expected to

flow down towards the corner features of the samples during manufacturing, therefore

42

generating resin-rich zones (Mazumdar, 2002). This may lead to significant differences

between the thickness of the composite sample in flat sections and those adjacent to the

corners. An optical microscope was used to measure the cross-sectional thickness at the flat

section of each sample, as well as at the corner section. The ratio between these two values

was defined as “thickness ratio”. Similarly, resin rich zones between layers were measured

(Figure 3.11). Bridging was calculated from the average of all the distances between layers in

the corner of each sample.

Figure 3.11 Measurements of the total (white arrows) thickness on: a ) the corner (Tc) and b) the flat

region (Tf). Thickness ratio defined by Tf /Tc; the layer bridging is defined by the distance between layers

in the corner (yellow arrow).

3.2.1.5 External Surface Defects

During the manufacturing process, corner areas were seen to be prone to surface porosity

under certain sample configurations (Figure 3.12). As a result, the surface defects were

quantified using the Omnimet® BUEHLER software. This software was used to determine

the total area of the corner and the size of the area containing surface porosity.

Tc Tf

a) b)

43

Figure 3.12 (a) Top and (b) lateral views of a typical corner surface defect

3.2.1.6 External Formability of Reinforcement

Due to the high flexural stiffness of the fabric reinforcement, the capacity of the fibers to

drape into the desired curvatures was affected by the sample geometry. Thus, a formability

parameter was developed by calculating the ratio between the target radius (defined by the

mold shape) and the actual radius of the outer reinforcement layer (measured with the use of

optical imaging (Figure 3.13).

Figure 3.13 (a) Design curvature, and (b) the actual reinforcement curvature at the outer surface (notice

the resin rich region in the corner area)

44

3.2.2 Multiple Criteria Decision Making (MCDM) Procedure

The measurements and statistical analysis of the above discussed quality parameters (also

listed in section 3.2.1) can provide useful information for open -moulding design conditions

yielding overall higher quality FRP parts (i.e., with less defects). However, as will be shown

in the results in Chapter 4, there are conflicts among different quality measures (e.g., higher

part angles may cause less surface defects, but increase the fiber bridging defect). For this

reason, a MCDM approach was employed in order to obtain the best overall solutions

considering all the measured quality variables based on two holistic application scenarios: (1)

design for structural purposes, and (2) design for aesthetic purposes. TOPSIS MCDM was

implemented with signal to noise (S/N) ratios and combinative weighting techniques. The

procedure for the proposed MCDM method is as follows:

Step 1: Linear Normalization of the Raw Data

The response values for each specific quality criterion (listed in section 3.2.1) were divided

by corresponding maximum value according to Equation 3.4:

𝑦𝑖𝑗 =𝑥𝑖𝑗

𝑥𝑗∗⁄

Where, 𝑥𝑖𝑗 corresponded to the measured j-th quality parameter (decision criterion; j=1 to n)

under the i-th (i= 1 to m) design configuration alterative (see Table 3.2) 𝑥𝑗∗ is the

corresponding maximum value among all configurations under the j-th parameter.

Equation 3.4

45

Table 3.2 Schematic of MCDM for the experimental methodology

Quality Criteria

Design Alternatives 1. CBS 2. Void Content

1. 40°, 5/16”, 3 layers x11 x11

x21 x21

x11 x11

2. 50°, 5/16", 3 layers x12 x12

x22 x22

x12 x12

x1j x1j

x2j x2j

x1j x1j

Weights W1 W2 Wi

Step 2: S/N Values

The corresponding Mean Squared Deviation (MSD) for each criterion was calculated

according to the characteristic type of quality parameter being evaluated. For the “higher the

better” attributes the corresponding expression was:

𝑀𝑆𝐷𝑗 = ∑1

𝑦𝑘𝑗2⁄

𝑛′

𝑛′𝑘=1

Where, 𝑦𝑘 corresponded to the normalized values for one specific combination of inputs

(calculated in step 1) under given quality criterion, where n’ was the number of repeats per

test (in this thesis n′=2).

For the “lower the better” characteristic, the corresponding MSD was obtained from:

𝑀𝑆𝐷𝑗 = ∑𝑦𝑘𝑗

2

𝑛′

𝑛′𝑘=1

Also, for parameters where a target value (m) was desired, the MSD was obtained from

Equation 3.7 as follows:

Equation 3.5

Equation 3.6

...𝑖𝑡ℎ

...𝑗𝑡ℎ

46

𝑀𝑆𝐷𝑗 = ∑(𝑦𝑘𝑗−𝑚)

2

𝑛′

𝑛′𝑘=1

Once the MSD values of each of the attributes were calculated, the S/N ratio was obtained by

substituting the corresponding MSD value in Equation 3.8.

𝑺/𝑵𝒋

= −10 ∗ 𝐿𝑜𝑔(𝑀𝑆𝐷𝑗) Equation 3.8

Step 3: Subjective Weights Calculation (Modified Digital Logic)

The outcomes obtained from the Modified Digital Logic (MDL subjective weighting

method) were based on two different application scenarios: (1) design for structural purposes,

and (2) design for aesthetic purposes. Based on each design premise, pair-wise comparisons

were performed between quality metrics. The purpose of the comparisons was to determine

which of the input (design) parameters was more relevant with respect to the target

(structural or aesthetic) performance measure. The parameters that were assumed to be more

important received a score of 3, while the less important parameters received a score of 1.

For situations where both parameters are deemed to be equally important, both received a

score of 2. The schematic of pairwise comparisons for the structural and aesthetic scenarios

are shown in Table 3.3 (note that only the assigned score values by the DM could change

from one scenario to another; as will be shown through results in Chapter 4).

Equation 3.7

47

Preference designation

between attributes

Table 3.3 Relative importance between criteria based on the MDL method

Attributes Number of possible decisions

1 2 …

Misalignment 1 1

CBS 3

Void content

3

…

The total number of pairwise decisions to be made by the DM was:

𝑁 = 2𝑛(𝑛 − 1)

Where, n was the number of attributes.

Once all the comparisons were scored, the total number of positive decisions per attribute,

𝑁𝑝𝑗 , is found and the final subjective weight for each attribute (𝑊𝑠𝑗) is determined by:

𝑊𝑠𝑗 =𝑁𝑝𝑗

𝑁

Step 4: Objective Weights Calculation (CRITIC)

The Pearson correlation coefficient concept was employed to establish the level of

interdependency between attributes. Considering two different attributes, j and k, the

correlation between them was obtained using the Pearson’s product moment correlation as:

𝑅𝑗𝑘 =∑ (𝑥𝑖𝑗−�̅�𝑗)(𝑥𝑖𝑘−�̅�𝑘)𝑚

𝑖=1

√∑ (𝑥𝑖𝑗−�̅�𝑗)2 ∑ (𝑥𝑖𝑘−�̅�𝑘)2𝑚𝑖=1

𝑚𝑖=1

Where, as before m was the number of design alternatives (possible geometry input

combinations), 𝑥𝑖𝑗 corresponded to the response of each design alternative under attribute j.

Equation 3.9

Equation 3.10

Equation 3.11

48

�̅�𝑗 was the average from all the 𝑥𝑖𝑗’s. Similarly, 𝑥𝑖𝑘 corresponds to the response of each

design alternative under the k-th attribute and �̅�𝑘 is the average value from all the 𝑥𝑖𝑘.

Then, total objective weight (𝑊𝑜𝑗) for each attribute was determined using Equation 3.12:

𝑊𝑜𝑗 =∑ (1−|𝑅𝑗𝑘|)𝑚

𝑖=1

∑ (∑ (1−|𝑅𝑗𝑘|)𝑛𝑘=1 )𝑚

𝑖=1

Step 5: Calculation of the Total Combinative Weights

Following the methodology proposed by Jaham et al. (2011), the total combinative weight

for each of the attribute was obtained via:

𝑊𝑗 =(𝑤𝑜𝑗∙𝑤𝑠𝑗)

1/2

∑ (𝑤𝑜𝑗∙𝑤𝑠𝑗)1/2

𝑛𝑗=1

Step 6: Weighted Normalized Ratings and TOPSIS Ideal Solutions

With the use of the combined weights 𝑊𝑗, and the total responses expressed in S/N ratios in

the decision matrix, the weighted normalized rankings, 𝑣𝑗 , were calculated using Equation

3.14:

𝑣𝑗 = 𝑤𝑗 ∙ 𝑟𝑖𝑗

Once the 𝑣j values were found, the ideal positive and the ideal negative solutions were

determined. At this point, the imaginary best and the worst design combinations for each

attribute were identified. Since all types of the signal to noise ratios in quality evaluations

were to be maximized, the positive ideal solution (𝑣𝑗+) corresponded to the highest 𝑣𝑗 score

Equation 3.12

Equation 3.13

Equation 3.14

49

obtained under each attribute, while the negative ideal solution (𝑣𝑗−) corresponded to the

lowest 𝑣𝑗 score.

Step 7: Separation Distances

The corresponding Euclidean distances of each of the design solutions should be calculated

for both the ideal positive and ideal negative solutions. The distance with respect to the

positive ideal solution (𝑆𝑖+) was calculated as:

𝑆𝑖+ = √∑ (𝑣

𝑗− 𝑣𝑗

+)2𝑛

𝑗=1

Similarly, the distance to the negative ideal solution (𝑆𝑖−) was obtained as:

𝑆𝑖− = √∑ (𝑣

𝑗− 𝑣𝑗

−)2𝑛𝑗=1

Finally, the relative degree of similarity with respect to the positive ideal solution was

obtained using:

𝐶𝑖+ =

𝑆𝑖−

𝑆𝑖++𝑆𝑖

−

The term 𝐶i+ provided a useful tool to help the DM to evaluate and rank different design

options. The alternative with the highest 𝐶𝑖+ value corresponds to the best design solution.

Equation 3.15

Equation 3.16

Equation 3.97

50

Experiment #2: Effective Flexural Rigidity Evaluation 3.3

Following the same manufacturing procedure described in Section 3.2, specimens with

-45o/+45

o fiber orientation were prepared, as shown in Figure 3.14.

(a) (b)

Figure 3.14 Reference of ply orientation for a) 0o /90

o degrees and b)-45

o /+45

o degrees

The differences between fabric flexural rigidity for different orientations of the reinforcement

were measured using the procedure described in the standard ASTM D1388 for stiffness of

fabrics using a cantilever bending tester (Figure 3.15).

Figure 3.15 Cantilever bending tester used of the stiffness characterization of the reinforcement

For this group of experiments, samples were manufactured only with the 1/8” radius

geometry. Under this design radius, a 23

full factorial design was established considering two

levels for the following inputs: part angle (40⁰, 70⁰), ply orientation (-45o/+45

o, 0

o /90

o) and

0⁰

90⁰ -45⁰ +45⁰

Fabric

bending

under its

own weight

51

the number of layers (3, 5). In total, 16 samples were manufactured for the eight possible

combinations of parameters considering two repeats per condition, as described in Table 3.4.

All the quality metrics previously discussed in Experiment #1 were evaluated for this group

of samples, except the misalignment parameter (this parameter was excluded since the

experiment itself considers a main change in the fiber orientation).

Table 3.4 Experimental matrix for flexural stiffness evaluation (Experiment #2)

Sample Angle Ply

Orientation Number of Layers

1 40⁰ -45/+45 3

2 40⁰ 0/90 5

3 40⁰ -45/+45 3

4 40⁰ 0/90 5

5 70⁰ -45/+45 3

6 70⁰ 0/90 5

7 70⁰ -45/+45 3

8 70⁰ 0/90 5

Experiment #3: Process Conditions Evaluation 3.4

A third set of specimens was manufactured to evaluate the effect of resin curing on the

critical geometrical condition according to the results obtained from Experiment 1. Thus,

specimens with a part angle of 70° and a radius of 1/8” were fabricated with the following

variables:

Number of layers: 3 and 5 layers.

Amount of initiator (MEKP): 1% and 2% of MEKP.

Post curing of specimens: no post-cure and a post curing cycle of 1.5 hours at 90 ⁰C.

52

Similar to the experimental design in Experiment #2, for the total possible combinations

between the above variables, 16 samples were manufactured. The specimens were evaluated

only for their CBS test using the procedure previously described in section 3.2.1.2. The

experimental matrix for Experiment #3 is presented in Table 3.5. It is worth adding that it is

well known that the part thickness is a critical factor defining the thermal history of resin and

hence interacting with other process parameters to define the final cure state (Strong, 2008).

Table 3.5 Experimental matrix for Experiment #3

Sample Post Curing Radii Number of Layers

1 Yes 1% 3

2 Yes 1% 5

3 Yes 2% 3

4 Yes 2% 5

5 No 1% 3

6 No 1% 5

7 No 2% 3

8 No 2% 5

53

Chapter 4: Results and Discussion

This chapter provides the results of the novel multi-criteria, statistical characterization

procedure developed in Chapter 3 for the evaluation of mechanical properties of open

moulded curved samples with woven reinforcements and varying geometries and process

conditions. The analysis of the CBS specimens is also related to a simplified finite element

model to explore the reasons for the observed non-linear trends for particular geometries.

Results of the MCDM and statistical analyses are discussed by closely relating the quantified

quality measures to the design parameters. All the raw data values for this section have been

included in Appendix C.

Experiment #1 Results: Influence of Geometrical Parameters 4.1

4.1.1 DIC for the CBS Test

The results obtained using the DIC approach for real time deformation studies on the CBS

tests are presented first. In general, the load vs. extension curves exhibited a response similar

to the classical behavior described earlier in Figure 3.6. One example of such material

behavior under CBS test is presented in Figure 4.1 for the configuration 1/8” (corner radius),

70⁰ (angle), and 3 layers.

54

Figure 4.1 Load vs. extension plot with DIC results, indicating: a) stage without failure, b) first

delamination on the upper region, and c) second delamination; specimen with a radius of 1/8”, part angle

of 70° and 3 layers.

As Figure 4.1 shows, the first delamination in the sample (between states (a) and (b))

corresponded to the separation in the upper space between reinforcement layers, with a

maximum load of approximately 400N. As can be seen in Figure 4.1(a), this region contained

micro-voids which likely have contributed to the initiation of the first failure. Also, a second

delamination was observed in the lower region of the cross-section between layers, with a

maximum load of approximately 300N. Both failure events are clearly visible in the load vs

extension curves as kinks corresponding to material’s sudden failure once the inter-laminar

resistance is reached.

It was observed that for geometry configurations with a part angle of 40°, the load vs

extension curves exhibited a unique response, which deferred from the classical (linear)

(400)

(300)

55

response in standard CBS test. The results obtained for sample with 5/16” (radius), 40⁰

(angle) and 3 layers, are shown in Figure 4.2.

Figure 4.2 Load vs. extension plot with DIC results, indicating: (a) stage without failure, (b) first

delamination on the lower region, (c) extension of the first delamination and (d) second delamination on

multiple regions; specimen with a radius of 5/16”, part angle of 40° and 3 layers.

The results indicate that the failure in this sample occurred after point (b), where the first

delamination appeared to originate at the voids surrounding the lower reinforcement layer of

the specimen. There was no DIC indication of failure in the non-linear region before point (a)

in Figure 4.2.

In order to further understand the source of this non-linear regime observed in the above CBS

test, an additional sample was prepared and evaluated 3 times under the non-linear region

(note that the same sample was loaded and unloaded). The results of this test are provided in

Figure 4.3.

56

Figure 4.3 Load vs. extension plot: Three different runs under with variable maximum loads to evaluate

repeatability on the curve for evaluation of the elastic region in a specimen with a radius of 1/4”, part

angle of 40° and 3 layers

Figure 4.3 shows the results of the three repeat runs of the CBS test for a same specimen of

with a radius of 1/4”. It can be observed that the curves overlapped and it confirmed the

earlier observation that no failure was recorded in the DIC images. Thus, the observed non-

linear behavior is not associated with failure in the composite layers and the material remains

elastic/undamaged (since the three re-loadings overlapped). Next, the FE model developed in

Chapter 3 was run for this test scenario to explore other potential sources of non-linearity for

the observed global behavior.

3.7

57

4.1.2 Non-linear Response Evaluation via FEM

The obtained FEM stress distribution in the transverse direction of the specimen with 5/16”

(radius), 40⁰ (angle) and 3 layers is presented in Figure 4.4.

Figure 4.4 Stress distribution of the sample on the y. direction

Figure 4.4 shows that the maximum stress location during the CBS test simulation was

coincident with the failure region observed in the DIC results (Figure 4.2). In the FE models,

the load vs. extension curves of the sample were also obtained from the summation of the

vertical reaction forces on points “a” and “b”. These points correspond to the upper support

of the 4 point bending test fixture (Figure 3.3). The resultant force vs. extension plot is

shown in Figure 4.5.

b

“

a

Y

X

58

Figure 4.5 Force vs. displacement response from the FEM simulation

Figure 4.5 suggest that the displacement for the specified geometry is ideally linear, although

it is contrary to the observed experimental response of the load vs. extension curve in Figure

4.2 for the same configuration. Hence, in the next step of analysis, a modification was made

in the composite part FE model considering the surface finish of the open side during open-

moulding. The actual difference between the two surfaces of the open moulded specimen is

also presented in Figure 4.6. The magnitude of roughness on the open surface was in the

range of 2mm.

Figure 4.6 Cross-section of a sample manufactured with manual wet lay-up

0

20

40

60

80

100

120

140

160

0 1 2 3 4

Forc

e (

N)

Extension (mm)

Force vs Displacementideal sample

Open Side

Mould Side

59

Figure 4.6 shows that in the open side, the architecture of the reinforcement defines the

surface of the part. This open side surface was the one in contact with the lower support in

the four point bending fixture during the CBS experiment. Figure 4.7 shows the force vs.

extension curve for a modified specimen in the FE model (with a rough texture in the open

side) when compared to the ideal specimen with no roughness (plain surface)

Figure 4.7 Comparison of force vs. extension plot between an ideal (plain) inner surface and an internal

surface with rough geometry

From Figure 4.7, the results suggest that the internal surface of the specimens can be the

main cause of non-linearity seen in the response of specimens with 40⁰ (angle) and 3 layers.

In order to confirm this conclusion obtained from the FEM, a complementary experimental

test was performed. Two specimens with 5/16” (radius), 40⁰ (angle) and 3 layers were

evaluated under the CBS test. One of the specimens was polished until the inner surface of

the specimen was plain. The results of the corresponding CBS tests are presented in Figure

4.8.

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5

Forc

e (

N)

Extension (mm)

w/ internal texture

Ideal Inner Surface

60

Figure 4.8 Comparison of experimental force vs. extension plots for a specimen with a modified (plain)

internal surface and the one with the original (rough) inner surface

From the results seen in Figure 4.8, it can be concluded that the inner surface of the open-

moulded part was the main source for the non-linear response in the specimens with 40°

(angle) and 3 layers. Also, the results of the tests show that the maximum failure load for

both specimens was about 80N. This suggests that the CBS failure load was “independent” of

the texture of the internal surface.

4.1.3 Sensitivity Analysis Results

This section provides the results of the statistical tests corresponding to the quality

parameters described in Section 3.2.1.

4.1.3.1 CBS Tests

Table 4.1 summarizes the ANOVA results of the measured CBS values with respect to the

design inputs.

0

10

20

30

40

50

60

70

80

90

0 2 4 6 8

Forc

e (

N)

Extension (mm)

Plain inner surface

Original inner surface

Failure Point

61

Table 4.1 ANOVA results for the CBS response (α=0.05)

Factors

Sum of

Squares

Degree of

Freedom SSMean F-value P-value

Percentage

Contribution

of SSMean

Significance

Angle (A) 168046 3 56015 6.955 0.001 4.77% Significant

Radius (B) 53646 3 17882 2.220 0.105 1.52% Insignificant

No. of layers (C) 1028820 1 1028820 127.736 0.000 87..62% Very high

AB 135302 9 15034 1.867 0.094 1.28% Insignificant

AC 29932 3 9977 1.239 0.312 0.84% Insignificant

BC 32433 3 10811 1.342 0.278 0.92% Insignificant

ABC 247931 9 27548 3.420 0.005 2.35% Very Low

Error 257736 32 8054 -- -- 0.69% --

The results in Table 4.1 suggest that the corner radius (factor B) was not significant in

controlling the CBS of the curved parts. On the other hand, the part angle (factor A) and the

number of layers (factor C) have a strong statistical significance (see the p-values in Table

4.1). The third-order interaction term (ABC) indicated some statistical relevance, however

with a less percentage contribution when compared to the significant main factors. Number

of layers has controlled the CBS values by 88%, followed by the part angle at ~5%

contribution. The corresponding main error plots of each parameter are also presented in

Figure 4.9.

62

Figure 4.9 Main effect plots of CBS vs. (a) part angle in degrees, (b) corner radii in inch and (c) number

of layers (note: vertical bars denote 0.95% confidence intervals; CBS values are in [N.mm/mm])

The difference between mean values due to the part angle (Factor A) change was statistically

relevant, presenting a decrease in the CBS response for every increase of the part angle

(Figure 4.9a). In contrast, increasing the radius increased the CBS, which supports the

theoretical trend in Figure 2.7; i.e., as the part radius increases, the maximum radial stress

decreases, hence increasing the CBS capacity (note that in Eq. 2.1 radial stress is highly

dependent of part radius). However, the latter effect was not statistically significant in Figure

4.9(b) given the large level of random errors. The CBS values were seen to be very highly

dependent on the number of reinforcement layers (Figure 4.9c), where specimens with 5

layers had a significantly higher average CBS value than parts made with 3 reinforcement

layers. This effect can be explained theoretically via thickness correlation to the part’s

mechanical strength. As described in Section 3.2.1., the CBS parameter represents a

a) b)

c)

63

measurement of flexural moment per unit of specimen width. Composite parts with a higher

number of layers (i.e., greater thickness) are expected to have a higher CBS strength.

The thickness of the corner region was not dependent of the number of layers of the part

only: the experimental observations indicate that the part angle also affected the ‘actual’

thickness of the corner area. Due to of fiber bridging and formation of resin rich area (this

will be discussed in more detail in section 4.1.3.4) the actual thickness increased. As a result,

‘thickness’ here in open-moulding represents a variable that cannot be directly/fully

controlled, but can be measured in the experiment for each sample; statistically, such a

variable is called a ‘covariant’ or ‘concomitant’ variable (Montgomery, 2009).

The dominant influence of the thickness in the CBS response can override the net effect of

part radius and part angle effect. In order to remove the effect of the thickness covariance, an

Analysis of Covariance or ANCOVA (Montgomery, 2009) was performed. A summary of

the ANCOVA results is presented in Table 4.2.

Table 4.2 ANCOVA results for the CBS response (α=0.05)

Factors Sum of

Squares Degree of

Freedom

SS Mean F-value P-value

Percentage

Contribution

of SS Mean

Significance

Thickness (A) 1004971 1 1004971 79.802 0.000 85.59% Significant

Radius (B) 347184 3 115728 9.190 0.000 9.86% Significant

Angle (C) 59297 3 19766 1.570 0.209 1.68% Insignificant

BC 189583 9 21065 1.673 0.123 1.79% Insignificant

Error 591883 47 12593 -- -- 1.07% --

The results in Table 4.2 suggest that the part radius next to thickness was a relevant

parameter for the CBS (as opposed to Table 4.1). This result suggests that the nuisance effect

of the thickness in the ANOVA analysis may have affected the correct statistical evaluation

64

of the effect of the radius parameter. In addition, the part angle in ANCOVA presented no

statistical significance. This result suggests that the significant effect of angle seen in Table

4.1 was highly dependent of the corner thickening (i.e., through factor interaction).

4.1.3.2 Void Content

The results of the ANOVA analysis for the void content response are presented in Table 4.3.

Table 4.3 ANOVA results for the void content response (α=0.05)

Factors

Sum of

Squares

Degree of

Freedom SSMean F-value P-value

Percentage

Contribution

of SSMean

Significance

Angle (A) 3.481 3 1.160 2.436 0.083 17.34% Insignificant

Radius (B) 10.033 3 3.344 7.020 0.001 49.99% Very high

No. of layers (C) 0.017 1 0.017 0.035 0.853 0.25% Insignificant

AB 4.894 9 0.544 1.141 0.364 8.13% Insignificant

AC 1.068 3 0.356 0.747 0.532 5.32% Insignificant

BC 1.726 3 0.575 1.208 0.323 8.59% Insignificant

ABC 1.958 9 0.218 0.457 0.892 3.26% Insignificant

Error 15.245 32 0.476 -- -- 7.12% --

The results in Table 4.3 indicate that the part radius had the highest impact to the void

content, with a total contribution of ~ 50%. The second most important parameter was the

part angle (A) with a 17.34% contribution (generally, tighter part angle would result in a

higher void content (Figure 4.10b)); however, the level of error relative to this effect has

been so high such that there was no statistical significance for Factor A in Table 4.3 (p-

value>5%). The number of layers had a negligible contribution on the variation of the void

content in the samples. The main effect plots of the radius and part angle are presented in

Figure 4.10.

65

Figure 4.10 Main effect plot of a) void content vs. corner radius in inch and b) void content vs. corner

angle (note: vertical bars denote 0.95% confidence intervals; void content is given in percentage values)

The results in Figure 4.10a show that specimens with a radius of 1/8” had a notably higher

void content. There was no statistical difference between specimens with radii of 3/16”, 1/4”

and 5/16”. It can be hence concluded that for radius over 1/8”, the modification of this

geometrical parameter would be ineffective to control void content at sharp corners.

a)

b)

66

4.1.3.3 Fiber Misalignment

The results of the ANOVA analysis for the fiber misalignment are presented in Table 4.4.

Table 4.4 ANOVA results for the misalignment response (α=0.05)

Factors

Sum of

Squares

Degree of

Freedom SSMean F-value P-value

Percentage

Contribution

of SSMean

Significance

Angle (A) 81.7 3 27.2 6.6 0.001 34.13% High

Radius (B) 62.6 3 20.9 5.0 0.006 26.22% High

No. of layers (C) 5.3 1 5.3 1.3 0.268 6.64% Insignificant

AB 51.2 9 5.7 1.4 0.242 7.15% Insignificant

AC 24.5 3 8.2 2.0 0.139 10.29% Insignificant

BC 6.1 3 2.0 0.5 0.694 2.51% Insignificant

ABC 56.0 9 6.2 1.5 0.191 7.78% Insignificant

Error 132.9 32 4.2 -- -- 5.26% --

The results in Table 4.3 show that the part angle (34.13%) and radius (26.22%) have had

significant effects on the fiber misalignment on the curvature areas of the parts. The

corresponding trends for part angle and radius are also presented in Figure 4.11.

Figure 4.11 Main effect plots of misalignment vs. (a) part angle in degrees, and (b) corner radii in

inch (note: vertical bars denote 0.95% confidence intervals; void content is given in percentage

values)

a) b)

67

Figure 4.11(a), shows that fiber misalignment is seen to gradually increase for every increase

of the part angle. Also, Figure 4.10(b) shows that only specimens with a part radius of 5/16”

had statistically different results when compared with parts of the smaller radii.

These results can be related to the relative movement of the reinforcement material during

the consolidation process of the part. In parts with low corner angles, the geometrical

restriction provided by the mold on the fabric against its bending is high (Figure 4.12a). As a

result, the reinforcement preserves its original position due to the high normal force and

thereby friction force from the mould. For open moulded specimens with 70° angle (i.e., less

sharp corners), the distortions are more significant. In this case, the mould provides a reduced

restriction to the fibers and hence their relative movement can occur during draping, thus

generate fiber misalignment (Figure 4.12b).

Figure 4.12 Draping comparison between a) mould with 40° and b) mould with 70° angle

Normal force

of the mould

Friction force

a) b)

68

4.1.3.4 Thickness Uniformity

The ANOVA analysis results for thickness uniformity are presented in Table 4.5.

Table 4.5 ANOVA results for the thickness uniformity response (α=0.05)

Factors

Sum of

Squares

Degree of

Freedom SSMean F-value P-value

Percentage

Contribution

of SSMean

Significance

Angle (A) 0.082 3 0.027 3.098 0.041 8.28% Significant

Radius (B) 0.559 3 0.186 21.163 0.000 56.53% Very High

No. of layers (C) 0.061 1 0.061 6.933 0.013 18.52% High

AB 0.149 9 0.017 1.879 0.092 5.02% Insignificant

AC 0.048 3 0.016 1.818 0.164 4.86% Insignificant

BC 0.009 3 0.003 0.335 0.800 0.89% Insignificant

ABC 0.096 9 0.011. 1.207 0.325 3.22% Insignificant

Error 0.282 32 0.009 -- -- 2.67% --

Table 4.5 shows that the variation of all the design factors had a significant contribution to

the thickness uniformity of the parts. The results also suggest that the most important

parameters were the curvature radius (56.53%) and the number of layers (18.36%). The part

angle had a lower contribution of 8.28%. The main effect plots for the part angle, radius, and

number of layers are presented in Figure 4.13.

69

Figure 4.13 Main effect plots of thickness uniformity vs. (a) part angle in degrees, (b) corner radii in inch

and (c) number of layers (note: vertical bars denote 0.95% confidence intervals)

Figure 4.13(a) suggests that a more uniform thickness can be obtained for parts with a high

angle (70°). Also, more uniform samples are observed in cases with high radius (1/4” and

5/16”) (Figure 4.13(b)). Figure 4.13(c) shows a more uniform thickness for specimens with

less number of layers.

a) b)

c)

70

4.1.3.5 Corner Bridging

The ANOVA analysis results for corner bridging response are presented in Table 4.6.

Table 4.6 ANOVA results for the bridging response (α=0.05)

Factors

Sum of

Squares

Degree of

Freedom SSMean F-value P-value

Percentage

Contribution

of SSMean

Significance

Angle (A) 2541695 3 847232 40.185 0.000 36.80% Very High

Radius (B) 1315908 3 438636 20.805 0.000 19.05% High

No. of layers (C) 505941 1 505941 23.998 0.000 21.98% High

AB 2274753 9 252750 11.988 0.000 10.98% Significant

AC 45117 3 15039 0.713 0.551 0.65% Insignificant

BC 516331 3 172110 8.163 0.000 7.48% Low

ABC 444816 9 49424 2.344 0.037 2.15% Low

Error 674658 32 21083 -- -- 9.16% --

The results in Table 4.6 suggest that all the input design parameters and some of their

interactions had a statistical impact on the bridging quality metric. The main effect plots for

angle, radius and number of layers are shown in Figure 4.14.

71

Figure 4.14 Main effect plots of bridging vs. (a) part angle in degrees, (b) corner radii in inch and (c)

number of layers (note: vertical bars denote 0.95% confidence intervals)

In Figures 4.14(a) and (b), the results indicate a decrease of bridging with the increase of the

part angle and radius. Also, the lowest extent of bridging was seen in specimens with less

layers of reinforcement. The presence of higher bridging under tighter radius was expected.

Under reduced dimensions in a corner, the reinforcement layers could not fully drape into

pre-defined concentric geometries; instead, they altered their curvatures, creating higher

spaces between layers (bridging). Meanwhile, in Table 4.6 it was observed that the

interaction between two geometrical design parameters (radius and part angle) was also

important. The latter notion is further scrutinized in Figure 4.15.

a) b)

c)

72

Figure 4.15 Bridging effect plot for AB interaction; bridging values are in [mm] (note: the curves have

been slightly shifted in x-axis for better visibility)

The interaction plot in Figure 4.15 indicates the differences between bridging values for

different combinations of part angle and part radius. For example, the tightest radii (1/8” and

3/16”) have induced significantly high bridging only on samples with a part angle of 40°.

Figure 4.16 shows a visual comparison for these two conditions.

73

Angle

40° 70°

Rad

ius

1/8

"

5/1

6"

Figure 4.16 Comparison between bridging for (a) sample with 40°, 1/8” (b) sample with 70°, 1/8” (c)

sample with 5/16”, 40° and (d) sample with 5/16”, 70°

In Figure 4.16(a), for a part angle of 40° it was observed that the upper layer draped into the

curvature radius of the mold. The reduced space made the subsequent layers to separate from

the previous one and form under a similar radius, thus producing high distance between the

layers. On the other hand, for the 70° specimens (Figure 4.16(b)), the layers could not

conform to the geometry of the mold. The parallel reinforcement layers draped to a radius

higher than that of the mould. This condition has produced a lower distance (less bridging)

between the layers, thus developing an external brittle area in the part corner due to the

absence of reinforcement fibers.

a) b)

c) d)

Higher bridging

74

4.1.3.6 External Formability of Reinforcement

The ANOVA analysis results for the formability parameter are included in Table 4.7.

Table 4.7 ANOVA results for the external formability response (α=0.05)

Factors

Sum of

Squares

Degree of

Freedom SSMean F-value P-value

Percentage

Contribution

of SSMean

Significance

Angle (A) 1.052 3 0.35076 42.008 0.000 42.37% Very High

Radius (B) 1.111 3 0.37027 44.344 0.000 44.73% Very High

No. of layers (C) 0.001 1 0.00054 0.064 0.801 0.07% Insignificant

AB 0.591 9 0.06568 7.966 0.000 7.93% Significant

AC 0.033 3 0.01097 1.313 0.287 1.33% Insignificant

BC 0.025 3 0.00845 1.012 0.400 1.02% Insignificant

ABC 0.115 9 0.01276 1.528 0.180 1.54% Insignificant

Error 0.267 32 0.00835 -- -- 1.01% --

From Table 4.7, parameter A (part angle) and B (part radius) have the most relevant effect on

the external formability response. Also, a statistically significant response was observed for

the interaction parameter AB. The trends corresponding to the part angle and part radius are

shown in Figures 4.17(a) and 4.17(b), respectively.

Figure 4.17 Main effect plots of external formability vs. (a) part angle in degrees, (b) corner radii in inch

(note: vertical bars denote 0.95% confidence intervals)

Figure 4.17(a) shows that the increase of the part angle decreased the capacity of the material

to properly drape onto the mould curvature. On the other hand, better formability results were

a) b)

75

obtained for every increment in the radius size, as indicated in Figure 4.17(b). The interaction

plot of factor AB is shown in Figure 4.18.

Figure 4.18 CBS effects plot for the interaction AB (note: the curves have been slightly shifted in x-axis

for better visibility)

The above interaction plot denotes that formability remains constant in specimens with a

radius of 5/16”. Nevertheless, a progressive decreasing trend is observed with every

reduction in the angle value. For larger angles, the effect to different radii is more

pronounced. On the contrary, parts with 40° angle present comparably a good formability

capacity for all the levels of part radius. The decrease of the part radius showed a negative

impact on the formability only for specimens with a part angle higher than 40°.

76

4.1.3.7 External Surface Defects

The ANOVA results corresponding to analysis of the external surface defects are presented

in Table 4.8.

Table 4.8 ANOVA results for the surface defects response (α=0.05)

Factors

Sum of

Squares

Degree of

Freedom SSMean F-value P-value

Percentage

Contribution

of SSMean

Significance

Angle (A) 6381543 3 2127181 20.12215 0.000 35.50% Very High

Radius (B) 2600065 3 866688 8.19847 0.000 14.46% High

No. of layers (C) 1710395 1 1710395 16.17955 0.000 28.54% High

AB 4799723 9 533303 5.04480 0.000 8.90% Significant

AC 304252 3 101417 0.95936 0.424 1.69% Insignificant

BC 878538 3 292846 2.77019 0.058 4.89% Insignificant

ABC 2295282 9 255031 2.41248 0.032 4.26% Very Low

Error 3382829 32 105713 -- -- 1.76% --

From Table 4.8, all the geometrical conditions studied in the experiments showed a

significant influence. The most relevant parameter was the part angle (35.5%) followed by

the number of layers (8.90%). The statistical trends for the part angle, radius, and number of

layers are presented in Figure 4.19.

77

Figure 4.19 Main effect plots of surface defects vs. (a) part angle in degrees, (b) corner radii in inch and

(c) number of layers (note: vertical bars denote 0.95% confidence intervals)

In Figure 4.19(a), the results show that specimens had less surface defects for parts with

angles between 40° to 60°. The 70° angle was statistically the worst condition. Also, lower

surface defects are clearly found in specimens with large part radius and large number of

layers.

4.1.3.8 Summary of Geometrical Parameters Effects

By comparing the above presented set of ANOVA results, it can be stated that the design

parameters having statistical contribution on different quality metrics are not completely

commensurate. For example, the part angle and number of layers were found to have a

a) b)

c)

78

significant effect on the CBS response, but not on the void content response. In the case of

part radius, a positive trend was observed in the CBS values with every size increase.

Nevertheless, only samples with 1/8” radius were seen to have a higher void content. In the

same relation, a summary of qualitative evaluation of the obtained results from the DIC tests

and optical imaging is presented in Tables 4.9 and 4.10.

Table 4.9 Comparison between DIC results and optical imaging for samples with 70° angle

79

Table 4.10 Comparison between DIC results and optical imaging for select samples with 40° angle

As suggested by images in Tables 4.9 and 4.10 (for specimens with corresponding 40° and

70° angles), the failure mechanism in the CBS test samples was mainly associated with

matrix cracking originating at the voids. These results show the relation between the level of

porosity in the samples and part failure. However, the presence of voids is not affected by the

geometrical parameters and is randomly distributed among all groups of specimens, except at

radius of 1/8”. As a result, it is not possible to make a full correlation between void content

and CBS. In turn, this suggests that in actual design practices it is necessary to consider all

the quality metrics. The following overall design guidelines may be helpful to GFRP

designers in this regard.

A general design guideline/chart for GFRP manufactures: As mentioned above from a

practical application perspective, it is important to establish the impact of design decisions on

the quality performance. This is summarized in Table 4.11, where the qualitative significance

80

between each design input and the quality outcome is described. The orientation of arrows

indicates the trend of the input parameter providing a desirable output result. Values in

brackets indicate the rank of corresponding variables in each column. The notation ‘N/A’

refers to the cases where the input variable showed no statistically significant effect on the

output variable in the overall results (considering the hand lay-up process had large random

errors). Regarding the output characteristics, the void content, fiber misalignment, and

surface defect metrics are of the ‘the lower the better’ type (i.e., defect-type metrics),

whereas the CBS was the mechanical strength and hence ‘the higher the better’. In the case

of bridging, formability, and thickness ratio all are of ‘the higher the better’ type. In Table

4.12, the optimum design configurations have been visualized based on the results of Table

4.11 for each metric. For instance, the thickness uniformity metric (Table 4.5) suggested that

the corner radius played the most important role, followed by the number of layers and the

part angle. Also it was noted that the best thickness uniformity ratio was obtained when the

part angle was large, the corner radius was small, and the number of layers was low.

81

Table 4.11 Trends of the influence of significant design inputs on the quality metrics; ranking of input

variables are given in brackets in each column; ‘No’ refers to statistical insignificance

Table 4.12 Images corresponding to the best quality designs under different quality metric criteria

4.1.4 MCDM Results and Discussions

The data in Tables 4.11 and 4.12 suggest the presence of conflicting results between different

quality metrics for design of GFRP parts with sharp corners. For example, surface defects

and bridging follow some inconsistent trends against changes in design factors. While both of

these metrics are positively influenced by increasing the radius of curvature of the part,

higher part angles cause less surface defects but increase the bridging. This type of a conflict

represents a typical scenario of multiple criteria decision making (MCDM) that engineers

frequently face in design of complex FRP parts.

Void Surface Thickness

Content Defect Ratio

2 2(3) N/A 1 (3) N/A 2

3

1 3 2 3 3 1

(2 )N/A 2 1 1 1

BridgingCBS Misalignment

Radius (B)

No. of layers (C)

Angle (A)

1

(3) N/A

Formability

2

N/A 40⁰ 40⁰ 40⁰ 70⁰ 40⁰ 40⁰

5/16" 5/16" 5/16" 5/16" 5/16" 5/16" 5/16"

N/A 5 layers N/A 5 layers 3 layers N/A N/A

Angle

Radius

N of layers

Void

ContentCBS Misalignment

Surface

Defects

Thickness

Uniformity

Best input

combination

Bridging Formability

82

The application of MCDM methodology in this section was aimed to assist designers to make

a final choice regarding the geometrical parameters of curved parts, given the conflicts

among quality metrics. Two different scenarios have been considered. These scenarios were

created merely based on the potential type of application for open-moulded parts: structural

applications (e.g., a GFRP boat hull), and aesthetic application (e.g., GFRP architectural

cladding). In both scenarios, the subjective weighting (i.e., via the DM’s input and

experience through the MDL method - section 2.2.1.1) and the corresponding objective

weighting (through CRITIC method in section 3.2.2) have been implemented. The summary

of the obtained MDL (subjective) weights per scenario are presented in Table 4.13 and Table

4.14.

Table 4.13 Relative importances between criteria based on the MDL method; structural scenario

Table 4.14 Relative importances between criteria based on the MDL method; aesthetic scenario

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Misalignment 1 1 2 2 3 1 10 0.125

CBS 3 3 3 3 3 3 18 0.225

Void content 3 1 3 3 3 2 15 0.188

Bridging 2 1 1 3 2 1 10 0.125

Surface defects 2 1 1 1 2 1 8 0.1

Thickness ratio 1 1 1 2 2 1 7 0.088

Formability 3 1 2 3 3 3 12 0.15

Positive

DecisionsWeights

Structural

Scenario

Number of possible decisions

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Misalignment 3 2 1 1 1 1 9 0.107

CBS 1 1 1 1 1 1 6 0.071

Void content 2 3 1 1 1 1 9 0.107

Bridging 3 3 3 1 2 1 13 0.155

surface defects 3 3 3 3 3 2 17 0.202

thickness ratio 3 3 3 2 1 1 13 0.155

Formability 3 3 3 3 2 3 17 0.202

Aesthetic

Scenario

Number of possible decisionsWeightsPositive

83

Next, the objective weights were obtained through the CRITIC technique, which as described

in section 3.2.2 accounts for Pearson’s correlations between decision attributes. The results

of the Pearson’s correlation factors are given in Table 4.15.

Table 4.15 Pearson's correlation results for criteria pairs; Rjk

Criteria CBS Void

Content Misalignment Bridging

Surface

Defects

Thickness

Uniformity Formability

CBS 1 -0.022 -0.324 0.275 -0.346 -0.119 0.213

Void Content -0.022 1 -0.012 0.355 0.195 -0.121 -0.091

Misalignment -0.324 -0.012 1 -0.333 0.343 0.037 -0.451

Bridging 0.275 0.355 -0.333 1 -0.363 -0.558 0.245

Surface Defects -0.346 0.195 0.343 -0.363 1 0.428 -0.598

Thickness Uniformity -0.119 -0.121 0.037 -0.558 0.428 1 0.039

Formability 0.213 -0.091 -0.451 0.245 -0.598 0.039 1

Table 4.15 shows that the highest correlation was present between the formability and

surface defect measures (Rjk = 0.598). As a result, these two quality measures should be

assigned lower objective weights for the MCDM analysis. A summary of the final weights

from the combinative method (equation 3.12) is presented in Table 4.16.

Table 4.16 Summary of weighting results under the combinative method for each design scenario

Misalignment CBS Void content Bridging Surface

Defects

Thickness

ratio Formability

Ws Structural 0.125 0.225 0.188 0.125 0.1 0.088 0.15

Ws Aesthetic 0.107 0.071 0.107 0.155 0.202 0.155 0.202

Wo CRITIC 0.145 0.151 0.168 0.125 0.12 0.151 0.14

Wc Structural 0.136 0.186 0.179 0.126 0.111 0.116 0.146

Wc Aesthetic 0.127 0.106 0.137 0.142 0.159 0.156 0.172

84

In Table 4.16, the results suggest that initially the weighting values were strongly influenced

by the DM opinion from the subjective method. However, after including the objective

CRITIC weights, the combinative weights present a different preference order. For example,

for the structural scenario, the DM assigns an equal importance to bridging and misalignment

measures (each 0.125). But the inclusion of the CRITIC weights modified this assignment,

providing a higher relevance to the misalignment quality metric than to fiber bridging.

4.1.4.1 Structural Scenario Ranking

Four possible set of design parameters were considered based on the general guideline results

in Table 4.12. A summary of the scores and the corresponding TOPSIS ranking for each of

these structural design options is presented in Table 4.17.

Table 4.17 TOPSIS results using four design alternatives for a structural application

Alternatives Angle Radius N of layers Ranking Score Design 1 40 5/16" 5 layers 1 0.695

Design 2 70 5/16" 5 layers 2 0.557

Design 3 70 5/16" 3 layers 3 0.510

Design 4 70 1/8" 3 layers 4 0.320

The results indicate that from a structural application perspective, the most desired solution is

given by the combination of a part angle of 40°, a radius of 5/16” and five fabric layers. The

most important quality parameters for this approach according to the weights presented in

Table 5.4 are CBS and the void content of the samples. Hence, the samples with the higher

number of layers and higher radius represent the best solution among the different

alternatives.

85

4.1.4.2 Aesthetic Scenario Ranking

Under the aesthetic application scenario, quality parameters such as formability, thickness

ratio and surface defects received the highest weights in the combinative method in Table

4.16. The results obtained from the selected possible solutions for the aesthetic scenario are

presented in Table 4.18.

Table 4.18 TOPSIS results using four design alternatives for an aesthetic application

Alternatives Angle Radius N of layers Ranking Score

Design 1 40 5/16" 5 layers 1 0.652

Design 2 70 5/16" 3 layers 2 0.564

Design 3 70 5/16" 5 layers 3 0.540

Design 4 70 1/8" 3 layers 4 0.361

In Table 4.18, the optimum solution was coincident with the structural approach best result.

It also corresponded to the case with a 40° angle, a 5/16” radius and 5 layers. However, the

second best solution now was obtained for a specimen with 3 layers.

Experiment #2 Results: Influence of Flexural Rigidity 4.2

A comparison of the measured flexural rigidity of the tested glass fabric (Figure 3.15) was

made in Table 4.19 for 0o/90

o (weft/warp) and -45

o /+45

o fabric orientations.

Table 4.19 Flexural rigidity values for the reinforcement material at different orientations

Fabric

bending/draping

angle

Flexural Rigidity

(μjoule/m)

0o /90

o 17284

-45o /+45

o 1227

86

In Table 4.19, the values of the flexural rigidity change significantly with the orientation of

the fibers under a defined curvature; this result indicates that a change in the reinforcement

orientation may improve the draping capacity of the reinforcement material (Pierce, 1930).

Next, new set of samples were prepared to represent the two different draping orientations

(0o/90

o and -45

o /+45

o). Subsequently, all ANOVA analyses were repeated to evaluate the

quality metrics (results are provided in Appendix A). A general comparison of the quality of

parts made via these two reinforcement orientation options is provided in Table 4.20.

Table 4.20 Comparison for all quality metrics between -45 o/45

o and 0

o/90

o specimens (green marks

indicate a statistically preferred condition)

Fabric Draping

Angle

Void

Content CBS Surface Defects Bridging

Thickness

Ratio Formability

-45o/+45

o -

- -

0o/90

o - - -

-

The response obtained for the ‘void content’ presented no “statistical” differences between

the two groups of samples. On the other hand, the ‘CBS’ metric (which would be the most

relevant to structural applications) had statistically significant improvement for the -45o /+45

o

specimens. This observation was attributed to the increase of the corner thickness in the

specimens, and can be further supported by the results of parameters such as bridging and

thickness tatio (Table 4.20) where specimens in the -45o /+45

o configuration were less

uniform (corner thickening).

The results indicate that among the four quality parameters that would be considered more

relevant for aesthetical applications, two (surface defects and formability) exhibited greater

87

sensitivity in response with the change of the material orientation from 0o/90

o to -45

o/+45

o,

and the other two (bridging and thickness ratio) were less sensitive. The interaction effect

plots for the formability and corner surface defects are also presented in Figures 4.20 and

4.21, respectively.

Figure 4.20 Effect plots for interaction between angle and layer orientations for formability metric

In Figure 4.20, the results suggest that the samples with a lower flexural rigidity (-45o/+45

o)

had no statistically significant change between two part angle levels (40° and 70°) for the

critical radius of 1/8”. At both angles, the formability index of (-45o/+45

o) reinforcement

orientation was fairly high (close to 0.9). This means that the flexural rigidity of the fibers

can serve as a direct control factor for optimizing the formability metric. Similarly, the

surface defect results (Figure 4.21) showed that no defects were found with the reinforcement

at (-45o/+45

o) orientation, regardless of the number of layers or the part angle.

88

Figure 4.21 Effect plot for interaction between angle, number of layers and reinforcement orientation for

the surface defects metric

Experiment #3 Results: Influence of the Cure 4.3

The results presented in this section were obtained for the CBS quality metric analysis under

a constant geometry and draping orientation, but different resin cure/process parameters, as

explained in Section 3.4. The summary of the results of the ANOVA analysis for this group

of experiments is shown in Table 4.21. Results in Table 4.21 suggest that none of the

evaluated process parameters on these experiments had an effect on the response obtained

from the CBS.

Table 4.21 ANOVA results for the CBS response as a function of process conditions (α=0.05)

Factors

Sum of

Squares

Degree of

Freedom SSMean F-value P-value

Percentage

Contributi

on of

SSMean

Significance

No. of layers (A) 122605.0 1 122604.0 32.758 0.000442 73.00% Very High

Initiator % (B) 3180 1 3180.0 0.850 0.383608 1.82% Insignificant

Post-curing (C) 6838.2 1 6838.2 1.827 0.213447 4.07% Insignificant

AB 87.4 1 87.4 0.023 0.882362 0.01% Insignificant

AC 3298.8 1 3298.8 0.881 0.375299 1.96% Insignificant

BC 1127.9 1 1127.9 0.301 0.598015 0.67% Insignificant

ABC 871.9 1 871.9 0.233 0.642277 0.52% Insignificant

Error 29941.7 8 3742.7 -- -- 17.83% --

89

A qualitative evaluation of the failure of the specimens for the CBS test under this group of

experiments is included in Appendix B. The failure of the samples was related to the

presence of voids in the matrix and interface areas. Any possible direct effect of the resin

cure properties on the CBS performance of the material was not detected under the selected

experimental conditions. Namely, the amount of initiator (1-2%) and the post-curing cycle

have not been significant enough to show statistical differences in the wet lay-up open

moulded specimens. This effect could be increased by increasing the temperature in the

initial curing stage. As previously demonstrated by Vilas et al. (2000), the degree of cure of

unsaturated polyester resins is highly sensitivity to the curing temperature. However, the

effect of thermally induced defects (e.g. significant spring-in or residual stresses) must also

be considered as a possible outcome during the application of extra heat in curing stages of

parts.

90

Chapter 5: Conclusions and Future Work

This chapter presents a summary of the key results obtained in this thesis along with the

research limitations and potential future work direction. For practical application purposes,

the findings of this research may be categorized into two general production stages: i) pre-

production (design) stage based on the characterization of open moulded curved parts with

the goal of targeting individual and general quality requirements through mould geometry

variations, and ii) post-production stage (i.e. for cases where the mould shape has been

finalized and only reinforcement configuration and/or processing conditions may be altered

to resolve a part quality issue).

Conclusions 5.1

The findings for the pre-production stage were:

The surface quality of the open-side of the composite brackets has an impact on the

response of the Curved Beam Strength (CBS). For example, non-linear behavior was

observed under specific geometrical conditions. The use of a modified four point

bending test in conjunction with digital image correlation provided an alternative

technique to identify the deformation of composite parts with non ASTM

configurations.

The main failure mechanism observed at the corner area was related to the nucleation

of cracks at voids (i.e., stress concentration zones).

91

The level of voids in the open moulded samples was not significantly affected by the

geometrical conditions investigated.

The CBS of the material increased as the thickness of the part increased. The radius

of the corner had a significant impact on the mechanical performance of the part.

Formation of resin rich zones did not have a detrimental impact on the interlaminar

resistance of the composite.

The geometrical parameters evaluated in this research (i.e. corner radius, angle, and

number of layers) provided statistically optimum design configurations for individual

quality metrics. These solutions (summarized in Tables 4.11 and 4.12) may be used as

an initial guide for designers in order to achieve specific quality requirements.

The use of S/N ratio in the MCDM method was a useful technique to enhance the

significance of data analysis and results obtained through experiments.

The use of statistical analysis for MCDM was an effective method to narrow down

the design alternatives. This procedure identified the best design configuration based

on statistically relevant observations.

The findings for the post-production stage were:

Misalignment of the fibers did not significantly influence the interlaminar properties

of curved open moulded specimens under bending. The modification of the layup

orientation to -45°/45° with respect to the forming direction significantly reduced the

92

flexural rigidity of the fibers, hence generating better draping properties which also

improved aesthetic quality of the final part.

Process conditions related to post-curing or the increase of the initiator had no effect

on the mechanical properties of the composite parts tested.

Research Limitations:

This research was limited by the lack of previous testing standards applicable to open

moulded composite parts. Further, the samples were manufactured using open moulding wet

lay-up technique for one material configuration (i.e. woven fiberglass and UP resin). Hence,

the obtained results may not be necessarily applicable to all composite parts manufactured

using different materials and process conditions. In addition, the evaluation of curing

parameters was carried out without the use of high temperature during the initial curing

process. This condition could modify the results obtained in this experimental work

regarding the statistical effect of degree of cure as presented in Section 4.3.

93

Future Work 5.2

This research provided insights and experimental work provided background on the effect of

design parameters and process conditions on the quality of open moulded fibre reinforced

parts. The focus of this research was to explore the preferred design scenarios based on

geometrical conditions and process parameters that can yield the highest quality in sharp

corner areas. In doing so, the MCDM was used to identify possible conflicts among design

criteria and arrive at an overall optimum solution. However, in order to establish a better

knowledge applicable to industry, several follow-up investigations could be carried out. For

example:

Evaluate other composite materials with different resin (e.g. epoxies and

thermoplastic resins) and fiber architectures (e.g. twill and unidirectional weaves)

configurations in order to create a design database for fabric reinforcements and

resins commonly used in the composite industries.

Apply the presented methodology to other manufacturing processes such as resin

transfer moulding and vacuum bagging, in order to study the differences and specific

solutions for each manufacturing process.

Study the influence of additional additives for UP resins (e.g. inhibitors, fillers, and

promoters) on the mechanical response of composite parts with sharp corners.

Include the study of spring-in as an additional quality metric, especially in

manufacturing processes with high temperature conditions.

94

Bibliography

American Society for Testing and Materials. (2007). ASTM D6415: Standard test method for

measuring the curved beam strength of a fiber-reinforced polymer-matrix composite.

American Society for Testing and Materials. (2009). ASTM D2734: Standard Test Methods

for Void Content of Reinforced Plastics.

American Society for Testing Materials. (2011). ASTM 3171: Standard test method for

constituent components of composite materials.

American Society of Testing Materials. (2014). ASTM D1388: Standard Test Methods for

Stiffness of Fabrics.

Avalon, S., & Donaldson, S. (2011). Strength of composite angle brackets with multiple

geometries and nanofiber-enhanced resins. Journal of Composite Materials, 45, 1017-

1030.

Berhe, B. (1961). Mechanical properties of textile fabrics. Part I: Shearing. Textile Research

Journal, 64, 346-362.

Bhatti, A. (2008). Stereo Vision. InTech. Doi: 10.5772/89.

Cambell, F. C., Mallow, A. R., & Browning, C. E. (1995). Porosity in carbon fiber

composites. An overview of causes. Journal of advanced composite materials, 18-33.

Cauberghs, J., & Hubert, P. (2011). Effect of tight corners and ply terminations on quality in

out-of-autoclave parts. SAMPE tech conference and exhibition. Long Beach, CA.

Cui, W., Tao, L., Len, J., & Ruo, R. (1996). Interlaminar tensilie strength (ITLS)

measurement of woven glass/polyester laminates using four-point curved beam

specimen. Composites Part A, 27A, 1097-1105.

Dahlberg, B. (1961). Mechanical properties of textile fabrics. Part II: Buckling. Textile

Research Journal, 31, 94-99.

DANTEC Dynamics. (2011). Q-400 DIC and ISTRA4D training.

Davoodi, M., Sapuan, S., Ahmad, D., Aidy, A., & Khalina, A. (2011). Concept selection of

car bumper beam with developed hybrid bio-composite material. Materials and.

Design., 32(10), 4857–4865.

95

Dehghan-Manshad, B., H. Mahmudi, Abedian, A., & Mahmudi, R. (2007). A novel method

for materials selection in mechanical design: Combination of non-linear

normalization and a modified digital logic method. Materials and Design., 28(1), 8-

15.

Delahaye, N., Marais, S., Saitter, J., & Metayer, M. (1998). Characterization of Unsaturated

Polyester Resin Cured with Styrene. Journal of Applied Polymer Science, 696-703.

Diakoulaki, D., Mavrotas, G., & Papayannakis, L. (1995). Determining objective weights in

multiple criteria problems: The critic method. Computer & Operation Research,

22(7), 763–770.

Donaldson, S. C., & Avalon, S. (2011). Strength of composite angle brackets with multiple

geometries and nanofiber-enhanced resins. Journal of composite materials, 1019-

1030.

Dridi, S., Morestin, F., & Dogui, A. (n.d.). Use of digital image correlation to analyse the

shearing deformation in woven fabrics. Experimental Techniques, 36(5), 46-52.

Farag, M. (1997). Materials selection for engineering design: New York, Prentice Hall.

Fishburn, P. (1967). Additive utilities with incomplete product set: applications to priorities

and assignments. Baltimore, MD, USA.

Grosberg, P. (1966). The mechanical properties of woven fabrics. Part II: The bending of

woven fabrics. Textile research journal. 36, 205-211.

Guo, Z.-S., Liu, L., Zhang, B.-M., & Du, S. (2006). Critical void content for thermoset

composite laminates. Journal of Composite Materials, 43, 1775-1790.

Hagstrand, P. O., Bonjour, F., & Manson, J. A. (2005). The influence of void content on the

structural flexural performance of unidirectional glass fibre reinforced polypropylene

composites. Composites Part A, 36, 705-714.

Hao, W., Ge, D., Ma, Y., Yao, X., & Shi, Y. (2012). Experimental investigation on

deformation and strength of carbon/epoxy laminated curved beams. Polymer Testing,

520-526.

Hitchon, J., & Phillips, D. (1978). The effect of specimen size on the strength of CFRP.

Composites, 9, 119-124.

Huang, Y.-J., & Leu, J.-S. (1993). Curing of unsaturated polyester resins. Effects of

temperature and initiato: 1. Low temperature reactions. Polymer, 34, 295-304.

96

Hubert, P., & Poursartip, A. (2001). Aspects of the Compaction of Composite Angle

Laminates: An Experimental Investigation. Journal of Composite Materials, 35.

Hwang, C., & Yoon, K. (1981.). Multiple attribute decision making making: Methods and

applications. Berlin: Springer-Verlag .

Jahan, A., Mustapha, F., Sapuan, S., & Ismail, M. (2011). A framework for weighting of

criteria in ranking stage of material selection process. International Journal of

Advanced Manufacutiring Technologies, 58(1-4), 411-420.

Jahan, A., Mustapha, S., Sapuan, S., Ismail, M., & Bahraminasab, M. (2011). A framework

for weighting of criteria in ranking stage of material selection process. International

Journal of Advanced Manufacutiring Technologies, 58(4), 411-420.

Jee, D., & Kang, K. (2000). A method for optimal material selection aided with decision

making theory. Mater. Des., 21(3), 199–206.

Kachlakev, D., & McCurry, D. (2000). Simulated full scale testing of reinforced concrete

beams strenghtened with FRP composites: Experimental results and design model

verification. Federal Highway Administration and Oregon DOT. Salem, OR.

Kedward, K., Wilson, R., & McLean, S. (1989). Flexure of simply curved composite shapes.

Composites, 20, 527-536.

Ko, W. (1988). Delamination stresses in semicircular laminated composite curved bars.

NASA.

Komeili, M. (2014). Multi-scale characterization and modeling of shear-tension interaction

in woven fabrics for composite forming and structural applications (Doctoral Thesis).

Kuhn, P. (1956). Stresses in aircraft and shell structures. New York: McGraw Hill.

Lekhnitskii, S. G. (1968). Anisotropic Plates. New York: Gordon and Breach Science

Publishers.

Liu, L., Zhang, B.-M., Wang, D.-F., & Jun, Z. (2005). Effects of cure cycles on void content

and mechanical properties. Composite Structures, 303-309.

Lomov, S., Boisse, P., Deluycker, E., Morestin, E., Vanclooster, K., Vandepitte, D., et al.

(2008). Full-field strain measurements in textile deformability studies. Composites

Part A, 39(8), 1232-1244.

97

Mabson, G., & Neal III, E. (1988). Analysis and testing of composite aricraft frames for

interlaminar tension failure. National specialists meeting on rotary wing test

technology of the american helicopter society. Bridgeport, CT.

Mazumdar, S. K. (2002). Composites Manufacturing, Materials, Product and Process

Engineering. Boca Raton, Florida: CRC Press.

Michel, L., Garcia, S., Chen, Y., Espinosa, C., & Lachaud, F. (2014). Experimental and

numerical investigation of delamination in curved-beam multidirectional laminated

composite specimen. Key Engineering Materials, 577-578, 389-392.

Montgomery, D. (2009). Design and Analysis of Experiments. New York: John Wiley &

Sons, Inc.

Pan, B., Qian, K., Xie, H., & Asundi, A. (2009). Two-dimensional digital image correlation

for in-plane displacement and strain measurement: a review. Measurement Science

and Technology, 20(6), 062001.

Pierce, F. (1930). The handle of cloth as a measurable quantity. Journal of the textile

institute, 21, 317-416.

Potter, K. (2004). Deformation properties of uncured reinforcements – a reappraisal.

International Journal of Materials and Product Technolgy, 21, 4–23.

Potter, K. D. (2009). Understanding the origins of defects and variability in composites

manufacture. ICCM 17th

. Edinburg, UK.

Potter, K., Khan, B., Wisnom, M., Bell, T., & Stevens, J. (2008). Variability, fibre waviness

and misalignment in the determination. Composites: Part A, 1343–1354.

Purslow, D. (1984). On the optical assesment of void content in composite materials.

Composites, 15, 207-210.

Saaty, T.L. (1980). The analytical hierarchical process: New York, Wiley.

Shah Mohammadi, M., Solnickova, L., Crawford, B., Komeili, M., & Milani, A. (2013). A

case study on dimensional change of glass fiber reinforced polymers: a combined

effect of cure progression and thermo-viscoelastic behaviour. 19th International

conference on composite materials. Montreal.

Stillwell, W., Seaver, D.A., & Edwards, W. (1981). A comparison of weight approximation

techniques in multiattribute utility decision making. Organizational Behavior and

Human Performance, 28, 62-67.

98

Strong, A. (2008). Fundamentals of composites manufacturing, Materials, Methods and

Applications. Dearborn, Michigan: Society of Manufacturing Engineers.

Taguchi, G. (1990). Introduction to Quality Engineering. Tokyo. Asian Productivity

Organization.

Tversky, A. (1972). Elimination by aspects: A theory of choice. Psychological Review.

79(4), 281-299.

Vilas, J., Laza, J., Garay, M., Rodriguez, M., & Leon, L. (2001). Unsaturated Polyester

Resins Cure: Kinetic, Rheologic, and Mechanical-Dynamical Analysis. I. Cure

kinetics by DSC and TSR. Journal of Applied Polymer Science, 79, 447-457.

Wisnom, M. R., & Jones, M. (1996). Size effects in interlaminar tensile and shear strength of

unidirectional glass fibre/epoxy. Journal of reinforced plastics and composites, 15:2.

Yoon, K., & Hwang, C.-L. (1995). Multiple attribute decision making. An Introduction. Sage

Publications, Inc.

Yuksekkaya, M., Howard, T., & Adanur, S. (2008). Influence of the fabric properties on

fabric stiffness for the industrial fabrics. Tekstil ve Konfeksiyon, 18(4), 263-267.

Zweben, C. (1994). Is there a size effect in composites? Composites, 25, 451-454.

99

Appendices

Appendix A: ANOVA Experimental Results for Samples of Group 2

Table A.1 ANOVA results for the CBS response (group 2) (α=0.05)

Factors

Sum of

Squares

Degree of

Freedom SSMean F-value P-value

Percentage

Contribution

of SSMean

Significance

Angle (A) 12940 1 12940 1.587 0.243 1.41% Insignificant

No. of layers (B) 599767 1 599767 73.544 0.000 69.02% Very High

Ply Orient. (C) 70959 1 70959 8.701 0.018 8.17% Significant

AB 15699 1 15699 1.925 0.203 1.81% Insignificant

AC 25548 1 25548 3.133 0.115 2.94% Insignificant

BC 42078 1 42078 5.160 0.053 4.84% Insignificant

ABC 36761 1 36761 4.508 0.066 4.23% Insignificant

Error 65242 8 8155 -- -- 7.51% --

Table A.2 ANOVA results for the void content response (group 2) (α=0.05)

Factors

Sum of

Squares

Degree of

Freedom SSMean F-value P-value

Percentage

Contribution

of SSMean

Significance

Angle (A) 2.614 1 2.614 1.277 0.291230 5.86% Insignificant

No. of layers (B) 9.080 1 0.186 4.436 0.068283 20.36% Insignificant

Ply Orient. (C) 1.563 1 0.061 0.764 0.407623 3.50% Insignificant

AB 12.044 1 0.017 5.884 0.041485 27.01% Very Low

AC 1.645 1 0.016 0.804 0.396139 3.69% Insignificant

BC 0.968 1 0.003 0.473 0.511155 2.17% Insignificant

ABC 0.305 1 0.011. 0.149 0.709413 0.07% Insignificant

Error 16.376 8 2.047 -- -- 36.72% --

Table A.3 ANOVA results for the formability response (group 2) (α=0.05)

Factors

Sum of

Squares

Degree of

Freedom SSMean F-value P-value

Percentage

Contribution

of SSMean

Significance

Angle (A) 0.281 1 0.281 58.975 0.000059 28.32% Significant

No. of layers (B) 0.006 1 0.006 1.198 0.305576 0.60% Insignificant

Ply Orient. (C) 0.176 1 0.176 36.795 0.000301 17.71.% Significant

AB 0.001 1 0.001 0.038 0.850590 0.02.% Insignificant

AC 0.488 1 0.488 102.259 0.000008 49.09% Significant

BC 0.001 1 0.001 0.099 0.761036 0.05% Insignificant

ABC 0.004 1 0.004 0.907 0.368713 0.44% Insignificant

Error 0.038 8 0.005 -- -- 3.82% --

100

Table A.4 ANOVA results for the thickness ratio response (group 2) (α=0.05)

Factors

Sum of

Squares

Degree of

Freedom SSMean F-value P-value

Percentage

Contribution

of SSMean

Significance

Angle (A) 0.101 1 0.101 8.717 0.018359 17.67% Significant

No. of layers (B) 0.013 1 0.013 1.125 0.319837 2.28% Insignificant

Ply Orient. (C) 0.306 1 0.306 26.299 0.000898 53.27% High

AB 0.011 1 0.011 0.912 0.367453 1.85% Insignificant

AC 0.002 1 0.002 0.193 0.672052 0.04% Insignificant

BC 0.020 1 0.020 1.754 0.221975 3.55% Insignificant

ABC 0.027 1 0.027 2.342 0.164496 4.75.% Insignificant

Error 0.093 8 0.011 -- -- 16.19.% --

Table A.5 ANOVA results for the bridging response (group 2) (α=0.05)

Factors

Sum of

Squares

Degree of

Freedom SSMean F-value P-value

Percentage

Contribution

of SSMean

Significance

Angle (A) 4227846 1 4227846 15.187 0.004564 33.61% Significant

No. of layers (B) 3595 1 3595 0.013 0.912319 0.03% Insignificant

Ply Orient. (C) 4267983 1 4267983 15.331 0.004447 33.93% Significant

AB 773881 1 773881 2.779 0.134014 6.15% Insignificant

AC 354 1 354 0.001 0.972416 0.00% Insignificant

BC 1070330 1 1070330 3.845 0.085552 8.51% Insignificant

ABC 9001 1 9001 0.032 0.861768 7.15.% Insignificant

Error 2227102 8 278388 -- -- 17.70.% --

101

Appendix B: DIC Qualitative Evaluations on Experimental Group 3

Table A.6 Comparison between DIC results and optical imaging for samples with 5 layers (group 3)

% Initiator Post-cured Optical imaging DIC first failure Observations

noFailure between layers 2-3, crack propagation

from voids on the same region.

no

noFailure between layers 2-3, high prescence

of voids in the corner region.

1

2

1

2

Failure between layers 1-2, crack propagation

from voids located in the same region.

noFailure between layers 1-2, high void content

in the same region.

Failure between layers 2-3. Large

void in the same region

2 yesFailure between layers 1-2, no significant

differences between layers.

1 yesFailure between layers 1-2, high void content

in the same region.

1 yesFailure between layers 1-2 regardless of

significant defect between layers 3-4.

2 yes

102

Table A.7 Comparison between DIC results and optical imaging for samples with 3 layers (group 3)

% Initiator Post-cured

Failure between layers 1-2. Cracks propagated

from voids in the same region.

Failure between layers 1-2. Simultaneous

resin rupture in lower resin rich area.

1 noFailure between layers 1-2. Regardless of void

content between layers 2-3.

DIC first failure Observations

1 noFailure between layers 1-2. Crack propagation

from void on the left side.

Optical imaging

2 no

2

1 yes

2 yesFailure between layers 1-2. Cracks propagated

from voids in the same region.

2 yesFailure between layers 1-2. Cracks propagated

from voids in the same region.

1 yesFailure between layers 1-2. Cracks propagated

from voids in the same region.

noFailure between layers 1-2. Not signifcant

void level observed on the corner area.

103

Appendix C: Experimental Raw Data

Table A.8 Raw data for experiment #1 (geometry effect)

Specimen Number

Angle Radius Number of

layers CBS

(N*mm/mm)

Void Content

(%)

Misalignment (Degrees)

Bridging (mm)

Surface defects (mm^2)

Thickness ratio

Formability

1 70 1/8" 3 layers 205.576 2.858 5.780 504.420 2701.344 1.022 0.335

2 70 1/8" 3 layers 188.728 2.082 3.670 576.050 1888.417 0.978 0.340

3 60 1/8" 3 layers 367.887 2.087 4.180 590.450 743.077 0.503 0.467

4 60 1/8" 3 layers 294.694 1.672 11.230 302.425 1606.887 0.982 0.410

5 50 1/8" 3 layers 208.610 3.034 4.440 820.870 12.987 0.780 1.000

6 50 1/8" 3 layers 334.163 0.757 5.960 777.665 0.000 0.713 0.755

7 40 1/8" 3 layers 321.654 2.565 1.280 979.280 76.206 0.744 0.984

8 40 1/8" 3 layers 227.493 3.185 4.950 1353.710 0.000 0.695 1.000

9 70 3/16" 3 layers 260.505 0.922 3.820 590.449 377.779 0.654 0.741

10 70 3/16" 3 layers 212.312 0.106 5.480 547.246 461.410 0.694 0.686

11 60 3/16" 3 layers 164.908 0.965 0.460 748.862 293.988 0.759 0.866

12 60 3/16" 3 layers 178.274 0.141 4.150 662.755 874.469 0.943 0.728

13 50 3/16" 3 layers 322.357 1.971 5.920 846.069 324.195 0.547 0.933

14 50 3/16" 3 layers 320.467 0.495 8.840 1036.886 24.494 0.594 0.912

15 40 3/16" 3 layers 246.194 0.930 5.300 1730.079 45.732 0.446 0.961

16 40 3/16" 3 layers 360.954 2.799 1.500 1627.335 83.617 0.467 1.000

17 70 1/4" 3 layers 305.932 1.066 7.930 620.690 1178.454 1.003 0.713

18 70 1/4" 3 layers 337.892 2.143 5.860 677.215 1793.753 0.946 0.680

19 60 1/4" 3 layers 239.417 0.743 9.300 734.885 0.000 0.713 0.930

20 60 1/4" 3 layers 246.429 1.139 6.870 849.905 0.000 0.736 0.962

21 50 1/4" 3 layers 302.512 1.159 5.770 633.655 757.787 0.918 0.904

22 50 1/4" 3 layers 236.579 1.678 1.660 980.605 113.231 0.721 0.979

23 40 1/4" 3 layers 203.634 3.119 8.030 1152.095 1130.369 0.787 1.000

24 40 1/4" 3 layers 247.018 1.783 5.610 518.820 1139.278 0.975 1.000

25 70 5/16" 3 layers 171.015 0.689 5.030 633.653 277.408 0.915 1.000

26 70 5/16" 3 layers 250.210 1.869 2.780 619.520 543.090 0.939 1.000

27 60 5/16" 3 layers 139.414 1.250 3.550 749.447 76.863 0.840 1.000

28 60 5/16" 3 layers 235.617 1.161 5.220 561.647 39.961 0.895 1.000

29 50 5/16" 3 layers 261.041 1.699 2.910 604.850 0.000 0.925 1.000

30 50 5/16" 3 layers 387.469 1.299 2.020 532.844 0.000 0.937 1.000

104

Table A.9 Raw data for experiment #1 (geometry effect) (continued)

Specimen Number

Angle Radius Number of

layers CBS

(N*mm/mm) Void Content

(%) Misalignment

(Degrees) Bridging

(mm)

Surface defects

(mm^2)

Thickness ratio

Formability

31 40 5/16" 3 layers 411.508 0.797 1.680 633.653 0.000 0.863 0.551

32 40 5/16" 3 layers 519.138 1.912 2.680 648.533 0.000 0.843 0.622

33 70 1/8" 5 layers 368.144 2.881 10.880 727.593 769.950 0.618 0.722

34 70 1/8" 5 layers 278.452 2.485 7.010 662.580 828.847 0.835 0.809

35 60 1/8" 5 layers 350.997 1.537 3.170 957.903 69.233 0.634 0.958

36 60 1/8" 5 layers 286.266 1.479 7.610 943.510 71.821 0.693 1.000

37 50 1/8" 5 layers 430.804 1.951 6.470 1015.285 0.767 0.742 0.659

38 50 1/8" 5 layers 434.114 2.246 4.870 1202.500 0.748 0.678 0.595

39 40 1/8" 5 layers 602.427 3.050 -2.380 2073.770 33.711 0.550 0.758

40 40 1/8" 5 layers 836.388 2.020 1.340 2138.580 0.000 0.900 0.776

41 70 3/16" 5 layers 397.716 1.263 6.390 705.797 496.242 0.644 0.735

42 70 3/16" 5 layers 678.961 0.446 7.140 777.665 92.395 0.606 0.903

43 60 3/16" 5 layers 693.142 2.140 3.120 1095.019 92.363 0.595 1.000

44 60 3/16" 5 layers 532.006 2.666 7.270 979.650 553.507 0.600 1.000

45 50 3/16" 5 layers 447.433 0.972 2.790 1117.337 18.988 0.635 0.782

46 50 3/16" 5 layers 464.146 1.881 4.760 864.072 8.713 0.572 0.742

47 40 3/16" 5 layers 500.778 2.771 2.020 1864.955 17.795 0.533 1.000

48 40 3/16" 5 layers 415.299 0.943 3.070 1310.509 0.000 0.593 1.000

49 70 1/4" 5 layers 439.730 1.016 4.850 613.030 2213.091 0.841 1.000

50 70 1/4" 5 layers 444.990 2.276 7.370 642.540 303.137 0.836 1.000

51 60 1/4" 5 layers 412.638 1.528 7.450 864.758 119.616 0.777 0.987

52 60 1/4" 5 layers 723.921 0.663 4.690 691.708 0.000 0.782 1.000

53 50 1/4" 5 layers 471.744 1.815 6.010 915.150 0.000 0.780 0.960

54 50 1/4" 5 layers 616.329 0.663 3.760 900.453 0.000 0.744 1.000

55 40 1/4" 5 layers 822.223 2.094 2.300 780.278 0.000 0.875 1.000

56 40 1/4" 5 layers 582.917 1.378 2.230 743.005 0.000 0.850 1.000

57 70 5/16" 5 layers 387.759 1.151 1.160 727.405 86.768 0.796 1.000

58 70 5/16" 5 layers 449.982 1.475 5.040 655.895 148.856 0.882 1.000

59 60 5/16" 5 layers 572.053 0.877 2.990 813.913 99.401 0.795 1.000

60 60 5/16" 5 layers 464.715 0.980 3.690 749.125 37.960 0.870 1.000

61 50 5/16" 5 layers 672.915 1.029 1.530 784.865 17.603 0.773 0.551

62 50 5/16" 5 layers 802.862 1.497 2.900 871.272 0.000 0.830 0.622

63 40 5/16" 5 layers 531.492 0.877 2.940 691.367 0.000 0.814 0.722

64 40 5/16" 5 layers 710.719 1.060 1.030 655.444 20.717 0.827 0.809

105

Table A.10 Experimental design alternatives for the MCDM (experiment #2)

Design Configurations

Specimen Number

Angle Radius Number of

layers CBS

(N*mm/mm) Void Content

(%) Misalignment

(Degrees) Bridging

(mm) surface defects

(mm^2) thickness ratio Formability

1 70 1/8" 3 layers 205.576 2.858 5.78 504.42 2701.344 1.022 0.335

2 70 1/8" 3 layers 188.728 2.082 3.67 576.05 1888.417 0.978 0.340

3 70 5/16" 3 layers 171.015 0.689 5.03 633.65 277.408 0.915 1.000

4 70 5/16" 3 layers 250.21 1.868 2.78 619.52 543.089 0.939 1.000

5 70 5/16" 5 layers 387.759 1.151 1.16 727.41 86.768 0.796 0.959

6 70 5/16" 5 layers 449.982 1.475 5.04 655.89 148.856 0.882 1.000

7 40 5/16" 5 layers 531.492 0.877 2.94 691.37 0 0.814 1.000

8 40 5/16" 5 layers 710.719 1.059 1.03 655.44 20.717 0.827 1.000

106

Table A.11 Raw data for experiment #2 (reinforcement orientation effect)

Input Parameters

Specimen Number

Angle Number

of layers

Reinforcement Orientation

CBS (N*mm/mm)

Void Content

(%)

surface defects

(mm^2)

Bridging (mm)

Thickness ratio Formability

1 70 3 0/90 205.576 4.858 2701.344 504.420 1 0.335

2 70 3 0/90 188.728 4.064 1888.417 576.050 0.978 0.340

3 70 3 -45/+45 168.034 2.483 0.000 1400.000 0.572 1.000

4 70 3 -45/+45 255.631 2.369 0.000 2857.000 0.592 0.837

5 70 5 0/90 368.144 6.640 769.950 727.590 0.617 0.391

6 70 5 0/90 278.452 7.229 828.847 662.580 0.835 0.418

7 70 5 -45/+45 869.556 7.350 0.000 1014.500 0.616 0.882

8 70 5 -45/+45 600.119 5.523 0.000 1293.314 0.639 1.000

9 40 3 0/90 175.961 2.473 76.206 979.280 0.744 0.984

10 40 3 0/90 174.909 6.467 0.000 1353.710 0.695 1.000

11 40 3 -45/+45 251.328 2.578 0.000 1957.415 0.484 0.861

12 40 3 -45/+45 192.688 5.963 0.000 3400.000 0.376 0.756

13 40 5 0/90 521.634 4.458 33.711 2073.770 0.549 0.958

14 40 5 0/90 715.579 3.593 0.000 2138.580 0.901 1.000

15 40 5 -45/+45 693.007 3.999 0.000 2610.120 0.403 0.957

16 40 5 -45/+45 664.149 4.516 0.000 2747.270 0.423 0.809

107

Table A.12 Raw data for experiment #3 (degree of cure effect)

Input Parameters

Specimen Number

Number of layers

Initiator %

Post-curing CBS

(N*mm/mm)

1 5 1 n 466.597

2 5 2 n 279.769

3 5 1 y 329.243

4 5 2 y 322.258

5 5 1 n 294.883

6 5 2 n 371.554

7 5 1 y 228.997

8 5 2 y 252.049

9 3 1 n 168.286

10 3 2 n 149.782

11 3 1 y 184.022

12 3 2 y 100.956

13 3 1 n 165.428

14 3 2 n 114.137

15 3 1 y 120.377

16 3 2 y 141.762