DEFORMATION CHARACTERISTICS OF KNITTED FABRIC COMPOSITES

Copyright Statement

The digital copy of this thesis is protected by the Copyright Act 1994 (New Zealand). This thesis may be consulted by you, provided you comply with the provisions of the Act and the following conditions of use:

• Any use you make of these documents or images must be for research or private study purposes only, and you may not make them available to any other person.

• Authors control the copyright of their thesis. You will recognise the author's right to be identified as the author of this thesis, and due acknowledgement will be made to the author where appropriate.

• You will obtain the author's permission before publishing any material from their thesis.

To request permissions please use the Feedback form on our webpage. http://researchspace.auckland.ac.nz/feedback

General copyright and disclaimer In addition to the above conditions, authors give their consent for the digital copy of their work to be used subject to the conditions specified on the Library Thesis Consent Form

DEFORMATION

CHARACTERISTICS OF KNITTED

FABRIC COMPOSITES

by

Miro Duhovic

A thesis submitted in partial fulfilment of the requirements for the degree of

Doctor of Philosophy in Engineering

Department of Mechanical Engineering

University of Auckland, New Zealand

December 2004

ii

Abstract

A relatively recent innovation in the field of thermoplastic composites is the

reinforcement with knitted structure that offers a number of potential advantages over

the more conventional straight-fibre reinforcements. They can be stretched in both

directions during forming, increasing the potential for forming complex and deeply-

curved components and have excellent impact, fracture toughness and energy

absorption properties. An understanding of some of the unique behaviour of these sheet

materials during forming and the practical viability of various forming processes are

crucial in assessing their applicability to given products and uses.

The first part of this study concentrates on identifying the types of micro-level

mechanisms that occur during the forming process of knitted fabric thermoplastic

composite sheets. It has been proposed that knitted fabrics and textile composite

materials, in general, follow a three-level hierarchy of deformation modes. The most

important of these levels are the micro-level fabric deformation modes, which have

been identified and specifically developed for study in this thesis.

In order to study these modes, the material has been subjected to a series of simple in-

plane, single and double curvature forming experiments. The main purpose of the in-

plane forming experiments was to record tensile data that would later be used to

establish the warp and weft direction modulus curves, important inputs for the

numerical simulations. Grid strain analysis (GSA) was also performed to investigate the

strains that occur during the forming of more complex shaped components and to verify

the numerical simulation results. The experiments highlighted that the behaviour of the

molten composite was very similar to that of the dry fabric at forming rates below

100mm/min and that the lubricating effects of chemical sizing on fibres in both the

composite and the fabric were present. It was also found that a more even surface strain

and thickness distribution could be attained using flexible tooling and higher forming

temperatures.

iii

High fibre volume fraction knitted fabric composites were produced from 1x1 rib fabric

made from commingled yarn at different pressures and temperatures. The material was

able to match the stiffness and strength of a commercially available woven fabric

product, Twintex®, for strains of up to 8%. An optimum forming pressure of 400kPa

was found to give the best consolidation without causing fibre damage due to excessive

compression.

During the forming experiments the importance of the reinforcing structure was realised

and provided the impetus for a detailed micro-level numerical investigation. The

simulation involved the production of a narrow strip of 1x1 rib fabric and subsequent

tensile testing. The model was verified in two ways: i) by comparing the physical and

numerical specimens geometrically and ii) by using force displacement curves

generated from the tensile tests on real specimens manufactured using the same knitting

machine parameters. A correlation factor was defined to allow the comparison of

numerical and physical specimens containing different numbers of fibres.

Comprehensive analysis of the model revealed bending as the most dominant micro-

level mechanism, followed by torsion, uniaxial tension and contact energy at low strain

levels and bending followed by uniaxial tension, contact energy and torsion at high

strain levels.

In addition, macro-level numerical modelling was performed using the data gathered

from molten tensile tests. A PAMFORM™ material model originally designed to model

the sheet behaviour of unidirectional and woven composites was used. Minimum

thickness strains showed close agreement. However, further development of the model

is required to allow more accurate predictions of the surface strains and stability at very

high strain values.

iv

Acknowledgments

First and foremost I would like to thank my family for their continued support and

encouragement throughout my studies, especially Mum and Dad whose dedication

towards providing the best opportunities for me and my two younger brothers has been

overwhelming.

I would like to thank my supervisors Professor Debes Bhattacharyya and Dr. Piaras

Kelly, especially Debes whose optimism, encouragement, support and patience over the

years has been hugely appreciated.

Thanks to CRC-ACS Australia, for providing me with many of the resources required

for this study, the knitted fabric material as well as the PAMFORM™ software. Their

support and hospitality during my visits has been exceptional, especially Michael

Bannister, whom I consider a co-supervisor, your encouragement and useful insights are

much appreciated. Thanks also to Rowan Paton and Bruce Cartwright whom I have had

many useful discussions.

To Pacific ESI, Damian McGuckin and Allen Chorr for their support with the

PAMFORM™ software. A very special thank you goes to Allen whose invaluable

support and lightning responses to my questions made working with the software a

pleasurable experience.

A very big thank you to the Strength of Material Laboratory technicians, Rex Halliwell,

Barry Fullerton, Ivan Bailey, Stephen Cawley and Jos Geurts, whom I have over the

years become good friends with. Special thanks goes to Ivan for his financial support,

your bus tickets were greatly appreciated mate and Barry for his masterful repair of my

glasses using a heavy duty gas torch.

To Luke Baxter, Andrew Douglas, Chris, Kelvin and Veena. Special thanks to Luke

whom I had the pleasure of working with personally and whose wealth of knowledge

and intellect never ceased to amaze me. The encouragement and motivational

discussions I had with you were greatly appreciated my friend.

v

Special thanks goes to Dr. Xun Xu whose almost therapeutic discussions regarding non-

thesis related engineering topic areas of interest, particularly CAD/CAM, kept me sane

throughout my studies. I sometimes wonder if I should have done my Ph.D in Computer

Aided Design and Manufacturing.

A big thank you to Mr. Roger Cobbley and the Auckland University of Technology

Fashion Design Department who kindly allowed the use of their knitting machinery.

Thank you to the Chemical and Materials Department and Steve Strover for his help in

taking some very nice images of my knitted fabric specimens.

Thanks to Fisher And Paykel for their financial support through the Maurice Paykel

Scholarship.

To my colleges, who made my stay in room 3.319 a pleasurable experience, as the only

composites person in the room at the beginning I was welcomed into the group which

contained postgrads of many disciplines, I thank you for your friendship which I hope to

maintain in the future, especially Yin Fai “Faister” Li, Derek “Big D” Philips and David

“Dave” Lee along with Rhys Star and Chris Philpot. Within the composites group,

special thanks to Yu “Roger” Dong, Mohamad “Zaki” Abdullah and Zhenbin “Jim” Cui

whom I have shared many fruitful discussions with over the years. To all the other

postgrads who have helped me in one way or another I thank you all.

vi

Table of Contents

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

Acknowledgments ...................................................................................................... iv

Table of Contents ....................................................................................................... vi

List of Figures............................................................................................................. xi

List of Tables ............................................................................................................ xvi

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

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

2.1 Introduction to Polymer Composites ............................................................ 5

2.2 Thermoplastic Composite Preform Materials ............................................. 6

2.2.1 Textile Preforms ....................................................................................... 8

2.2.1.1 Fibres .................................................................................................... 9

2.2.1.2 Yarns..................................................................................................... 9

2.2.1.3 Manufacturing Textile Preforms......................................................... 10

2.2.1.4 Manufacturing Textile Composite Preforms ...................................... 12

2.2.2 Fabric Structures & Terminology ........................................................... 12

2.2.2.1 Woven Fabrics .................................................................................... 13

2.2.2.2 Braided................................................................................................ 15

2.2.2.3 Knitted ................................................................................................ 16

2.2.3 The 1x1 Rib and Milano Rib Structures ................................................. 17

2.2.3.1 Why choose these knit structures? ..................................................... 18

2.3 Manufacturing Processes for Thermoplastic Textile Composite Preforms

........................................................................................................................ 18

2.4 Textile Composite Deformation Mechanisms ............................................ 20

2.4.1 Prepreg Flow Mechanisms...................................................................... 21

2.4.2 Macro-Level Fabric Deformation Modes ............................................... 23

2.4.3 Micro-Level Fabric Deformation Modes................................................ 23

2.4.4 Textile Fabric Force-Displacement Curve.............................................. 26

2.4.5 The Role of the Matrix............................................................................ 27

vii

2.5 Research Trends ........................................................................................... 27

2.6 Review of Modelling Approaches and Analysis Tools............................... 28

2.6.1 Kinematic................................................................................................ 28

2.6.1.1 Numerical Strain Mapping Technique (Grid Strain Analysis (GSA)) 28

2.6.1.2 Kinematic Strain Mapping Technique................................................ 31

2.6.2 Mechanics, Micromechanics and Homogenisation ................................ 33

2.6.2.1 The Development of Analytical Models............................................. 35

2.6.2.2 Numerical Methods............................................................................. 48

2.7 Review of Other Relevant Literature.......................................................... 52

2.7.1 A Note on the Particular Forming Method ............................................. 52

2.7.1.1 Forming of Commingled Thermoplastic Composites ........................ 53

2.7.2 Shear Deformation Testing of Fabrics.................................................... 54

Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheets ......... 55

3.1 Manufacture of Sheet and Raw Materials.................................................. 55

3.2 In-Plane Forming Behaviour ....................................................................... 56

3.2.1 Unidirectional Behaviour: Tensile Testing............................................. 56

3.2.2 Shear Behaviour: The Picture Frame Test .............................................. 59

3.2.2.1 Picture frame rig ................................................................................. 60

3.2.2.2 Test parameters ................................................................................... 60

3.2.2.3 Test results .......................................................................................... 62

3.2.2.4 Parametric study using spring and dashpot systems........................... 67

3.3 Single Curvature Forming ........................................................................... 72

3.3.1 Vee-Bending (Interply Shear and Stretch Behaviour) ............................ 72

3.3.2 Vee-Bending Equipment......................................................................... 73

3.3.3 Test Results............................................................................................. 75

3.4 Double Curvature Forming ......................................................................... 80

3.4.1 3D Forming: The Dome Forming Test ................................................... 80

3.4.2 The Dome Forming Rig.......................................................................... 82

3.4.3 Test Results............................................................................................. 83

3.4.3.1 Surface Strains and Thickness Contours ............................................ 83

3.4.3.2 Draw-in Behaviour ............................................................................. 91

3.4.3.3 Surface Finish ..................................................................................... 93

viii

3.5 Extreme Forming.......................................................................................... 94

3.5.1 Deep Drawing (The Cup Forming Test)................................................. 94

3.5.2 Extreme Component ............................................................................... 95

3.5.2.1 Surface Strains and Thickness Contours ............................................ 97

Chapter 4 High Fibre Volume Fraction Knitted Fabric Composites..................... 101

4.1 Background ................................................................................................. 101

4.2 Comparison of Common Materials........................................................... 102

4.2.1 Variations in RibTEX specimens ......................................................... 104

4.2.2 Test Results........................................................................................... 106

Chapter 5 Explicit Finite Element Modelling and Analysis................................... 112

5.1 PAMFORM™/PAMCRASH™ and Explicit Modelling......................... 112

5.2 PAMFORM™/PAMCRASH™ Basics ..................................................... 113

5.2.1 Preprocessing (PAMGENERIS™)....................................................... 114

5.2.2 Simulation (PAMFORM™/PAMCRASH™ Solver)........................... 114

5.2.3 Postprocessing (PAMVIEW™)............................................................ 114

5.3 Modelling the Manufacture of the Reinforcement Architecture............ 114

5.3.1 Model Set-up......................................................................................... 115

5.3.2 Model Input: Knitting Machine Parameters ......................................... 116

5.3.3 Model Input: Material Property Parameters ......................................... 118

5.3.4 Model Input: Non Physical Parameters ................................................ 119

5.3.5 Simulating the Mechanics of the Knitting Process ............................... 120

5.3.6 Model Verification.................................................................................... 123

5.3.6.1 Geometrical Comparisons................................................................. 123

5.3.6.2 Experimental vs. Numerical F-D Curves.......................................... 126

5.3.7 Investigating the Mechanisms in Detail................................................ 128

5.3.7.1 Energy Derivation............................................................................. 129

5.3.7.2 Simulation Results: Energy Contributions ....................................... 132

5.3.7.3 Beam Elements in PAMCRASH™ and Discussion of Results........ 141

5.4 Macro-Level Material Definition .............................................................. 144

5.4.1 Material Model ..................................................................................... 144

5.4.1.1 Existing Material Models.................................................................. 144

ix

5.4.1.2 Material Model Calibration .............................................................. 146

5.4.2 Experimental Comparisons................................................................... 151

5.4.2.1 Double Curvature Forming............................................................... 151

5.4.2.2 Cup Forming ..................................................................................... 158

5.4.2.3 Extreme Forming .............................................................................. 161

5.4.2.4 Summary........................................................................................... 163

Chapter 6 Conclusions and Recommendations for Further Work ........................ 165

6.1 Conclusions.................................................................................................. 165

6.1.1 Literature Survey .................................................................................. 166

6.1.2 Experimental Tensile, Picture Frame, Vee-bend, Dome, Cup and

Extreme Forming .................................................................................................. 168

6.1.3 High Fibre Volume Fraction Knitted Fabric Composites..................... 169

6.1.4 Micro-level Modelling of the Reinforcing Structure............................ 170

6.1.5 Macro-level Modelling ......................................................................... 171

6.1.6 Summary............................................................................................... 171

6.2 Recommendations for Further Research ................................................. 172

References................................................................................................................ 112

Glossary of Terms................................................................................................... 179

Appendices............................................................................................................... 181

Appendix A. Material Property Data Sheet for Cotene 9800 ....................................... 181

Appendix B. Force Displacement Curves for Knitted Fabric Composite .................... 182

Appendix C. Typical Knitted Fabric Tensile Test Data (Single Ply Dry Milano)

Specimen Size 150 X 50mm......................................................................................... 183

Appendix D. Full Scale Y-Axis Plot for Warp and Weft Modulus Curves.................. 184

Appendix E. Empty Frame Friction Data for All Temperatures and Rates.................. 185

Appendix F. Knitted Fabric at Room Temperature (20°C) All Rates .......................... 187

Appendix G. Knitted Fabric at Elevated Temperature (180°C) All Rates ................... 189

Appendix H. Knitted Fabric at Room and Elevated Temperature 10mm/min ............. 191

Appendix I. 4-Component Model Parameter Variation E1,E2,η1,η2............................. 192

Appendix J. Comparison of Pressure and Matched Die Formed Domes ..................... 194

x

Appendix K. Full Mesh Thickness Contour Plot for Dome 22 .................................... 195

Appendix L. Comparison of Experimental and Numerical F-D Curves ...................... 196

Appendix M. Comparison of All Experimental and Numerical F-D Curves ............... 197

Appendix N. Full Milano Rib Structure and Unit Cell................................................. 198

Appendix O. Rigid Matched Die Dome at High Material Viscosity............................ 199

Appendix P. Sample Input Code for Numerical Knitting Simulation .......................... 201

xi

List of Figures

Figure 1-1. Overview and comparison of some composite properties of the main

existing reinforcements 1 .................................................................................................. 2

Figure 2-1. A range of applications for textile reinforced thermoplastic materials 3 ....... 5

Figure 2-2. Comparison of viscosities for (a) Polyester(thermoset) and (b)

Polypropylene(thermoplastic) 5 6 ...................................................................................... 6

Figure 2-3. A range of currently available thermoplastic composite preform/prepreg

materials............................................................................................................................ 7

Figure 2-4. Methods for combining thermoplastic matrices with reinforcement fibres ... 8

Figure 2-5. A comparison of (a) continuous glass fibre and (b) typical discontinuous

woollen yarn structures 2................................................................................................. 10

Figure 2-6. Forming of 2D and 3D commingled knitted fabric thermoplastic composite

preforms .......................................................................................................................... 11

Figure 2-7. 3D model of a plain woven fabric 15 ............................................................ 13

Figure 2-8. Weaving procedure 3 .................................................................................... 14

Figure 2-9. Woven fabric terminology 8 ......................................................................... 14

Figure 2-10. 3D model for balanced 2/2 twill fabric 15 .................................................. 15

Figure 2-11. 3D model of a flat braided fabric made from five yarns 15 ........................ 15

Figure 2-12. Braiding a shaft with varying cross section 16............................................ 16

Figure 2-13. Schematic of knitted fabrics 18 (a) Weft knit (b) Warp knit..................... 17

Figure 2-14. Schematic of (a) 1× 1 Rib and (b) Milano Rib structures.......................... 17

Figure 2-15. 3D schematic of the 1×1 Rib structure 20 ................................................... 18

Figure 2-16. Manufacturing routes for composite materials 21....................................... 19

Figure 2-17. Hierarchy of deformation modes in textile composite materials ............... 21

Figure 2-18. Hierarchy of top-level (or prepreg) deformation modes ............................ 22

Figure 2-19. Macro-level fabric deformation modes...................................................... 23

Figure 2-20. Micro-level fabric deformation modes ...................................................... 24

Figure 2-21. Textile fabric force displacement curve..................................................... 26

Figure 2-22. Deformation of a triangle element described by three adjacent grid points

........................................................................................................................................ 29

Figure 2-23. 1-D Cubic Hermite basis function ............................................................. 30

Figure 2-24. The Bi-Cubic Hermite element .................................................................. 30

xii

Figure 2-25. Micromechanics model of plain weft knit by Takano et al 38 .................... 34

Figure 2-26. Peirce’s model of a plain woven fabric unit cell 11 .................................... 36

Figure 2-27. Continuous multifilament yarn cross sections 11........................................ 38

Figure 2-28. The Elastica as proposed by Olofson 11 ..................................................... 38

Figure 2-29. Considering an incremental arc length on the elastica............................... 39

Figure 2-30. Olofson’s kinetic modelling approach for woven fabric implemented...... 41

Figure 2-31. Models of the plain weave (a) and plain knit (b) structures 55 ................... 45

Figure 2-32. Establishing forces due to yarn bending 56................................................. 47

Figure 2-33. Textile composite modelling strategy by Lomov et al 57 ........................... 49

Figure 2-34. Finite element model for braiding by Pickett 59 ......................................... 50

Figure 2-35. Bar element braiding models generated by PAM SOLID™ 58.................. 51

Figure 2-36. (a) Constraining the yarn to the solid and (b) Comparison of yarn force for

solid and bar models, (graph shows force variation from upper to lower faces) 59 ........ 51

Figure 2-37. Mechanical property variation of glass fibre polyethylene terephthalate

with various stretch ratios and amorphous or semicrystalline matrices 28...................... 52

Figure 2-38. Schematic of migration pattern in commingled yarn 60 ............................. 53

Figure 3-1. Warp and weft true stress-strain curves for molten knitted composite (180°C

100mm/min).................................................................................................................... 57

Figure 3-2. Close up of warp and weft modulus curves for knitted fabric composite

(180°C 100mm/min) ....................................................................................................... 58

Figure 3-3. Picture frame shear test experimental setup................................................. 59

Figure 3-4. The picture frame mechanism...................................................................... 60

Figure 3-5. Fabric orientations (a) Force applied at 45° to warp and weft (b) Force

applied parallel to warp and weft.................................................................................... 61

Figure 3-6. Comparison between fabric reinforcement orientations (a) and (b) ............ 62

Figure 3-7. Knitted fabric at room temperature (20°C) 10mm/min ............................... 62

Figure 3-8. Knitted fabric at elevated temperature (180°C) 10mm/min......................... 63

Figure 3-9. Comparison of knitted fabric at all temperatures and strain rates................ 64

Figure 3-10. Knitted fabric composite at elevated temperature (180°C) all rates .......... 65



Figure 3-13. Four-component spring and damper model ............................................... 68

Figure 3-14. Fitting curves derived from the 4-componet model................................... 69

xiii

Figure 3-15. Ideal molten knitted fabric composite spring and damper model .............. 71

Figure 3-16. Schematic of vee-bending rig (a) Apparatus prior to forming (b) Post

forming............................................................................................................................ 74

Figure 3-17. Post formed vee-bend specimen showing “edge fraying” ......................... 75

Figure 3-18. Clamping force versus strain (for all specimens)....................................... 77

Figure 3-19. Clamping force versus springforward for all specimens ........................... 78

Figure 3-20. (a) Molten and (b) softened vee bending specimens.................................. 79

Figure 3-21. Springforward versus forming temperature with clamping force as marker

identifier.......................................................................................................................... 79

Figure 3-22. Dome forming experimental set-up ........................................................... 82

Figure 3-23. Close up of (a) Pressure forming and (b) Matched die forming equipment

........................................................................................................................................ 83

Figure 3-24. Dome 12..................................................................................................... 84

Figure 3-25. Dome 13..................................................................................................... 85

Figure 3-26. Dome 15..................................................................................................... 86

Figure 3-27. Dome 16..................................................................................................... 87

Figure 3-28. Dome 18..................................................................................................... 88

Figure 3-29. Dome 22..................................................................................................... 89

Figure 3-30. Dome 27..................................................................................................... 90

Figure 3-31. Comparison of draw-in behaviour ............................................................. 92

Figure 3-32. Comparison of surface finish in (a) molten and (b) softened domes ......... 93

Figure 3-33. Comparison of domes formed from rubber and metal male stamping dies93

Figure 3-34. Tearing in cup wall ................................................................................... 95

Figure 3-35. (a) Deformed grid points of the fairing and (b) Plan view showing draw-in

of flange .......................................................................................................................... 96

Figure 3-36. (a) Progressive development of rubber punch and (b) surface finish quality

........................................................................................................................................ 97

Figure 3-37. Extreme component overall surface strains ............................................... 98

Figure 3-38. Extreme component highly detailed region ............................................... 99

Figure 3-39. Percentage thickness strains in extreme component ............................... 100

Figure 4-1. RibTEX commingled preform fabric and consolidated sheet.................... 102

Figure 4-2. Calculated fibre volume and mass fractions .............................................. 105

Figure 4-3. Stress strain curves for all compared specimens........................................ 106

Figure 4-4. Specific stress strain curves for all compared specimens .......................... 107

xiv

Figure 4-5. Warp direction stress strain curves for all RibTex specimens (300kPa) ... 108



Figure 4-8. Warp direction stress strain curves for all closed edge RibTex specimens

(400kPa)........................................................................................................................ 110

Figure 4-9. Stress strain curves for weft and specially formed warp RibTex specimens

(400kPa)........................................................................................................................ 110

Figure 4-10. Weft direction stress strain curves for all weft insert RibTex specimens

(400kPa)........................................................................................................................ 111

Figure 5-1. Stages and file relationships of a PAMFORM™/PAMCRASH™ analysis

...................................................................................................................................... 113

Figure 5-2. Real five needle knitting of 1x1 rib weft knitted fabric ............................. 116

Figure 5-3. Initial state of knitting simulation .............................................................. 121

Figure 5-4. The six stages of the knitting simulation ................................................... 122

Figure 5-5. Geometrical comparisons of complex 1x1 rib formation .......................... 123

Figure 5-6. Comparison of loop geometry for (a) Numerical and (b) Physical specimens

...................................................................................................................................... 124

Figure 5-7. Test set-up for 1x1 rib strip tensile test...................................................... 126

Figure 5-8. Average experimental F-D curve for 1x1 rib specimen............................. 127

Figure 5-9. Comparison of experimental and numerical F-D curves ........................... 128

Figure 5-10. Individual filament readings for axial elongation energy ........................ 132

Figure 5-11. Total yarn axial elongation energy........................................................... 133

Figure 5-12. Individual filament readings for s-axis bending moment energy ............ 135

Figure 5-13. Total yarn s-axis bending moment energy............................................... 135

Figure 5-14. Individual filament readings for t-axis bending moment energy............. 136

Figure 5-15. Total yarn t-axis bending moment energy ............................................... 136

Figure 5-16. Individual filament readings for torsional energy.................................... 137

Figure 5-17. Total yarn torsional energy ...................................................................... 138

Figure 5-18. Total yarn contact energy......................................................................... 139

Figure 5-19. Comparison of yarn deformation energy components............................. 140

Figure 5-20. The co-rotational technique used in PAMCRASH™ for beam elements 142

Figure 5-21. Definition of material Type 140 in PAMFORM™ 67.............................. 145

Figure 5-22. Comparison between PAMFORM™ warp direction tensile tests and

experimental results, viscosity parameter η variation .................................................. 148

xv


experimental results, shear modulus parameter G variation......................................... 149


experimental results, parent sheet and displacement rate variation.............................. 150

Figure 5-25. Calibrated warp and weft modulus curve points...................................... 150

Figure 5-26. Rigid matched die dome forming of molten knitted fabric composite η =

0.001MPa.s ................................................................................................................... 152

Figure 5-27. Flexible matched die dome forming of molten knitted fabric composite η =

0.001MPa.s ................................................................................................................... 154


0.005MPa.s ................................................................................................................... 156


0.010MPa.s ................................................................................................................... 157

Figure 5-30. Fully clamped cup forming to strain failure using low tool friction

coefficient μ = 0.05....................................................................................................... 159

Figure 5-31. Fully clamped cup forming to strain failure using high tool friction

coefficient μ = 0.5......................................................................................................... 161

Figure 5-32. Wing mirror component forming using a clamping force of 100N ......... 163

xvi

List of Tables

Table 2-1. Fibre materials for textile composites 10.......................................................... 9

Table 2-2. Manufacturing options for thermoplastic textile composite preforms .......... 20

Table 3-1. Specifications for the types of materials used ............................................... 55

Table 3-2. Summary of data collected from shear deformation experiments................. 61

Table 3-3. Vee-bending test parameters ......................................................................... 73

Table 3-4. Vee-bending results table .............................................................................. 76

Table 3-5. Dome forming test parameters ...................................................................... 81

Table 3-6. Cup forming .................................................................................................. 94

Table 4-1. List of materials used in the mechanical property comparison of high fibre

volume fraction knitted fabric composites.................................................................... 103

Table 4-2. Theoretical and average measured density for all test specimens............... 105

Table 5-1. Summary of important knitting machine parameters .................................. 116

Table 5-2. Yarn material properties.............................................................................. 119

Table 5-3. Important non-physical parameters ............................................................ 119

Table 5-4. List of material models available in PAMFORM™ software..................... 145

Table 5-5. Material Type 140 physical input parameters ............................................. 147

Table 5-6. Material Type 140 numerical input parameters .......................................... 147

Table 5-7. Comparison data for experimental and numerical forming experiments .... 164

1

Chapter 1 Introduction

Over the past decade research regarding the understanding of the forming characteristics

of fibre reinforced thermoplastic composite materials has steadily progressed. New

polymer materials are constantly being developed to provide more favourable forming

as well as final mechanical property characteristics. On the other hand fibre

reinforcements seem to have followed a similar trend ranging from the development of

simple and random to highly structured configurations. This trend has lead to research

in the area called textile composite materials.

Textile Composite Materials (TCMs) are a form of fibre reinforced polymer where the

reinforcing fibres are structured in such a way as to provide favourable forming

characteristics while preserving the fibre continuity needed for final component

strength. TCMs have been an important development as far as composite preform

materials are concerned since they allow for much easier handling of raw materials.

However, the biggest potential of these materials must lie in the fact that the technology

required to produce the complicated reinforcing structures economically, exists and has

existed for a number of years in the apparel industry. The challenge now is being able to

combine this technology reliably and economically with composites processing and

develop a scientific understanding of these materials that will allow reasonable

predictions of both the forming behaviour and end product’s overall mechanical

property characteristics.

One of the current problems associated with Fibre Reinforced Plastics (FRPs) seems to

be the trade off between final component strength and processability. FRPs for

structural applications usually consist of long continuous inextensible reinforcing fibres

in the loading directions. This is very favourable for the final component but poses

significant problems during the forming stages in many manufacturing processes where

virtually inextensible fibres restrict the movements required to form the part. TCMs


2

partially relieve this restriction by allowing for fibre movement through certain modes

of compliance present in the geometric structure of the textile reinforcement.

The main focus of this research is the study of these deformation modes during the

forming process through practical and numerical experimentation.

Although this study will mainly be concerned with processability; stiffness, strength,

interlaminar fracture toughness and material cost also play an integral role in

determining the relative advantages and disadvantages of certain FRPs. Figure 1-1

presents a general comparison of these properties for the main existing types of FRP

materials available today 1.

Figure 1-1. Overview and comparison of some composite properties of the main existing reinforcements 1

Positioned roughly in the centre of Figure 1-1 knitted fabrics generally posses a stiffness

and strength that is lower than woven or braided fabrics but higher than continuous or

short fibre mats. Their geometry, which allows a considerable amount of intermingling,

results in an interlaminar fracture toughness far superior to that of any two-dimensional

weave or braid. As far as processability of complex shapes is concerned this is where

knitted fabrics show their biggest advantage, allowing large strains and shear angles

without the occurrence of wrinkling. Although continuous and short fibre mat may seem

to have an upper hand with regards to processability, their composites are often

susceptible to tearing resulting in weak spots and inhomogeneous fibre content

something, which does not arise so easily in knitted fabrics. Degree of isotropy is

low

high

low

low

high

low

high

high

?

Material + production

cost

Stiffness & strength

Processabilityof complex

shapes

Interlaminar fracture

toughness

UD laminates

Non crimp fabrics

Woven &braided

fabrics Knitted fabrics

Continuous fibre mats

Short fibres

Degree of isotropy

low high


3

another favourable characteristic 1, a material property only bettered by continuous and

short fibre mats.

Finally, given that knitted fabric composites are still in the developmental stage, raw

material and subsequent composite production cost is an unknown factor for now.

However, industrial knitting is a technologically advanced production technique which

has gone through many years of refinement in the garment industry making the initial

cost image for knitted fabric composites seem very favourable.

It is not suggested that knitted fabric composites are the single solution for FRPs but

that they fit neatly into the broad family of FRP composite materials. Certainly for

applications requiring moderate stiffness and strength and excellent processability they

will be the obvious choice.

The following Chapters of this thesis examine the deformation mechanisms in knitted

fabric thermoplastic composite forming processes both experimentally and numerically.

The study concentrates on two particular knit structures both produced from continuous

filament E-glass fibre yarn embedded in a polypropylene matrix. A gross understanding

of the materials forming behaviour is gained through a series of experiments and

resulting grid strain analyses, while a more detailed examination is performed

numerically on a cellular level.

In Chapter 2, an overview of fabric structures, their associated terminology along with

an overview of fibre reinforced thermoplastics including their textile preforms and

manufacturing processes is presented. Particular attention is focussed on textile

composite deformation mechanisms and explaining the hierarchical deformation modes

that these materials posses. Finally, a review of the literature covering the modelling

approaches taken, from pure kinematics, to analytical and numerical mechanics for

predicting the forming behaviour of these materials is given.

Chapter 3 explores the deformation characteristics experimentally through a series of in-

plane, single and double curvature forming experiments. The experiments also consider

two different types of manufacturing processes for the material. The methodology


4

behind the experiments is to subject the material to individual isolated macro level

deformation modes and analyse its response to these modes separately.

Chapter 4 presents a short study on the solid-state mechanical properties of high fibre

volume fraction knitted fabric composites. Knitted fabrics are well known for their

forming flexibility but not so good stiffness and strength. This chapter compares the

stiffness and strength of high quality knitted fabric composite panels, with competing

materials.

Chapter 5 considers micro and macro level numerical simulations of the material for the

purposes of analysis and material behaviour prediction. The Chapter explains the

development of a unit cell model by actually simulating the mechanics of the knitting

process. The validity of the simulation is verified by comparing the geometry and

mechanical response of the model with knit samples manufactured using the same

machine parameters. Once verified the mechanics of the unit cell is investigated in

detail with the intention of identifying and ranking the importance of the micro level

deformation mechanisms.

Macro level material modelling is also investigated. The results of simulations using

existing material models originally designed for continuous and woven fabric

composites are presented and compared with corresponding characterisation

experiments along with suggestions of a user defined model based on the results of the

micro structural analysis.

The development of material models for complex structures such as knitted fabrics and

their composites is essential for the efficient use of these materials. If developed

correctly, a single knitting simulation could be capable of producing a number of

different knit structures by changing a few boundary conditions, just as real knitting

machinery can and their unit cells could serve as a database for a variety of the

material’s physical properties.

5

Chapter 2 Literature Review

2.1 Introduction to Polymer Composites

A composite can be defined as a combination of two dissimilar materials whose

combined properties outperform the sum of the properties from the individual parts.

Considering the synergistic effects that are achievable by some of today’s composite

materials it is not uncommon to hear expressions amongst composite circles like 1 + 1 =

11. While such expressions may disgruntle mathematicians it remains one of the

principal advantages pertaining to the use of composite materials today. It is no mystery

that engineers have long used nature as a source of inspiration and examples of

composite materials are to be found in mammals, plants as well as geological

formations 2. Wood, a natural composite containing cellulose fibres and lignin (a natural

polymer) is one of the most common materials used in the construction industry today.

Even man-made composites have existed for many years with the use of clay plus grass

to form bricks and other building materials as the classic example 2. However, it wasn’t

until the 1950’s that a feasible synthetic composite, fibre reinforced plastic (FRP),

emerged, which was able to replace wood and metal in applications 2.

As research progressed, manufacturing processes and materials were developed to meet

the demands of high tech applications such as the aircraft/aerospace and defence

industries. The opportunity was there to use FRPs for commercial applications but the

cost of producing them was still too high. Continued progress in manufacturing

techniques over the last ten years, including the evolution of more structured types of

Figure 2-1. A range of applications for textile reinforced thermoplastic materials 3


6

fibre reinforcements, has allowed FRPs to become prime candidates for consumer

products such as sports equipment, appliances, electronic and corrosion resistant

equipment and most of all transportation 3, 4. Figure 2-1 shows the wide range of current

applications for reinforced thermoplastic composite materials, in particular, those that

benefit from textile reinforcements.

2.2 Thermoplastic Composite Preform Materials

Perhaps the biggest factor contributing to the increasing use of fibre-reinforced plastics

(FRPs) has been the development of their composite preforms. This is true for

thermoplastic composites in particular, where advantages such as safe processing

environment and potential for high volume production have been offset by relatively

difficult-to-achieve impregnation quality. Composite preforms eliminate some of the

processing difficulties with regards to fibre impregnation quality and allow for quicker

and more manageable processing at the end user level. For typical fibre volume

fractions of around 0.4 - 0.6, the level of impregnation difficulty can be compared to the

task of spreading one gram of butter evenly over 36 slices of bread, on both sides. For

thermoplastic composites with their high melt viscosities, in the range of 100 – 10000

Nsm-2, compared to 0.1 to 10Nsm-2 for thermosetting composites, ensuring good

impregnation quality becomes an even greater challenge (see Figure 2-2).

Figure 2-2. Comparison of viscosities for (a) Polyester(thermoset) and (b) Polypropylene(thermoplastic) 5 6

Examples of early commercially available thermoplastic preform materials consist of

unidirectional E-glass fibres impregnated in a polypropylene matrix or commingled E-

glass and polypropylene yarn woven into a mat. The latter classified as a textile preform

Shear rate (s-1)

(a)

Visc

osity

(Pa

.s)

Shear rate (s-1)

(b)

Visc

osity

(Pa

.s)


7

material, which have become more and more popular in recent years. These textile

structures differ from ordinary FRPs by structuring fibres into yarns and weaving,

braiding, knitting or intertwining the yarn into the reinforcement for the composite

material. The geometric configurations of the yarn play an important role in determining

the desired mechanical properties of the final component and also make the fibres much

easier to handle. Figure 2-3 shows a selection of currently available thermoplastic

composite preform and prepreg materials, two of which use textile composite

technology, Twintex®, which can be classified as a textile preform, since no bonding

between the constituent materials has taken place and Towflex®, a textile prepreg that

uses powder coating technology. Plytron® can also be classified as a composite prepreg

(preimpregnated material) but is not considered a textile.

Figure 2-3. A range of currently available thermoplastic composite preform/prepreg materials

The development of textile preforms and prepregs, knitted structures in particular, have

attracted much interest mainly for two reasons. 1. Their ability to preserve fibre

continuity for strength while allowing for increased forming flexibility and 2. The fact

that processing techniques known for many years from the textile industry can be

readily applied in high volume production and low cost. Preforms such as bidirectional

woven mats provide a low degree of forming flexibility but high final strength. Staple or

chopped fibres provide a forming flexibility close to that of the thermoplastic alone,

however the final strength of the component is compromised. Knitted fabric preforms

attempt to bridge the gap between forming flexibility and strength while offering a

Twintex ® 2/2 Twill Weave

Saint-Gobain Vetrotex’s

Thermoplastic Preform

(France)

Towflex ® 2/2 Twill Weave

Hexcel Composite’s

Thermoplastic Prepreg

(US)

Plytron ® Unidirectional

Thermoplastic Prepreg

Manufactured by Borealis

(Europe)


8

greater in-plane shear resistance than either of the aforementioned 2. One main

disadvantage associated with textile preforms is that they commonly rely on

impregnation subsequent to shaping and depend on the component manufacturer rather

than the specialist manufacturer to ensure impregnation quality.

2.2.1 Textile Preforms

The specific assemblage or arrangement of continuous (or discontinuous) fibrous

materials into a form, which becomes the reinforcement for a composite is known as the

textile composite preform 2. Of course, there literally exist an infinite number of

configurations for these preforms ranging from simple to complex 3D geometric fibre

orientations. The architecture used is in many cases tailored to best fit the application,

which explains why many of these materials are not produced commercially. For knitted

structures, it is common practice to obtain the preform material in a more unrefined

form such as continuous filament yarn or roving, and to produce the fabric using

industrial knitting machines obtained from specialist textile manufacturers. Twintex®-

roving manufactured by Vetrotex of France is one example of a commonly available

roving. It consists of commingled continuous thermoplastic and glass fibre yarns. Other

techniques used to combine matrix and reinforcement include film stacking, powder

coating reinforcement yarns, (TOWFLEX®) and commingling continuous glass fibre

and thermoplastic staple yarns, air-textured or friction spun for cohesiveness, (see

Figure 2-4(b)) 7. To make up the required amount of matrix and to further ensure good

wetting between matrix and reinforcement, rovings can also be co-knitted with

conventional thermoplastic yarn 7. Although the focus here is on suitable thermoplastic

impregnation techniques, moulding using thermosetting matrices is far more common

and established in industry. These are processes such as resin transfer moulding (RTM),

structural reaction injection moulding (SRIM) and resin film infusion (RFI) 8.

Figure 2-4. Methods for combining thermoplastic matrices with reinforcement fibres (a) Film stacking (b) Commingling (c) Powder coating

Polymer film Textile

reinforcement Polymer fibre Reinforcing

fibre Reinforcing

fibre

Polymer powder


9

2.2.1.1 Fibres

A fibre or filament can be defined as the smallest unit of a fibrous material. They can be

produced by drawing materials from a molten bath and can have diameters ranging from

1 – 25 μm 9. The length of a fibre or filament is usually no less than 100 times its

diameter 9. To qualify for primary and secondary load bearing applications textile

preforms and prepregs must be made from high modulus fibres 2. Amongst the common

types of commercially available fibres used are glass, carbon, aramid and steel (see

Table 2-1). With each type comes a different set of favourable and unfavourable

properties. However availability and cost are usually the determining factors for their

use. At around $2.00US per kg and considering their relatively good performance

compared to other materials, E-glass fibres remain one of the most extensively used

reinforcement fibres in industry today. For comparative purposes the cost of Twintex®

roving which is made from continuous E-glass and Polypropylene filaments is also

given.

Table 2-1. Fibre materials for textile composites 10

Material Density Failure Stress Failure Strain

(%) Young’s Modulus Fibre Cost

(g/cm3) (MPa) (GPa) (US$/kg)

E-Glass 2.58 2400-3450 3.5-4.8 73 2.00

S-Glass 2.48 3100-4590 4.0-5.4 88 11.00

Aramid

(Kevlar 49) 1.45 3500-3600 2.5-2.7 133 24.00

High

Strength

Carbon

1.76-1.80 3.30-6.37 1.5-2.2 230-300 16-24

High

Modulus

Carbon

1.83-1.90 2.60- 4.70 0.6-1.4 345-590 ~96

Steel 7.9 0.275Y/0.430UTS 20 205 0.64

Twintex®

Vf 60%/75% - - - - 2.93/3.04

Note: costs are approximate average values collected from various sources on the internet as well as direct communications with suppliers

2.2.1.2 Yarns

As mentioned before a textile composite preform comes in many different forms. The

yarn itself may be an assemblage of chopped or continuous fibres plied together a


10

number of times. The most important form of yarn for use in textile structural

composites is multi-filament continuous yarn. Although there is no strict definition, a

yarn normally contains around 1000 filaments whereas larger assemblies are commonly

referred to in the glass fibre industry as rovings or tows 2. The tensile property of this

parallel assembly of monofilament fibres is simply the sum of the individual fibre

tensile properties. However, because parallel assemblies have no lateral cohesion

manufacturers will usually add a degree of twist to hold the yarn together. A typical

amount of twist is about 1 turn/cm 2. It is also common to pass the yarn through an air

jet which gives a certain degree of cohesion and is sometimes referred to as “false

braiding” 2. These processes have little effect regarding the improvement of yarn tensile

properties, and in fact, reduce tensile strength. The main role of twist is to provide a

satisfactory resistance to abrasion, fatigue and produce a coherent structure that cannot

be easily damaged by lateral stresses; in other words knitting, weaving or braiding

processes 11. It is also interesting to note, (for modelling purposes later) the influence of

twist on the fabrics flexural rigidity. A yarn of 100 filaments has only 100times the

flexural rigidity of a single filament whereas if the filaments were cemented together to

form a rod its bending stiffness would increase by 10,000 times (Bending stiffness ∝ I) 11. In woven fabric containing spun yarn it has been found that the bending stiffness of

the fabric is of the same order of magnitude as the total bending stiffness of all the

individual filaments in a given cross section. That is, twist produces its favourable

effects without significantly increasing bending stiffness 11.

2.2.1.3 Manufacturing Textile Preforms

Producing a knitted fabric composite preform using conventional knitting machinery is

indeed feasible, however slight modifications need to be made to account for fibre

inextensibility and increased yarn stiffness. The difference between a continuous-glass

and wool fibre yarn can be clearly distinguished by comparing the structures shown in

Figure 2-5.

Figure 2-5. A comparison of (a) continuous glass fibre and (b) typical discontinuous woollen yarn structures 2

(a) (b)


11

Most natural textile fibres exhibit viscoelastic behaviour and inter-fibre friction much

different to commonly used reinforcement fibres 12. In fact, many of the reinforcing

fibres used such as glass and carbon exhibit strong linear elastic behaviour. The

knittability of high performance yarns has been shown to be dependent on the frictional

properties, pliability (bending stiffness) and strength of the yarn 12. Because glass fibres

are very brittle in nature and have a high stiffness and coefficient of friction, they

require a low input tension and minimal metal surface contact for knitting 12. Knitting

speeds also need to be slower than usual to avoid needle damage. All these requirements

can be met using automated or manually operated knitting machinery.

For general usage a textile preform is usually manufactured in the form of a mat, relying

on the formability properties of the flat preform to produce complex 3D components.

Another option, referred to as integral knitting, is where the near net shape of the final

component is manufactured on the knitting machine and subsequently used as the

preform for the component to be produced, the added advantages being low material

wastage and labour costs 12. With next generation knitting machinery such as Shima-

Seiki’s “wholegarment” flat bed knitting machines, it is possible to produce gaugeless

(loops of any size) and seamless three-dimensional preforms directly by specifying the

geometry using KnitCAD data. The process is illustrated in Figure 2-6.

Figure 2-6. Forming of 2D and 3D commingled knitted fabric thermoplastic composite preforms

3D preform no stretching

2D preform stretching,

clamped edges


12

Depending on the type of knitted preform produced, (2D or 3D) the matched die

forming process will consist of either compression only, or in the case of the two

dimensional preform, both stretching and compression.

2.2.1.4 Manufacturing Textile Composite Preforms

The manufacture of thermoplastic textile composite preforms will usually involve one

of the processes discussed briefly at the beginning of Section 2.2.1. Detailed

information on how some of these processing techniques, such as commingling, are

achieved is difficult to obtain as the technology behind them is well protected. In one of

their technical papers 13, Vetrotex comments that it is not the commingling of matrix and

reinforcement fibres that defines Twintex® as an original product, but the actual

process by which this is achieved. According to Vetrotex, the commingling process

occurs during glass fiberizing ensuring a homogeneous mix of matrix and reinforcing

fibres to the desired proportions. The manufacturing advantages of the product are that

the distance the thermoplastic polymer must move to surround the glass fibres never

exceeds 100microns 13. The commingled fibre yarn is also more pliable than standard E-

glass fibre yarn and therefore presents no additional problems with weaving, knitting or

braiding machinery. However, even though many 2D/3D shapes can be produced using

the weaving, knitting or braiding process, this does not mean commingled preforms are

always suitable. Tong, Mouritz and Bannister 14 raise an important issue regarding 3D

preforms manufactured from commingled yarn. To achieve a suitable volume fraction

and ensure that the resin completely fills the fibre reinforcement the preform must be

dramatically reduced in thickness during consolidation. For 3D preforms a large

reduction in thickness may cause severe distortions in the fibre architecture and possible

fibre damage, therefore limiting this type of material to simple 3D shell structures.

2.2.2 Fabric Structures & Terminology

As in any field of study a body of language usually evolves which helps describe and

characterise the various phenomena occurring in that area of research. However, much

of the terminology associated with textile composites has been borrowed directly from

the textile industry. The following sections briefly discuss the three main fabric

categories, woven, knitted and braided fabrics to help clarify some of the terminology

frequently encountered throughout this thesis. For quick reference the reader can refer

to the glossary.


13

2.2.2.1 Woven Fabrics

A textile composite preform can come in many different structural configurations but

can basically be categorised as woven, knitted or braided fabric. Non-crimp and non-

woven fabrics including stitch bonded yarn assemblies or even chopped fibre mat where

fabric integrity is achieved via bonds between fibres are another fabric category, which

will not be discussed here. Textile composite preforms can be produced in the form of

2D flexible sheets or even as three-dimensional solid shapes. The first textile preform

introduced commercially was the plain 2D woven fabric. A 3D model of the 2D woven

fabric configuration is shown in Figure 2-7.

Figure 2-7. 3D model of a plain woven fabric 15

The fabric is produced by running a continuous weft yarn, across the width of the fabric,

over and under the warp yarns running along the length of the fabric as shown in Figure

2-8. The resulting fabric has a modulus lower than the fibre materials due to the

existence of crimp. Crimp is the existence of bends in the woven structure. A fabric

containing a high degree of fibre crimp is one that has a very high frequency of yarn

interlacing. Plain weave contains the highest level of fibre crimp giving it the best

flexibility of any woven fabric. However the greater the crimp the lower the fabric

strength compared to the yarn. This is sometimes referred to as the fibre to composite

translational strength.


14

Figure 2-8. Weaving procedure 3 Twill or Satin weaves, shown diagrammatically in Figure 2-9 have a lower preform

structural integrity than plain weaves. However, because they don’t have a great deal of

interlacing they are capable of higher fibre volume fractions and fibre to fabric

translational strengths. This means a stronger composite component in the fibre

directions. In a twill weave the weft yarn passes over two and under one (or two) warp

yarns with a single yarn progression to the left or right creating a characteristic diagonal

pattern. A satin weave has the weft yarn passing over n and under one warp yarn where

n is any number greater than 2. Basket weaves are another type of configuration where x

warp yarns interlace with x weft yarns where x is a number greater than two.

Figure 2-9. Woven fabric terminology 8

A weave is termed balanced if it has the same properties and geometric dimensions in

both the warp and weft directions. For example, the plain weave shown in Figure 2-9 (a)

is balanced while the schematic diagrams for the twill and satin weaves shown are not.

A plain weft knitted fabric (see Section 2.2.2.3) is also unbalanced, which explains why

some knitted mats roll up on themselves when laid out flat. To more accurately classify

(a) Plain weave (b) Twill weave (c) 8–harness satin weave

Weft yarn Warp yarn


15

woven structures prefixes like 2/2, indicating the number of warp and weft crossovers,

are used. Figure 2-10 shows a 3D model for a balanced 2/2-twill fabric 15.

Figure 2-10. 3D model for balanced 2/2 twill fabric 15

Woven fabrics can also be classified by the tightness of the weave. Tightly packed

structures are referred to as closed-packing weaves whereas loosely packed structures

(i.e. gaps between parallel fibres) are referred to as open-packing weaves.

2.2.2.2 Braided

The second category of textile composite preform is the braided fabric. Braided fabrics

are produced by the intertwining of yarns, or in other words interlacing of yarns at

angles other than 0° and 90° 15. At any one time half of the yarns travel in the + θ

direction while the others travel in the - θ direction as shown in Figure 2-11. θ is termed

the braid angle and the yarns following the braid angle are usually termed braid

yarns/tows. For a braid angle of ± 45° interlacing is half that for the plain weave, which

means reduced crimp and better yarn to composite translational strength.

Figure 2-11. 3D model of a flat braided fabric made from five yarns 15


16

The structure of braided fabrics makes them highly deformable in the axial and radial

directions. This makes them particularly suitable for producing near-net shape structures

such as cones, nozzles and shafts such as the one shown in Figure 2-12.

Figure 2-12. Braiding a shaft with varying cross section 16

2.2.2.3 Knitted

Knitting is the process of manufacturing textile structures with a single yarn or set of

yarns moving in only one direction. Unlike weaving where the yarns cross-over one

another, knitted fabrics are produced by looping the yarn through itself to make a chain

of stitches which are then connected together, as shown in Figure 2-13 17. There are two

types of knitted fabric, those produced by weft knitting and those produced by warp

knitting, where warp and weft refer to the knitting directions. In a weft knit, the fabric is

essentially produced with one yarn whereas in a warp knit the number of yarns used

depends on the required fabric width. The knitting directions are also termed wale and

course as shown in Figure 2-13.


17

Figure 2-13. Schematic of knitted fabrics 18 (a) Weft knit (b) Warp knit

2.2.3 The 1x1 Rib and Milano Rib Structures

To improve manufacturability and mechanical performance 3D knit structures such as

the 1x1 Rib and Milano Rib can be used, see Figure 2-14. Both fabrics are essentially

2D but unlike the plain knitted structure, knit loops now occupy two planes with a

mirrored geometric configuration that ensures the fabric is balanced. This characteristic

also allows for the addition of multiaxial insert yarns without the occurrence of any

crimp 19.

Figure 2-14. Schematic of (a) 1× 1 Rib and (b) Milano Rib structures

(a) Weft knit (b) Warp knit

width of fabric

leng

th o

f fa

bric

width of fabric

leng

th o

f fa

bric

(b) Milano Rib

Rib Structure

Plain Structure

(a) 1X1 Rib


18

For example, the 3D schematic shown in Figure 2-15 illustrates how the 1x1 Rib knit

structure can be used to accommodate weft wise insert yarns. The insert yarns are

placed between the planes of loops in the course direction and remain perfectly straight,

giving maximum yarn to fabric translational strength.

Figure 2-15. 3D schematic of the 1×1 Rib structure 20

2.2.3.1 Why choose these knit structures?

It is inevitable that at some stage the reader may ask the question, “why choose the rib

structures as the main reinforcement type for this study?” One reason is that the rib

structure in general possesses an unusually high degree of elasticity. As a result, yarns

made from high performance fibres with very little inherent elasticity can produce a

reinforcing fabric with decent stretchability. For the Milano Rib structure this is even

more the case. They are also, because of through thickness symmetry, the simplest knit

structures exhibiting balanced properties. In the garment industry these structures are

primarily employed in the manufacture of sleeve trims, collars and waistbands for

jerseys and sweaters as well as underwear apparel because of their excellent width wise

stretchability.

2.3 Manufacturing Processes for Thermoplastic Textile Composite

Preforms

Most of the forming processes used in the manufacture of ordinary fibre reinforced

thermoplastics are used and applied to thermoplastic textile composites. The reason

being that in many cases manufacturers will look at existing manufacturing methods


19

and equipment to do the job. Figure 2-16 shows the possible manufacturing path for

composites materials 21.

Figure 2-16. Manufacturing routes for composite materials 21

Like ordinary thermoplastic composite prepregs, textile composite prepregs or preforms

can also be consolidated into sheets or blanks, however not all methods of consolidation

are suitable for all textile structures. For example, knitted and braided fabric preform

materials cannot be consolidated into sheets using the vacuum bagging technique

because of their undulating structures which give a rough surface finish. For these

structures matched die press consolidation is the required method with rigid tools

applying pressures of up to five times that required by woven prepregs and preforms to

achieve the same volume fractions. But is this two-step process of sheet forming and

subsequent shaping really necessary for these materials? Does consolidating the

material into a sheet first then subsequent shaping provide us with a better quality

component or defeats the whole purpose of a textile preform?

Having a preform in the form of a textile permits better formability by allowing the

manufacturer to drape or place a flat or integrally knitted preform into their mould. One

of the main difficulties is how to heat the preform. For thermoplastic commingled

preforms there are two options, either heat the mould which requires a large amount of


20

energy but essentially ensures good consolidation since forming is isothermal with

minimal matrix flow paths, or heat the blank separately and form into a mould which

provides the cooling. This is essentially a non-isothermal process but is possible since

the forming window exhibited by polypropylene allows for a temperature drop of

several degrees without significant change in the melt viscosity. Unless a novel method

of heating the fabric preform material, with small amounts of energy when the matched

die mould is closed under pressure, is found, then forming using the second method is

the manufacturers cheapest and therefore preferred option. Therefore, considering the

forming properties of a preheated flat piece of fabric against cold tooling becomes

important. The deformation of such a material is that of the knitted structure with the

hindrance of a viscous matrix provided by the melted polypropylene filaments or

powder.

Table 2-2 shows a selection of manufacturing options available to thermoplastic

composites, but not all are compatible with and can be used to process the different

types of textile composite preforms.

Table 2-2. Manufacturing options for thermoplastic textile composite preforms

2.4 Textile Composite Deformation Mechanisms

When thermoforming parts from textile composite materials it is useful to understand

the deformation mechanisms, which take place in them so that the forming process can

be optimised to produce the best quality parts.

For example, it is well established from previous studies that a major deformation

mechanism in woven fabrics and multi-layered continuous fibre reinforced plastics is

inter-yarn/fibre shear or the “trellis effect”. In order to achieve a better understanding of

Manufacturing Process Option 2D Fabric Structure Compatibility Manufacturing Issues

Rubber Punch Matched Die Forming Knit, Braid, Weave

Rigid Matched Die Forming Knit, Braid, Weave

Vacuum Forming Weave

Pressure Forming using Diaphragms (>101.3kPa) Weave

Large undulations in the structure of knitted and braided fabrics require the use rigid or semi-rigid matching dies to ensure adequate surface finish


21

knitted fabric composites and textile composite materials in general the deformation

mechanisms for these materials need to be considered and identified.

The hierarchy of deformation modes for this family of composite materials can be

broken down into three broad categories: prepreg flow mechanisms, macro-level fabric

deformation modes and micro-level fabric deformation modes as shown in Figure 2-17.

Each of these categories contains a number of different mechanisms, which will be

looked at in more detail in the following sections.

This hierarchical definition is a method by which a textile composite material can be

studied at different levels of its material structure although it must be appreciated that

these levels are not mutually exclusive and the behaviour of a composite sheet is

slightly different to that of a fabric sheet warranting intra-ply shear and/ or inter-ply (in

the case of multi-ply sheets) to be included at both the 1st and 2nd levels.

Figure 2-17. Hierarchy of deformation modes in textile composite materials

2.4.1 Prepreg Flow Mechanisms

When the textile fabric reinforcement is combined with the matrix to form the

composite prepreg a set of deformation modes are introduced. These can be referred to

as top-level deformation modes since they involve the movement of the reinforcement,

(macro and micro-level fabric deformation mechanisms), and the matrix. They are in

fact the conformation modes of the composite prepreg sheet or group of sheets, as is

usually the case, during the forming process. The hierarchy of the top-level deformation

modes is shown in Figure 2-18.

Prepreg flow mechanisms

Macro-level fabric deformation modes

Micro-level fabric deformation modes


22

Figure 2-18. Hierarchy of top-level (or prepreg) deformation modes

The simplest of these top-level deformation modes is matrix percolation, which is

achieved by using a compliant mould or the vacuum bagging process as shown in

Figure 2-18(a). Both methods apply an even pressure over the prepreg to assist the flow

of matrix through the textile reinforcement. This is usually coupled with minimal

transverse compression, which can hinder the mechanism by decreasing the

permeability of the textile.

Consolidation between rigid matching moulds introduces transverse or squeeze flow as

shown in Figure 2-18(b). Here transverse compression of the textile reinforcement

becomes an important factor.

For the shaping of flat preform sheets into singly curved components, shown in Figure

2-18(c), interply shear is required along with out-of-plane bending of the fabric which

can easily be accommodated by any number of different textiles. Knitted fabric

composite laminates are of particular interest since their geometric structure gives them

interlaminar strength superior to other textile preforms.

Up until the shaping of singly curved components there is not much problem with

regards to reinforcement conformability since most of the deformations can be taken

Conformation Mode: Consolidation:

(a) Compliant mould or vacuum bag

(b) Matching mould

Shaping:

(c) Single curvature (d) Double curvature

Flow Mechanism:

Resin percolationthrough fibre bed

Transverse (squeeze) flow

+ + +

Interply shear Intraply shear transverse

and in-plane


23

care of by the top-level deformation modes. However, forming double curvature and

complex shaped components from preform sheets requires intraply shear, Figure

2-18(d), which inherently involves in-plane shear of the textile reinforcement and a

selection of micro-level textile deformation modes relevant to the reinforcing textile

structure.

2.4.2 Macro-Level Fabric Deformation Modes

The four deformation modes termed macro-level fabric deformation modes as shown in

Figure 2-19 describe the deformations observed when looking at the fabric as a whole.

However, the way in which each fabric complies to these modes is different and can be

attributed to the deformations occurring within the textile structure itself. These sub-

structure or micro-level deformation modes are the real mechanisms behind textile

deformations and need to be identified in order to understand the materials behaviour.

Figure 2-19. Macro-level fabric deformation modes

2.4.3 Micro-Level Fabric Deformation Modes

Micro-level fabric deformation modes exist through the interaction of structured yarns

within the fabric. Figure 2-20 shows what are believed to be the eight micro-level

deformation modes for textile fabrics in general.

(a) Transverse compression (b) In-plane tension (c) In-plane shear (d) Out-of-plane bending


24

Figure 2-20. Micro-level fabric deformation modes

Inter-yarn slip as shown in Figure 2-20(a) occurs when the yarns that construct the

fabric move over one another. It is one of the modes of deformation belonging almost

exclusively to knitted fabrics. In this mode of deformation the friction between the

yarns becomes important since it determines where the onset of buckling will be as well

as the magnitude of the forming forces required. Fortunately the matrix and fibre

chemical sizing (coatings) usually lubricate the yarn to help this mode of deformation.

Inter-yarn shear is a common mode of deformation in many woven fabrics. This is

where the yarns rotate about their crossover points to accommodate the required

deformation (see Figure 2-20(b)). In fact, this type of mechanism has been reported to

occur in multi-layered continuous fibre-reinforced composites also as outlined by Krebs

et al, Martin and Christie 22 23 24 and is commonly referred to by many researchers as the

“trellising effect”. In knitted fabrics depending on the orientation of the reinforcement

large in-plane tension and in-plane shear can be accommodated, but not in the same

direction as will be demonstrated in Chapter 3.

(a) Inter-yarn slip (b) Inter-yarn shear (c) Yarn bending (d) Yarn buckling

(e) Intra-yarn slip (Inter-fibre friction)

(f) Yarn stretching (g) Yarn compression (h) Yarn twist


25

Yarn bending or “straightening” shown in Figure 2-20(c) is in many cases the most

significant deformation mode in many textiles. It is the most influential mode in knitted

fabrics because of the knit loop geometry. Straightening also occurs to a lesser degree in

woven and braided fabrics depending on the amount of crimp or yarn undulation present

in the fabric structure.

Out of all the different deformation modes fibre buckling is the only unfavourable one

since material movement through this mode creates what are considered as defects,

although this can be quite difficult to notice with complex structures such as knits and

braids. Out-of-plane buckling usually occurs when the in-plane modes cannot

accommodate the required deformation. In-plane buckling can also occur but is less

likely due to in-plane geometric constraints (see Figure 2-20(d)).

Intra-yarn slip shown in Figure 2-20(e) coupled with yarn bending, Figure 2-20(c), are

the biggest contributors to a textile fabric’s force displacement curve. Intra-yarn slip is

where the continuous fibres within the yarn slide past one another along the length of

the fibre because of changes in fibre curvature during bending and unbending.

Yarn stretching while not so prominent at early stages of fabric deformation is certainly

present and becomes a significant contributor to the deformation at larger strains.

Although the reinforcing fibres used in composites are very brittle and exhibit very high

stiffness moduli (e.g. glass, carbon, aramid) strains of up to 5% through this mode can

still occur (see Figure 2-20(f)) and Table 2-1).

Another fabric deformation mechanism to consider is yarn compression. Figure 2-20(g)

shows this mode where, forces at yarn cross-over points compress the filaments in the

yarn and cause them to flatten out and conform to the curvature of perpendicular yarns.

Like fibre stretching this can also be considered relatively insignificant and only really

starts to contribute to the load extension curve once the aforementioned mechanisms

have been exhausted.

Finally, yarn twist, shown in Figure 2-20(h), which has been observed in knitted fabrics

and not so much in woven fabrics contributes further resistance to fabric deformation.

This is where the yarn is subjected to one full turn during the manufacture of the fabric


26

in order to create the looping structure of the knit. The twist creates a resistance to the

increase in yarn curvature during fabric deformation.

2.4.4 Textile Fabric Force-Displacement Curve

The relative importance of each of these deformation mechanisms is fabric specific and

in some cases certain deformation modes may not be utilised at all. During the

deformation of a textile fabric combinations of these mechanisms occur simultaneously

and the influence of each changes continuously throughout the entire deformation.

Figure 2-21 shows the force displacement curves for both woven and knitted fabrics in

general, with regions of the curves identified to show where certain deformation modes

are of greatest influence.

Figure 2-21. Textile fabric force displacement curve

It can be seen that the curves for both the woven and knitted fabrics follow similar

trends. Intra-yarn or inter-fibre friction is most influential at initial stages (1) of both

curves starting out as the static friction that needs to be overcome to initiate the sliding

of long fibres past one another. That is, if you can imagine a yarn made up of

continuous fibres upon the commencement of bending or unbending due to changes in

curvature of individual fibres in the yarn there will be sliding.

For both fabrics the next major region (2) and (3) is that caused by bending/unbending

and resistance to twist. Friction is still present from here on but is in the form of a lower

Force Woven Fabric Knitted Fabric

Displacement (in warp & weft directions)

(3) c,h

(4) a,b

(5) g

(6) f

(2) c

(1) e


27

dynamic friction force. Because of its structure, a knitted fabric has more curved yarn to

extend, whereas a woven fabric no matter what its degree of crimp is still far lower.

For knitted fabrics inter-yarn slip (4) also contributes to the shape of the curve in this

central region starting at around 10% extension and ending once the forces at the yarn

crossover points become too large.

Finally yarn compression and extension (5) and (6), no doubt present throughout the

entire extension become most dominant at the latter part of the curves and can

contribute up to 5% of the total extension up to failure. Although the knitted and woven

fabrics have been compared side by side it is important to note that Figure 2-21 is not a

scale comparison between the two materials since in reality knitted fabrics can exhibit

strains 100 times greater than their woven counterparts.

2.4.5 The Role of the Matrix

With the previous three sections in mind it is interesting to consider what role the

thermoplastic matrix plays. Besides allowing for the top-level or prepreg deformation

modes to occur it will, depending on its physical state, affect the behaviour of the lower

level deformation modes in different ways. As a result, the forming characteristics of

the material may change to become more or less favourable.

2.5 Research Trends

Up until the present, the bulk of literature has focussed on characterising mechanical

performance of knitted fabric composite materials, both thermoset 18, 25, 26 and

thermoplastic 27, 28. Fatigue resistance 29, fracture mechanisms 30 31, the influence of knit

architecture 32, fibre volume fraction and pre-stretching on the mechanical properties 33,

34, are examples of some of the areas that have been explored. Modelling the mechanical

properties (mainly stiffness and tensile) has also been popular 8, 35-37. Even the

mechanical properties of dry preforms have been investigated 12. However, limited

literature exists on the forming property characteristics of knitted fabric reinforced

thermoplastics 38, 39 and their processing properties are still poorly understood. In fact,

most of the literature on forming properties deals with unidirectional 24, 40, mostly woven 22, 41-44, and to a lesser extent, braided reinforcements 45 rather than knitted


28

reinforcements. If they are to have any commercial viability the forming behaviour of

knitted fabric thermoplastic materials need to be more thoroughly investigated.

2.6 Review of Modelling Approaches and Analysis Tools

An important feature of any material study is to acquire enough knowledge and

information to be able to predict that material’s behaviour. However, the inherent

complexities that exist with these types of materials make modelling any aspect of their

behaviour difficult. To achieve efficient solutions researchers usually resort to making

assumptions based on practical and experimental observations. However, sometimes the

modelling tools themselves can provide useful detailed information. This section

presents some of the approaches taken in this field of research. While some of the

methods and techniques presented here may not be simulating the behaviour of the

material directly, they serve as useful tools to aid in their understanding.

2.6.1 Kinematic

2.6.1.1 Numerical Strain Mapping Technique (Grid Strain Analysis (GSA))

Grid Strain Analysis (GSA), used extensively in Chapter 3 of this thesis, is a method by

which the macroscopic deformation of a sheet may be evaluated, without needing to

know any constitutive information about the particular material being deformed. First

developed by Sowerby et al 46 and later extended by Schedin, Melander and more

recently by Duncan, Zhang and Christie 24, 47-49 the method provides a means for

establishing a mathematical relationship between a series of points marked on the

surface of a sheet before and after deformation. The fundamental assumption made in

the analysis is that the deformed component may be represented by a two-dimensional

surface in 3-D space, thus allowing the principal in-plane strains of the sheet to be

quantified through the use of a 2×2 deformation gradient tensor. The direction of the

thickness strains can also be defined by using surface normals and their magnitudes

calculated by applying the constraint of material incompressibility.

In the simplest case the deformed sheet can be modelled as a polyhedral surface, by

treating each element as a 2-D segment in 3-D space as shown in Figure 2-22. This

approach is reasonable when the surface contains small degrees of curvature however,

in regions of severe curvature the calculated strains will be less accurate unless a large


29

number of elements are used. There is also the issue of how to deal with the strain

within and between elements. One method is to treat the strain distribution as

discontinuous and the strains within the elements as homogeneous so that an exact

solution will be attained as the number of elements tends towards infinity 46, 47.

Figure 2-22. Deformation of a triangle element described by three adjacent grid points

A better method for calculating the strains can be developed if a convected curvilinear

coordinate system is used to describe the deformation. When the surface geometry is

defined using bicubic parametric elements, the basis or weighting functions provide a

method for determining the continuous strain variation across the surface by considering

displacement gradients 48.

Consider a one-dimensional data set where the raw data is assumed to be inherently

smooth and continuous. One approach for finding a mathematical expression for the

data would be to use a polynomial expression. In this way, an Nth order polynomial can

be used to exactly interpolate (N – 1) data points. However, unacceptable oscillations

uncharacteristic of the actual nature of the data begin to occur for higher order

polynomials.

By dividing the domain into a finite number of regions, a low-order polynomial can be

used to best interpolate the data. The parametric cubic equation is the lowest-order

polynomial function, which can be forced to meet four constraint conditions (i.e. the

values of position and gradient at both the nodes for a one-dimensional data set) by an

appropriate selection of its coefficients. After solving for these coefficients the resulting

z

x y

A’ B’

O’

A

O

B

(a) In 3-D space

B’

O,O

B

A’ A

y

x

(b) After 3-D coordinate system transformation


30

cubic equation can be rearranged to express the interpolation of the nodal parameters in

terms of a parameter ξ and its basis functions. The four basis functions are given in

Equation (1) and their plots are shown in Figure 2-23.

320

1 ξ2ξ31)ξ( +−=Ψ , 211 1)-ξ(ξ)ξ( =Ψ , ξ)23(ξ)ξ( 20

2 −=Ψ , 1)-ξ(ξ)ξ( 212 =Ψ (1)

In a GSA analysis bi-cubic Hermite elements are used to describe both the undeformed

and deformed geometry. The element, shown in Figure 2-24, stores four vector

quantities at each one of its four nodes, the nodal position 1x , the slopes 1

1

ξ∂∂x and

2

1

ξ∂∂x of the element sides along the 1ξ and 2ξ directions as well as a twist vector

21

12

ξξ ∂∂∂ x to control the surface behaviour inside the element.

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 2-23. 1-D Cubic Hermite basis function Figure 2-24. The Bi-Cubic Hermite element

Using both the deformed and undeformed grid data points, the bi-cubic Hermite

elements are fitted to both sets of data points to give smooth representations of both the

deformed and undeformed 2-D geometry. The surface fitting is carried out using the

method of least squares as defined in Equation (2) where iv is termed the error, P is the

total number of points and ix and iu are the fitted surface approximation and actual

data respectively. Also included is a weighting function iw , which can be used to

control points, which are suspected to have a larger degree of measurement error. By

φ1 φ3

φ4

φ2

φ(ξ)

ξ


31

differentiating Equation (2) and setting the result to zero a matrix equation can be

formed to calculate the vector coordinates of the approximated surface.

221

16

11

221

1

2 )ˆ)ξ,ξ(()ˆ)ξ,ξ(( pi

pni

n

pi

P

p

pi

pi

pi

P

pi uuwuxwv −φ=−= ν

===∑∑∑ i =1,2,3 (2)

To finish off the analysis the relationship between the deformed and undeformed

geometries are related through the deformation gradient tensor 50, which is used directly

to calculate the magnitude and directions of the principal strains in all the bi-cubic

Hermite elements approximating the deformed surface.

There are certain limitations associated with the GSA technique, one being that the

accuracy of the results is dependent on the accuracy of the nodal point measurements.

Usually the deformed grid points are physically measured using digitising equipment,

which means that if the strains are too small they can easily be overwhelmed by the

error associated with the measurement. It is also important to be aware of surface fit

errors associated with the type of elements that are used. Another limitation is the fact

that it can only be assumed that the grid strains are representative of the surface

laminate. In other words for multi-layered composite sheets, the behaviour of

subsurface plies is unknown, although qualitative information about the effect of sub-

surface plies on the surface ply can be established.

While GSA in this case is purely a post manufacturing kinematic analysis tool, several

authors including Van West 51 and Heisley et al 52 have outlined the use of a kinematic

model by considering the draping of fabric over arbitrary surfaces. A review of the

various approaches is given by Lim and Ramakrishna 53 and is summarised in Section

2.6.1.2.

2.6.1.2 Kinematic Strain Mapping Technique

The paper titled “Modelling of Composite Sheet Forming: A Review” by Lim and

Ramakrishna 53 details how the earliest research on the forming of composite sheets

began with unidirectional and has slowly progressed towards woven, braided and even

knitted composites. The review focuses on providing an overall account of sheet


32

forming modelling techniques for all these reinforcement types. Since knitted fabrics are

the focus of this thesis only the relevant sections from this review are discussed. Two

categories of modelling approaches are highlighted in this paper, 1. Mapping

Approaches and 2. Mechanics Approaches. Mapping approaches consider draping of the

material onto smooth tool surfaces and the GSA technique discussed in Section 2.6.1.1.

As most researchers have done for unidirectional and woven fabrics, the yarn is

assumed to be inextensible. In the case of woven materials, yarn crossover points act as

trellising pivots and yarn slippage is ignored. The same constraints are applied to

knitted fabrics, except yarn stretching is added to account for yarn loop straightening.

The analysis uses stretch ratios λ, which describe the relationship between the projected

and actual side and head loop lengths, along with γ for the extent of shearing. Surface

mapping equations are then related to λ and γ, meaning that the values of these ratios

can be evaluated for the given undeformed sheet and tool surface. For simple tool

geometries such as cylinders and domes, analytical expressions can be set up describing

the exact mapping scheme. In his analysis on knitted fabric sheet forming over a

hemispherical (or cylindrical) punch geometry, Lim assumes a uniformly distributed

meridional strain (which is an oversimplification, yet necessary in order to develop a

solution), and considers both stretch forming and deep drawing. A zero or positive value

strain along the flat face of the cylindrical punch indicates the difference between

stretch forming and deep drawing. By taking the lower of the two stretch ratios λc or λw the maximum achievable product depth in terms of knit structural geometry and tool

geometry can be obtained.

For more complicated tool surfaces, which is usually the case, analytical equations

describing tool geometry may not be possible and numerical mapping techniques are

required. Here the mapping is based on algorithms that take into consideration a number

of constraints such as, fibre inextensibility, constant fibre spacing and sticking friction

to generate the nodes defining the fibre-tool contact points. An alternative method is to

map elements to the tool geometry and use minimisation of strain energy over the

elemental surface as the defining constraint.


33

The mapping technique proposed by Van der Ween54 could also be applied to knitted

fabrics since the equation that minimises strain energy incorporates only stretch ratios.

However, unlike the straight forward geometry of unidirectional and woven fabrics the

mapping of knitted fabrics would need to refer to something like a database of strain

states in order to present a picture of the mapping geometry, which means that the

establishment of an accurate micromechanical model is very important.

2.6.2 Mechanics, Micromechanics and Homogenisation

A common approach to the prediction of the mechanical properties of textile composite

materials is the use of the micromechanics approach. The micromechanics or

homogenisation approach is a procedure for determining the effective properties of a

representative volume of composite material from its known constituents. The

heterogeneous properties of the composite at the micro-scale are idealised as a

homogeneous medium with effective anisotropic properties at the macro-scale level

paving the way for computationally efficient prediction of composite properties. While

this method has been used mainly for predicting the solid-state composite mechanical

properties, most of the techniques and methodology can be readily applied to simulating

forming behaviour as well. The fact that processing or forming simulations are an

important aspect of composite technology that can help the development of cost

effective composite solutions, provides the impetus for such research. The purpose of

this section is therefore to investigate and review some of the work done by various

researchers in this specific topic area. Most of the articles deal with forming rather than

solid-state material property simulation although these are also reviewed where

relevant.

The work by Takano et al. 38 presents some of the most significant pieces of work

related to this thesis. The paper looks at simulating the deep drawing process of single

layer plain weft-knitted fibre reinforced thermoplastic using the homogenisation

approach. The authors explain how the multi-scale modelling approach, first developed

in the late 70s early 80s by various European researchers only requires the mechanical

properties of the constituent materials as inputs parameters. This is a particular

advantage since experiments for characterising these types of materials in their

processing state are not only difficult to perform but difficult to get reliable data from.

Rather than use the conventional micro-macro algorithm where microscopic equations


34

are solved everywhere in the composite’s domain before the macroscopic equation is

solved, Takano et al. construct a database of some representative microstructural

deformation states. These results are then used to solve the macroscopic equation. If

other loading cases that are not in the database are required then simple linear

interpolation is used.

The most important part of the entire simulation has to be the micromechanics model

since this is where all available physical information is applied and is what generates

the values for the macroscopic material database. For their microscopic simulation

Takano et al. make the following assumptions. 1. The constituents are isotropic and

linear elastic. 2. The process is isothermal at 443K. and 3. Large deformation of knitted

fibre bundles is considered, but more microscopic deformation in the fibre bundle is

neglected, therefore, the fibre bundle itself is supposed to be orthotropic and linear

elastic 38.

Figure 2-25. Micromechanics model of plain weft knit by Takano et al 38


35

It is not clear whether the models consider inter-yarn friction, or how properties for the

yarn compression stiffness are calculated. Indeed, if the yarn properties are orthotropic,

then the transverse behaviour of the yarn will need to be known to ensure that the

bending stiffness of the yarn is not too high. It is also unclear as to how many

microscopic stress states are solved for. The number of stress states in the

micromechanics model should be large enough to capture the true shape of the stress

strain curve.

The micromechanics approaches presented by Tong, Mouritz and Bannister 14 consider

rules of mixtures, Mori-Tanaka (which is modified rule of mixtures) and classical

laminated plate theory, all of which require linear constituent material property data.

These models are for predicting the solid-state mechanical properties of textile

composites. The most challenging part of the analysis is actually understanding the

complex interactions between the constituent materials 14. More can be found in Chapter

4 of 3D Fibre Reinforced Polymer Composites by Tong, Mouritz and Bannister14.

2.6.2.1 The Development of Analytical Models

Analytical methods for the prediction of the forming properties and deformation of

textile composites begin with an understanding of the reinforcing fabric. Understanding

the mechanical behaviour of fabrics has been in the interest of textile manufacturers

who benefit from such understanding by being able to produce better quality garments

and use their textiles with greater efficiency. However, literature addressing the

mechanics of fabrics seems to be scarce with very few publications appearing since the

1960’s. Early work has perhaps been complete enough to satisfy the textile industry, but

a renewed interest within the composites and computer modelling community is starting

to develop. The next few pages review early work done in this area and perhaps the best

modern account, written by S. Kawabata in Chapter 3 of Textile Structural Composites 55.

The analysis of a fabric begins by establishing the geometrical properties. Considering

geometry allows, 1. Calculation of the resistance of the fabric to mechanical

deformation such as initial extension, bending or shear in terms of the resistance to

deformation of individual fibres and 2. Direct information on the relative resistance of


36

the fabric to the passage of air, light (important for the textile industry) or matrix

materials in the case of composites by giving a guide to the calculation of properties like

packing density (i.e. fibre volume fraction).

Grosberg 11 who summarises the works of Peirce describes the most elaborate account

of early work. Peirce built up a purely geometrical model of a woven fabric involving

no consideration of internal forces. He assumed the yarn was circular in cross section

and considered the bending resistance of the yarns as negligible, (yarns have zero

bending resistance). In other words it was assumed that the geometry was not the result

of the balance of various internal forces, since no forces were needed to produce the

geometry postulated.

If bending resistance is neglected then the yarn will be straight at all points except at the

crossovers where it wraps itself around the circular crossing yarn. Figure 2-26 shows

the unit cell of woven fabric with the various parameters defined as suggested by Peirce 11.

Figure 2-26. Peirce’s model of a plain woven fabric unit cell 11

The nine parameters are….

h1 = Crimp height in warp direction

h2 = Crimp height in weft direction

P1 = Yarn spacing in warp direction

P2 = Yarn spacing in weft direction

l1 = Unit cell yarn length in warp direction

D

d

P

h/2 θ

l/2

h


37

l2 = Unit cell yarn length in weft direction

D = Sum of yarn diameters

θ1 = Angle of yarn to horizontal in warp direction

θ2 = Angle of yarn to horizontal in weft direction

d1,2 = Warp and Weft yarn diameters (known parameters)

It is possible to write the five equations, as shown in (3) - (7), which means that four of

the nine parameters need to be measured. These will usually be P1 ,P2 and l1, l2 since

they are the easiest to obtain physically. Although the measurement of D is not required,

since D = d1 + d2, it is useful for verifying the values of d1 + d2. To avoid the problems

of solving these difficult simultaneous equations, graphs of P versus θ can be generated.

Dhh =+ 21 (3)

11111 )( θθθ DSinCosDlP +−= (4)

22222 )( θθθ DSinCosDlP +−= (5)

)1()( 11111 θθθ CosDSinDlh −+−= (6)

)1()( 22222 θθθ CosDSinDlh −+−= (7)

Therefore, Peirce’s approach gives five equations for five unknowns, but for the case of

P1 = P2, i.e. the yarn spacing is equal in both the warp and weft directions, equations (4)

and (5) combine to give an expression relating θ1 to θ2. An equation containing the

measured parameter P no longer exists. Therefore, there will now only be four

equations for the five unknowns θ1, θ2, h1, h2, and D, which suggests an infinitely

variable geometry. However, for a relaxed woven fabric with P, l1 and l2 fixed, there

must only be one geometry, because of the fact that the force required to bend the warp

yarn into its crimped shape must be equal and opposite to the force required to bend the

weft yarn into shape. To find this geometry is beyond the scope of Peirce’s model

which uses the approximation shown in equation (8) 11 to calculate the various fabric

parameters h, P, l or the commomly used crimp, c if two parameters are already known.

The model can also be used to calculate woven fabric geometry jamming conditions

using assumed yarn shapes including circular, race track and elliptical cross sections.


38

cPl

Ph

⎟⎠⎞

⎜⎝⎛≡⎟

⎠⎞

⎜⎝⎛ −⎟

⎠⎞

⎜⎝⎛=

341

34 2

1

(8)

It was soon realised that yarn cross sections were far from circular and that even highly

twisted yarns showed large scale deviations from circularity. Figure 2-27 shows the

cross sectional shape of low-twist continuous multifilament yarn in a woven fabric,

which is typical in composite reinforcing fabrics.

Figure 2-27. Continuous multifilament yarn cross sections 11

It became obvious that the bending resistance of the yarn produced forces that can

completely distort the cross section of the yarn. The concept of a given yarn cross

section was difficult to maintain and a completely different approach was taken to

define what governs cloth geometry. In 1964 Olofson proposed that the yarn cross-

sectional shape could be obtained by assuming that the yarn is bent into shape by point

loads acting at the yarn crossover points. The yarn takes up the shape of an “elastica”, as

shown in Figure 2-28.

Figure 2-28. The Elastica as proposed by Olofson 11

V

V

ψ

θ

s

P (yarn spacing)


39

The assumption is made that the yarn cross-section is so easily distorted that it can be

ignored in determining the yarn’s cross-sectional shape and instead, the yarn flows into

the space made available for it by the perpendicular yarns. The analysis proceeds by

summing moments about the inflection point of the elastica as given in equation (9)

where m = the flexural stiffness or bending modulus of the yarn, and ρ = the radius of

curvature at any point on the elastica.

VxmREIM −≡≡=

ρ (9)

Additionally, consideration of an incremental arc length as shown in Figure 2-29 gives

the relationships shown in equation (10).

ψρψ

ddsdsCosdx

==

(10)

Figure 2-29. Considering an incremental arc length on the elastica

Therefore, it is possible to write the differential equation shown in equation (11), which

can then be integrated to give the x coordinate parameter formulae required to establish

the shape of the elastica curve, see equation (12).

VxdxdmCos −=ψψ (11)

ψθ

ψθ

SinSinVmx

SinSinmVx

−=

−=

2

)(21 2

(12)

+

ds

S2

S1

ρ

dψ

ψ1

ψ2


40

When 2Px = and ψ = 0 then an expression giving the size of the force V needed to

form the relaxed cloth geometry at each crossover point can be written in terms of m,

the bending rigidity, θ, the yarn crimp angle and P, the yarn spacing, see equation (13).

2

8P

mSinV θ= (13)

To obtain the other two equations for defining the shape and length of the elastica

requires the integration of the differential equation shown in equation (11) in terms of y

and ψ and s and ψ. The equations are given here for reference, (14) and have been taken

directly from Hearle 11. They involve elliptical integrals, which can only be solved using

numerical integration techniques.

[ ][ ])()2(

))(2)(()2(2)2(

0

00

φπ

φφππ

FFVms

EFEFVmy

−=

−−−= (14)

where

)42sin()1(sin)42sin(sin1

)(

sin1)(

0 22

0

22

πψφπθ

φ

φ

φφ

+=+=

−=

−=

∫

∫

kk

kdxF

dkxE

x

x

0φφ = when 0=ψ so that 21sin 0 k=φ

Therefore, the geometry of a plain-woven fabric and the value of the forces at the yarn

crossover points can be generated using only information on yarn spacing P, bending

rigidity of the yarn, m and the yarn crimp angle θ. Furthermore, if another approximate

relationship, c106=θ , also developed by Peirce, is used with equation (8), then only

P, l and m are required.


41

In addition, the equation given in (13) can be rearranged using part of equation (9) to

give an expression which evaluates the minimum radius of curvature ρ, which again

occurs at 2Px = and ψ = 0, giving equation (16). This information can then be used to

generate the elliptical cross sectional shape of the yarn.

θρ

sin4P

= (15)

The method of analysis was implemented by the author of this thesis as it was thought

that a similar strategy could be employed for the calculation of knitted fabric geometric

and mechanical properties. The code was written using a high level programming

language called Tcltk (Tool command language tool kit) and used visualisation libraries

from Vtk (Visualisation tool kit) for the Opengl 3D graphics instructions. A screenshot

from the program is shown in Figure 2-30.

Figure 2-30. Olofson’s kinetic modelling approach for woven fabric implemented

Following the consideration of geometry, the next step is to consider the warp and weft

extension behaviour, and how to analytically derive expressions for the tensile

properties. The general behaviour of the load extension curve for woven and knitted

fabrics was discussed in Section 2.4.4. In a woven (and knitted) fabric, major

Inputs: weave angle, bending stiffness, yarn

spacing, no, of iterations.

Outputs: cross-over forces, length of yarn, 3D fabric

geometry.

¼ of unit cell (½ elastica)


42

geometrical changes take place at fairly low forces, so it is reasonable to initially

neglect the extension and compression of yarns.

The analysis proceeds by first deriving expressions for Poisson’s ratio in both the in-

plane and thickness directions of the fabric in terms of the same parameters established

in the geometric considerations, l, P, h and c. The following assumptions are made. 1.

Yarn extension is zero; 2.Yarn crossover compression is zero; 3. Length of yarn in a

unit cell is constant; 4. Sum of the crimp height h, for the warp and weft yarn is

constant. Using these assumptions and the expression given in equation (8) the

following two equations shown in (16) and (17) can be derived. More details of the

derivation are given in Hearle 11.

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−=2

1

1

2

2

1

11

cc

cc

dPdP

(16)

⎟⎟⎠

⎞⎜⎜⎝

⎛ −−=

cc

dPdh

5.11

(17)

Equation (16) defines the poisson’s ratio in the in-plane direction while equation (17)

the poisson’s ratio in the thickness direction for the fabric. The equations make it

possible to consider the modulus for several different assumption variations of loading

in a woven material.

From here, five different cases are considered each giving a function defining the

stiffness curve which can be combined to give the overall generalised behaviour of a

woven fabric. These are considering the deformation when, 1. Stresses are significantly

large therefore there is negligible internal energy change due to bending; 2. Yarn

extension also occurs; 3. Only bending energy changes are considered; 4. Cases 1 and 3

combined; 5. Cases 4 and 2 are combined giving the most complete general model of

woven fabric stress strain behaviour.

For case 1, a function representing the modulus behaviour of the fabric can be

developed by considering the energy equation as written in (18), where the total

extension of the fabric in the warp direction = 12dPn and the total extension in the weft


43

direction = 21dPn . This equation corresponds to the static equilibrium under biaxial

extension.

212121 dPnfdPnf −= (18)

If nfF −= is the force per yarn then it is possible to write (19).

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=−==2

1

1

2

1

2

22

11

2

1

11

cc

cc

dPdP

nfnf

FF

(19)

The modulus of the woven fabric can be defined as the change in the force per unit

width of cloth 2

1

PdF per fractional increase in length

1

1

PdP , giving equation (20).

constFdPdF

PP

PdP

PdF

21

1

2

1

1

1

2

1

,⎟⎟⎠

⎞⎜⎜⎝

⎛≡ (20)

Evaluating 1dF in equation (19) with respect to the crimp c, by taking F2 to be constant

gives (21).

( ) ( ) 1

21

23

121

22

221

122

21 22, dcccFdcccFconstFdF

−−−

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

(21)

Which, by substituting for 2dc and 1dc using the expression given for crimp in terms of

P and l given previously in an indirect manner, in equation (8) and shown in equation

(22), gives the expression for the stiffness of the woven fabric in terms of F2, P1, P2, c1

and c2, for the case where no yarn extension or bending energy changes are considered,

see equation (23).

1

111

)1(P

dpcdc +−=

2

222

)1(P

dpcdc +−=

(22)


44

Stiffness for Case 1 (A) ( ) ( )⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛++= 1

21

1

2

2

12

12

2 112

ccc

PPc

cPF

(23)

The complexity of the model increases by deriving the expressions giving the stiffness

due to yarn extension, Case 2 and yarn bending energy changes, Case 3. Yarn extension

is relatively simple to derive using dl = KdF where K is the stiffness of the yarn and

again using l = P(1+c) and differentiating assuming c to be constant. The expression for

this case is given in equation (24).

Stiffness for Case 2 (B) ⎟⎟⎠

⎞⎜⎜⎝

⎛ +=

1

1

2

1 1K

cPP

(24)

For yarn bending energy, the derivation is more complex, again involving the elastica

with additional variables added to the differential equation to give the expression shown

in (25) for case 3.

Stiffness for Case 3 (C) 2

1223

2

31

1

2

113

1

1 )(1)( P

Pf

PP

mm

fPm

⎥⎦

⎤⎢⎣

⎡+= θ

θ

Where ∫ −=

1

022

2

)41()(tan)()(

PxPxdPyf ψθ

(25)

To complete the analysis and to obtain a complete expression for the stiffness

behaviour, the stiffness expressions for cases 1 and 3 are added, since the bending work

done against the external load and that due to the bending energy changes in the yarn,

work like springs in parallel. To incorporate yarn extension, its equation is then

combined in series to give the final equation as shown in (26), where A, B and C have

already been given in equations (23) - (25).

Total Stiffness of Woven Fabric BCA

BCA++

+=

)( (26)

The extent of the analysis involved in simply analysing the mechanical properties of

woven fabrics has meant that knitted fabrics, with their more complex geometry, have

been treated rather sketchily. Most of the theoretical extension behaviour has been of a

qualitative nature, involving the empirical approaches of Pierce, Munden, Nutting and


45

Leaf 11. The previous section if anything was meant to highlight the complexities

involved in the considerations of even the simplest type of textile, the woven fabric, let

alone the complex three dimensional structures found in knits. In the final pages of his

chapter in Hearle 11,Grosberg states that because the resistance to the extension of

knitted fabrics is mainly due to bending and torsion and is quite small (compared to

woven fabrics) the frictional restraint plays a much bigger role in the shape of the stress

– strain curve, however this is very difficult to analyse. There are two statements here

that have provided most of the impetus for the work carried out in Chapter 5. They are

that no successful prediction of the mechanical behaviour of plain weft knit fabrics has

yet been made and that no successful analysis of the frictional restraint in knitted fabrics

has yet been made either.

In more recent publications, Kawabata 55 considers the biaxial extension theory of both

plain woven and knitted fabrics allowing for the calculation of their tensile properties.

The models are based on simplified structural models of the unit structures of both

materials as shown in Figure 2-31.

Figure 2-31. Models of the plain weave (a) and plain knit (b) structures 55

Plain Weave

Plain Knit

(a)

(b)


46

In his consideration of the plain weave, the curved geometry of the yarn in the structure

is simplified by assuming straight lines running along the centreline of the yarn,

bending along the X3 axis at their crossover points. The four basic structural constants

that are initially required and measured off the fabric are shown in equation (27). It can

be seen that the equations here are identical to those presented by Grosberg in Hearle 11,

where again, as in equation (8), the crimp of the fabric is evaluated with respect to the

size of and length of yarn in the unit cell.

=01n undeformed warp yarn density (yarns/unit length)

=02n undeformed weft yarn density (yarns/unit length)

01010101 /)( yylS −= = warp crimp caused by weaving

01010101 /)( yylS −= = warp crimp caused by weaving

(27)

Kawabata also makes use of stretch ratios, which are defined as the stretched length

over the undeformed length of the fabric, λi, and is equal to 1 + the tensile strain of the

fabric. At first, the case of a perfectly flexible and incompressible yarn is considered

and expressions for the equal and opposite yarn compression forces are derived as

shown in equation (28).

2200 )/2(/)/4)(( iiiiiyiici yHyHgF λλ += (i=1,2 warp and weft)

(28)

where )( yiig λ is a function describing the tensile behaviour of either the warp or weft

yarn, in terms of its own stretch ratio yiλ , which can also be given in terms of the

geometric parameters shown in Figure 2-31, and the overall fabric stretch ratio, see

equation (29). Note that a subscript of zero is used for the initial state.

)( yiiyi gF λ= (i=1,2 warp and weft)

1)/2(/)/2(/ 20

2200 ++== ioiiiiiiyi yHyHll λλ (i=1,2 warp and weft)

(29)

From here there are two more formulae which are used, that of force equilibrium,

21 cc FF = and that of yarn incompressibility 020121 HHHH +=+ . Therefore the


47

tensile force of one yarn in the fabric can be calculated by equating 21, cc FF using

equation (28) and solving for H1 (H2 is eliminated in 2cF using

020121 HHHH +=+ ) for a given fabric stretch ratio, i.e. λ1 and λ2 are selected and

the corresponding F1 and F2 are calculated using the equation shown in (30) and the

relationships given previously in (29).

220 )/2(/ iiiiyii yHFF λλ += (i=1,2 warp and weft) (30)

Kawabata expands on the analysis for the cases where yarn compression and yarn

bending are considered, similar to cases 2 and 3 in the analysis given by Grosberg in

Hearle. To incorporate the effects of yarn compression he uses an experimental method

to determine the yarn diameter decrease as a function of the yarn compression force, to

simplify the analysis.

In the case of including the effects of bending rigidity of the yarn, small deflection

theory of an elastic beam is used as shown in Figure 2-32, where B is the bending

rigidity of the yarn and all the other parameters can be related to the geometric

parameters that were shown in Figure 2-31.

Figure 2-32. Establishing forces due to yarn bending 56

φ0

φ

FB

FCB

)4/sin/(3 20 φφ lBF iB Δ=

where

)/2(tan 01

0 λφφ yH−−=Δ

)4/cos/(6tan2 20 φφφ lBFF BcB Δ==


48

Kawabata also adds a hysteresis term to FcB and the new equilibrium equation to equate

becomes 2211 cBccBc FFFF −=− . Again the equations are solved for H1 under

selected values of the stretch ratios λ1 and λ2, then 2211 ,,, cBccBc FFFF can all be

evaluated and the tensile force in the fabric per yarn in the warp and weft direction is

given by equation (31). In equation (32) δ is the decrease in the yarn diameter for a

given cross-over compression force and is determined experimentally.

icBicii FFF φtan2/)( += (i=1,2 warp and weft) (31)

Where

)/(tan 10111

1 λφ yH−=

)/)((tan 202102011

2 λδφ yHHH −−+= − (32)

The analysis starts to bear a close resemblance to a finite element analysis as the curved

geometry of reality is simplified to eliminate the difficulties associated with complex

mathematical expressions.

With knitted fabrics, stretch ratios are again utilised and the analysis is divided into two

steps. The first step considers the stretching of the curved yarn up to a critical stretch

state, while the second step considers elongation, compression and slippage of the yarn

separately, even though these deformation processes actually occur in tandem.

2.6.2.2 Numerical Methods

The general procedure for predicting the mechanical properties of textile composite

materials using finite element analysis usually involves a two-step process. Generating

and analysing the mechanical properties of the unit cell, then, using this information,

construct and simulate the entire composite geometry to predict its solid state or

forming properties. An example of the scope of an overall modelling strategy is given

by Lomov et al 57 and is shown in Figure 2-33.


49

Figure 2-33. Textile composite modelling strategy by Lomov et al 57

Following the section on analytical methods, it was established that even simplified

analytical techniques of molten knitted fabric tensile property analysis would prove too

difficult to establish and would provide no significant contribution or addition to the

information which all ready exists on the topic. Also, adapting the theory to the case of

a molten composite would be an extremely difficult task. There was also the

requirement that instead of simply developing a predictive tool, a micro mechanical

model be developed that could gather information in a form that could be easily

processed to find out the type of quantitative information that had never been explored

before. Emphasis was therefore placed on developing the most accurate and flexible

numerical model for the analysis of knitted fabrics and their composites.

No known authors have dealt with knitted fabrics at the filament level before. Most, like

the works of Takano 38 and Pickett 58 have dealt with micro structural models with the

yarn as the smallest element. However, the work done by Pickett on the micro

modelling of yarn architecture in 3D braids using explicit dynamic finite element

techniques provided a preview to the type of information that could be gathered using

these types of numerical analysis tools.

Using a fine mesh of one dimensional linear bar or membrane elements, the braiding

process was simulated incorporating 21 moving and 15 stationary yarns, where the

moving yarns where given a prescribed velocity path to describe their motion. Yarn feed

in and feed out was modelled using non-linear bar elements, which maintained the


50

correct yarn tension conditions during braiding. All bar or membrane elements were

identified and continuously checked for potential contact with one another and in the

case of the membrane elements yarn friction was also incorporated. The basic set up of

Pickett’s model is shown in Figure 2-34. Notice that there are very few elements other

than the ones representing the yarns required, as many of the boundary conditions

including the take-up velocity, and horn gear velocity and displacement loci can be

readily applied to element nodal points.

Figure 2-34. Finite element model for braiding by Pickett 59

Figure 2-35 shows the computer graphics visualisation of the simulation showing that it

is possible to involve a significant number of yarns. Although the possibility of

developing a knitting simulation looked promising, there were some fundamental

differences that had to be considered before proceeding. The type of knitted fabrics that

are considered in this research are produced from a single yarn, which means that

during the process of knitting the yarn would come into contact with itself many times.

This would be an extreme test for robustness of the software’s contact algorithm. There

is also a large amount of contact with knitting machine elements, for example needles

and the knitting machine bed, which means it would not be possible to simply apply the

boundary conditions to nodes. Along with this, it was planned that the simulation be


51

done at the filament level using a high order beam element, which would give more

information than just the stress strain response along an element’s axial direction.

Figure 2-35. Bar element braiding models generated by PAM SOLID™ 58

In Pickett’s work, once the braid has been generated it is used as a basis to construct a

macro-mechanical model of the braided composite. Bar and solid elements are

combined by assembling both element types over one another and defining new bar

nodes at the intersection of each solid facet as shown in Figure 2-36 (a) 58. During the

simulation the internal forces of the bar nodes are transferred to the solid nodes using

standard element shape functions 58. Nodal quantities for the solid elements are

calculated and then mapped back to the bar elements using the same shape functions.

The validity of the method has been verified using simple yarn-in-matrix models, shown

in Figure 2-36 (b).

Figure 2-36. (a) Constraining the yarn to the solid and (b) Comparison of yarn force for solid and bar models, (graph shows force variation from upper to lower faces) 59

close up view

(a) (b)


52

2.7 Review of Other Relevant Literature

The following section is a brief review of literature dealing particularly with relevant

knitted fabric composite questions that have arisen during the course of this study and

have been answered by other researchers.

2.7.1 A Note on the Particular Forming Method

Knitted fabric composite components can be produced by the stretching of a flat 2D

preform or the draping of a 3D shape as was shown in Figure 2-6. One of the questions

that have arisen during the course of this study was, does stretching actually make the

knitted composite mechanical properties better? In the work done by Putnoki et al 28

composite specimens made from weft knitted 1x1 rib glass fibre and poly(ethylene

terephthalate) Twintex® commingled yarn, were stretched in the wale direction to

various degrees before consolidation. The effect of having a semicrystalline (C) or

amorphous (A) matrix was also investigated. Some of their results are summarised in

Figure 2-37, which shows clearly that mechanical properties in the stretching direction

are enhanced while in the transverse direction the properties are reduced.

Figure 2-37. Mechanical property variation of glass fibre polyethylene terephthalate with various stretch

ratios and amorphous or semicrystalline matrices 28


53

Therefore the work has highlighted that the material exhibits an increase in anisotropy

due to the stretching and contracting of the wale and course directions. Another

interesting observation was that the transverse impact toughness remained constant

since an increase in strength is accompanied by a reduced ability for deformation.

Overall it has been shown that rather than improving the mechanical properties of the

material, stretching during forming provides a means of redirecting strength and

stiffness in the directions that may be required by the component being manufactured.

2.7.1.1 Forming of Commingled Thermoplastic Composites

Since their inception, research on commingled thermoplastic composites has become

popular with researchers concentrating on optimising forming parameters such as

forming rate, temperature, pressure, and consolidation time to minimise void content,

cycle time and maximise quality 60, 61. With commingled yarn there are again two

options for forming the composite. 1. The compaction of the commingled fabric to the

required thickness and subsequent heating/consolidation within the mould or 2. External

heating and transfer into a cold tool for forming and consolidation. Of course, the

second option is more practical these days as quick in-mould heating techniques are

currently unavailable. However, technologies such as radio frequency heating like that

used in the ply wood industry could change that. In the work by Long et al 60 it was

found that heating commingled preform with no application of pressure caused

migration of the constituents as shown in Figure 2-38, increasing the potential for void

formation. The causes of the migration were described as being caused by the shrinkage

of polypropylene upon heating which tends to coalesce within and between the yarns.

Figure 2-38. Schematic of migration pattern in commingled yarn 60


54

It is stated that the problem of migration can also be caused by differences in the

constituent fibre sizes, and in the case of fabrics, this coupled with the yarn crossover

forces cause the migration of the smaller diameter fibres towards the contact point.

Therefore, an ideal process might be one where the yarn contains equally sized fibres

and migration during consolidation is controlled by precompaction.

2.7.2 Shear Deformation Testing of Fabrics

Shear deformation testing of woven fabrics has been quite common, the aim being to

determine material properties such as the shear modulus, and determine the particular

fabric-locking angle. More information on the experimental techniques used in this type

of testing is given in the works by Prodromou 62 and Mohammed et al 63 and is

explained and utilised in Chapter 3.

55

Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic

Sheets

3.1 Manufacture of Sheet and Raw Materials

The experimental study of the deformation of knitted fabric composites concentrated on

two basic knit structures, the 1x1 rib and full milano the reasons for which are detailed

in Section 2.2.3. Most of the experimental work carried out was performed on the full

milano fabric with the specifications listed in Table 3-1. During the course of the study

the E-glass fibre yarn used to manufacture the fabric was acquired which meant that

different structures could be produced, including the simpler 1x1 rib structure, which

was subsequently used for experimental verifications of the simulation work, detailed in

Chapter 5. Along with this, a short study of the post forming mechanical properties of a

heavier high volume fraction commingled (E-glass/Polypropylene) 1x1 rib fabric was

also investigated and compared to materials including Aluminium and Vetrotex’s

balanced twill weave. When these other materials are specifically involved it will be

clearly stated, otherwise the reader may assume that it is the full milano structure that is

being used.

Table 3-1. Specifications for the types of materials used

Fabric Structure Yarn Size

(Linear Density) Tex g/km

Areal Weight

g/m2

Resulting Fibre Volume Fraction

Single Fabric Sheet Thickness

(mm)

Full Milano 68 700 -750 0.20 1.6mm

1 X 1 Rib 68 - 0.20 1.6mm

1 X 1 Rib(Commingled) 790 1000 –1100 0.35 5.0mm

Full Milano (Commingled) 790 1000 –1100 0.35 5.0mm

Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet

56

The main focus of this chapter is to investigate the forming behaviour of

preconsolidated thermoplastic composite sheets made from the full milano fabric

specified in Table 3-1. Before any experiments were performed the composite sheets

had to be manufactured using the knitted fabric and a chosen thermoplastic material. A

rotational moulding grade of polypropylene in powdered form, Cotene 9800 (material

property data given in Appendix A) was chosen and the two constituent materials were

consolidated together between two aluminium plates under vacuum pressure at 180°C,

to form single layered preform sheets 1.8mm thick with a fibre volume fraction of 20%.

Multi layered sheets with up to four plies of the fabric were also manufactured and

depending on how many plies and how they were oriented, measured up to 6.4mm thick

and contained an average fibre volume fraction of 15%.

For standard glass fibre reinforced materials, fibre volume fractions between 15 and

20% are considered to be quite low. The reasons for the low fibre volume fractions

come from the knitted fabric, which has a low-density structure compared to something

such as a weave and needs to be knitted tightly and compressed in the thickness

direction in order achieve higher fibre volume fraction values. However, there are

drawbacks to the formability if the structure is compressed too much and reheating

preconsolidated sheets that have been severely compressed re-inflate, which can be

undesirable for the sheet forming process. Along with this, severe compression can

cause fibre damage, compromising the integrity of the fabric. At this stage of the

material’s development, a general understanding of the forming behaviour can be

obtained using specimens of low fibre volume fraction.

3.2 In-Plane Forming Behaviour

In-plane forming deformations involve two out of the four macro-level deformation

modes, namely in-plane tension and in-plane shear, as was shown in Figure 2-19. To

examine the material’s behaviour under these two modes individually, a series of simple

tensile tests and more detailed shear deformation experiments were performed.

3.2.1 Unidirectional Behaviour: Tensile Testing

Characterisation methods for ordinary materials such as steel and aluminium usually

involve the extraction of relevant material property parameters from reliable tensile test

data. These parameters are then used together with the appropriate material model to


57

describe the material’s deformation behaviour. In this set of experiments, samples of 2-

ply, 4mm thick, milano rib fabric thermoplastic composite material were tested in order

to gather material data, which could be used during the macro modelling stages of this

work. The specimens, which measured 100 x 25mm with a gauge length of 80mm, were

heated to 180°C and stretched at a rate of 100mm/min. Although the experiments were

not performed under isothermal conditions, as could be the case in industry, the curves

shown in Figure 3-1 show a reasonable level of consistency due to the forming window

presented by polypropylene. The true stress strain curves have been plotted assuming a

condition of volume constancy.

Figure 3-1. Warp and weft true stress-strain curves for molten knitted composite (180°C 100mm/min)

Appendix B shows the same curves plotted using force versus extension which gives a

more intuitive look as to how much the warp and weft material specimens have

stretched. The curves show engineering strains of up to 87.5% for the warp direction

and 125% for the weft direction as well as different levels of failure stress. In

experiments involving a single layer of fabric similar characteristics appear. However,

considering all the dimensional ratios it can be concluded that the failure stress of the

composite is more than double that of the fabric, which means that the molten matrix

Weft

Warp


58

does have a significant effect on the material behaviour. A specimen width of 25mm

was large enough to avoid any edge effects caused by cutting, see Appendix C for fabric

only data.

To convert the data shown in Figure 3-1 into something that is useful for simulation

purposes, the modulus or stiffness curves versus strain in both the warp and weft

directions need to be calculated. True modulus values at various points of the material’s

deformation are extracted using true stress-strain rather than engineering stress-strain

data since the magnitude of the deformations occurring in the material are extremely

large. Figure 3-2 shows a close up of the initial portion of the modulus curves generated

using the moving average of five points from the true stress-strain data points. The full-

scale y-axis plot is given in Appendix D.

Figure 3-2. Close up of warp and weft modulus curves for knitted fabric composite (180°C 100mm/min)

The ripples introduced by numerical differentiation make it difficult to examine the two

curves accurately, however there is a definite indication that the warp direction

stretching gives a greater modulus throughout the deformation range. With the modulus

data in hand, numerical tensile tests can be set-up using different material models to see


59

which one best matches the behaviour of the material. This is done in the second part of

Chapter 5.

3.2.2 Shear Behaviour: The Picture Frame Test

The key idea behind this set of experiments was to study the differences in forming

behaviour between the prepreg material and the knitted fabric alone under one of the

prepreg deformation modes, namely intra-ply shear. The macro-level fabric deformation

mode associated is in-plane shear and the details of the micro-level fabric deformation

modes, were unknown at the time. The so-called “picture frame shear test” applies an

almost pure shear strain to see how both the knitted fabric and composite material react

to this mode of deformation.

Figure 3-3. Picture frame shear test experimental setup

The picture frame rig, mounted in an environment chamber and Instron tensile testing

machine as shown in Figure 3-3, was used to perform the experiments and generate

analysis data in the form of F-D curves and GSA specimens.


60

3.2.2.1 Picture frame rig

The picture frame rig itself basically consists of four spring-loaded pin jointed linkages

with mounted clamps on each to hold the composite or fabric specimen in place as

shown in Figure 3-4. Grids were printed on the composite specimens using a digitiser to

form a matrix of points with a spacing of 4mm; therefore four points approximately

enclosed a unit cell of the knitted fabric. The specimens were then subjected to a 40mm

vertical displacement, which corresponded to a shear angle of 24°. This was the largest

shear angle that could be accommodated in all of the experiments without the onset of

buckling.

Figure 3-4. The picture frame mechanism

3.2.2.2 Test parameters

Force displacement data was gathered for several situations including the knitted fabric

alone at room temperature (20°C) as well as elevated temperatures of 180 190 and

200°C. F-D data for the composite specimens at these temperatures was also collected.

Strain rate was another parameter considered with each specimen tested at rates of 10,

100, 300 and 500mm/min for each temperature. Along with this, empty frame data was

collected at the required test temperatures and test speeds so that it could be subtracted

from the raw data to give only the response of the material. These experiments showed

no real difference in behaviour as can be seen in Appendix E. A summary of the data

collected is given in Table 3-2.

Fv

Φ

Shear Angle: θs = 90 - 2Φ

Shear Force: Fs = Fv/(2cosΦ)


61

Table 3-2. Summary of data collected from shear deformation experiments Test Temperature (°C) Test Speed (mm/min) 20°C 170°C 180°C 190°C 200°C 10 100 300 500 Empty Frame b b* b b b b b b b Fabric b b* b b b b b b b Composite - - b b b b b b b

*data available but not processed

Another part of the experiment involved measuring the displacement in the grid pattern

after deformation and visualising the results using a GSA software package. The

orientation of the fabric when mounted in the picture frame rig was a further

consideration. The fabric could either be cut so that the force was applied at 45° to the

warp and weft directions or parallel to the warp and weft directions as shown in Figure

3-5(a) and Figure 3-5(b). This would allow the identification of different micro-level

fabric deformation mechanisms that might come into play based on the different fabric

orientations.

Figure 3-5. Fabric orientations (a) Force applied at 45° to warp and weft (b) Force applied parallel to warp and weft

With the fabric placed in orientation (a) the composite sample experienced the

immediate onset of buckling. The experiment indicated that this particular knitted fabric

could not accommodate any magnitude of inter-yarn shear and that the other micro-level

fabric deformation mechanisms such as inter-yarn slip and yarn bending are effectively

switched off in this orientation. For fabric sample (b) however, wrinkling occurred at a

much later stage. Therefore, to compare the differences between fabric and composite

deformation behaviour, the rest of the experiments were done with the fabric in

(a) (b)


62

orientation (b). The difference in behaviour between the two fabric reinforcement

configurations is shown in Figure 3-6.

Figure 3-6. Comparison between fabric reinforcement orientations (a) and (b)

3.2.2.3 Test results

Figure 3-7 shows the force displacement curve for the knitted fabric at room

temperature, at a displacement rate of 10mm/min.

Figure 3-7. Knitted fabric at room temperature (20°C) 10mm/min


63

The experiment was performed in the forward and reversed directions to gain a better

understanding of the material’s behaviour. The force displacement curves indicate that

the repeatability of the experiment is quite good and that friction, the intra-yarn or inter

fibre friction along with yarn bending seem to be the dominant deformation

mechanisms. This can be verified by studying the shape of the reverse cycle curve. In

reverse cycle deformation the material again needs to overcome the static friction

component of deformation and then settles into the dynamic friction component along

with a helping bending force evidenced by the slightly lower gradient of the reverse

curve. For these test parameters the largest magnitude of force is around 20N at a

maximum shear angle of 24°. A vertical displacement of 40mm, which corresponds to a

shear angle of 24° was found to be the maximum displacement that could be

accommodated with no occurrence of wrinkling. The experiment was also performed at

test speeds of 100, 300 and 500mm/min, given in Appendix F, which showed no

obvious change in behaviour.

Figure 3-8. Knitted fabric at elevated temperature (180°C) 10mm/min


64

In Figure 3-8 only the temperature parameter has been changed from room temperature

(20°C) to 180°C, again for the fabric on its own. The force displacement curves show

that the static and dynamic friction components of the deformation have significantly

reduced due to the lubrication introduced by the molten chemical sizing on the fibres.

The force at the maximum shear angle is now just below 14N, however, the linear

slopes of the curves remain similar, although slightly lower indicating that lubrication is

occurring between the fibres as they are bent. The room temperature test also shows a

slight increase in the slope of the curve between 20 – 25mm displacement, which is

characteristic of the yarn stretching component becoming more prominent as it should,

given the higher friction at this temperature. Again, there were no apparent differences

in the behaviour of the heated fabric at the higher test speeds, which are given

individually in Appendix G.

A comparison of the average curves at elevated and room temperature for all test speeds

and temperatures is shown in Figure 3-9.

Figure 3-9. Comparison of knitted fabric at all temperatures and strain rates


65

While it is difficult to identify individual curves on the graph, Figure 3-9 gives an

overall picture of the effects of temperature and strain rate on the fabric and shows that

that the only influential factor is the large temperature difference activating the

lubricating effect of the sizing. In fact, no strain rate effects seem to be present at all,

except in the room temperature curves, which show shifts in the forward and reverse

curves, but have the same encompassing area, suggesting that this is more likely to be

an inconsistency caused by the high levels of friction and hysteresis at this temperature

rather than strain rate effects. Appendix H shows curves for 20 and 180°C at

10mm/min, which are representative of the difference, for more clarity.

Figure 3-10 shows F-D data for the composite specimen at 180°C. It can be seen that

for a displacement rate of 10mm/min, the addition of the molten matrix has had a

further effect on the shape of the curve, again slightly reducing the static and dynamic

friction components.

Figure 3-10. Knitted fabric composite at elevated temperature (180°C) all rates


66

Assuming that the molten matrix does not infiltrate the yarn can help explain the shape

of the forward and reverse curves. At higher displacement rates the yarn-bending

component of the forward curves is subjected to the viscous effects of the thermoplastic

polymer, therefore the slope of the curves increase. If the polymer infiltrated the yarn

then we would expect an increase in the friction component, for example the curve

would have the same slope but be shifted upwards. The reverse curves however, show a

slightly different trend. This can be explained by considering the restoring bending and

twisting forces, which try to keep all the yarns at the minimum curvature given the

initial configuration or “minimum energy state” of the fabric reinforcement. Therefore

in the reverse cycle the restoring force adds an extra component to the curve giving it a

slightly different shape.

As the temperature parameter is increased from 180°C to 190 and 200°C the viscosity

of the matrix decreases and the large differences in the curves at different rates shown in

Figure 3-10 begin to narrow. The graphs for these temperatures are shown in Figure

3-11 and Figure 3-12.



67

3.2.2.4 Parametric study using spring and dashpot systems

A simple modelling approach to study the behaviour of the mechanisms occurring in the

knitted fabric and its composite would be to represent the unit cell using a viscoelastic

system such as the one shown in Figure 3-13. The difficulty though with this implicit

form of modelling is identifying which element corresponds to which deformation

mechanism. However, using the methodology discussed in Chapter 2 Section 2.6.2.1 the

different stiffness and viscous components can be assembled and experiments such as

the picture frame test, provide the data required for comparison and verification. In

theory if the micro-level fabric deformation mechanisms described in Chapter 2, Section

2.4.3 are in fact all of the mechanisms occurring, then the force displacement curve

could be perfectly described by eight elements (five elastic and three viscous, although

the arrangement of these elements are uncertain). Examining this concept in more detail

it can be seen that the number of mechanisms can actually be reduced to six, since yarn



68

buckling and yarn bending are essentially the same mechanism. This is also true for

inter-yarn slip and inter-yarn shear. The draw back of this method is that such a model

would give no information about the geometry of the fabric in the composite below the

macro-level.

Initially, to examine the characteristics of the curves generated from the picture frame

experiments, a general purpose four-component model is assembled; see Figure 3-13.

Using this model, a curve can be fitted to the forward part of the experimental results

and the magnitude of the elements varied to assess their influence on the curve’s

behaviour. The deformation mechanisms can be assigned to the elements by considering

the behaviour of the material as was considered in the literature review in Section

2.6.2.1. Developing an idealised model means using this knowledge to put spring and

dampers in the appropriate positions to properly represent the interaction between the

different mechanisms. The methodology is discussed as follows.

In the fabric on its own, yarn bending and twist must occur in parallel with intra-yarn

slip and can be represented by E2 and η2 respectively. Yarn compression and stretching

however, appear in series with inter yarn slip and the viscous effects of the matrix,

which are represented by E1 and η1. The explanation for the assignment is as follows.

Figure 3-13. Four-component spring and damper model

E2

η2

E1

η1

Viscoelastic

Viscous Flow

Elastic

E1 = Yarn compression + Yarn stretching

E2 = Yarn bending + Yarn twist

η1 = Viscous effects of the matrix + Inter-yarn slip

η2 = Viscous effects of fibre coating or Intra-yarn slip friction


69

The material consists of two parts; the reinforcement and the matrix, which experience

the same force during deformation but not the same amount of strain, assuming the

fabric is able to pass through the molten matrix, and therefore work together in series.

For the matrix material, its viscous and elastic components also work in series because

of the same reason, although in this model it is only represented as a viscous element.

For the reinforcement (or fabric), its elastic component E2 represents the sum of all the

elastic components of the yarn including bending and twist, which work in parallel with

the viscous element η2 representing the friction or viscous effects between the

individual fibres.

Given the explanation for choosing what each element represents, the model can be

fitted to the forward portion of the picture frame test curves. This is shown in Figure

3-14 where the model has been fitted to the knitted fabric at room (20°C) and elevated

(180°C) temperatures and shows that the 4-component model is almost good enough to

Figure 3-14. Fitting curves derived from the 4-componet model


70

do the job. The effects of varying the parameters on the shape of the model curve are

examined in Appendix I.

Variation of E1, which is specified as being the combination of yarn compression and

yarn stretching, is shown in Appendix I. It can be seen that increasing this parameter

does not modify the size of the curve after the best fit, as would be the case if yarn

bending and tensile stiffness were independent parameters. Increasing this parameter

also increases the slope of the curve in the initial displacement region. In relation to the

real life system, this tends to suggest that yarn tensile stiffness plays an important role at

the initial stages of deformation when friction is being overcome.

Increasing E2, also shown in Appendix I, which represents yarn bending and yarn twist,

increases the slope of the curve in the initial and latter parts of the curve, which is

reasonable and what would be expected in the real life system if the bending and

torsional stiffness were higher.

Variation of η1 is again a simple parameter to verify. It represents the viscous effects of

the matrix and inter-yarn slip. The graph in Appendix I can be compared with the

experimental results of the picture frame test for the composite at varying displacement

rates (i.e. different viscosity, as shown in Figure 3-10 - Figure 3-12), which show very

similar effects on the shape of the force displacement curve.

η2, which has been assigned to represent the intra-yarn slip also follows an expected

trend and increases the slope and size of the curve at the early and latter stages of

deformation, again see Appendix I. The assignment of this parameter has been verified

in Figure 3-14, which only uses variation in η2 to match the model with the

experimental effects of increased intra-yarn lubrication. Note that an increase in

temperature should affect both intra-yarn and inter-yarn friction. Inter-yarn friction is

reflected in the experimental curves by an increase in the slope during the second half of

the forward curve, which is where inter-yarn slip tends to come into effect.

The picture frame experiments have highlighted some important issues associated with

knitted fabric composites. The lubrication effect that the chemical sizing produces at


71

typical forming temperatures in not only the fabric but the composite, delays the onset

of buckling and reduces forming forces significantly. Perhaps designing a sizing that not

only provides good fibre to matrix cohesion but also lubricates well at forming

temperatures would be a worthwhile project to look into. The experiments have also

helped highlight the importance of friction and bending as the major components of

deformation, which is important information for macro modelling purposes.

Following the study using the four-component model, an ideal six-component model for

molten knitted fabric composites is suggested. There are two major differences in this

model which now incorporates all six of the mechanism elements. 1. The viscous effects

of the matrix are now assumed to have the same strain as the fabric, meaning that the

matrix moves with the fabric resulting in its dashpot element being placed in parallel

with all the other elements. 2. Yarn compression has been separated and placed in series

with the element group of yarn bending and yarn twist since it involves the movement

and interaction of individual filaments under similar forces applied to these elements.

Figure 3-15. Ideal molten knitted fabric composite spring and damper model

E3

η2

E1

η1

E1 = Yarn stretching

E2 = Yarn compression

E3 = Yarn bending

E4 = Yarn twist

η1 = Viscous effects of fibre coating or Intra-yarn slip friction

η2 = Viscous effects of the matrix + Inter-yarn slip

E2

E4


72

If the arrangement of the elements has been guessed correctly, this model would give

very good predictions of the material behaviour. However, it can be difficult to know

what values need to be assigned and the model is purely predictive in nature. For this

reason it was decided that micro-level modelling where a quantative prediction and

analysis of the material behaviour would be possible should be carried out. This major

section of work is presented in Chapter 5.

3.3 Single Curvature Forming

If three out of the four macro-level deformation modes are involved, this is termed

single curvature forming. Here, forming takes place as the specimen bends about one of

its three orientation axes. For multiply specimens, this also introduces the sliding of

plies past one another, or, interply shear.

3.3.1 Vee-Bending (Interply Shear and Stretch Behaviour)

Unless some form of three-dimensional reinforcing structure is used, most 2D textile

composite material sheet forming processes will involve multiple plies. During woven

and unidirectional sheet forming, interply shear plays a big role in the successful

forming of the part, because in these structures, the reinforcement is practically

inextensible. With knitted fabrics, the plies of the material can either stretch or slide past

one another (interply shear), or both, to achieve the desired shape. The purpose of the

Vee-bending experiments was to investigate the competing mechanisms of interply slip

fabric stretch as well as draw-in and shape fixability.

The tests involved the matched die forming of V-shaped specimens from flat strips of

the material subject to various forming parameters including the number of plies used,

orientation of the plies, forming temperature and applied clamping mass, which

controlled the amount of stretch versus draw-in occurring in the material. A summary of

the test parameters is shown in Table 3-3. Notice that in most cases, except for the cross

ply specimens, only the warp direction has been selected for testing since previous

testing, Figure 3-1, has shown the two directions behave in an analogous fashion.


73

Table 3-3. Vee-bending test parameters

Specimen Number No. of Plies Thickness

(mm) Orientation Temperature (°C)

Applied Clamping Mass (kg)

1 2 4 Xply, warp top 160 0.5 2 2 4 Xply, warp top 160 1 3 2 4 Xply, weft top 160 1.5 4 2 4 Xply, weft top 160 2 5 2 4 Xply, weft top 180 1.5 6 2 4 Xply, weft top 150 1.5 8 3 6 warp 160 3 9 3 6 warp 160 3 10 3 6 warp 160 4 11 2 4 warp 160 2 12 2 4 warp 160 2 13 2 4 warp 160 1 15 2 4 warp 160 0.5 19 2 4 warp 160 4 20 2 4 warp 160 1.5 21 3 6 warp 160 0 22 3 6 warp 160 1.5 23 2 4 Xply, weft top 160 0 24 2 4 Xply, weft top 160 0.5 25 2 4 Xply, weft top 160 1 29 3 6 warp 180 2 30 3 6 warp 180 2 31 3 6 warp 180 6 32 3 6 warp 180 6 33 3 6 warp 180 0 34 3 6 warp 180 0 41 3 6 warp 170 2 43 3 6 warp 160 2 50 3 biaxial 6 warp 160 2 51 3 biaxial 6 warp 180 0 52 3 biaxial 6 warp 170 2

Note: Missing specimen numbers are for specimens not tested or discarded

biaxial = woven fabric specimen

3.3.2 Vee-Bending Equipment

The vee-bending equipment itself, consisted of a matching male and female 45° vee,

with an inner nose radius of 7.5mm, clamping frame, cylinders, and masses as shown in

Figure 3-16. The specimens were heated to an equilibrium temperature, in an oven

adjacent to the rig and were then transferred for forming. Up to 6kg of mass (depending

on the thickness of specimen used) was applied to the clamping frame, which

transferred a holding force into the drawbead like cylinders, to control the amount of

stretching in the specimen. Forming rate (movement of the male die) was held constant

at 350mm/min.


74

The matched die forming process was chosen in order to correct the “puffing up” and

“edge fraying” that occurred in the neatly consolidated blank, once reheated for vee-

bending. Lubrication effects introduced at the forming temperature caused edge fraying

in the molten blank that was even more severe than in the original dry fabric. Overall,

the knitted reinforcement showed no signs of relaxation and would reinflate readily

upon reheating, see Figure 3-17.

The tests also involved a simple form of the GSA technique whereby lines were marked

on the upper and lower surfaces of the specimens at 10mm intervals perpendicular to the

length of the specimen, both sides exactly aligned prior to forming. Following

processing, the surface strain on each side of the specimen was measured along with the

average amount of interply shear, indicated by the misalignment of corresponding

Figure 3-16. Schematic of vee-bending rig (a) Apparatus prior to forming (b) Post forming

Clamping Masses

Clamping Cylinder

Female Vee Block Specimen

Spring Connection

(a)

(b)


75

marks on the upper and lower surfaces. The assumption was made that the strains

occurring on the exposed surfaces of the top and bottom plies was indicative of the

strain throughout these plies. Justification for this was that the lines remained coherent

during forming and yielded strains, which concurred with a visual assessment of strain

from the changes in the fabric pattern.

3.3.3 Test Results

Table 3-4 summarises the measurements obtained from all the experiments.

Figure 3-17. Post formed vee-bend specimen showing “edge fraying”


76

Table 3-4. Vee-bending results table

Specimen Number

Outer Grid Spacing (mm)(bottom)

Outer True Strain

Inner Grid Spacing (mm)(top)

Inner True Strain

Average IP Shear (mm)

Spring Forward °

1 12 0.182 11 0.095 -2 3.5 2 12.5 0.223 13 0.262 -2 4.5 3 14 0.336 14 0.336 -2 4.5 4 17 0.531 17 0.531 -3 0 5 14 0.336 15 0.405 - 1.5 6 14 0.336 14 0.336 -2 4.5 8 15 0.405 14 0.336 -0.5 3 9 14 0.336 13.5 0.300 0 3 10 17 0.531 16.5 0.501 -1 1.5 11 16 0.470 16 0.470 -2 0.5 12 15.5 0.438 15 0.405 -2 0.5 13 14.5 0.372 14.5 0.372 -2 2 15 12 0.182 11.5 0.140 -2 3.5 19 16 0.470 16 0.470 -2 1.5 20 13 0.262 13 0.262 - 3.5 21 11 0.095 10 0.000 -2.5 4.5 *22 15 0.405 14 0.336 -2 3 **23 10 0.000 10 0.000 -1 3.5 **24 10.5 0.049 12.5 0.223 -1 2 25 14 0.336 14 0.336 -1 3 29 13.5 0.300 12 0.182 -1 3 30 14 0.336 12.5 0.223 -3 2.5 31 19 0.642 16.5 0.501 - 0.5 32 18.5 0.615 16 0.470 - 0 33 10 0.000 9 -0.105 -2 4 34 11 0.095 10 0.000 -2.5 3 ***41 12 0.182 12 0.182 0-2 1.5 ***43 10 0.000 10 0 0 -3.5 ***50 10 0.000 10 0 2-3 2.5 ***51 10 0.000 10 0 - 3 ***52 10 0.000 10 0 2-3 2

*22 = Specimen experienced sticking on forming

**23,24 = Specimen formed using incorrect die

***41,43,50,51,52 = Specimen formed in soft rather than molten state

The graph shown in Figure 3-18 shows the trend lines for the inner and outer

engineering strains versus the clamping force per unit width for all the specimens tested.

An expected trend of increasing strain with increasing clamping force is observed in the

inner and outer plies of all the specimens. With both sets of 2ply specimens it is very

difficult to identify any trend in the interply shear behaviour (even more the case for the

X-ply specimens) due to the variability of the experiment. The 3ply specimens show a

marginal trend of widening of the strain levels in the inner and outer plies as the

clamping force increases, indicating that some interply shear may be taking place.

However, this could also be attributed to uneven stretching through the thickness.


77

Shape fixability due to thermal expansion and shrinkage is a common consideration in

many thermoplastics forming processes. When fibre reinforcements are involved, the

behaviour seems to not only be altered by the directionality of the fibres, but in the case

of knitted fabrics, the amount of strain in the knitted structure as well. In these

experiments, the vee-bend specimens exhibited a springforward behaviour, which

means that a smaller vee-angle is achieved in the final consolidated part once removed,

than that of the forming die.

In Figure 3-19 the correlation between the springforward behaviour and the clamping

force is presented. Again, the 3ply 6mm specimens showed the most convincing trend

that the springforward behaviour actually diminishes with increasing clamping force.

This is a particularly important trend because it means that a manufacturer could ensure

a component’s shape fixability by applying the correct clamping force to the material

during forming.

Figure 3-18. Clamping force versus strain (for all specimens)


78

The results presented thus far have dealt with the material in a molten state. A small set

of experiments were performed to see whether the material could be formed in a

softened state and alleviate some of the problems of edge fraying and untidy

consolidation. Rather than fully melting the specimens, they were heated to

temperatures of 160°C and 170°C, specimens 41 through 52 in Table 3-3 and Table 3-4.

Figure 3-20 shows the difference in quality between the molten and softened vee-bend

specimens. Even at 170°C, because of the melt characteristics of polypropylene, the

specimens remained fairly stiff, but formable.

To compare the interply shear behaviour of the knitted fabric to a material more widely

used and studied, specimens of biaxial straight fibre (woven) reinforced polypropylene

of the same volume fraction and thickness were also tested at the temperatures of

160°C, 170°C and 180°C(molten).

Figure 3-19. Clamping force versus springforward for all specimens


79

Inspection of the lines on the samples shown in Figure 3-20 (b) reveals that the knitted

material deforms through pure bending (no interply shear) at 160ºC, with slight interply

shear occurring at 170ºC. The biaxial material, by contrast, must deform purely through

interply shear at all temperatures as indicated by the stepwise patterns, with buckling

observed at the inner nose radius of the 160ºC test specimen due to the lack of allowable

interply shear when the material forming temperature becomes too low.

Figure 3-20. (a) Molten and (b) softened vee bending specimens

Figure 3-21. Springforward versus forming temperature with clamping force as marker identifier

(a) (b)

0% 20% 90%

Biaxial 160°C170°C

170°C Knitted 160°C


80

Another interesting observation involves the variation in the springback/springforward

behaviour at the tested temperatures. In the softened state, the knitted material

demonstrated a wider band of springforward behaviour and even springback at these

lower temperatures, rather than the narrower band of purely springforward behaviour

observed in the molten samples, see Figure 3-21. The trend of decreasing springforward

behaviour at a fixed temperature is still apparent even though each marker may be

representing a slightly different configuration of the material.

3.4 Double Curvature Forming

3.4.1 3D Forming: The Dome Forming Test

A well-established method of assessing the ability of a particular material to form

doubly curved components is through the production of hemispherical domes. The

purpose of the dome forming tests was to examine the behaviour of knitted fabric

composites when thermoforming three-dimensional parts.

The two different forming methods investigated were matched die forming, and

pressure forming using diaphragms. A test rig was constructed which allowed the

forming of hemispherical domes under controlled parameters such as blank temperature,

blank size, shape and thickness, die temperature, forming speed, in the case of match die

forming, as well as pressure and rate of pressure release for pressure forming. To obtain

a physical measure of the specimen’s behaviour, the grid strain analysis technique was

used to investigate the surface and thickness strains in the material as outlined in

Section 2.6.1.1. Table 3-5 shows an overall account of the number of experiments

performed.


81

Table 3-5. Dome forming test parameters

Disc No.

Diameter (mm)

No. of Plies

Thickness (mm)

Tool Temperature (°C)

Air Temperature (°C)

Material State Forming Process

1s 100 1 1.8 160 180 molten 180°C MD 2s 100 1 1.8 160 180 molten 180°C PF 1 100 2 3.5 165 180 molten 180°C MD 2 100 2 3.7 170 180 molten 180°C MD 3 100 2 3.1 165 180 molten 180°C MD 4 100 2 3.6 160 180 soft @ 155°C MD 5 100 2 3.7 25 20 molten 180°C MD 6 100 2 3.7 160 180 molten 180°C MD 7 100 2 4 155 200 soft @ 155°C MD 8 100 2 4.1 130 145 soft @ 145°C MD 9 100 2 4.1 180 200 molten 170°C MD 10 70 2 4.1 160 180 molten 175°C MD 11 70 2 4.1 25 180 molten 175°C MD +12 100 3 5 160 160 molten 175°C MD +13 100 3 5.1 160 160 soft @ 160°C MD 14 100 3 5.5 160 180 molten 170°C MD +15 100 3 5.3 150 180 soft @ 150°C MD +16 100 3 5.4 25 20 molten 180°C MD 17 100 3 biaxial 5.5 22 20 molten 180°C MD +18 100 3 biaxial 5.2 22 20 molten 180°C MD 19 100 3 biaxial 5.7 130 170 soft @ 160°C MD 20 100 3 5.8 160 170 molten 180°C MD 21 70 3 5.8 160 180 molten 180°C MD +22 70 3 5.6 160 180 molten 180°C MD 23 70 3 5.6 160 180 molten 180°C MD 24 70 3 5.6 160 180 soft @ 160°C MD 25 70 3 6.4 22 20 molten 180°C MD 26 70 3 5.7 23 20 soft @ 160°C MD +27 70 3 5.1 23 20 soft @ 160°C MD 28 70 3 5.6 22 20 molten 180°C MD 29 70 3 biaxial 5.5 160 180 molten 180°C MD 30 70 3 biaxial 5.6 160 180 molten 180°C MD

*PF = Specimen formed using the pressure forming process

**MD = Specimen formed using the matched die forming process

+ = Indicates the specimen has been selected for grid strain analysis

biaxial = woven fabric specimen

s = single ply specimen

Due to the large number of parameters the forming rate for all the experiments was held

constant at 350mm/min.


82

3.4.2 The Dome Forming Rig

Figure 3-22 shows a photo of the hemispherical dome forming experimental set-up. The

rig is capable of a number of different forming scenarios including isothermal/non

isothermal, pressure/matched die/rubber plug assisted forming and is equipped with

cooling channels and an interchangeable male dome forming tool to allow for different

specimen sheet thickness.

The entire tooling is mounted inside an environment chamber for temperature control of

the blank and tool surfaces, while the top half of the die is attached to the Instron tensile

testing machine crosshead, to allow forming speed control. In Figure 3-22 the rig has

been set-up for the pressure forming process and the two grey heat resistant hoses apply

vacuum pressure between the diaphragms that enclose the blank and the air pressure

required to form the dome via the top half of the tooling. In the matched die forming

process, the pressure plate and vacuum frame are removed and a male mould allowing

interchangeable dome inserts is used. The yellow hoses exiting the heating chamber

apply water-cooling to the attachment arm leading to the load cell as well as the die so

Figure 3-22. Dome forming experimental set-up


83

that the cycle time for the experiment is greatly reduced. The cycle time for pressure

forming a dome is approximately 35mins. A slightly shorter cycle time is required for

the matched die forming process if the blank is heated in-situ, however when forming

using a cold tooling condition the blank may be heated externally which reduces the

cycle time significantly (approx. 10mins). Thermocouples are used to monitor the blank

temperature and the die temperature and in the case of the matched die forming set-up,

forming forces (which did not yield any significant information on the forming

behaviour) could also be recorded. A close-up of the pressure forming in progress and

matched die forming equipment is shown in Figure 3-23. Because of the complexity of

the set-up and cycle time, pressure forming was only used as a comparison to the more

efficient matched die forming process with which most of the experiments were

performed. However, Appendix J shows a comparison of two single ply domes made

using the two processes.

3.4.3 Test Results

The most useful information comparing the behaviour of the material when

manufacturing domes under different forming conditions was obtained using the grid

strain analysis technique. A selection of seven domes were chosen as identified in Table

3-5 and analysed with regards to surface strains, thickness variation and draw-in

behaviour. Figure 3-24 – Figure 3-30 present the detailed results of all the selected

domes.

3.4.3.1 Surface Strains and Thickness Contours

Figure 3-23. Close up of (a) Pressure forming and (b) Matched die forming equipment

(a) (b)


84

Specimen Forming Parameters Diameter Size = 100mm No. of Plies = 3 Original Thickness = 5mm Tool Temperature = 160°C Air Temperature = 160°C Material State = molten 175°C

Surface Strain Arrow Diagram

Surface and Thickness Strain Max Surface Strain = 62.8% Min Surface Strain = -25.1% Max Thickness Strain = 15.4% Min Thickness Strain = -30.4%

Percentage Thickness Strain Contours

Observations Significant levels of surface strain occur in both the flange and hemispherical regions of the dome. The strains are distributed smoothly, indicating the dominance of the reinforcing structure. Around the base of the dome draw-in has caused a region of negative strain or thickening, more so towards the warp direction axis while in the weft direction this effect has been offset by the amount of weft direction stretching that has occurred. The maximum surface strain reaches a value of 62.8% which is half of the maximum strain that can be accommodated by the weft direction and approximately 72% of the warp direction maximum. In-plane shear deformation occurs readily as indicated by the gradual rotation of the surface strain arrows with respect to the warp and weft directions.

Figure 3-24. Dome 12

weft warp


85

Specimen Forming Parameters Diameter Size = 100mm No. of Plies = 3 Original Thickness = 5.1mm Tool Temperature = 160°C Air Temperature = 160°C Material State = soft @ 160°C




Observations The forming parameters are identical to those used in Dome 12 except for the specimen itself, which is now heated to a softened state at 160°C. Looking first at the surface strains indicates that a very small amount of strain has occurred in the flange region. The thickness strains confirm this, although there is a small amount of overall thickening in the flange and again definite thickening at the base of the dome along with a clear strain gradient moving towards the apex of the dome. While the scale is similar to Dome 12 the actual thickness strain range, (indicated by the line markers to the right of the contour scale) shows a larger strain range (more strains occurring on the positive thickness side) and a lower maximum surface strain compared to Dome 12 (a more even positive and negative strain distribution). Note that the contour bars are always symmetrical, have different scales and that the “contour scale trimming” lines to the right of the bars show the range in which the actual “linear” thickness strains reside. The arrow diagram and maximum and minimum surface and thickness values given, are all “Lagrange” strains. Lagrange strains are more accurate since large displacement gradient taken into account.


weft warp


86

Specimen Forming Parameters Diameter Size = 100mm No. of Plies = 3 Original Thickness = 5.3mm Tool Temperature = 150°C Air Temperature = 180°C Material State = soft @ 150°C




Observations With a tool and material temperature 10°C lower than Dome 13 and air temperature elevated to 180°C (of insignificant influence), the results are much the same to those shown in Dome 13. Again, the strain occurring in the flange is negligible as shown by both the surface strain and thickness strain plots. The only notable difference is perhaps a more uniform strain gradient from the flange to the apex of the dome.


weft warp


87

Specimen Forming Parameters Diameter Size = 100mm No. of Plies = 3 Original Thickness = 5.4mm Tool Temperature = 25°C Air Temperature = 20°C Material State = molten 180°C




Observations Forming the material in its molten state at 180°C against a cold tool (25°C) reintroduces stretching in the flange region once again, as was observed in Dome 12 Figure 3-24. Compared to Dome 12 the specimen exhibits higher maximum and minimum surface and thickness strains, a larger strain range and a more pronounced region of draw-in thickening around the base perimeter of the dome.


weft warp


88

Specimen Forming Parameters Diameter Size = 100mm No. of Plies = 3 (biaxial weave) Original Thickness = 5.2mm Tool Temperature = 22°C Air Temperature = 20°C Material State = molten 180°C




Observations Forming the biaxial weave using parameters almost identical to those in Dome 16 Figure 3-27 shows very small variations in the thickness strain profile over the entire surface of the dome suggesting either no deformation or pure shear deformation has occurred. The surface strain arrow diagram confirms this, showing most of the strain occurring in the region 45° from the warp or weft direction and very little strain in the fibre directions.


weft warp


89



Surface and Thickness Strain Max Surface Strain = 62.1% Min Surface Strain = -11.7% Max Thickness Strain = -6.4% Min Thickness Strain = -35.7%


Observations Using a 70mm diameter blank size the flange area draws in almost completely. A small mesh area has been used to allow a finer thickness contour resolution (see Appendix K for an alternative plot). The plot suggests stages of stretching and draw-in (then stretching again) as can be seen by the contours pattern along the edges of the mesh representing the warp and weft directions. Note that in this plot the strains shown are all negative and that the blue contours still represent negative strains. The surface strain arrow diagram coupled with the thickness contour plot confirm that rather than trellising when deformation is required at 45° to warp or weft (down the middle of the dome), the material deforms in both the directions which will result in thinning (or more negative thickness strain contours).


weft warp

Stretch

Stretch/Draw

Stretch


90





Observations Using the same diameter blank as that used in Dome 22 Figure 3-29 but using a cold tool surface temperature of 23°C the dome seems to exhibit less overall stretching than Dome 22. It is thought that this could be due to the cold tool effect of matrix shrinkage interacting with the deforming fibres. Using a hot tool the reinforcement is in a fixed position since the tooling is fully closed before cooling commences which may help decrease the effects of shrinkage.


weft warp


91

3.4.3.2 Draw-in Behaviour

Another important aspect of the material’s behaviour is the amount of draw-in that

occurs. A comparison of the draw-in behaviour can be established by comparing the

angular deviation of the gridlines representing the warp and weft directions to their

original 90º configuration as shown in Figure 3-31. The most significant differences can

be seen in domes 15 and 16 where the three-ply knitted specimens have been formed at

softened and molten conditions respectively. In the softened state (dome 15) more

stretching has occurred, especially in the weft direction, while the less accommodating

warp direction has experienced some draw-in.

Dome 12 Blank Diameter Size = 100mm Tool Temperature = 160°C Material State = molten 175°C

warp

weft

Original Blank Mesh

Dome 13 Blank Diameter Size = 100mm Tool Temperature = 160°C Material State = soft @ 160°C

warp

weft

warp

weft

warp

weft

Dome 15 Blank Diameter Size = 100mm Tool Temperature = 150°C Material State = soft @ 150°C


92

Figure 3-31. Comparison of draw-in behaviour

In dome 16, where the material is molten, draw-in has occurred in both directions. An

extreme case of draw-in behaviour can be seen in dome 18, which shows a biaxial

woven specimen. The tool temperature has little effect on the draw-in behaviour as is

demonstrated by domes 12 and 16. In Domes 22 and 27, which use a 70mm blank

diameter size, it is difficult to see any significant differences, however, this

demonstrates the dominance of the fabric reinforcing structure regardless of the forming

parameters when the material is in the molten state.


warp

weft


warp

weft

warp

weft



warp

weft Woven


93

3.4.3.3 Surface Finish

While surface finish was not an issue with pressure forming, achieving a smooth, glossy

surface finish on the domes using the ridged aluminium dies for the multiply specimens

was difficult due to the differences in the amount of stretching (and therefore thinning)

in the flange and hemispherical regions of the dome. Figure 3-32 shows close up images

of the outer surface of (a) the molten and (b) the softened domes. In both cases, the

formation of dimples, due to the matrix squeezing out of the closing loops of the

stretching knit structure was evident. In the softened dome this would be difficult to

correct, but in the molten case, using a flexible rubber male insert allowed the

redistribution of the matrix material during stamping. These were manufactured from

high temperature silicone rubber and designed to fill out the dome before coming into

contact with the flange area and produced an excellent surface finish as shown in Figure

3-33.

Figure 3-32. Comparison of surface finish in (a) molten and (b) softened domes

Figure 3-33. Comparison of domes formed from rubber and metal male stamping dies

(a) Dome 12 (b) Dome 15

Rubber Stamp Metal Stamp


94

3.5 Extreme Forming

So far the forming experiments performed have not tested the material to its forming

limits. The forming problems that may arise when the reinforcing knit structure is

stretched to its fullest is the subject of Sections 3.5.1 and 3.5.2.

3.5.1 Deep Drawing (The Cup Forming Test)

The dome forming tests had indicated that a molten material – male rubberstamp

matching die combination was the most appropriate forming method. However, these

experiments had not taken the material up to its forming limits. The cup forming

experiments, even though not a matching die forming process allowed the observation

of any further potential forming problems when the material is taken to its forming

limit.

The experiments were performed using a 38mm diameter cylindrical aluminium punch

with a nose radius of 5mm. The female die cavity was able to accommodate a cup wall

thickness of 6mm and a maximum depth of 50mm. Using 120mm diameter, molten 3ply

(5mm) blanks, cups of various heights were formed up to a depth where either

wrinkling or tearing was observed for a particular clamping force as shown in Table

3-6.

Table 3-6. Cup forming

Clamping Force (N) Depth (mm) Forming Defect Observed

40 25 Flange Wrinkling

120 30 Flange Wrinkling

Fully Clamped 42 Tearing

When the specimen was fully clamped, the material reached its maximum cup depth and

tearing occurred while wrinkling was totally avoided. Interestingly, the forming defect

occurred in the region of the cup subjected to the highest single direction strain, the wall

of the cup, a good distance away from the punch nose radius, which is where failure

would be expected. The magnitude of strain present in the knit structure is indicated by

the amount of matrix flow from the closing loops of the reinforcement in the bottom


95

part of the cup, no longer in contact with the die. Figure 3-34 shows the warp direction

failure that could have occurred on either side of the cup wall.

3.5.2 Extreme Component

Having studied the behaviour of the knitted fabric under controlled circumstances with

standardised test specimens and geometries, a product demonstrating the key attributes

of the material was manufactured. The product chosen was based on the shape of a

deeply curved wing mirror fairing that would require the material to stretch to its limit

and draw-in. Once it had been shown that the fairing could be satisfactorily formed

from knitted fabric composite material using the rubberstamp matched die-forming

process, a more detailed investigation of the material's deformation during forming was

conducted.

The component, which would also serve as the physical reference for the sheet forming

simulation of the same part described in Chapter 5, was manufactured from a 2mm thick

single ply sheet of the material. Similar to the previous experiments, a reference grid

was inscribed on the surface of the raw blank, and the deformed grid points shown in

Figure 3-35 (a) were digitised. Figure 3-35 (b) shows the material not only had to fully

stretch but also draw-in as indicated by the rectangle showing the original shape of the

blank. The grid density was highest over the areas of highest curvature, with a 2.5 mm

Figure 3-34. Tearing in cup wall

Warp

Weft


96

grid spacing in this region. Elsewhere, (in the flange region), the grid spacing was

increased to 5 mm to reduce the number of points; in total 3,800 points were digitised to

generate a 3-D numerical representation of the part. The digitised grid data points were

used to generate a GSA model of the formed fairing, which was used to assess the in-

plane material strains during forming and the variations in thickness in the final article.

The digitised grid data points were also used as the reference for creating the geometry

data for the stamping simulation.

Two of the most important parameters during the manufacturing stages were the blank

holder force and shape of the rubber punch. As long as the material remained molten,

deformation was dominated by the strain transmission properties of the fabric. The

blank holder force, although not recorded, was maintained at a level, which, for the

formation of an extreme component, was enough to facilitate full stretching in both the

warp and weft directions but allow draw-in once the knitted fibre loops had fully

stretched. The shape of the rubber punch, designed to accommodate a uniform 2mm

thickness was not able to initially produce a component with an accurate shape

definition and quality surface finish. The reason for this comes from the distortion that

occurs in the plug during the transfer of forming forces. To correct this, the punch was

refined by adding or removing silicone material to areas where lack of contact or

premature contact was evident. Figure 3-36 (a) shows the components produced during

the development of a suitable punch shape by the progressive reduction of the problem

areas highlighted. The optimum punch shape allowed full contact with the surface of the

female die giving a very good surface finish as shown in Figure 3-36 (b).

Figure 3-35. (a) Deformed grid points of the fairing and (b) Plan view showing draw-in of flange


97

3.5.2.1 Surface Strains and Thickness Contours

Figure 3-37 shows an overall plot of the surface strains on the component, highlighting

four distinct regions. Near the top of the component, region 1, biaxial stretch can be

observed as the forming punch stretches the material in both the warp and weft

directions. Towards the middle of the component, region 2, uniaxial stretching is clearly

visible. In region 3, the strain pattern characteristic to material drawing, can be

observed. However, the most interesting strain pattern occurs in region 4 where the

material exhibits warp and weft direction trellising without the onset of wrinkling. In

the shear deformation experiments performed in Section 3.2.2.1 it was observed that

warp and weft direction trellising could not be accommodated without wrinkling. The

strain pattern presented in region 4 shows that in a more constrained fabric the

introduction of biaxial stretching can help alleviate the wrinkling effects caused by warp

and weft direction trellising.

In Figure 3-37 the maximum surface and thickness strain values were not given, since

surface fitting errors in some regions of the overall component were as high as 2mm

(80%), due to the high curvature regions of the component where wrinkling had

occurred. Using the portion of the mesh shown in Figure 3-38, where the maximum and

the average surface fit errors were reduced to 1.3mm (50%) and 0.3mm (12%)

respectively, gave more accurate maximum thickness and surface strain readings.

Figure 3-36. (a) Progressive development of rubber punch and (b) surface finish quality

(b) (a)


98

Specimen Forming Parameters Blank Size = 200 x 200mm No. of Plies = 1 Original Thickness = 2mm Tool Temperature = Warm Air Temperature = 20ºC Material State = molten 180ºC Forming Rate = 350mm/min

Surface and Thickness Strain Note that caution is required when reading the maximum and minimum values of surface and thickness strain as they also reflect surface fit errors


Figure 3-37. Extreme component overall surface strains

It is important to note that the largest surface fit error could occur in a region which

experiences very little strain. By examining the location of the largest surface fit error, it

was observed that this was indeed the case. This means that the maximum surface strain

value presented in Figure 3-38 is likely to be the subject of around 12% error which is

verified by the maximum weft direction strain value (125%) that was measured in

Section 3.2.1.

1

2

4

3

warp weft


99

Specimen Forming Parameters Blank Size = 200 x 200mm No. of Plies = 1 Original Thickness = 2mm Tool Temperature = Warm Air Temperature = 20ºC Material State = molten 180ºC Forming Rate = 350mm/min

Surface and Thickness Strain Max Surface Strain = 136% Min Surface Strain = -34.5% Max Thickness Strain = 76.3% Min Thickness Strain = -39.8%


Figure 3-38. Extreme component highly detailed region

While the method of digitising and precision of the equipment limited the strain value

accuracy to 88%, another possible source of error, can be smearing of the surface during

forming. However, the maximum strain observed within the circled region of the strain

arrow diagram shown in Figure 3-38 is believed to be representative of the strains

throughout the entire thickness of the part as this matches the maximum strain value in

the weft direction of the fabric closely, given the average surface fit error.

Finally, looking at the percentage thickness strains of Figure 3-39 shows a pattern of

thickening, drawing and stretching moving from the base to the top of the component.

The values represent the percentage increase or decrease in thickness based on the

Maximum Strain

warp weft


100

original thickness (2mm) of the component. Using the values of the maximum and

minimum thickness strains given in Figure 3-38 (rather than the thickness strain contour

bar limits) translates to a minimum thickness of 1.20mm near the top of the component

and a maximum thickness of 3.53mm near the flange region.

Figure 3-39. Percentage thickness strains in extreme component

101

Chapter 4 High Fibre Volume Fraction Knitted Fabric Composites

4.1 Background

It is well known that the exceptional forming properties of knitted fabric composites

come at a cost to the stiffness and strength of the final component produced from the

material. Compared to other types of textile composite materials made from the same

constituent materials, the two properties of stiffness and strength are mainly influenced

by fibre/yarn directionality and the fibre volume fraction. In Chapter 3 the knitted fabric

material used in the forming experiments was of a relatively low fibre volume fraction,

(20%). This allowed the preconsolidation of composite sheets without using high

compression loads (consolidation using vacuum pressure) and during the forming

process allowed the knitted structure to deform normally under the impediment of the

molten thermoplastic matrix.

To create a knitted fabric composite of higher fibre volume fraction requires a slightly

different approach. The forming of preconsolidated sheets is now not feasible because

the compression load required to achieve the high fibre volume fraction distorts the

fabric structure and its formability benefits are lost. There are also the other difficulties

of achieving good wet-out of the fibres since the porosity of the fabric decreases more

as the material is compressed as well as reinflation of the fabric in the preconsolidated

sheet upon reheating.

Here the option taken for forming high fibre volume fraction knitted fabric composite

materials is using a commingled fabric of a given fibre volume fraction and

compressing it until adequate consolidation is achieved, which is characterised by a

smooth specimen surface finish, indicating that the matrix has filled most of the internal

voids and has made its way to the outer surfaces of the panel. Figure 4-1 shows a

picture of the material in raw commingled fabric and consolidated sheet form. Each

individual layer of the fabric is approximately 5mm in thickness. To produce a

consolidated sheet of average thickness between 2.2 – 3.0mm required


102

four layers of fabric, which then needed to be compressed to one tenth of its original

thickness.

4.2 Comparison of Common Materials

Knitted fabric composites of low fibre volume fraction are usually only compared with

ordinary plastics as their mechanical property improvements are not good enough to

compete with other types of composites made from the same materials, let alone

materials such as aluminium. The objective of this chapter is to test the mechanical

performance of high volume fraction knitted fabric composites and compare it with

woven fabric of the same volume fraction as well as aluminium and ordinary

polypropylene.

Table 4-1 shows the list of the materials tested ranging from RibTEX, which has been

made from a 1x1 rib knit preform material manufactured from commingled roving, to

Twintex®, a 2/2-twill woven fabric, both having a nominal fibre volume fraction of

35% (or Vf = 60% by weight) and made from yarn with a linear density of 790tex. The

commingled knitted fabric was manufactured on a 3.5 gauge, manually operated v-bed

knitting machine, producing a continuous strip of fabric 80mm wide. All composite

specimens were formed in a 5kN heated platen press, with platen temperature set to

220ºC, since the press was fully exposed to ambient temperature and using forming

pressures ranging from 100 – 500kPa. A temperature of 220ºC was necessary in order

for the specimen to reach at least 180ºC (melt temperature of polypropylene), upon

which it could be seen that forming had taken place. The forming pressure then

remained as the specimen was cooled down.

Figure 4-1. RibTEX commingled preform fabric and consolidated sheet


103

Initially it was unknown what level of pressure would be required to produce properly

consolidated sheets. Based on the values of average thickness shown in Table 4-1, it can

be seen that the compression plateau is somewhere close to 400kPa. This is a

characteristic, which would be unique to the size and type of yarn, as well as the

geometric structure of the fabric, that is being used. As for the number of layers,

because the stacks of fabric behave like springs in series, the pressure required to reach

the same layer to thickness ratio should remain unchanged. In fact, the layer to thickness

ratio and required consolidation pressure should decrease due to nesting.

Table 4-1. List of materials used in the mechanical property comparison of high fibre volume fraction knitted fabric composites

Specimen Average Thickness (mm)

Weight(g)

Consolidation Pressure (kPa) Notes Density

(g/cm3)RibTEX3.1 2.2 5.9 500kPa 4 layers folded (no vacuum) 1.68 RibTEX3.2 2.3 5.9 500kPa 4 layers folded (no vacuum) 1.60 RibTEX3.3 2.3 5.9 500kPa 4 layers folded (no vacuum) 1.60 RibTEX3.4 2.4 6.3 500kPa 4 layers folded (no vacuum) 1.64

**RibTEX3.weft 2.3 6.2 500kPa 4 layers folded (no vacuum) 1.68 TWINTEX4.1 2.9 7.2 100kPa 8 layers stacked (no vacuum) 1.55 TWINTEX4.2 2.9 7 100kPa 8 layers stacked (no vacuum) 1.51 TWINTEX4.3 3 6.8 100kPa 8 layers stacked (no vacuum) 1.42 TWINTEX4.4 3.1 7.2 100kPa 8 layers stacked (no vacuum) 1.45 RibTEX5.1 2.7 7.2 300kPa 4 layers folded (no vacuum) 1.67 RibTEX5.2 2.8 7 300kPa 4 layers folded (no vacuum) 1.56 RibTEX5.3 2.8 7.2 300kPa 4 layers folded (no vacuum) 1.61 RibTEX5.4 3 7.5 300kPa 4 layers folded (no vacuum) 1.56 RibTEX6.1 2.3 6.4 400kPa 4 layers folded (no vacuum) 1.74 RibTEX6.2 2.3 6.1 400kPa 4 layers folded (no vacuum) 1.66 RibTEX6.3 2.3 5.9 400kPa 4 layers folded (no vacuum) 1.60 RibTEX6.4 2.3 6 400kPa 4 layers folded (no vacuum) 1.63

RibTEXSpecial1 2.4 6.3 *V.O.L 210ºC 4 layers folded 1.64 RibTEXSpecial2 2.6 6.9 *V.O.L 190ºC 4 layers folded 1.66

P1 3.2 4.7 - - 0.92 P2 3.2 4.9 - - 0.96 P3 3.2 4.6 - - 0.90

Aluminium1 1.6 7.1 - - 2.77 Aluminium2 1.6 6.7 - - 2.62

RibTEXClosedEdge1 2.3 8.2 400kPa 4 layers folded (no vacuum) 1.49 RibTEXClosedEdge2 2.2 8.2 400kPa 4 layers folded (no vacuum) 1.55 RibTEXClosedEdge3 2.2 8.2 400kPa 4 layers folded (no vacuum) 1.55 RibTEXClosedEdge4 2.2 8.2 400kPa 4 layers folded (no vacuum) 1.55 **RibTEXWeftInsert1 2.9 7.5 400kPa 4 layers folded (no vacuum) 1.62 **RibTEXWeftInsert2 2.8 8.0 400kPa 4 layers folded (no vacuum) 1.79 **RibTEXWeftInsert3 2.8 7.4 400kPa 4 layers folded (no vacuum) 1.65 **RibTEXWeftInsert4 2.9 7.9 400kPa 4 layers folded (no vacuum) 1.70

*Vacuum consolidation in oven for long period of time

**All specimens tested in the wale direction except for these, a weft direction control and four weft insert specimens


104

4.2.1 Variations in RibTEX specimens

In addition to the specimens manufactured in the hot platen press, two were

manufactured in an oven under isothermal conditions at 190ºC and 210ºC using vacuum

pressure but significantly larger plate size (3-4 times larger in area) than the specimen

itself in order to achieve the necessary compression force for proper consolidation. It

was expected that these specimens, which were allowed a significant time to reach

forming equilibrium (30 – 40mins) and for which a vacuum was used, would represent

the highest quality specimens that could then be compared to the quality of those

formed on the heated platen press.

Another consideration was the issue of whether the tensile test specimens had been cut

from larger specimens meaning that they had open loop edges. Most of the specimens

were produced in this way and for the manufacture of real components it is usually

necessary to do this for trimming and finishing of the product. Four closed loop edge

specimens were manufactured in order to check if the open loop edges had any effect on

the tensile strength of such narrow specimens. The closed loop edge specimens

contained five columns of loops per width of specimen and measured 30mm wide by

80mm long while the open loop edge specimens contained only four columns of loops

and measured 20mm wide by 80mm long.

A final consideration was the improvement and comparison of the tensile strength in the

weft direction when incorporating a weft direction insert yarn. Here the fabric is still

produced using a continuous strand of yarn that is inserted between the planes across

each row of rib loops. Table 4-2 gives the theoretical density of a composite made from

the constituent materials of E-Glass and Polypropylene at two different fibre volume

fractions and can be compared with the average measured density of each of the

composite specimens. For the knitted fabric composite specimens, the average measured

density is higher than the theoretical value at 35% fibre volume fraction, especially in

the weft insert specimens, where the average measured density equals 1.69g/cm3. It was

suspected that these specimens contained a higher fibre volume fraction than the 35%

that was previously assumed. Individual calculations of the fibre mass and fibre volume

fractions for each specimen confirmed this and a graph of the results is shown in Figure

4-2.


105

Table 4-2. Theoretical and average measured density for all test specimens

Material Theoretical Density (g/cm3) Material Average Measured Density (g/cm3)

E-Glass 2.54 RibTEX 1.64 Polypropylene 0.90 Aluminium 2.70

Aluminium 2.80 TWINTEX 1.48 *Composite 1.47 Polypropylene 0.92 **Composite 1.75 RibTEXClosedEdge 1.54

RibTEXWeftInsert 1.69

*Composite produced from E-glass and Polypropylene with fibre volume fraction of 35% (Mass Fraction 60%)

**Composite produced from E-glass and Polypropylene with fibre volume fraction of 52% (Mass Fraction 75%)

Although the exact void contents were unknown, they were checked indirectly by

incorporating void volume content percentages of 2, 5 and 10% into the calculation. The

specimen numbers shown in Figure 4-2 are in the same order as the composite

specimens presented in Table 4-1.

It can be seen that the Twintex® 2/2-twill woven fabric composite, represented by

specimens 6 – 9, does show a fibre volume fraction of approximately 35% while the

other specimens appear to have much higher volume contents. It is uncertain how much

quality control Vetrotex places on its product with regards to fibre volume fraction,

however, it can be concluded that the Twintex® yarn used to manufacture the knitted

Figure 4-2. Calculated fibre volume and mass fractions


106

fabric composite preforms are of a mass fraction closer to 75% (Vf = 52%, which is a

commercially available ratio). This should be taken into account when considering the

results in the rest of this chapter. It can also be concluded that the void content of the

RibTEX specimens is unlikely to exceed 10% as this would mean an unusually high

mass fraction for this type of product.

4.2.2 Test Results

Figure 4-3 shows the engineering stress strain curves for all of the tested specimens.

There are four main clusters of curves showing the behaviour of Twintex®, Aluminium,

RibTEX and Polypropylene. It can be seen that the low fibre volume fraction knitted

fabric composite does not provide much improvement over polypropylene. RibTEX on

the other hand is able to match the stiffness and strength of the woven fabric composite,

Twintex® for strains of up to 8%, where it then begins to follow a unique failure path.

To provide a better comparison, the specific stress strain curves of all the materials can

be compared as shown in Figure 4-4. Here the knitted fabric composite is able to attain

Figure 4-3. Stress strain curves for all compared specimens

Twintex®

Aluminium

RibTEX

Polypropylene


107

the same maximum specific strength as aluminium, although the amount of strain it can

sustain at this maximum specific strength is not as high.

A closer examination of the knitted fabric composite tensile curves indicates some

important differences between the RibTEX specimens themselves. Figure 4-5 to Figure

4-7 highlight the warp direction tensile test results of specimens manufactured using

300 – 500kPa of forming pressure. It can be observed that for this type of material an

optimum forming pressure seems to exist, which would also be the case for any type of

commingled knitted fabric composite preform. Figure 4-6 shows that the group of

specimens with the highest warp direction yield stress are those that have been formed

using 400kPa of forming pressure. Using a higher forming pressure, as shown in Figure

4-7, does not result in any further improvement in the quality and even starts to become

detrimental to the strength properties of the formed material. It is postulated that the

reduction in strength occurs because of fibre damage caused by over compressing the

specimen. A minimum forming pressure of 300kPa was chosen because it was the

lowest pressure at which the material by visual inspection appeared to be fully

consolidated.

Figure 4-4. Specific stress strain curves for all compared specimens

Twintex®

Aluminium

RibTEXPolypropylene


108

Figure 4-5. Warp direction stress strain curves for all RibTex specimens (300kPa)



109

Having established the suitable forming pressure, specimens were also manufactured

with closed loop edges to see whether this had any effect on the tensile strength of the

material. Figure 4-8 shows that the closed loop edge specimens actually performed

worse than the open loop edge specimens, probably due to the geometric irregularities

introduced at the edges, or surfaces in the thickness direction, which are difficult to

consolidate to the quality of the in-plane surfaces. This suggests that a clean (cut) edge

is more important than closed loops at the edges. In Figure 4-9, the weft direction

specimen exhibits the worst performance, while the other two curves show warp

direction tensile data for specimens that have been formed isothermally, in an oven

under vacuum at 190 and 210ºC for short (10mins) and long periods (45mins) of time

respectively. The important observation here is that the highest performance curve when

the material is produced in this way, is not significantly better than those produced in

the heated platen press at the same optimal pressure.



110

Figure 4-8. Warp direction stress strain curves for all closed edge RibTex specimens (400kPa)

Figure 4-9. Stress strain curves for weft and specially formed warp RibTex specimens (400kPa)

Vacuum formed long duration 210ºC

Vacuum formed short duration 190ºC

Weft specimen


111

Finally, in Figure 4-10 the effect of adding a weft insert yarn is demonstrated and can be

seen to increase the strength of the material in the weft direction to an equivalent level

of that in the warp direction. Unfortunately, the drawback of this is that the insert yarns

now limit the material’s most stretchable direction. If the preform is knitted to the shape

of the component to be formed, this does not pose a problem, but if the component is to

be made by stretch forming then the issue of inextensibility, as found in woven fabrics,

again arises.

The experimental investigation performed in this chapter has shown that the

manufacture of high fibre volume fraction knitted fabric thermoplastic composite

material is possible. For a particular type of knitted preform structure, an optimum

forming pressure appears to exist. In the case of a 1x1 rib structure used in this study,

400kPa has been found to be the most suitable forming pressure, any further increase in

the pressure lowers the quality due to severe compression which may start to damage

the fibres at their cross-over points. The experiments have also shown that forming

using a hot platen press can produce very good quality specimens and that weft insert

yarns can bring the tensile strength of the weft direction up to same level as the warp

direction at the expense of forming flexibility in this direction.

Figure 4-10. Weft direction stress strain curves for all weft insert RibTex specimens (400kPa)

112

Chapter 5 Explicit Finite Element Modelling and Analysis

5.1 PAMFORM™/PAMCRASH™ and Explicit Modelling

Many of the problems encountered in structural mechanics are difficult to solve using

the conventional analytical techniques, especially the mechanics of knitted fabrics as

seen in Chapter 2, Section 2.6.2.1. Because of the complexity of the geometry and

loading arrangements it is not always easy to develop mathematical expressions that

accurately represent the relationships between stress and strain of the system while at

the same time satisfying the boundary conditions of force and displacement. This is why

the basis for many engineering analysis software involves the use of the finite element

method, which has been chosen as the primary tool for simulation and analysis in this

study.

PAMFORM™/PAMCRASH™ is a very powerful engineering simulation program

based on the finite element method. The software uses an explicit dynamic finite

element formulation (also implemented in several other FEA software packages

including LSDYNA™, ABAQUS™ and RADIOSS™). Originally designed for

modelling systems where the events occur over a very short period of time and where

inertial effects of the system are important (e.g. impact, explosions), its formulation

characteristics make it very efficient for solving problems involving changing contact

conditions, such as knitting and forming simulations. While knit manufacturing is

relatively well represented as a high-speed impact problem, forming processes occur

over much longer periods of time and adjustments are required to ensure a solution is

obtained within a reasonable time frame.

In this Chapter the behaviour of knitted fabric composites is examined at two different

levels. The first part considers the micromechanics of the reinforcing knit structure by

simulating the production of a narrow strip of 1x1 rib fabric. The model is verified

using tensile tests of physical specimens and then used to analyse the importance of


113

individual reinforcement deformation mechanisms described in Section 2.4.3 and their

influence throughout the forming process.

Following the micromechanical analysis, the deficiencies of the most suitable existing

macro-level composite material model are investigated by performing a series of one,

two and three-dimensional forming simulations and comparing these with

complimentary experimental data. Based on the results of the micromechanical

modelling, suggestions for an ideal macro-level model for textile composites are

discussed.

5.2 PAMFORM™/PAMCRASH™ Basics

Before exploring the details of the modelling section, consider a brief overview of the

software’s program structure. A complete PAMFORM™/PAMCRASH™ analysis

usually consists of three distinct stages; preprocessing, simulation and postprocessing.

Each of these stages are linked together by the software modules and various file types

as shown in Figure 5-1.

Figure 5-1. Stages and file relationships of a PAMFORM™/PAMCRASH™ analysis

Preprocessing

PAMGENERIS™

Simulation

PAMFORM™/PAMCRASH™

Solver

Postprocessing

PAMVIEW™

solver model

(.ps/.pc file)

time history plot

(.THP file)

results visualisation

(.DSY file)

solver log

(.out file)

visualisations

screen shots

(.tiff file)

Pro/ENGINEER™

(.pat file)

DeltaMESH™

(.dsy file) Solver

BatchFile

Algorithm


114

5.2.1 Preprocessing (PAMGENERIS™)

PAMGENERIS™ is the graphical interface module of PAMFORM™/PAMCRASH™

used for defining the various parameters of a physical problem such as element types,

materials, motion constraints, contacts, loading conditions and kinematic behaviour. It

also contains tools for the construction of simple geometry. In most cases though, the

geometry is created using a dedicated CAD package such as Pro/ENGINEER™ and

imported into PAMGENERIS™ via DeltaMESH™ or Pro/MECHANICA™ which

generates the mesh or finite element representation of the geometric model.

5.2.2 Simulation (PAMFORM™/PAMCRASH™ Solver)

The actual simulation is executed using the PAMFORM™/PAMCRASH™ solver,

which takes the input deck (.pc/.ps file), solves the numerical problem and generates the

output files (.DSY and .THP) required for post processing. Depending on the

complexity of the model and the power of the computer, the simulation run time can

range from seconds to days. To automate the process of parameter optimisation the

simulation can be run in the form of a batch file. Parameter values within the input

deck, which is simply a structured text file, can also be changed based on some criteria

using simple batch file commands. For more complicated solving criteria and

optimisation functionality, third party software such as HyperWorks™ is available.

5.2.3 Postprocessing (PAMVIEW™)

Once the simulation is complete, useful visualisations like static and animated finite

element mesh plots, as well as output time history curves for element, nodal and contact

interface variables such as stress, strain, force, displacement and energy can be

generated using PAMVIEW™. Data not generated by the software directly can be

obtained by operating on data in PAMVIEW™ or exported into Excel for further

processing.

5.3 Modelling the Manufacture of the Reinforcement Architecture

In Section 2.4.3 it has been established that the most dominant factors influencing the

sheet forming behaviour of knitted fabric thermoplastics are associated with the

micromechanics of their reinforcing structures. Therefore, understanding the

deformation behaviour of the reinforcing structure on its own becomes extremely

important. In this section, a model is developed to quantitatively analyse the


115

contributions of the deformation mechanisms described in Section 2.4.3. By setting up a

model flexible enough to evaluate these mechanisms for some specific knit structures,

more accurate simplified models can be developed for describing the forming behaviour

of textile composite materials in finite element software such as PAMFORM™.

Furthermore, the model could be developed to analyse the behaviour of the knitted

reinforcement in different forms of the matrix (i.e. molten and solid), along with their

failure modes, which could also be analysed in detail. There may also be application in

the textile industry for the design of flatbed knitting machinery. Although the knit

manufacturing model is capable of producing models of many different weft-knit

structures; the number is only limited by what could be produced on actual flatbed

knitting machinery; in this study, the 1x1 rib structure has been chosen to develop the

model.

5.3.1 Model Set-up

The manufacture of knitted fabric is a high-speed dynamic contact problem, where

knitting needles move back and forth at speeds of up to 1.5m/s. This makes knit

manufacture particularly suitable for modelling using the explicit dynamics code

commonly utilised for crash and forming simulations. PAMCRASH™ has been utilised

because of its extensive range of material models and contact algorithms most suited to

the knitting process, the reason being that most of the software functionality required in

a crash simulation is also required for knitting, (beam self contact, function on/off

sensors, simulation restart etc).

Only a small quantity of the fabric is required for the analysis, therefore the number of

needles used in the simulation has been limited to five. On real weft knitting machinery

there are hundreds of needles, the actual number that are engaged is dependent on the

desired fabric width and structure. For the 1x1 rib, it is possible to produce a coherent

narrow strip of fabric that captures the repeating unit and can be used for experimental

comparisons using only five knitting needles as shown in Figure 5-2.


116

Figure 5-2. Real five needle knitting of 1x1 rib weft knitted fabric

5.3.2 Model Input: Knitting Machine Parameters

Simulating the operation of a flatbed-knitting machine requires in-depth knowledge of

all the physical parameters that make the machine work. Some of these important

knitting machine parameters include; the relationship between the knitting bed

movement and displacement profiles of the front and back knitting needles or the cam

profiles, the needle spacing or gauge, needle and bed geometries, yarn feed friction and

take-up spring stiffness, fabric take-up velocity and take-up spring stiffness, and

knitting needle latch kinematics and friction as summarised in Table 5-1.

Table 5-1. Summary of important knitting machine parameters

Knitting Machine Parameters Description

Cam Dimensions (mm)

(Identical for both cams)

A = 12.5

B = 72

C = 21.5

Parameter A defines the knitting loop length

and is controlled via movable cams 1 and 2.

Parameter B defines the needle cycle duration

Parameter C defines the needle stroke

Geometrical

Needle Spacing

10 Gauge

Distance between adjacent knitting needles,

10 gauge equals a 2.54mm spacing.

A

B

C1 2


117

10 gauge

Needle Geometry

5 Needles

Yarn Feed Friction and

Feed Take-up Spring

Fabric Take-up Velocity

Fabric Take-up Spring

Mechanical

Needle Latch Friction

5x10e-07N.m(kN.mm)

The needle latch friction moment is measured physically and then further reduced using needle only simulations until a value, which sustains inertial effects of the needle movement, is obtained.

While many of the knitting machine parameters can be modelled directly, the yarn feed

mechanism including feed friction and the take-up spring is simulated using non-linear

0.00E+00

1.00E-06

2.00E-06

3.00E-06

4.00E-06

5.00E-06

0 50 100 150 200

Displacement (mm)

Forc

e (k

N)

Unloading

20

30.00

22.50 7.50

1.176.95

Needle Head Diameter = 0.5mm

0

0.05

0.1

0.15

0.2

0.25

0.3

0 20 40 60

Time (ms)

Velo

city

(mm

/ms)

0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

0 1 2 3 4 5 6 7 8 9 10 11 12

Displacement (mm)

Forc

e (k

N)


118

bar elements to simplify the model. Each filament in the yarn uses its own non-linear

bar element describing the yarn feed properties, this way the definition is not dependent

on the number of filaments and more or less filaments can be added depending on the

computer resources that are available. Parameters such as the fabric take-up velocity

and the yarn feed friction which are difficult to measure physically are estimated and

adjusted according to the visual quality of the resulting knit, just as is done by

technicians with real knitting machinery, (i.e. an insufficiently large numerical value for

the fabric take-up velocity will cause poor loop formation, tangling and needle jamming

as occurred in many simulations). The fabric take-up mechanism, a spring-loaded

rotating roller, is simulated by moving springs attached to the take-up bar, applying a

near constant tension.

All five knitting needles include kinematic pin joints that simulate the needle

mechanism required to produce the fabric structure. The needle latches open and close

according to the movements made by the needles and contacts encountered by the

needles against the yarn and needle latches against the main body of the needle itself. A

needle latch rotational friction resistance is also prescribed to restrict latch movement

under its own inertial forces.

5.3.3 Model Input: Material Property Parameters

Material property parameters form another important part of the model. Fortunately,

continuous filament glass fibre yarn can be accurately represented as a purely linear

elastic material. Each filament in the yarn is represented by a series of interconnected

linear elastic circular beam elements whose bending, tension and torsion forces are

transmitted between one another. The element size, 0.2mm, has been carefully chosen to

allow accurate representation of the fabric geometry but also keep the solving time

reasonable. Other elements of the machinery such as knitting needles and the machine

bed are treated as rigid bodies since information on stresses and strains in these

elements is not required. A summary of the yarn’s material properties is given in Table

5-2.


119

Table 5-2. Yarn material properties Material Property Value

Filament Diameter 17μm

Density, E-Glass 2.54e-06kg/mm3

Poisson’s Ratio, ν 0.2

Tensile Modulus, E 73 GPa

Second Moment of Area, Ix 4.1e-09 mm4

Second Moment of Area, Iy 4.1e-09 mm4

Polar Second Moment of Area, J 8.2e-09 mm4

To simulate contact between the glass filaments and other elements of the knitting

machinery, the code uses contact algorithms that check for penetrating nodes within a

space around each element. In this simulation the space is defined using the average

diameter of the filaments, 17μm. Any penetration is then resisted by a contact stiffness,

(filament-filament, filament-needle compression stiffness in the presented case),

calculated by averaging the tensile moduli of the two materials in contact 64. For

additional control a scaling variable called the penalty scale factor (PSF) is also

introduced. Using the self-impacting contact type, contacts between individual

filaments, filaments and the knitting machinery as well as filaments contacting

themselves at different points can all be accounted for.

5.3.4 Model Input: Non Physical Parameters

Apart from the physical parameters many non-physical parameters such as the time step

scale factor (TSSF), contact search accelerator (CSA), penalty scale factor (PSF) and

material damping factors all play an important role in the simulation ensuring solution

stability and results within a sensible timeframe. A list of the most important non-

physical parameters and their descriptions are presented in Table 5-3.

Table 5-3. Important non-physical parameters

Important Non Physical Parameter Abbreviation Description

Time Step Scale Factor TSSF Time step control multiplier

Contact Search Accelerator CSA Controls search frequency per n cycles

Penalty Scale Factor PSF Contact stiffness multiplier based on E values

Material Damping Ratios - Controls material oscillations


120

In explicit dynamic finite element procedures the stable time step is calculated by using

information about element size, material density and stiffness. To ensure the stability of

the solution this value is multiplied by the TSSF. For large strain simulations using shell

elements such as sheet metal forming a suitable TSSF usually lies between 0.7 and 0.9.

For crash simulations where elements undergo more radical movements during a single

time step, the factor may need to be set as low as 0.3 64. In the knitting simulation where

only bar and beam elements are used, the factor lies between 0.1 and 0.2. The reason for

such a low value may arise because of the ambiguity of one-dimensional element nodal

rotations. For example, if a beam element undergoes rigid body rotation larger than a

certain value during one time step then it maybe unclear which direction that element

has rotated in order to get to that position. It is this shortcoming of the Lagrange (or

even Updated Lagrange) formulation when using bar or beam elements, which is the

main factor influencing the solution stability in a knitting simulation. This is discussed

in more detail in Section 5.3.7.3

With the large number of contacts involved, the contact search accelerator, or CSA is

another important non-physical parameter determining the frequency of the contact

search per n time steps. To ensure contacts are detected and maintained throughout the

simulation the search is performed at every time step. A sample listing of the input file

for the simulation is given in Appendix P.

5.3.5 Simulating the Mechanics of the Knitting Process

The duration of the model covers two and a half full knitting cycles, producing enough

fabric for the second stage of the simulation where all the knitting machine elements are

stationary and a numerical tensile test of the specimen is performed. Given the linear

density of the yarn, the density of E-glass and filament diameter, the number of

filaments in the real yarn can be calculated as approximately 120. While the current

simulation uses only 20 filaments to help reduce solving time, a force-displacement

curve of the resulting simulated fabric should exhibit a curve similar to that of the actual

fabric, (which contains 6 times the number of filaments), only lower in magnitude. The

yarn itself is modelled as a hexagonal close packed arrangement of all the filaments, a

simplification over real yarn, which is usually spun, or air textured to provide lateral

cohesion and resistance to damage during knitting 11. However, it is even possible to

simulate these characteristics. Extra boundary conditions can be applied to the ends of


121

the yarn or the filaments can be assembled together with centre distances smaller than

their diameters, causing the filaments to fly apart initially, as if under the external force

of an air jet. A simplified version of the initial state of the simulation is shown in Figure

5-3.

Figure 5-3. Initial state of knitting simulation

The duration of the entire knitting simulation is 50ms, somewhat faster, around 5 times,

than practically achievable knitting speeds on conventional machines due to the loss in

yarn feed control and dangerously high needle bed movements. However, simulating at

a faster than normal knitting speed is necessary in order to keep the solving time

reasonable. The production stages of the simulation are shown in Figure 5-4. The

simulation performs two and a half full cycles, or 5 passes, producing enough fabric for

the second stage of the analysis. An animated filmstrip of the simulation can be viewed

by flicking through the pages of this thesis.

Knitting Bed 20 Filament

Yarn

Yarn Feed

Hole

Fabric Take-Up Bar

Knitting Needles

Needle Latches


122

Figure 5-4. The six stages of the knitting simulation

STATE: 60

STATE: 120

STATE: 240

STATE: 180

STATE: 300

STATE: 0


123

5.3.6 Model Verification

5.3.6.1 Geometrical Comparisons

The first and most obvious way of checking the simulation is by geometrical

comparisons. Visual checks of the geometry during the knitting process are of particular

importance and are analogous to the visual checks made by knitting machine operators.

Any problems are almost certainly due to incorrect knitting machine parameters or in

the simulation case, incorrect boundary conditions. Figure 5-5 shows plan and isometric

views of the real and simulated five-needle knitting process showing very close

structural similarities.

Figure 5-5. Geometrical comparisons of complex 1x1 rib formation

Further comparisons can be made after the knitting procedure is completed on a relaxed

portion of the fabric specimen, where a relaxed specimen is one that is not acted upon

by any forces other than its own internal reaction forces. For the numerical case, the

tensioning bar used during the knitting phase was relieved until it gave a flat-lined force

reading of 0.06N. The geometry data was then exported back into a CAD package for


124

accurate measurement. The physical specimen was analysed and measured using

microscopic digital images taken at 10X magnification. Figure 5-6 shows the two

specimens in their relaxed state along with their average loop height, width and length,

where the averages reflect measurements taken from nine fully formed loops across

three rows of both specimens. While the two specimens were produced using exactly

the same knitting parameters, their resulting 1x1 rib geometries look quite different with

the average loop height, width and length all measuring larger in the physical specimen.

One obvious reason for the difference is that the physical yarn contains six times the

number of filaments used in the numerical specimen. Therefore, its significantly higher

yarn bending rigidity results in a different relaxed state geometry and force

displacement behaviour of the specimen.

Another reason why the structures look different can be attributed to friction and shear

resistance between individual fibres (inter-fibre shear). The fact that the numerical

specimen contains no inter-fibre frictional restraint, which is also a function of the

number of fibres in the yarn, tends to suggest that the forces here are large enough to

have an influence at least on the relaxed geometry of the fabric. That is, the order of

magnitude of the forces generated by inter-fibre friction, is comparable to the forces

generated by bending for the specimen in its relaxed state and is therefore a significant

factor in determining what the geometry of the relaxed structure should look like.

Average loop height = 1.41mm Average loop height = 2.06mm

Average loop width = 1.88mm Average loop width = 1.89mm

Average loop length Lav = 4.58mm Average loop length Lav = 7.05mm

Figure 5-6. Comparison of loop geometry for (a) Numerical and (b) Physical specimens

(b) (a)


125

At this stage a difficulty arises in the undertaken analysis because the specimens,

although knitted using the same knitting machine parameters, exhibit significant relaxed

state geometric discrepancies. The absence of an inter-fibre friction effect and the

correct number of filaments in the yarn, which could only be implemented using super

level computing resources, means that a method to compare knitted structures made

from yarn of different bending rigidity and different loop sizes needs to be found out.

A summary of the generalised behaviour and the mechanics of knitted fabrics by

Grosberg in Hearle 11 highlights an important observation made by several researchers

relevant to this course of study. It has been found empirically that the load to give a

fixed extension is proportional to either m/l3 or G/l3, where m and G are the bending and

shear moduli respectively and l is the knit loop length (or average knit loop length, l =

Lav). Depending on the type of fibres that are involved (i.e. continuous or discontinuous,

as shown in Figure 2-5) and their frictional properties, the elongation resistance will be

largely due to bending energy changes or shear energy changes 11. In the case of high

modulus continuous filament yarn, the relationship between the force-displacement

curves generated from 1x1 rib fabric yarn containing different number of filaments and

different loop lengths (which occurs as a consequence of having more or less filaments

since the loop length or loop size depends on the yarn bending stiffness) seems more

likely to be correlated using m/l3. However, from the difficulties experienced during

knitting it is known that the friction coefficient between E-glass fibre filaments along

with their sizing is very high. In fact, an attempt to measure yarn friction using the

WRONZ (Wool Research Organisation of New Zealand) yarn friction-testing machine

at Auckland University of Technology’s textile research facility, proved unsuccessful

because readings were off the scale.

The loop length L or average loop length Lav, two measures commonly used by textile

researchers and shown in Figure 5-6 become particularly important now, since they can

be used to calculate the correlation factor Xcf, now formally defined in equation (33).

33 lGor

lmX cf = (33)


126

Using an Xcf governed by m/l3 and the geometrical measurements made on both the

experimental and numerical specimens in Figure 5-6, it can be shown how well the

simulation represents the real life system without incorporating the effects of inter-fibre

or intra-yarn friction.

5.3.6.2 Experimental vs. Numerical F-D Curves

To provide a form of experimental verification which would prove the validity of force

and energy readings taken from the simulation, warp direction tensile tests were carried

out on 68 tex E-glass fibre yarn 1x1 rib fabric specimens, 5 needles wide, with a

specimen length defined by five full knitting cycles. The set-up is shown in Figure 5-7.

To prevent any distortion or damage to the knitting structure, the hat-shaped specimen

holders were placed into position during the knitting procedure.

Figure 5-7. Test set-up for 1x1 rib strip tensile test

The experiment used a 20N load cell and the average curve for 5 tests is shown in

Figure 5-8. Note the specimens show a small amount of mechanical property variation

as no two loops had exactly the same geometry and might have incurred a varying

degree of yarn damage during knitting. The curves also show that the initial inter-fibre

friction, or region (a) in Figure 2-21, is a relatively small contributor to the total energy.

However, the overall behaviour is similar to that shown in Figure 2-21.


127

Figure 5-8. Average experimental F-D curve for 1x1 rib specimen

Figure 5-9 compares the numerical and experimental force displacement curves. Both

curves follow a similar trend and only appear to be different in size. Using an Xcf value

of 1.64, calculated from the known and measured ratio values of m(6) and l(1.54)

respectively, the experimental curve is redrawn and compared with the numerical results

to show a very good agreement. The fact that the curves match so closely in the absence

of any provision in the simulation for inter-fibre friction tends to suggest that for this

type of yarn, contact and friction are very small contributors to the total deformation

energy while bending plays an overwhelmingly dominant role. This is proved in the

subsequent analysis performed in Section 5.3.7 and shown in Figure 5-19. Another

interesting characteristic of the numerical curve and further proof of the validity of the

curve, is that its gradient up until 3.5mm extension falls below the experimental curve,

again indicating the absence of a viscous friction effect between fibres during yarn

bending, which indeed has been left out of the simulation (see Appendix L for a larger

graph without the original experimental curve). The fact that no filament failure

criterion has been set-up might also explain the steeper gradient near the peak load of


128

the numerical curve. The drop off in load exhibited in the numerical curve is not due to

failure in the filaments themselves but is a result of a boundary condition failure at the

yarn feed hole. At a certain level of tensile loading, more yarn begins to pull through the

yarn feed hole. It was difficult to fully constrain the specimen as the numerical

procedure only allowed reallocation of the boundary conditions rather than a complete

redefinition. The actual readings from the simulation are presented in Section 5.3.7.

Appendix M shows all of the numerical tensile tests performed against the modified

experimental curve.

Figure 5-9. Comparison of experimental and numerical F-D curves

5.3.7 Investigating the Mechanisms in Detail

In Chapter 2 Section 2.4.3 eight micro-level fabric deformation mechanisms were

identified and discussed in detail, inter-yarn slip, inter-yarn shear, intra-yarn slip, yarn

bending, yarn twist, yarn stretching, yarn compression and yarn buckling. These

mechanisms can be separated into two further categories, those influenced by friction

and those influenced by the material properties and geometry of the fibres. Inter-yarn


129

slip, inter-yarn shear and intra-yarn slip are all forms of inter-fibre friction the

difference being that inter-yarn slip and inter-yarn shear involve the relative translation

or rotation of groups of fibres whereas intra-yarn slip considers the axial sliding

movements within these group reference frames.

Yarn bending, compression, stretching, twist and yarn buckling, which can be viewed as

the reverse of yarn stretching or the result of axial compression upon a filament, are all

part of the second category. These mechanisms are all directly related to the material

properties and geometry of the fibres and their energy contributions can be obtained

directly from the simulation.

5.3.7.1 Energy Derivation

From the curves presented in Figure 5-8 and Figure 5-9, it is starting to become clear

that friction forces play a small role in the deformation energy contribution of high

modulus continuous fibre 1x1 rib knitted fabric. Even though interfibre friction effects

are not active in the simulation, its significance can still be assessed by comparing the

difference in the magnitude of the contact energy compared to the other energy

components. To clarify which components of energy can actually be extracted from the

simulation, a summary of the energy balance taking place is presented before

proceeding any further. For the knitting, or specimen generation, Phase 1 of the

simulation, the energy balance follows the expression shown in equation (34) (Note that

energy terms not relevant to the simulation are not shown).

WEEEEE EXT

StructKIN

SIFINT

SISINT

StructINTTOT −+++=

(34)

where ETOT = is the total energy present at any time in the system

EStructINT = is the internal energy stored and absorbed by the material of the

structure

ESISINT = is the elastic energy stored by the sliding interface contact springs

ESIFINT = is the energy dissipated by the sliding interface contact friction

(currently not available for beam contact in PAMCRASH™)

EStructKIN = is the kinetic energy of the structure

0


130

W EXT = is the work done by externally applied forces (which only includes

the velocity boundary conditions applied to the knitting needles)

The frictionless interaction between the filaments means that equation (34) can be

simplified to equation (35).

WEEEE EXT

StructKIN

SISINT

StructINTTOT −++=

(35)

In the tensile testing phase of the simulation, Phase 2, the kinetic energy of the structure, EStruct

KIN becomes small and equation (35) reduces to equation (36).

WEEE EXT

SISINT

StructINTTOT −+=

(36)

To examine the deformation mechanisms of the structure in detail the internal energy stored and absorbed by the structure, EStruct

INT needs to be decomposed into its components as shown in equation (37).

EEEEEEE StructTSF

StructSSF

StructTBM

StructSBM

StructTORSION

StructAXIAL

StructINT +++++=

(37)

where EStructAXIAL = is the total axial energy present at any time in the system

EStructTORSION = is the total torsional energy present at any time in the system

EStructSBM = is the total s-axis bending moment energy present at any time in

the system

EStructTBM = is the total t-axis bending moment energy present at any time in

the system

EStructSSF = is the total s-axis shear force energy present at any time in the

system

EStructTSF = is the total t-axis shear force energy present at any time in the

system

0


131

In simple beam theory the shear force is estimated by using the condition of force

equilibrium, i.e. a shear force exists because of the bending stress. For the beam theory

used in PAMCRASH™ and by most FEA software, EStructSSF and EStruct

TSF are

complementary quantities and should therefore not be added as part of the energy

balance. As a result the internal energy of the structure reduces to equation (38).

EEEEE StructTBM

StructSBM

StructTORSION

StructAXIAL

StructINT +++=

(38)

where EStructAXIAL = ∑

n

i

ii lF2δ

, for i = 1, n

EStructTORSION = ∑

n

i

iiT2δϑ

, for i = 1, n

EStructSBM =

222211 sisi

n

i

sisi MM δϑδϑ∑ + , for i = 1, n

EStructTBM =

222211 titi

n

i

titi MM δϑδϑ∑ + , for i = 1, n

(39)

Note that because of the way in which beam elements are formulated in

PAMCRASH™, moments are calculated about both nodal points of each element and

are different for the common nodal points of different elements. See Section 5.3.7.3 for

a detailed explanation on the beam elements used.

Finally, to define a complete formula for the total deformation energy of the knit

structure, EKnitStructTOTAL , the ideal case would be to include ESIF

INT and ESISINT .

PAMCRASH™ provides ESISINT already, but ESIF

INT is currently not available since

friction has not been activated for contact Type 46. Nevertheless it is included for

completeness and the total deformation energy of a knit structure can be defined as

presented in equation (40). Note that ESISINT and ESIF

INT have been renamed to EKnitStructSIS

and EKnitStructSIF respectively with all other quantities previously defined in equation (39).

EEEEEEE KnitStructSIF

KnitStructSIS

KnitStructTBM

KnitStructSBM

KnitStructTORSION

KnitStructAXIAL

KnitStructTOTAL +++++=

(40)


132

5.3.7.2 Simulation Results: Energy Contributions

In Figure 5-9 the force displacement curve for the numerical simulation was shown to

be in very good agreement with experimental results with even the minor discrepancies

readily explainable (i.e. the effects on the curve due to the absence of inter-fibre

friction). Therefore, it is with a good level of confidence that the energy readings for the

quantities defined in equation (40), are presented. However, this does not mean that the

results presented hereafter should be taken for granted. There may be aspects of the

physical specimen that are not accurately represented and a high level of care should be

taken to recognise and identify them.

Figure 5-10. Individual filament readings for axial elongation energy

The first set of curves presented focus on the axial elongation component of yarn

energy. Figure 5-10 shows the energy versus specimen extension for all twenty of the

filaments in the yarn. The energy curves show a significant amount of variation, which

is expected, but the trend for each is consistent. It can be seen that the filaments

experience different levels of axial elongation energy depending on their location in the


133

yarn. The largest energy spike on the graph corresponds to a filament that has become

slightly separated from the rest of the yarn. The result is shortening of the filament

length in sections of the specimen, which therefore experiences more axial elongation

energy. All of the curves exhibit a very low energy contribution at early stages of the

tensile test before rising steeply towards tensile failure.

Figure 5-11. Total yarn axial elongation energy

In Figure 5-11 the total yarn axial elongation energy curve is shown along with six

sample data points identifying the model specimen’s state in the mesh plot key. Only

after the fourth data point does the tensile energy begin to increase, once fibres in the

specimen begin to straighten. At the peak axial elongation energy a maximum stress of

2058MPa and maximum axial strain of 2.8% is achieved in filament 687 (Beam

Element: 234605 State: 682). The maximum axial stress and axial strain at any time

during the tensile test, is 2198MPa and 3.0% in filament 672 (Beam Element: 219638

State: 729). Both maxima occur at the edges of the specimen in regions of high

curvature and contact. Comparing these to the documented values of E-glass fibre

mechanical properties 65 and Table 2-1, shows that the values here are very close to the

failure range (2400MPa – 3450MPa).

E KnitStructAXIAL


134

Although the graphs show the characteristics of a material property failure, it must be

noted that no failure criterion has been assigned to the model. It is possible to do so by

using a different material model and the element elimination function in

PAMCRASH™ but this further complicates the model. Failure is detected by

identifying element stress levels exceeding the ultimate tensile stress. As mentioned

already, this may explain why the numerical F-D curve shown in Figure 5-9 becomes

steeper than its experimental counterpart at the latter stages of the tensile test.

Fortunately, failure of the specimen is quite catastrophic, as shown in Figure 5-8, and

the total specimen failure in the simulation can be assumed once a single element

reaches the ultimate tensile stress. The peak load and drop off which are exhibited in all

of the graphs is the result of leftover yarn pulling through into the specimen once a

certain tensile loading is reached, increasing the size of one of the loops, and relieving

the load on the specimen. This is a boundary condition failure rather than an actual

material property failure but because it occurs at a sufficiently high load, valid tensile

test readings for the simulation can still be made.

The next set of graphs shown in Figure 5-12 and Figure 5-13 show a very different

trend. For the s-axis bending moment energy the curves show a more gradual increase

in energy as well as an initial fabric specimen internal bending energy, created in the

structure during the knitting process. At the peak energy level, the bending energy has

increased by a factor of five compared to its initial internal energy value and is four

times larger than the maximum energy level of axial elongation.

The t-axis (perpendicular to the s-axis) bending moment energy curves shown in Figure

5-14 and Figure 5-15 show a significantly lower level of energy than the s-axis energy

curves. Its initial internal energy is half that of the s-axis bending moment energy and

the increase in energy during the tensile test is very low, reaching a peak value which is

four times lower than that of the s-axis bending moment energy.


135

Figure 5-12. Individual filament readings for s-axis bending moment energy

Figure 5-13. Total yarn s-axis bending moment energy

E KnitStructSBM


136

Figure 5-14. Individual filament readings for t-axis bending moment energy

Figure 5-15. Total yarn t-axis bending moment energy

E KnitStructTBM


137

Since the filaments have been defined with a circular symmetrical cross-section and all

have their orientation node pointing in the same direction, this indicates that to create

the 1x1 rib fabric, the yarn needs to be bent twice as much about one axis compared to

the other. This phenomenon could be used to measure how three-dimensional the

structure is. This characteristic continues during the tensile test with bending moment

energy increasing more about one axis compared to the other.

While the contribution of the bending moment energy was always expected to be high,

it was difficult to even guess how much of a part the torsional energy would play.

Magnified images of the milano and 1x1 rib fabric specimens always display a certain

level of twist in the structure (see Appendix N) even if the yarn itself does not exhibit

much initial twist, which is what was assumed for the yarn in the simulation exercise.

Figure 5-16 and Figure 5-17 show how small the contribution of torsional energy is,

with an initial internal torsional energy level of 0.01mJ, a factor of twenty to forty times

less than that of the bending moment energy.

Figure 5-16. Individual filament readings for torsional energy


138

Figure 5-17. Total yarn torsional energy

It is also interesting to note the way in which this energy component changes, with its

almost linear increase up until point 3 and then exponential increase afterwards,

indicating a certain amount of dependence on the axial elongation energy curve. If a

certain degree of yarn twist was incorporated into the model, it is anticipated that this

would not change the shape of the curve by much, but would only shift its position

upward along the energy axis.

The final energy component curve presented here shows the total yarn contact energy,

Figure 5-18. Its characteristics are similar to that of the axial energy curve, however, it

does not increase as much and is about four times smaller at its peak energy level. A

closer inspection of this curve, compared with the axial energy curve, reveals an

average energy level 4.7 times smaller after 2mm extension (13.3 times smaller prior to

2mm extension).

E KnitStructTORSION


139

The contact energy curve can also help give a clue as to how much energy is dissipated

through friction effects. Using a coulomb friction law with a coefficient of friction of

0.5 and assuming that the contact force is the normal force acting on an element, the

only difference between friction and contact energy is lδ , the movement of the fibres.

For friction energy, sliding displacements are much greater than the compression

displacements experienced by the contact interface springs. The magnitudes of these

displacements can be sampled in the model by looking at relative movements of nodal

points at the heads of the knit loops and by measuring how much loop crossover points

have moved with respect to one another. Typical crossover movement is around 0.6 -

0.8mm while inter-fibre movement, depending on the location, ranges from 0.02mm at

the sides of the loops and 0.1mm at the head of the loop. These movements are 10 to

100 times larger than the contact spring compression displacements, so the frictional

energy would certainly be of more significance than the contact energy. Another clue is

in the fact that the force displacement curve shown in Figure 5-9 agrees so well,

indicating that the frictional energy is not as dominant as the bending moment energy.

Based on the above arguments, an estimate of the total frictional energy dissipation

Figure 5-18. Total yarn contact energy

E KnitStructSIS


140

before failure would be between 0.64 and 6.4mJ. A curve representing the total

frictional energy dissipation versus specimen extension would probably lie within the

sum of all yarn energy components curve and have similar shape characteristics to the

contact and axial elongation energy curves, meaning that bending energy would still

dominate throughout most of the deformation.

Due to the unconventional nature of some of the information required, most of the

quantities were calculated element by element using the expressions for the various

energies as presented in equation (39) and programmable macros to generate the

required curves. To check the correctness of the energy calculations, all the energy

components shown in equation (40) without the terms EKnitStructSIF

and EKnitStructSIS were

added and compared to the total internal energy output given by PAMCRASH™ minus

the non-yarn energy components of the model (i.e. knitting machine elements). Figure

5-19 shows the graphical form of equation (40) and the quantitative results of each of

the components versus specimen extension.

Figure 5-19. Comparison of yarn deformation energy components


141

In this figure, it is clear how dominant the bending moment energy is. The summation

of the s and t-axis bending moment energy curves practically fit the shape of the total

internal energy curve except in the region closest to tensile failure. The internal energy

calculated by the software can be seen to match exactly with the sum of the calculated

energy component curves, verifying that the calculations have been done correctly.

An interesting question, which arises as a result of this analysis, is that with the given

information, is it possible to determine which of the deformation components causes

strain failure? The obvious choice is the bending moment stress, but although the

energy readings for this component are the highest, this does not necessarily mean that

this is the component that initiates failure. Axial elongation energy while much lower

also reaches stress levels very close to the tensile failure as discussed after Figure 5-11.

An analysis of the bending moments shows maximum values that exceed the ultimate

tensile stress of E-glass by a factor of 4.5 (maximum s-axis bending moment occurs at

n1 5.28994e-06kN.mm, σUTS for E-glass taken as 2400MPa). Furthermore, the UTS

value is first reached at fairly modest levels of specimen elongation. The concern here is

that the level of mesh refinement is not good enough to give the correct readings for

bending moments. However how is it possible that the force displacement readings for

the numerical and experimental case match so well? These issues are addressed and

discussed in Section 5.3.7.3, which is a dedicated section on the type of beam elements

used in PAMCRASH™.

5.3.7.3 Beam Elements in PAMCRASH™ and Discussion of Results

The knitting procedure subjects a yarn to large displacements and the subsequent

geometric structure has many regions of high curvature. To cope with such large

displacements PAMCRASH uses the Belytschko beam element formulation, part of a

family of structural elements that employ the ‘co-rotational technique’ 66.

In a large displacement formulation, the idea is to separate deformation displacements

from rigid body displacements since it is only deformation displacements that generate

strain energy. In order to perform the separation it requires a complete description of the

deformed body at its current and reference (previous time step) configuration (i.e. the

orientation and location of all elements and nodes at both configurations).


142

To do this, the co-rotational technique assigns a co-ordinate system to each individual

node and element. The coordinate system attached to a node is termed the body

coordinate system (xb, yb, zb) and moves with the nodes while the element coordinate

system (xe, ye, ze) is defined firstly by its x-axis, which originates at node n1 and then

through n2 of the element. The remaining axes of the element coordinate system are

defined by the element’s principal inertial axes (i.e. using an orientation node n3).

Body and element coordinate system unit vectors are used to relate the translational and

rotational transformations between the global coordinate system and both the coordinate

systems. For a rigid body rotation the unit vector of the element coordinate system will

be the same in the initial and rotated configuration with respect to the body coordinate

system, the same applies for the other rigid body transformations. If the unit vectors are

not the same then a deformation displacement has taken place.

It is in this way that all the deformation components are calculated and subsequently the

forces, bending moments and torques in each of elements. These are calculated using

known quantities including the Young’s and shear moduli, second moments of area, the

effective cross-sectional area in shear and element lengths.

One quantity that immediately comes into question is the effective area in shear, which

was taken in the simulation to be equivalent to the actual cross sectional area. What

should the effective area in shear in a solid circular beam be?

Figure 5-20. The co-rotational technique used in PAMCRASH™ for beam elements

X

Y

Z

n1

n2

n3

Global coordinate system

zbyb

xb

ye

xe

ze

zb yb

xb


143

Shear area represents the area of the cross section that is effective in resisting shear

deformation. It is used in finite element analysis to calculate a member's deformation

due to shear stress. Replacing the actual area with shear area reduces the effective cross

sectional area to reflect the parabolic distribution of shear stress in the section, resulting

in a better approximation of the maximum shear stress. It can usually be ignored for

long, slender beams where deflections due to shear stress are negligible compared to

bending stress deflections, but is of significant importance in short, deep beams 66,

therefore, in this case the use of actual cross sectional area is acceptable.

The reason why the force displacement readings for the numerical and experimental

case match so well, while local moment readings seem inaccurate, can be attributed to

the way in which connectivity between beam elements is addressed in PAMCRASH™.

Beam element moments are calculated by defining their nodal connection points as a

type of hinge where the stiffness of the hinge is dictated by whatever stiffness and

second moment of area values (about the two perpendicular transverse axes) are

specified by the user. Therefore, the dependence on which material model is used (in

this study only linear elastic is used since glass fibres adhere to this model very well)

and how much the hinge node between the two beam elements rotates, determines the

moment at the beam endpoint, the element itself remains perfectly straight. With this

type of formulation the overall structural response of the numerical specimen

approaches the exact response of the physical specimen as the number of elements used

in the simulation approaches infinity. If the beam element size is small enough then

correct energy readings for the entire specimen should also be achieved. However, local

moment readings will not be so accurate because of the inadequate mesh resolution in

localised regions of high curvature.

The axial moment calculation in the beam elements is based on Timoshenko's torsion

theory, which is only relevant for very small rotations and is where the problem of

"large rotation error", which frequently occurred in the simulation, may arise. The

problem occurs when the axial rotation of an element is larger than that which can be

handled by theory in one time step. When a very small time step scale factor is used,

this problem is eliminated.


144

The fact that the simulation does not consider initial yarn twist and friction may explain

why maximum axial force readings are fairly low. More twist means a larger transverse

force applied to the filaments. This coupled with interfibre friction causes a significant

amount of energy loss. Even with a significant amount of lateral pressure, if the friction

coefficient is zero, as it is in the current simulation, two adjacent fibres will still slide

over one another very easily. If friction was incorporated then its influence could be

closely analysed, and its contribution to the deformation energy could actually be

quantified for different coefficient of friction values. There is, however, the problem of

element size which might be introducing an artificial form of friction creating the

potential for incorrect results or results corresponding to a particular unknown value of

coefficient of friction. The effect is analogous to a chain as opposed to a piece of wire

sliding around a sharp corner.

5.4 Macro-Level Material Definition

Unfortunately the level of detail described in the previous section cannot be applied to

simulations on a larger scale because of the overwhelming computing power

requirements, which will no doubt be available in the future. However, it would suffice

to have accurate simplifications of the materials behaviour using the information gained

in this and previous chapters.

5.4.1 Material Model

In Chapter 3, hot tensile tests using 2-ply specimens of milano rib knitted fabric

composite were performed to gather data that could be used together with an

appropriate material model. In this section, these data are used to perform numerical

tensile tests, which are compared to the results presented in Chapter 3.

5.4.1.1 Existing Material Models

PAMFORM™ offers a wide range of material models, which can handle many different

types of materials. Table 5-4 shows a list of the material models that could be used to

describe the forming behaviour of molten knitted fabric composite material.


145

Table 5-4. List of material models available in PAMFORM™ software Material Model

(for shell and membrane elements) Description

Type 121 Plastic forming non-linear thermo-visco-elastic (G’Sell model)

Type 132 Multi-layered fabric composite (linear fibres)

Type 140 Thermo-visco-elastic matrix with elastic fibres

Type 151 Thermo-visco-elastic matrix with non-linear fibres

Type 180-183 User defined material

The closest descriptions to molten knitted fabric composite are material model types

140 and 151, both of which are able to consider the strain dependency of the Young’s

modulus for the two definable fibre directions. In type 140, “elastic fibres” means that

the loading and unloading curves follow the same path, whereas in type 151 this is may

not be the case and there are allowances for specifying an energy dissipation factor and

the magnitude of permanent plastic deformation to account for frictional energy losses.

To consider the forward loading behaviour of the material only, material type 140 is

ideal. It defines a composite triple-phase shell element material with a thermo-visco-

elastic matrix and elastic fibres 67. A description of the material model and the

parameters that it requires is given in Figure 5-21. It is made up of three basic

components, a stabilising parent sheet, a visco-elastic matrix component and a fabric

component.

The parent sheet helps avoid numerical instabilities (due to oscillation) that can

sometimes occur when defining unidirectional materials by providing a means of

Figure 5-21. Definition of material Type 140 in PAMFORM™ 67

G, v

Max(E1,E2)

E2

E1

Stabilizing optional “parent sheet”

Thermo-visco-elastic “matrix” phase

Non-linear elastic “fabric” phase


146

defining an additional resistance to deformation. It behaves like a linear elastic shell

element and its properties are based on a user specified Poisson’s ratio and shear

modulus, which can be entered as a single value or function of the shear strain. The

component is not essential and is sometimes ignored in the case of unidirectional and

woven fabrics that have a very low intra-ply shear stiffness. However, it is not deemed

as ignorable in the case of knitted fabric composites. It can be neglected by defining a

zero value, or zero value shear modulus versus strain curve.

In the thermo-visco-elastic component, which is of the Maxwell type, the effective

viscosity can be given by specifying a constant in the case of an assumed isothermal

condition or by Cross or Power law equations that define viscosity as a function of

temperature 67.

In the fabric component, the behaviour of E1 and E2 can be defined by a constant or as a

function of strain, which is necessary for knitted fabrics. The fibres not only contribute

to stresses in the fibre direction but also transverse shear and bending moments,

computed using classical beam theory 67. However, in the case of fabrics, to account for

the fact that an individual assembly of fibres has a bending stiffness much lower than a

solid beam of equivalent area, (as discussed in Section 2.2.1.2), a scale factor is used to

reduce the size of the transverse shear and bending moments.

The model also allows the definition of fibre directions other than 90 degrees that can

change and evolve during the course of the simulation.

5.4.1.2 Material Model Calibration

Many of the parameters required for the simulation are difficult to measure; however,

given the modulus curves defining E1 and E2, the rest of the required parameters can be

calibrated numerically. The methodology used is to first run the simulation using the

measured input modulus curves for E1 and E2 and estimate values for the parent sheet

shear modulus G, poisson’s ratio ν, and matrix viscosity η. These values are based on

typical values for the viscosity of polypropylene and an educated guess for the initial

values of G and ν of the stabilizing parent sheet. The order of magnitude for the value

of G is known since it must not be larger than the minimum value of the modulus in the

warp and weft direction otherwise the properties of the parent sheet will overpower

those of the fibres in the warp and weft direction.


147

The input parameters derived from the physical properties of the molten knitted fabric

material are presented in Table 5-5.

Table 5-5. Material Type 140 physical input parameters Material Property Value

*Density, Composite 1.23e-09tonne/mm3

Thickness 4mm

Tensile Modulus E1 Warp Curve Modulus (MPa) versus Strain

Tensile Modulus E2 Warp Curve Modulus (MPa) versus Strain

Bending Factor 0.01

Out of Plane Shear Factor 0.01

**Parent Sheet Shear Modulus, G 0.02MPa

Parent Sheet Poisson’s Ratio, ν 0.3

Viscosity, η 0.001MPa.s (1000Pa.s)

Fibre Orientation 90°

***Void Parameters -

*Composite density calculated on basis of 20% fibre volume fraction

**Locking angle and post locking Shear Modulus may also be defined, but not used here. Minimum E

values = 0.09 warp direction, 0.13 weft direction

***Void parameters for discontinuous fibre mats, (ao, bo, wo, phi) not used

Table 5-6 lists the numerical parameters, most of which are left as default values.

Table 5-6. Material Type 140 numerical input parameters Numerical Property Value

*Number of Integration Points 3

*Membrane Hourglass Coefficient 0.01

*Out of Plane Hourglass Coefficient 0.01

*Rotation Hourglass Coefficient 0.01

*Transverse Shear Correction Factor 0.8333

**Damping Ratio -

**Frequency -

* Numerical parameters, mostly damping coefficients to maintain stability, default values used

**Extra material damping parameters not used


148

To calibrate the model, a comparison of the influence of varying the unmeasured

parameters G and η, can be undertaken to make sure that the values chosen for these

parameters are correct and that their variation causes a change in behaviour that would

be expected. The study is performed using the warp direction tensile tests only, since

the values of G and η are the same for the material in either direction.

Figure 5-22 shows the variation in the viscosity parameter η ranging from 0.0001 to

10MPa.s. It can be seen that the best fit corresponds to a viscosity value of 0.001MPa.s

(1000Pa.s), which is a typical order of magnitude for polypropylene at forming

temperature, as was discussed in Figure 2-2.

The other important parameter to investigate is the effect of the parent sheet shear

modulus, G, which can have a large influence on the response, especially if the value

chosen is too high. In Section 5.4.1.1 it has been stated that this parameter may not be

required at all, but can help avoid numerical instabilities due to unwanted oscillations if

they occur. Figure 5-23 shows that any value below 0.02MPa shows a very similar

response and can be used without influencing the overall behaviour of the curve.

Figure 5-22. Comparison between PAMFORM™ warp direction tensile tests and experimental results, viscosity parameter η variation


149

A further check of the behaviour without the parent sheet at all can be seen in Figure

5-24, which shows that slight oscillations start to occur at very low viscosities when the

value of the parent sheet shear modulus is set to zero. A test simulation at a lower

displacement rate is also shown to make sure that the numerical test, which is done at a

much faster speed than in real life is in fact representative of the real life situation, and

that rate effects are not present.

At this stage the material model can be optimised so that the numerical tensile data fits

the experimental data exactly. A more rigorous calibration could be performed once it

becomes clear that the material model is capable of simulating the material to a

reasonable level. The warp and weft direction tensile results of the optimised modulus

curves points are presented in Figure 5-25.

Figure 5-23. Comparison between PAMFORM™ warp direction tensile tests and experimental results, shear modulus parameter G variation


150

Figure 5-24. Comparison between PAMFORM™ warp direction tensile tests and experimental results, parent sheet and displacement rate variation

Figure 5-25. Calibrated warp and weft modulus curve points

Oscillations at very low viscosity


151

5.4.2 Experimental Comparisons

Using the calibrated material property data developed in Section 5.4.1, an attempt was

made to simulate and compare the production of domes, cups and a wing mirror fairing

component with their GSA counterparts.

5.4.2.1 Double Curvature Forming

In Section 3.4 a number of 50mm diameter domes were formed using the matched die

forming process and the behaviour of the material was investigated at softened and

molten temperatures. The differences in strain patterns exhibited in the softened and

molten domes were evident. In this section matched die forming simulations are

performed on 100mm diameter blanks at viscosities of 1000 and 5000Pa.s to represent

the material behaviour in both states. Other numerical parameters to consider in the

three-dimensional forming simulations are the bending factor and out of plane shear

factor, which help account for the very low bending stiffness of the fabric. To achieve

reasonable bending and out of plane shear properties (and stability) values of up to 0.99

can be used instead of default value of 0.01, since the tensile stiffness of the molten

knitted fabric material model is very low. Warp direction numerical tensile tests

performed using values of 0.99 instead of 0.01 show that this parameter has no effect on

the tensile properties as expected. Once again the simulations have been performed at a

displacement rate of 2.5m/s.

Specimen Forming Parameters Blank Diameter Size = 100mm Original Thickness = 5mm Density = 1.23g/cm3

Parent Sheet Shear Modulus = 0.02MPa Material Viscosity = 0.001MPa.s Bending and Out of Plane Shear Factors = 0.99 Friction Coefficient Between All Contacts = 0.3

weft warp

Warp and Weft fibremodulus properties asdefined in Section 5.4.1.2


152

Figure 5-26. Rigid matched die dome forming of molten knitted fabric composite η = 0.001MPa.s

The first simulation shown in Figure 5-26 modelled the tooling as rigid, which in

practical experiments always produced a dome of uneven thickness and significant

thinning in the hemispherical region of the dome unless the blank was made thicker

than the final mould gap. The maximum warp and weft direction true strains were 0.180

and 0.152 respectively while a minimum thickness of 3.7mm or 26.0% thinning is

exhibited by the specimen. Domes 12, 13, 15 and 16 in Section 3.4 showed typical

weft warp

weft warp

weft warp


153

minimum thickness strains (thinning) between 30.4 – 35.2%. The physical specimens

produced in Section 3.4.3.1 used flexible rubber dome tooling therefore this was

subsequently incorporated into the simulation. Specimen Forming Parameters Blank Diameter Size = 100mm Original Thickness = 5mm Density = 1.23g/cm3


weft warp

weft warp

weft warp



154

Figure 5-27. Flexible matched die dome forming of molten knitted fabric composite η = 0.001MPa.s

There is not much difference between the domes formed using the rigid and flexible

tooling, only a slight variation exists in the uniformity of each of the contour plots due

to the compliance of the rubber punch. A punch gap of 5mm was again used, so the

simulation did not fill out the dome as in the practical experiments. Simulations using a

3mm punch gap on the 5mm thick blanks were also performed, however at the latter

stages of the simulation when transverse flow of the matrix material should occur, the

model was unable to proceed any further with the calculation. The simulation

highlighted the inability of the material model to adequately model large amounts of in-

plane flow by the matrix around the knitted fabric reinforcement during rubber stamp

forming. The properties of the rubber punch were modelled using a simple linear elastic

model with a Young’s Modulus of 4MPa, Poisson’s ratio of 0.45 and density of

0.86g/cm3.

The contour plots in Figure 5-27 show similar maximum warp direction true strain of

0.180 and maximum weft direction true strain of 0.173. This does not compare well

with the overall range of maximum engineering surface strains exhibited in domes 12,

13, 15 and 16 in Section 3.4 (46.8 – 79.9%). The thickness and angle contours are very

similar to the rigid tool simulation of Figure 5-26, with ranges of 3.4 – 5.2mm and 63.8

– 90.0° respectively. However, the minimum thickness, 3.4mm, has decreased slightly,

now corresponding to 32.4% thinning which is now closer to the GSA results. It should

be noted that in the numerical contour plots, tensile fibre surface strains are given as

positive values. In the GSA contour plots this is also the case, therefore comparisons

should made between maximum surface strain values. In the case of thickness strains,

weft warp


155

the GSA results display a decrease in thickness as a negative percentage thickness

change while the numerical results simply show actual thickness values.



weft warp

weft warp

weft warp



156


In Figure 5-28 and Figure 5-29 only the viscosity parameter has been increased to see if

a reasonable prediction of the material behaviour can be achieved. As in the physical

experiments the simulations did not apply any flange clamping pressure to the

specimens and with the larger viscosity value it can be seen that wrinkling begins to

appear in the flange regions of the specimens. This is more prominent in Figure 5-29

where the viscosity of the material has been increased to 10000Pa.s. In the 5000Pa.s

simulation the maximum warp and weft direction fibre true strains were 0.152 and

0.145 respectively while the thickness and angle contours range from 3.8 – 5.4mm and

67.5 – 90.0° respectively. Specimen Forming Parameters Blank Diameter Size = 100mm Original Thickness = 5mm Density = 1.23g/cm3


weft warp

weft warp



157


In the 10000Pa.s simulation the higher viscosity causes higher localised warp and weft

true strains of 0.240 and 0.337 midway up the apex of the dome. The thickness range is

shifted upwards between 4.0 – 6.6mm and the angle between warp and weft, probably

due to the wrinkling has a large range of 48.1 – 90.0°. Appendix O shows the same

simulation done using rigid tooling, which shows less wrinkling but more thinning at

the higher viscosity values.

weft warp

weft warp

weft warp


158

5.4.2.2 Cup Forming

In Section 3.5.1 a 120mm diameter, 5mm thick blank was deep drawn into a cup using a

38mm diameter rigid aluminium punch. The experiment was done using varying levels

of clamping force as well as the fully clamped condition, which is simulated in Figure

5-30 and Figure 5-31. In the practical experiment, cup failure was observed to occur in

the warp direction at a specific region in the wall of the cup just below the punch nose

radius. The failure also occurs at a particular cup height and it was hoped that this

height could be predicted in the simulations. Both the cup forming and extreme

component simulations were performed at a displacement rate of 1m/s in order to

increase solution stability.


Parent Sheet Shear Modulus = 0.02MPa Material Viscosity = 0.001MPa.s Bending and Out of Plane Shear Factors = 0.99 Friction Coefficient Between All Contacts = 0.05 Clamping Force = 1000N

weft warp

weft warp



159

Figure 5-30. Fully clamped cup forming to strain failure using low tool friction coefficient μ = 0.05

Figure 5-30 shows the results from the low friction simulation. The maximum warp and

weft direction true strains are 0.470 and 0.516 respectively, at a cup height of 28.4mm,

where the simulation is no longer able to converge upon a solution. Unfortunately, these

values fall short of the warp and weft direction failure strains (0.670 for the warp

direction and 0.830 for the weft direction) as shown in Figure 5-25.

For the case of a low tool friction coefficient, it is difficult to even predict the location at

which failure might occur as the simulation indicates that fibre strain failure could occur

anywhere in the top face of the cup, not really a good prediction of what happened in

the physical experiment since fibre strain failure occurred at a particular location on the

cup.

Fibre angles in the cup range from 63.9 – 90.0° and the thickness ranges from 0.4 –

5.0mm with no prediction of the matrix migration due to knit loop closing, since the

material model is unable to account for this type of behaviour.

weft warp

weft warp


160



weft warp

weft warp

weft warp



161

Figure 5-31. Fully clamped cup forming to strain failure using high tool friction coefficient μ = 0.5

In the high friction cup forming simulation shown in Figure 5-31, the location of likely

fibre strain failure is now evident and matches the location observed in the physical

experiment, indicating that large amounts of tool to blank friction is indeed involved.

The warp and weft direction true strains are 0.553 and 0.701 respectively and are

interestingly within 2% of one another with respect to their failure strain percentage

values (0.553/0.670 = 82.5% and 0.701/0.830 = 84.4%) making it difficult to predict

whether tearing will occur in the warp or weft direction. The cup height achieved in this

case is 26.8mm before the simulation was no longer able to continue with the

calculation.

5.4.2.3 Extreme Forming

In the cup forming simulations it was found that the PAMFORM™ material model

Type 140 was unable to converge at very large fibre strain values. This made it difficult

to simulate the forming of the wing mirror component properly, since the manufacture

of this component relied on full stretching before allowing any draw-in into the mould.

The only complete simulation was one which allowed significant amounts of draw-in

behaviour by relieving the blank holder force. However, in this case the warp and weft

strain values were well below actual values of strain failure, see Figure 5-32.

weft warp


162

Specimen Forming Parameters Blank Size = 200 X 200mm Original Thickness = 2mm Density = 1.23g/cm3


weft warp

weft warp

weft warp



163

Figure 5-32. Wing mirror component forming using a clamping force of 100N

In the GSA experiment shown in Figure 3-38, the minimum thickness strain recorded

was –39.8%. This corresponds to a minimum thickness of 1.2mm, which is reasonably

predicted by the thickness contour plot in Figure 5-32. However, the surface strains in

the simulation are fairly inaccurate. The simulation predicts warp and weft direction

true strains of 0.100 and 0.548 respectively, while GSA measured a maximum

engineering surface strain of 136.0% (0.859 true strain) corresponding to the weft

direction, which is consistent with the method of forming (full stretching then draw-in).

Although lower surface strains were expected, since a small blank holder force was

used, the model seemed to exhibit excessive stiffness in the warp direction. Increasing

the blank holder force to 1000N or increasing friction to facilitate more stretching

caused instability and divergence.

5.4.2.4 Summary

The numerical simulations presented in Section 5.4.2 have shown that no reasonable

predictions of molten knitted fabric composite behaviour can be achieved using the best

available material model (Type 140) in PAMFORM™. Table 5-7 shows an overall

summary of the numerical and experimental data that have been used in the comparison.

The warp and weft direction strains from the numerical forming simulations are

compared with the maximum tensile surface strains obtained from the GSA experiments

and show lower than anticipated values. Note that the numerical strains have been

converted into engineering strains for the comparison. The minimum thickness strains

are the only values that seem to show any close agreement. For simulations that require

very high values of true warp and weft direction strains, the model always failed to

weft warp


164

converge. The instability was observed in the tensile testing, cup forming and wing

mirror forming simulations when larger strain values were required. It is believed to be

a shortcoming of the material model which has been designed for very stiff linear fibres

unlike knitted fabric fibres whose structure gives them non-linear, very low modulus

values during most of the deformation. Further development of the current material

model or the definition of an entirely new model is recommended before more

reasonable predictions can be made.

Table 5-7. Comparison data for numerical and experimental forming experiments

Type Tooling Variable Parameters εmax warp εmax weft

*εmin

thickness Fibre

Angles

Rigid η = 0.001MPa.s 19.7% 16.4% -26.0% 63.9 - 90.0°

η = 0.001MPa.s 19.7% 18.9% -32.4% 63.8 - 90.0°

η = 0.005MPa.s 16.4% 15.6% -24.2% 67.5 - 90.0° Dome

Flexible

η = 0.010MPa.s 27.1% 40.1% -19.4% 48.1 - 90.0°

μ = 0.05 60.0% 67.5% -92.8% 63.9 - 90.0° Cup Rigid

μ = 0.5 73.8% 101.6% **-100.0% 48.1 - 90.0°

Numerical

Wing Mirror Flexible

η = 0.001MPa.s μ = 0.3

Clamping Force =100N

10.5% 73.0% -60.5% 13.0 - 90.0°

Dome 12 Molten 175°C 62.8% (-25.1%) -30.4% -

Dome 13 Soft 160°C 49.3% (-21.5%) -30.7% - Dome 15

Soft 150°C 46.8% (-18.6%) -32.6% - Dome Flexible

Dome 16 Molten 180°C ***79.9% (-18.0%) -35.2% -

Experimental (GSA)

Wing Mirror Flexible Molten 180°C 136% (-34.5%) -39.8% -

*Percentage by which the thickness of the component has changed (negative indicates decrease in

thickness, or thinning)

**Actual minimum thickness reading given by the software is –0.2mm

***Experiment performed using an air and tool temperature of 20 and 25°C respectively

Note that for the experimental (GSA) surface strains, the maximum elemental strain

(tensile) is given together with the minimum strain (compressive) in brackets and

should correspond to the larger of the warp and weft direction tensile strains.

165

Chapter 6 Conclusions and Recommendations for

Further Work

6.1 Conclusions

The main focus of this research was to study the deformation mechanisms that occur

during the forming process of knitted fabric thermoplastic composites. This was done

by performing a series of practical and numerical experiments to reveal and record the

forming characteristics of the material. The major outcomes of the study can be divided

into five major sections.

• A literature survey of the current trends in knitted fabric composites research,

and comparison of this type of material with other forms of textile composite

materials. The focus was on surveying research that had been done on the

forming characteristics, rather than on the solid-state properties, and on

identifying analysis methods and deformation mechanisms that exist in the

hierarchical levels of the material.

• An experimental study of the material, involving a number of forming

experiments to find the best forming method, and to yield information on the

strain behaviour in two and three-dimensional test cases that were to be used to

validate the results of a macro scale numerical model.

• A brief investigation into the solid-state tensile properties of high fibre volume

fraction knitted fabric composites, comparing stiffness and strength with

common competing materials.

• A detailed numerical investigation into the deformation mechanisms of the

reinforcing structure with the aim of developing a model that can quantatively

Chapter 6 Conclusions and Future Work Recommendations

166

establish the energy weighting of the structural deformation mechanisms in any

weft knitted structural configuration produced on v-bed knitting machinery.

• Finally, the development, implementation and testing of macro-level models

using existing material models originally developed for unidirectional and

woven fabric composites.

6.1.1 Literature Survey

The following summarises the knowledge gained and developed from the literature

survey.

• The literature survey revealed that while much work had been done on the solid-

state properties of knitted fabrics composites, research on the forming properties

of these types of materials was limited. In general, the best research on textile

composites seems to have come from researchers who had previously been

involved in textile-only research. While large amounts of background

information was borrowed directly from the textile-only literature, research that

had been done on the structural mechanics of textiles, yarns and fibres by textile

researchers seems to have been overlooked by composite material researchers.

The main reason for this is that there are a limited number of publications in the

area of pure textile mechanics, possibly due to the complexity of the topic.

• After becoming familiar with the terminology and geometrical characteristics of

the many different types of textile structures, it became apparent that knitted

fabric structures are the most complex of all the textile geometries. However it is

not only the textile geometry that plays a part in the deformation behaviour, the

structure of the yarn and the types of fibres used in the yarn also play an

important role in the material’s deformation characteristics.

• To form the composite material the fibres need to be mixed with resin, either

thermoplastic or thermoset. Thermoplastic resins are highly viscous and require

innovative techniques such as commingling or powder coating to make sure the

two constituents mix together well. As a result, forming techniques can involve


167

dry or wet forms of the composite material. A raw material where the two

constituents have been wet-mixed, or consolidated, can be called a prepreg,

while dry-mix constituent materials are termed preforms.

• Manufacturing methods for forming three-dimensional shapes using knitted

fabrics can involve the stretch forming of a flat sheet of fabric or the forming of

an integrally knitted shape. Stretching the knit structure in one direction

increases the mechanical properties in that direction at the expensive of the

properties in the transverse direction. Forming can be performed using a variety

of techniques involving matching or single dies, heat and pressure.

• During the forming process there are mechanisms at different levels of the

material’s structure that allow deformation. From the knowledge gained in the

literature it is suggested that knitted fabric composites and even other textile

composite materials follow a three-level hierarchy of (1) prepreg flow

mechanisms, (2) macro-level fabric deformation modes and (3) micro-level

fabric deformation modes. Of these levels the micro-level modes are the most

important and are the ones that have been studied in this thesis.

• Modelling approaches for the forming of knitted fabric composites can be

divided into two categories, kinematics and mechanics. Kinematic approaches

are popular with woven fabrics but are not too relevant for knitted fabrics since

their geometry is so complex. However, kinematic approaches are very good for

strain mapping and can produce informative contour plots showing strain

distributions no matter what the reinforcing structure. Analytical mechanics

approaches are very difficult to execute. Even for woven fabrics the analysis is

complicated and lengthy. Analytical methods for the study of knitted fabric

deformation involves significant amounts of simplification, but computer

technology is now becoming powerful enough to perform numerical methods of

analysis at sufficient levels of detail.


168

6.1.2 Experimental Tensile, Picture Frame, Vee-bend, Dome, Cup and Extreme Forming

The experimental part of this study involved subjecting the knitted fabric composite

sheets to a number of in-plane, single curvature and double curvature forming

experiments. For in-plane forming, tensile testing of the molten knitted fabric composite

material was performed to establish modulus curves for the warp and weft directions of

the material and the in-plane shear deformation was examined using the picture frame

test. Single curvature forming, or vee-bending, was performed to investigate the interply

shear versus stretch behaviour of multiply specimens, while dome, cup and an

extremely deep curved component were designed to push the material to its forming

limits. From these experiments it can be concluded that:

• The elastic behaviour of the molten (180°C) composite is very similar to the

dry fabric at low forming rates (<100mm/min);

• In the shear deformation experiments it was apparent that the chemical sizing

(coating) on the yarn produces significant lubrication effects at elevated

temperatures for both the knitted fabric alone and the knitted fabric composite,

aiding the micro-level deformation mechanisms. Visual inspection of the

specimens at elevated temperatures exhibited buckling much later in the

deformation process. Only the composite specimens were affected by varying

displacement rates due to the rate dependency of the polypropylene matrix.

• In the vee-bending experiments, forming between 150°C and 180°C using

molten material showed consistent strains and amounts of interply shear with

constant clamping force and springforward behaviour. With an increase in

clamping force the springforward behaviour was observed to decrease.

Softened specimens did not exhibit springforward behaviour.

• For the dome forming experiments, choosing a higher forming temperature

resulted in a more uniform strain and thickness distribution. Using a silicone

rubber male stamp as opposed to a rigid mould allowed an even redistribution


169

of matrix material in regions where severe thinning or oozing of molten plastic

due to closing of knit loops had occurred.

• As the material stretches during forming, the minimum allowable angle

between the warp and weft directions without any occurrence of buckling

decreases.

6.1.3 High Fibre Volume Fraction Knitted Fabric Composites

Knitted fabric composites have been accepted as having lower stiffness and tensile

properties than other types of textile composite materials. It is possible to produce

higher volume fraction values of knitted fabric thermoplastic composite using

commingled preforms and significant levels of compaction. Tensile test specimens of

the 1x1 rib configuration were manufactured, tested and compared with a woven fabric

composite containing a fibre volume fraction of approximately 35% as well as

aluminium and ordinary polypropylene. The experiments showed that:

• The manufactured high volume fraction knitted fabric composite material

named RibTEX can match the stiffness and strength of a commercially

available equivalent woven fabric product Twintex®, for strains of up to

8%.

• Comparing RibTEX on the basis of specific strength showed that it is

capable of achieving the same maximum specific strength as aluminium,

although the amount of strain it can sustain at this maximum specific

strength is not as high.

• From the tensile tests, specimens manufactured using forming pressures

between 300 to 500kPa indicated that an optimum forming pressure exists.

This was found to be at 400kPa, which allowed the material to become

fully consolidated, but not cause any fibre damage due to severe

compression.


170

• Closed edge loop specimens performed worse than open edge loop

specimens, due to the geometric irregularities introduced at the edges and

the fact that it is very difficult to achieve a clean edge for a closed loop

specimen. This highlights the importance of a clean-cut edge.

• Material formed in the hot platen press at its optimal pressure for 10mins is

of the same quality as material produced isothermally by vacuum forming

in an oven for 45min at the same pressure.

• The addition of a weft insert yarn increases the strength of the material in

the weft direction to an equivalent level of that in the warp direction at the

expense of forming flexibility in the material’s most stretchable direction.

6.1.4 Micro-level Modelling of the Reinforcing Structure

The micromechanics of the 1x1 rib structure was studied by first simulating the

production of a narrow strip of 1x1 rib fabric. The model was then verified by

comparing tensile tests of the physical and numerical specimens before the energy

contributions of the structure’s deformation mechanisms were evaluated. It was found

that:

• In the case of continuous high modulus fibres such as E-glass, the load to give a

fixed extension is proportional to m/l3, where m is the bending modulus and l the

average knit loop length. This allowed the physical specimen, which contained 6

times the number of fibres in the numerical specimen, to be compared with the

numerical model.

• Bending was by far the largest deformation mechanism contributing to the 1x1

rib structure’s total deformation energy and was at no point overpowered by any

of the other deformation mechanisms. This was followed by torsion at low strain

levels, which is surpassed by uniaxial tension at very high strain levels and

finally the total yarn contact energy, which also surpasses torsion at very high

strain levels.


171

• Although the overall energy level readings for the entire specimen were correct,

it was not possible to predict which mechanism would be the cause of strain

failure since localised bending stress readings were vulnerable to the mesh

resolution in high curvature regions.

6.1.5 Macro-level Modelling

In this section a macro-level numerical model of knitted fabric composite was

developed using data gathered from molten tensile testing experiments. It was found

that:

• Of the many types of models available in PAMFORM™, material Type 140

describing a thermo-visco-elastic matrix phase with elastic fibres was deemed

most suitable. This material model was, however, designed for modelling woven

and unidirectional materials where the elastic fibre stiffness is closer to the

actual modulus of the constituent fibre, which is between 10,000 to 100,000

times the stiffness exhibited by weft knitted fabrics used in this study in the

warp and weft directions.

• The model was unable to give any reasonable predictions of surface strains

although the minimum thickness strain predictions did show close agreement.

For simulations involving very large strain values the model was unable to

converge upon a solution, which showed strains as high as the failure strains in

the warp and weft directions. Stability of the model up to the failure strains of

the material is necessary to be able to predict the location of strain failure.

6.1.6 Summary

Overall this study has shown that knitted fabric composites deformation is dictated by

eight micro-level fabric deformation mechanisms. These are; inter-yarn slip, inter-yarn

shear, yarn bending, yarn buckling, intra-yarn slip, yarn stretching, yarn compression

and yarn twist. In the practical forming experiments, forming using non-rigid tooling

and higher temperatures allow these mechanisms to occur unhindered.


172

To analyse these mechanisms in terms of deformation energy they need to be grouped

into five energy components; axial energy, torsional energy, bending energy, contact

energy and frictional energy. This was done and the energy contributions for a 1x1 rib

knit specimen during stretching in the warp direction have been quantified. Results

show that bending followed by torsion, uniaxial tension then contact energy are the

contributors in this order at low strain values, while at larger strain values the torsional

energy is surpassed by both uniaxial tension and the contact energy.

For macro-level modelling, the existing material models originally designed for

unidirectional and woven fabric composites cannot adequately simulate knitted fabric

composite forming behaviour up to the failure strains of the material.

It was also found that it is possible to produce higher volume fraction knitted fabric

thermoplastic composite whose stiffness and strength properties are good enough to

compete with woven fabric composites, along with more traditional materials such as

aluminium using the appropriate forming pressure and temperature.

6.2 Recommendations for Further Research

It is recommended that further research be carried out in two main areas. These are the

development of the macro and micro-level numerical models used to describe and

analyse the behaviour of knitted fabric thermoplastic composites.

• A macro-level model that can give good predictions of knitted fabric

thermoplastic composite forming behaviour needs to be developed. This could

mean modifying the most appropriate existing model so that it can accommodate

the unique behaviour of knitted fabrics or the definition of a new textile

composite material model.

• There are certain aspects of the micro-level model such as incorporating the

effects of interfibre friction via beam element edge-to-edge contact friction,

which has now become possible using explicit codes such as ANSYS LSDyna.

Also, the model has been set up in such a way to allow the addition of more

fibre elements; therefore if computer resources are available, the same number


173

of filaments as there are in a physical specimen could be used and there would

be no need for the use of the correlation factor.

• The model has all the same parameters that exist on v-bed knitting machinery,

therefore by adjusting the boundary conditions various other weft knit structures

could be knitted and analysed.

• Investigate the possibility of contact stress preservation during a rezone. In the

current micro-level model it is only possible to perform a specimen tensile test

in the knitting (warp) direction, since a rezone of the model for a subsequent

tensile test only allows the preservation of stresses and strains in the material but

does not record the contact residuals.

• Investigate the possibility of adding a matrix component to the model and

analyse interaction of the matrix with the reinforcing structure in both the solid

and molten state.

• Use the results of the micro-level model in homogenisation theories of macro

behaviour.

• The model may have specific relevance to particular research being done in the

textile industry and could be used to aid in the advancement of knitting

technologies.

174

References

1. Houtte, P.V., Verpoest, I., and Gommers, B., Analysis of knitted fabric reinforced composites: part I. fibre orientation distribution. Composites - Part A: Applied Science and Manufacturing, 1998. 29: p. 1579-1588.

2. Chou, T.-W. and Ko, F.K., Textile Structural Composites. Composite Materials Series, 1989. Vol. 3: p. 2.

3. Astrom, B.T., Manufacturing of Polymer Composites. Chapman & Hall, 1997: p. 103.

4. Ko, F.K., van Vuure, A.W., and Balonis, R.J., Textile Preforming for Complex Shape Structural Composites, in 44th International SAMPE Symposium and Exhibition. 1999.

5. Abdullah, M.Z., Initial Experimental Investigation of Injection/Compression Moulding and Validation of an Injection Pressure and Tool Forces, in Department of Mechanical Engineering. 2001, The University of Auckland: Auckland.

6. Friedrich, K., Hou, M., and Krebs, J., Thermoforming of continuous fibre/thermoplastic composite sheets, in Composite Materials Series, D. Bhattacharyya, Editor. 1997, Elsevier Science B.V. Amsterdam. p. 119-128.

7. Stumpf, H., Otto, T., and Schulte, K., New Textile Preforms and Processing Concepts for the Manufacture of Low-Cost Thermoplastic Composite Components. Eleventh International Conference on Composite Materials, 1997: p. 249-259.

8. Tan, P., Tong, L., and Steven, G.P., Modelling for predicting the mechanical properties of textile composites - a review. Composites Part A, 1997. 28A: p. 903-922.

9. Handbook, A.I., Engineered Materials Handbook. Vol. 1. 1987. 10-11.

10. Miravete, A., ed. 3-D textile reinforcements in composite materials. 1999, Woodhead Publishing Limited: Cambridge England.

11. Hearle, J.W.S., Structural mechanics of fibers, yarns and fabrics. Vol. 1. 1969, USA: John Wiley and Son.

12. Savci, S. and Curiskis, J.I., Weft-Knitted Glass-Fibre Preforms for Composite Materials. Eleventh International Conference on Composite Materials, 1997: p. 338-347.

13. Bricout, A., Composite Materials: Performance of Twintex for Automotive Weight Saving, Vetrotex International.

References

175

14. Tong, L., Mouritz, A.P., and Bannister, M.K., 3D Fibre Reinforced Polymer Composites. 2002: Elsevier.

15. Liao, T. and Adanur, S., 3D Modeling of Textile Composite Preforms. Composites Part B: Engineering, 1998. Vol. 29: p. 787-793.

16. Herakovich, C.T., Mechanics of Fibrous Composites. 1998: p. 26.

17. Collier, B.J. and Tortora, P.G., Understanding Textiles. Sixth Edition ed. 2001: Prentice-Hall Int.

18. Ramakrishna, S., Characterisation and modelling of the tensile properties of plain weft-knit fabric-reinforced composites. Composites Science and Technology, 1997. 57: p. 1-22.

19. Ko, F. and Du, G.-W., Analysis of Multiaxial Warp-Knit Preforms for Composite Reinforcement. Composites Science and Technology, 1996. Vol. 56: p. 253-260.


21. Bourban, P.-E., et al., Material phenomena controlling rapid processing of thermoplastic composites. Composites Part A: Applied Science and Manufacturing, 2001. 32(8): p. 1045-1057.

22. Krebs, J., Friedrich, K., and Bhattacharyya, D., A direct comparison of matched-die versus diaphragm forming. Composites Part A: Applied Science and Manufacturing, 1998. 29A: p. 183-188.

23. Martin, T.A., Christie, G.R., and Bhattacharyya, D., Grid strain analysis and its application in composite sheet forming, in Composite Sheet Forming, D. Bhattacharyya, Editor. 1997, Elsevier. p. 217 - 245.

24. Christie, G.R., Numerical modelling of fibre-reinforced thermoplastic sheet forming, in Department of Mechanical Engineering. 1997, University of Auckland Ph.D Thesis.

25. Bannister, M.K., et al., The effect of architecture on the impact properties of knitted fabrics. First Asian-Australasian Conference on Composite Materials (ACCM-1), 1998. 1: p. 402.

26. Houtte, P.V., Verpoest, I., and Gommers, B., Analysis of knitted fabric reinforced composites: part II. stiffness and strength. Composites - Part A: Applied Science and Manufacturing, 1998. 29: p. 1589-1601.

27. Haan, J.D., et al., Tensile properties of plain weft knitted carbon fibre reinforced polyamide 12 composites. First Asian-Australasian Conference on Composite Materials (ACCM-1), 1998. 1: p. 403.

References

176

28. Putnoki, I., Moos, E., and Karger-Kocsis, J., Mechanical performance of stretched knitted glass fibre reinforced poly(ethylene terephthalate) composites produced from commingled yarn. Plastics, Rubber and Composites, 1999. 28(1): p. 40-46.

29. Mouritz, A.P., Baini, C., and Herszberg, I., Mode I Interlaminar Fracture Toughness Properties of Advanced Textile Fibreglass Composites. Composites - Part A: Applied Science and Manufacturing, 1999. Vol. 30: p. 859 - 870.

30. Karger-Kocsis, J., Czigany, T., and Mayer, J., Fracture behaviour and damage growth in knitted carbon fibre fabric reinforced polyethylmethacrylate. Plastics, Rubber and Composites, 1996. 25(3): p. 109 - 114.

31. Karger-Kocsis, J. and Czigany, T., Effects of Interphase on the Fracture and Failure Behaviour of Knitted Fabric Reinforced Composites Produced From Commingled GF/PP Yarn. Composites Part A: Applied Science and Manufacturing, 1998. Vol. 29: p. 1319-1330.

32. Anwar, K.O., et al., The Effect of Architecture on the Mechanical Properties of Knitted Composites. Eleventh International Conference on Composite Materials, 1997: p. 328-337.

33. Khondker, O.A., Leong, K.H., and Herszberg, I., Effects of biaxial deformation of the knitted glass preform on the in-plane mechanical properties of the composite. Composites Part A: Applied Science and Manufacturing, 2001. 32(10): p. 1513-1523.

34. Khondker, O.A., Leong, K.H., and Herszberg, I., Study of composite compressive properties due to biaxial deformation of the weft-knitted glass fabrics. Composites Part A: Applied Science and Manufacturing, 2001. 32(9): p. 1303-1309.

35. Ramakrishna, S., Hamada, H., and Cheng, K.B., Analytical procedure for the prediction of elastic properties of plain knitted fabric-reinforced composites. Composites - Part A: Applied Science and Manufacturing, 1997. 28: p. 25-37.

36. Huang, Z.M. and Ramakrishna, S., Micromechanical modelling approaches for the stiffness and strength of knitted fabric composites: A review and comparative study. Composites - Part A: Applied Science and Manufacturing, 2000. 31: p. 479-501.

37. Houtte, P.V., Grommers, B., and Verpost, I., Modelling the elastic properties of knitted-fabric-reinforced composites. Composites Science and Technology, 1996. 56: p. 685-694.

38. Takano, N., et al., Microstructure-based deep-drawing simulation of knitted fabric reinforced thermoplastics by homogenization theory. International Journal of Solids and Structures, 2001. 38(36-37): p. 6333-6356.

39. Lim, T.C., Ramakrishna, S., and Shang, H.M., Improvement of knitted fabric composite sheet formability by simultaneous deep drawing and stretch forming.

References

177

First Asian-Australasian Conference on Composite Materials (ACCM-1), 1998. 1: p. 409.

40. Pickett, A.K. and Cunningham, J.E., Numerical Techniques for the Pre-Heating and Forming Simulation of Continuous Fibre Reinforced Thermoplastics. SAMPE European Conference and Exhibition, 1996.

41. Clifford, M.J., Long, A.C., and Luca, P., Forming of Engineered Prepregs and Reinforced Thermoplastics. The Minerals, Metals & Materials Society (TMS) 2001 Annual Meeting, 2001.

42. Boisse, P., Gasser, A., and Hivet, G., Analyses of fabric tensile behaviour: determination of the biaxial tension-strain surfaces and their use in forming simulations. Composites Part A: Applied Science and Manufacturing, 2001. 32(10): p. 1395-1414.

43. Ye, L. and Daghyani, H.R., Characteristics of woven fibre fabric reinforced composites in forming process. Composites - Part A: Applied Science and Manufacturing, 1997. 28A: p. 869-874.

44. Cherouat, A. and Billoet, J.L., Mechanical and numerical modelling of composite manufacturing processes deep-drawing and laying-up of thin pre-impregnated woven fabrics. Journal of Materials Processing Technology, 2001. 118(1-3): p. 460-471.

45. Kuo, W.-S. and Fang, J., Processing and characterization of 3D woven and braided thermoplastic composites. Composites Science and Technology, 2000. 60(5): p. 643-656.

46. Sowerby, R., Chu, E. and Duncan, J.L., Determination of large strains in metal forming. J. Strain Analysis, 1982. 17: p. 95-101.

47. Schedin, E. and Melander, A., The Evaluation of Large Strains from Industrial Sheet Metal Stampings with a Square Grid. J.Applied Metalworking, 1986. 32: p. 143-156.

48. Zhang, Z.T. and Duncan, J.L., Developments in Nodal Strain Analysis of Sheet Forming. Int. J. Mech. Sci., 1990. 32: p. 717-727.

49. Duncan, J.L. and Zhang, Z.T., Strain Measurement and Modelling of Sheet Metal Forming. Materials Forum, 1990. 14: p. 109-114.

50. Malvern, L.E., Introduction to the Mechanics of a Continuous Medium. 1969: Prentice-Hall Inc.

51. Van West, B.P., et al., The Draping and Consolidation of Commingled Fabrics. Composites Manufacturing, 1991. 2: p. 10-22.

52. Heisley, F.L. and Haller, K.D., Fitting Woven Fabric to Surfaces in Three Dimensions. J. Textile Inst, 1988. 2: p. 250-263.

References

178

53. Lim, T.C., and Ramakrishna, S., Modelling of Composite Sheet Forming: A Review. Composites Part A: Applied Science and Manufacturing, 2001.

54. Van der Ween, F., Algorithms for Draping Fabrics on Doubly-Curved Surfaces. International Journal of Numerical Methods, 1991. 31: p. 1415-1426.

55. Chou, T.-W. and Ko, F.K., Textile Structural Composites. Composite Materials Series, 1989. Vol. 3.


57. Lomov, S.V., et al., Textile composites: modelling strategies. Composites Part A: Applied Science and Manufacturing, 2001. 32(10): p. 1379-1394.

58. Pickett, A.K. MicroModelling of Yarn Architecture in 3D-Braids and Transfer to Macromodelling of Composites. in Techtextil Symposium Asia. 1998. Osaka, Japan.

59. Pickett, A.K., Review of Finite Element Simulation Methods Applied to Manufacturing and Failure Prediction in Composite Structures. ESI Internal Report Document, 2001: p. 1-19.

60. Long, A.C., Wilks, C.E., and Rudd, C.D., Experimental characterisation of the consolidation of a commingled glass/polypropylene composite. Composites Science and Technology, 2001. 61(11): p. 1591-1603.

61. Bernet, N., et al., Commingled yarn composites for rapid processing of complex shapes. Composites Part A: Applied Science and Manufacturing, 2001. 32(11): p. 1613-1626.

62. Prodromou, A.G. and Chen, J., On the relationship between shear angle and wrinkling of textile composite preforms. Composites Part A: Applied Science and Manufacturing, 1997. 28(5): p. 491-503.

63. Mohammed, U., et al., Shear deformation and micromechanics of woven fabrics. Composites Part A: Applied Science and Manufacturing, 2000. 31(4): p. 299-308.

64. Pam-System-International, PAM-CRASH™ version 2000 level 18 Notes Manual. 2000.

65. Owen, M.J., Middleton, V., and Jones, I.A., Integrated design and manufacture using fibre-reinforced polymeric composites. 2000: Woodhead Publishing Limited, Cambridge, England.

66. Hallquist, J.O., LS-Dyna Theoretical Manual. 1998, Livermore Software Technology Corporation: California.

67. Pam-System-International, PAM-FORM™ version 2000 Notes Manual. 2000.

179

Glossary of Terms

• Areal density, g/m2 = mass of fabric in grams divided by the area of fabric in square

metres (i.e. fabric weight).

• Average length, Lav(mm) = total length of yarn required to form one repeat or row

of loops in the fabric divided by the number of loops in one repeat.

• Balanced Fabric = a fabric whose properties and geometric dimensions are the

same in both the warp and weft directions or in knitted fabrics, whose properties are

mirrored across the thickness direction.

• Commingling = the combining of two different types of fibres to form a yarn, in the

case of Twintex® the combining of matrix and reinforcement fibres.

• Course density, c/cm = number of horizontal rows of loops per cm.

• Crimp = the amount of yarn undulation or waviness in the fabric.

• Denier = g / 9000m.

• Gauge = a measure of the number of needles per inch on a knitting machine.

• GSA = Grid Strain Analysis, the use of a reference grid (squares or circles marked

on the sheet before processing) to determine the local strains in a sheet material

following forming, by analysing the changes in the grid dimensions.

• Interfibre = interactions between reinforcing fibres.

• Interyarn = interactions between reinforcing fibres, relative movement between the

yarn.

• Intrayarn = interactions between reinforcing fibres, relative movement between

fibres.

• Loop length, L(mm) = length of yarn to form one complete knitted stitch.

• Metric number = km / kg.

• Micromechanics = the study of mechanics at the fibre or filament level.

• Milano Rib = a common type of two-dimensional knitted structure used in this

study.

Glossary of Terms

180

• Prepreg (preimpregnated) = a composite precursor material in which both the fibres

and matrix material have already been combined in a way that establishes bonding

between the two materials.

• Preform = a composite precursor material which may only consist of the fibre

material, or both the fibre and matrix material, but where no bonding between the

two has taken place.

• RibTEX = 1x1 rib knit fabric preform manufactured from Twintex® commingled

yarn.

• Roving = anything from 6 up to hundreds of individual parallel strands or bundles of

fibres.

• Springforward/Springback = the tendency of a component formed by bending to a

given angle to deflect from this angle once the bending force is removed. If the

included angle of the bend becomes smaller due to this effect, this is termed

springforward and vice versa.

• Tex, T = linear density in g/km (ISO standard).

• Textile = the structured (woven, knitted, braided) arrangement of fibres.

• Tightness factor, K = √Tex / Lav.

• Twintex® = a thermoplastic roving consisting of commingled unidirectional

thermoplastic and glass fibres.

• Vee – Bending = the matched die forming of vee shaped specimens in order to

assess the amount of interply shear and springforward/springback in a material.

• Wale density, w/cm = number of vertical columns of loops per cm.

• Warp direction = the direction defining the length of the fabric.

• Weft direction = the direction along which loops are produced defining the width of

the fabric.

• Yarn = individual strands or bundles of fibres twisted and doubled together.

• 1 X 1 Rib = the simplest two-dimensional configuration producing a balanced

knitted fabric.

181

Appendices

Appendix A. Material Property Data Sheet for Cotene 9800

Appendices

182

Appendix B. Force Displacement Curves for Knitted Fabric Composite

Appendices

183

Appendix C. Typical Knitted Fabric Tensile Test Data (Single Ply Dry

Milano) Specimen Size 150 X 50mm

Appendices

184

Appendix D. Full Scale Y-Axis Plot for Warp and Weft Modulus Curves

Appendices

185

Appendix E. Empty Frame Friction Data for All Temperatures and Rates

180°C

190°C

Appendices

186

200°C

Appendices

187

Appendix F. Knitted Fabric at Room Temperature (20°C) All Rates

20°C

20°C

Appendices

188

20°C

Appendices

189

Appendix G. Knitted Fabric at Elevated Temperature (180°C) All Rates

180°C

180°C

Appendices

190

180°C

Appendices

191

Appendix H. Knitted Fabric at Room and Elevated Temperature 10mm/min

Appendices

192

Appendix I. 4-Component Model Parameter Variation E1,E2,η1,η2

Variation in E1

Increasing

Increasing

Variation in E2

Appendices

193

Increasing

Variation in η1

Increasing

Variation in η2

Appendices

194

Appendix J. Comparison of Pressure and Matched Die Formed Domes

The differences between hemispherical domes manufactured using the pressure forming

method and matched die forming method can be seen above. Equivalent forming

parameters were used where ever possible including blank temperature, die temperature

and blank size for both the specimens. The images shown clearly highlight the differences

in surface finish. The pressure formed domes have a mat surface finish while matched die

formed domes have a glossy surface finish. This difference however, is more a

characteristic of the forming processes rather than the material itself. Another obvious

difference, which is more a material characteristic, is reinforcement draw-in. For the

pressure formed specimen the reinforcing fabric has been almost completely drawn in

leaving only the polymer in the flange region of the dome. For the matched die formed

dome no draw-in at all is observed, in fact the flange diameter of the dome has exactly the

same size diameter as the blank from which it was formed.

Pressure Formed Dome 1s Disc Diameter Size = 100mm No. of Plies = 1 Original Thickness = 1.8mm Tool Temperature = 160°C Air Temperature = 180°C Material State = molten 180°C

Matched Die Formed Dome 2s Disc Diameter Size = 100mm No. of Plies = 1 Original Thickness = 1.8mm Tool Temperature = 160°C Air Temperature = 180°C Material State = molten 180°C

Appendices

195

Appendix K. Full Mesh Thickness Contour Plot for Dome 22

Note: Any occurrence of positive and negative thickness strain automatically gives a

symmetrical contour bar. The range of the entire mesh thickness strain in this case is almost

all in the negative region as shown by the range marker.

Appendices

196

Appendix L. Comparison of Experimental and Numerical F-D Curves

Note: The maximum displacement rate in the numerical tensile test reaches 6m/s. Inertial

effects are avoided below 10m/s.

Appendices

197

Appendix M. Comparison of All Experimental and Numerical F-D Curves

Note: The numerical tensile test was run a number of times to compare different methods

of constraining the yarn feed to prepare the numerical model for the tensile test part of the

simulation. Because of the limitation on boundary condition control, i.e. it is not possible

to abruptly add fixed displacement boundary conditions to nodes on the yarn at any stage

of the simulation, the yarn feed hole was fully constrained at the end of the last pass and it

was relied upon that the yarn would not feed in any further during the tensile test up to a

certain loading value due to the sharp bend it had to go through to do so.

Appendices

198

Appendix N. Full Milano Rib Structure and Unit Cell

Note: The top plane of rib loops are visible while the bottom plane has been shifted to the right as the fabric

has been compressed. The connecting loops seem to contain fewer fibres but this is due to the fact that they

don’t need to bend and flatten as much as the rib loops and therefore remain more circular in cross section. It

is in fact the same piece of continuous yarn. The photograph shows clearly that the yarns are by no means

circular even when the fabric is at its lowest internal energy state, which is when the photograph was taken.

Because the fabric is made from continuous high modulus fibres its minimum internal energy state is not

zero but is dependent on the bending stiffness of the fibre material and the structural configuration of the

knit.

3D Unit Cell

Appendices

199

Appendix O. Rigid Matched Die Dome at High Material Viscosity

Specimen Forming Parameters Diameter Size = 100mm Original Thickness = 5mm Density = 1.23g/cm3

Parent Sheet Shear Modulus = 0.02MPa Material Viscosity = 0.010MPa.s Bending and Out of Plane Shear Factors = 0.99

weft warp

weft warp

weft warp


Appendices

200

weft warp

Appendices

201

Appendix P. Sample Input Code for Numerical Knitting Simulation

$ $ This file is generated by PAM-GENERIS version 2001.1 on 2003/08/25 at 15:27:19 $ PAM-GENERIS Version 2001.1 - Compiled 2002/01/10 $ FREE SOLVER CRASH NOLIS NOPRINT SIGNAL YES FILE kin9MultiFullFilaESIVX10rBEAM775 DATACHECK NO TIMESTEP SMALL BEND ALLOCATE 10000000 RESTARTFILES 1 THPLOT KINE INTE TOTE TEXT TCNT CNTF CNTE DLOC BEAPLOT ALL NODPLOT DFLT PCNT FACM CRUP PIPE NO DEBUG NO TITLE / $ $ CONTROL CARDS $ $ TIME TIOD PIOD IRD NLOG DTO SLFAC ISTR IPHG IS $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 CTRL / 17 0.05 0.166666 0.1 10 0 1 0 0 0 $ $ SOLID VISCOSITY AND TIME STEP CARDS $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 1.2 0.06 0 0.2 0 0 1 0 0 0 0 0 1 0 0 0 $ $ MATERIAL DATA CARDS $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 MATER / 1 200 7.86e-006 Needle1 0.2827 0 0 0 MATER / 5 200 2.54e-006 Latch1 0.001 0 0 0 MATER / 7 201 7.86e-006 LatchEnd1 200 0 0.001 0 0 0 0 0 0 0 0 0 0 (….Definition repeated for all five needles….) MATER / 255 200 7.86e-006 NeedleBed1 0.2827 0 0 0 MATER / 256 200 7.86e-006 NeedleBed2

Appendices

202

0.2827 0 0 0 MATER / 263 203 2.54e-006 TakeDownBar1 0 0 0 0 0 0 0.000227 3 0 0 0 0 0.1 0.0002 12 0.0002 0 0 MATER / 264 203 2.54e-006 TakeDownBar2 0 0 0 0 0 0 0.000227 3 0 0 0 0 0.1 0.0002 12 0.0002 0 0 MATER / 265 200 2.54e-006 TakeDownBar3 0.0874 0 0 0 MATER / 606 200 7.86e-006 YarnFeedHole 0.2827 0 0 0 MATER / 607 203 2.54e-006 FTension1 0 0 0 0 20 0 0.000227 3 2 2 0 0 0.8 4e-006 200 4e-006 0 0 0 0 20 4e-006 0 0 0 0 0 0 0.8 4e-006 0 0 0 0 MATER / 608 203 2.54e-006 BTension1 0 0 0 0 0 0 0.000227 2 0 0 0 0 10 5e-005 0 0 0 0 (….Definition repeated for all twenty filaments….) MATER / 667 201 7.86e-006 NeedleHeadEnd1 200 0 0.2827 0 0 0 0 0 0 0 0 0 0 (….Definition repeated for all five needles….) MATER / 672 201 2.54e-006 FILAMENT 1 73 0.2 0.000227 0.000227 4.1e-009 4.1e-009 8.2e-009 0 0 0 0.2 0.2 0.2 (….Definition repeated for all twenty filaments….)

Appendices

203

$ $ FRAME DATA CARDS $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 #GPNAM F1 FRAME / 1 0 0 10.856381 6.44828 0 579 #GPNAM F2 FRAME / 2 0 0 -1 6.448280.856381 0 580 $ $ NODAL POINT CARDS $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 NODE / 35 35.7828 2.57574 19.18 NODE / 38 36.1828 2.65186 19.18 (....Many Nodes….) NODE / 235763 178.302 141.49 36.2802 NODE / 235770 36.4559 1.05906 37.4802 $ $ BEAM ELEMENTS CARDS $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 BEAM / 219488 672 215781 215782 216732 BEAM / 219489 672 215782 215783 216732 (....Many Beam Elements….) BEAM / 239465 691 235729 235730 235770 BEAM / 239466 691 235730 235731 235770 $ $ BAR ELEMENTS CARDS $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 BAR / 51 1 54 576 BAR / 603 1 576 35 (....Many Bar Elements….) BAR / 219486 670 10492 215730 BAR / 109743 671 4983 107865 $ $ DISPLACEMENT BOUNDARY CONDITION $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 #GPNAM NeedleB1 BOUNC / 0 111111 MAT 255 END #GPNAM NeedleB2 BOUNC / 0 111111 MAT 256 END #GPNAM ZTrans BOUNC / 0 110111 MAT 606 END #GPNAM TDBar2 BOUNC / 4920 101111 1 -1 0 1 1 0 BOUNC / 4921 101111 1 -1 0 1 1 0 #GPNAM TopNew BOUNC / 12036 111111 BOUNC / 12537 111111 BOUNC / 13038 111111 BOUNC / 13539 111111 BOUNC / 14040 111111 BOUNC / 14541 111111 BOUNC / 15042 111111 BOUNC / 15543 111111 BOUNC / 16044 111111 BOUNC / 16545 111111 BOUNC / 17046 111111 BOUNC / 17547 111111 BOUNC / 18549 111111

Appendices

204

BOUNC / 19050 111111 BOUNC / 19551 111111 BOUNC / 20553 111111 BOUNC / 21054 111111 BOUNC / 21555 111111 BOUNC / 20052 111111 BOUNC / 18048 111111 #GPNAM TDBar1 BOUNC / 4918 101111 -1 1 -1 0 1 1 0 BOUNC / 4919 101111 -1 1 -1 0 1 1 0 #GPNAM AllFixed BOUNC / 11538 111111 BOUNC / 12039 111111 BOUNC / 12540 111111 BOUNC / 13041 111111 BOUNC / 13542 111111 BOUNC / 14043 111111 BOUNC / 14544 111111 BOUNC / 15045 111111 BOUNC / 15546 111111 BOUNC / 16047 111111 BOUNC / 16548 111111 BOUNC / 17049 111111 BOUNC / 17550 111111 BOUNC / 18051 111111 BOUNC / 18552 111111 BOUNC / 19053 111111 BOUNC / 19554 111111 BOUNC / 20055 111111 BOUNC / 20556 111111 BOUNC / 21057 111111 #GPNAM TDBar BOUNC / 21563 101111 1 1 -1 0 1 1 0 $ $ RIGID BODY CARDS $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 BOUNC / 577 011111 0 RBODY / 1 0 577 RB1 NOD 580 MAT 1 667 END RBODY / 2 0 578 RB2 NOD 579 MAT 5 END BOUNC / 1169 011111 0 RBODY / 3 0 1169 RB3 NOD 1168 MAT 8 668 END RBODY / 4 0 1170 RB4 NOD 1167 MAT 12 END BOUNC / 2339 011111 0 RBODY / 5 0 2339 RB5 NOD 2338 MAT 22 669 END RBODY / 6 0 2340 RB6 NOD 2337 MAT 26 END BOUNC / 2412 101111 0 RBODY / 7 0 2412 RB7

Appendices

205

NOD 11019 MAT 266 671 END RBODY / 8 0 11023 RB8 NOD 11020 MAT 270 END BOUNC / 2435 101111 0 RBODY / 9 0 2435 RB9 NOD 11021 MAT 538 670 END RBODY / 10 0 11024 RB10 NOD 11022 MAT 542 END RBODY / 11 0 21563 1 TDBAR MAT 265 END $ $ FUNCTIONS CARDS $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 #GPNAM KinJoint FUNCT / 1 3 1 1 0 0 -3.14 0 0 0 3.14 0 #GPNAM YFHVel FUNCT / 7 26 1 1 0 0 0 0 3.1146 0 5.8333 8.4598 6.5 8.4598 9.2187 0 10 0 13.1146 0 15.8333 -8.4598 16.5 -8.4598 19.2187 0 20 0 23.1146 0 25.8333 8.4598 26.5 8.4598 29.2187 0 30 0 33.1146 0 35.8333 -8.4598 36.5 -8.4598 39.2187 0 40 0 43.1146 0 45.8333 8.4598 46.5 8.4598 49.2187 0 50 0 #GPNAM BarTDVel FUNCT / 8 3 1 1 0 0 0 0 10 0.25 50 0.25 #GPNAM D1 FUNCT / 23 250 1 1 0 0 X Y (Function containing 250 data points) #GPNAM D2 FUNCT / 24 253 1 1 0 0 X Y

Appendices

206

(Function containing 253 data points) #GPNAM D3 FUNCT / 25 256 1 1 0 0 X Y (Function containing 256 data points) #GPNAM D4 FUNCT / 26 251 1 1 0 0 X Y (Function containing 251 data points) #GPNAM D5 FUNCT / 27 252 1 1 0 0 X Y (Function containing 252 data points) #GPNAM Sensor1 FUNCT / 28 4 1 1 0 0 0 0 29.269 0 29.2691 1 50 1 $ $ 3D BOUNDARY CONDITION $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 #GPNAM DLocus1 DIS3D / 23 0 0 1 1 1 0 0 NOD 2339 END #GPNAM DLocus2 DIS3D / 0 24 0 1 1 1 0 0 NOD 2412 END #GPNAM DLocus3 DIS3D / 25 0 0 1 1 1 0 0 NOD 1169 END #GPNAM DLocus4 DIS3D / 0 26 0 1 1 1 0 0 NOD 2435 END #GPNAM DLocus5 DIS3D / 27 0 0 1 1 1 0 0 NOD 577 END $ $ SLIDING INTERFACE CARDS $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 SLINT2/ 1 0 46 0.5 0 0.5 1 0.1 1 Contact 1 - type 46 0 0 1 1 40 0 $ MAT 1 7 END SLINT2/ 2 0 46 0.5 0 0.5 1 0.1 1 Contact 2 - type 46 0 0 1 1 40 0 $ MAT 8 14 END SLINT2/ 3 0 46 0.5 0 0.5 1 0.1 1 Contact 3 - type 46 0 0 1 1 40 0 $ MAT 22 28 END

Appendices

207

SLINT2/ 4 0 46 0.5 0 0.5 1 0.1 1 Contact 4 - type 46 0 0 1 1 40 0 $ MAT 266 272 END SLINT2/ 5 0 46 0.5 0 0.5 1 0.1 1 Contact 5 - type 46 0 0 1 1 40 0 $ MAT 538 544 END SLINT2/ 7 0 46 0.5 2 0.017 1 0.1 1 Contact 7 - type 46 8.66664 0 1 1 40 0 $ MAT 265 263 264 672 673 674 675 MAT 676 677 678 679 680 681 682 MAT 683 684 685 686 687 688 689 MAT 690 691 END SLINT2/ 9 0 46 0.5 2 0.017 1 0.1 1 Contact 9 - type 46 0 0 1 1 40 0 $ MAT 1 8 22 266 538 606 672 MAT 673 674 675 676 677 678 679 MAT 680 681 682 683 684 685 686 MAT 687 688 689 690 691 END SLINT2/ 10 0 46 0.5 2 0.017 1 0.1 1 Contact 10 - type 46 0 0 1 1 40 0 $ MAT 255 256 5 12 26 270 542 MAT 667 668 669 670 671 672 673 MAT 674 675 676 677 678 679 680 MAT 681 682 683 684 685 686 687 MAT 688 689 690 691 END SLINT2/ 11 0 46 0.5 2 0.017 1 0.1 1 Contact 11 - type 46 0 0 1 1 40 0 $ MAT 672 673 674 675 676 677 678 MAT 679 680 681 682 683 684 685 MAT 686 687 688 689 690 691 END $ $ VELOCITY BOUNDARY CONDITION CARDS $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 #GPNAM YFHVel VELBC / 0 7 3 -1 MAT 606 END #GPNAM BarTDVel VELBC / 0 8 4 -1 1 1 0 NOD 4920 4921 END $ $ SENSORS DATA CARDS $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 #GPNAM Sensor1 SENSO / 1 5 28 $ $ KINEMATIC JOINTS $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 #GPNAM K1 KJOIN / 1REVOLUTE 579 580 100000 1 1 111011 23 #GPNAM K2 KJOIN / 2REVOLUTE 1167 1168 100000

Appendices

208

1 1 111011 23 #GPNAM K3 KJOIN / 3REVOLUTE 2337 2338 100000 1 1 111011 23 #GPNAM K4 KJOIN / 4REVOLUTE 11020 11019 100000 2 2 111011 23 #GPNAM K5 KJOIN / 5REVOLUTE 11022 11021 100000 2 2 111011 23 $ $ TIME HISTORY PLOT FOR KINEMATIC JOINTS $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 THLKJ / 1 2 3 4 5 $ $ MATERIAL 230 $ $---5---10----5---20----5---30----5---40----5---50----5---60----5---70----5---80 MATER / 20 230 1e-015 NL1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 03.5e-005 1e-020 0.001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (….Definition repeated for all five needle latch pin joints….) ENDDATA $ The full duration of the knitting simulation is 50 milliseconds. The model is stable $ using a time step scale factor of 0.2 up to 17 milliseconds. To ensure stability during $ the most complex stage of initial knit generation, the time step scale factor is further $ reduced to 0.08 from 17.2 - 18 milliseconds. It can then be set back to 0.2 for the $ remainder of the run. A batch file algorithm has been used to establish the stability $ of the model by attempting to solve using the highest value for the time step scale $ factor.

DEFORMATION CHARACTERISTICS OF KNITTED FABRIC COMPOSITES

Documents

Transcript of DEFORMATION CHARACTERISTICS OF KNITTED FABRIC COMPOSITES