DEFORMATION CHARACTERISTICS OF KNITTED FABRIC COMPOSITES
Transcript of DEFORMATION CHARACTERISTICS OF KNITTED FABRIC COMPOSITES
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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 3-11. Knitted fabric composite at elevated temperature (190°C) all rates .......... 66
Figure 3-12. Knitted fabric composite at elevated temperature (200°C) all rates .......... 67
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 4-6. Warp direction stress strain curves for all RibTex specimens (400kPa) ... 108
Figure 4-7. Warp direction stress strain curves for all RibTex specimens (500kPa) ... 109
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
Figure 5-23. Comparison between PAMFORM™ warp direction tensile tests and
experimental results, shear modulus parameter G variation......................................... 149
Figure 5-24. Comparison between PAMFORM™ warp direction tensile tests and
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
Figure 5-28. Flexible matched die dome forming of molten knitted fabric composite η =
0.005MPa.s ................................................................................................................... 156
Figure 5-29. Flexible matched die dome forming of molten knitted fabric composite η =
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
Chapter 1 Introduction
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
Chapter 1 Introduction
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
Chapter 1 Introduction
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
Chapter 2 Literature Review
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)
Chapter 2 Literature Review
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)
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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)
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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.
Chapter 2 Literature Review
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.
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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.
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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.
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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.
Chapter 2 Literature Review
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)
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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.
Chapter 2 Literature Review
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)
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
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)
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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)
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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==
Chapter 2 Literature Review
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.
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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)
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 2 Literature Review
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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.
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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)
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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)
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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.
Figure 3-11. Knitted fabric composite at elevated temperature (190°C) all rates
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Figure 3-12. Knitted fabric composite at elevated temperature (200°C) all rates
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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.
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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.
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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)
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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”
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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.
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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)
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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.
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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.
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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)
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Surface Strain Arrow Diagram
Surface and Thickness Strain Max Surface Strain = 49.3% Min Surface Strain = -21.5% Max Thickness Strain = 45.9% Min Thickness Strain = -30.7%
Percentage Thickness Strain Contours
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.
Figure 3-25. Dome 13
weft warp
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Surface Strain Arrow Diagram
Surface and Thickness Strain Max Surface Strain = 46.8% Min Surface Strain = -18.6% Max Thickness Strain = 39.8% Min Thickness Strain = -32.6%
Percentage Thickness Strain Contours
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.
Figure 3-26. Dome 15
weft warp
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Surface Strain Arrow Diagram
Surface and Thickness Strain Max Surface Strain = 79.9% Min Surface Strain = -18.0% Max Thickness Strain = 43.0% Min Thickness Strain = -35.2%
Percentage Thickness Strain Contours
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.
Figure 3-27. Dome 16
weft warp
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Surface Strain Arrow Diagram
Surface and Thickness Strain Max Surface Strain = 79.3% Min Surface Strain = -29.8% Max Thickness Strain = 74.3% Min Thickness Strain = -26.0%
Percentage Thickness Strain Contours
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.
Figure 3-28. Dome 18
weft warp
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
89
Specimen Forming Parameters Diameter Size = 70mm No. of Plies = 3 Original Thickness = 5.6mm Tool Temperature = 160°C Air Temperature = 180°C Material State = molten 180°C
Surface Strain Arrow Diagram
Surface and Thickness Strain Max Surface Strain = 62.1% Min Surface Strain = -11.7% Max Thickness Strain = -6.4% Min Thickness Strain = -35.7%
Percentage Thickness Strain Contours
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).
Figure 3-29. Dome 22
weft warp
Stretch
Stretch/Draw
Stretch
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
90
Specimen Forming Parameters Diameter Size = 70mm No. of Plies = 3 Original Thickness = 5.1mm Tool Temperature = 23°C Air Temperature = 20°C Material State = molten 160°C
Surface Strain Arrow Diagram
Surface and Thickness Strain Max Surface Strain = 43.3% Min Surface Strain = -21.8% Max Thickness Strain = 33.3% Min Thickness Strain = -25.6%
Percentage Thickness Strain Contours
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.
Figure 3-30. Dome 27
weft warp
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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.
Dome 18 Blank Diameter Size = 100mm Tool Temperature = 22°C Material State = molten 180°C
warp
weft
Dome 22 Blank Diameter Size = 70mm Tool Temperature = 160°C Material State = molten 180°C
warp
weft
warp
weft
Dome 27 Blank Diameter Size = 70mm Tool Temperature = 23°C Material State = molten 160°C
Dome 16 Blank Diameter Size = 100mm Tool Temperature = 25°C Material State = molten 180°C
warp
weft Woven
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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)
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Surface Strain Arrow Diagram
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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%
Surface Strain Arrow Diagram
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
Chapter 3 Deformation of Knitted Fabric Reinforced Thermoplastic Sheet
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
Chapter 4 High Fibre Volume Fraction Knitted Fabric Composites
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
Chapter 4 High Fibre Volume Fraction Knitted Fabric Composites
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
Chapter 4 High Fibre Volume Fraction Knitted Fabric Composites
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.
Chapter 4 High Fibre Volume Fraction Knitted Fabric Composites
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
Chapter 4 High Fibre Volume Fraction Knitted Fabric Composites
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
Chapter 4 High Fibre Volume Fraction Knitted Fabric Composites
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
Chapter 4 High Fibre Volume Fraction Knitted Fabric Composites
108
Figure 4-5. Warp direction stress strain curves for all RibTex specimens (300kPa)
Figure 4-6. Warp direction stress strain curves for all RibTex specimens (400kPa)
Chapter 4 High Fibre Volume Fraction Knitted Fabric Composites
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.
Figure 4-7. Warp direction stress strain curves for all RibTex specimens (500kPa)
Chapter 4 High Fibre Volume Fraction Knitted Fabric Composites
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
Chapter 4 High Fibre Volume Fraction Knitted Fabric Composites
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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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
Chapter 5 Explicit Finite Element Modelling and Analysis
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.
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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)
Chapter 5 Explicit Finite Element Modelling and Analysis
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.
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
122
Figure 5-4. The six stages of the knitting simulation
STATE: 60
STATE: 120
STATE: 240
STATE: 180
STATE: 300
STATE: 0
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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)
Chapter 5 Explicit Finite Element Modelling and Analysis
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)
Chapter 5 Explicit Finite Element Modelling and Analysis
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.
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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)
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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.
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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).
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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.
Chapter 5 Explicit Finite Element Modelling and Analysis
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.
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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.
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
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
weft warp
weft warp
Warp and Weft fibremodulus properties asdefined in Section 5.4.1.2
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
155
the GSA results display a decrease in thickness as a negative percentage thickness
change while the numerical results simply show actual thickness values.
Specimen Forming Parameters Blank Diameter Size = 100mm Original Thickness = 5mm Density = 1.23g/cm3
Parent Sheet Shear Modulus = 0.02MPa Material Viscosity = 0.005MPa.s Bending and Out of Plane Shear Factors = 0.99 Friction Coefficient Between All Contacts = 0.3
weft warp
weft warp
weft warp
Warp and Weft fibremodulus properties asdefined in Section 5.4.1.2
Chapter 5 Explicit Finite Element Modelling and Analysis
156
Figure 5-28. Flexible matched die dome forming of molten knitted fabric composite η = 0.005MPa.s
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
Parent Sheet Shear Modulus = 0.02MPa Material Viscosity = 0.010MPa.s Bending and Out of Plane Shear Factors = 0.99 Friction Coefficient Between All Contacts = 0.3
weft warp
weft warp
Warp and Weft fibremodulus properties asdefined in Section 5.4.1.2
Chapter 5 Explicit Finite Element Modelling and Analysis
157
Figure 5-29. Flexible matched die dome forming of molten knitted fabric composite η = 0.010MPa.s
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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.
Specimen Forming Parameters Blank Diameter Size = 120mm 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 = 0.05 Clamping Force = 1000N
weft warp
weft warp
Warp and Weft fibremodulus properties asdefined in Section 5.4.1.2
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
160
Specimen Forming Parameters Blank Diameter Size = 120mm 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 = 0.5 Clamping Force = 1000N
weft warp
weft warp
weft warp
Warp and Weft fibremodulus properties asdefined in Section 5.4.1.2
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
162
Specimen Forming Parameters Blank Size = 200 X 200mm Original Thickness = 2mm 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 Clamping Force = 100N
weft warp
weft warp
weft warp
Warp and Weft fibremodulus properties asdefined in Section 5.4.1.2
Chapter 5 Explicit Finite Element Modelling and Analysis
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
Chapter 5 Explicit Finite Element Modelling and Analysis
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
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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
Chapter 6 Conclusions and Future Work Recommendations
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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.
Chapter 6 Conclusions and Future Work Recommendations
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
Chapter 6 Conclusions and Future Work Recommendations
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.
Chapter 6 Conclusions and Future Work Recommendations
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.
Chapter 6 Conclusions and Future Work Recommendations
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.
Chapter 6 Conclusions and Future Work Recommendations
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
Chapter 6 Conclusions and Future Work Recommendations
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
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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
Warp and Weft fibremodulus properties asdefined in Section 5.4.1.2
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
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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.