Structure and Mechanics of Textile Fibre Assemblies (Woodhead Publishing in Textiles)

Structure and mechanics of textile fibre assemblies

The Textile Institute and Woodhead Publishing The Textile Institute is a unique organisation in textiles, clothing and footwear. Incorporated in England by a Royal Charter granted in 1925, the Institute has individual and corporate members in over 90 countries. The aim of the Institute is to facilitate learning, recognise achievement, reward excellence and disseminate information within the global textiles, clothing and footwear industries. Historically, The Textile Institute has published books of interest to its members and the textile industry. To maintain this policy, the Institute has entered into partnership with Woodhead Publishing Limited to ensure that Institute members and the textile industry continue to have access to high calibre titles on textile science and technology. Most Woodhead titles on textiles are now published in collaboration with The Textile Institute. Through this arrangement, the Institute provides an Editorial Board which advises Woodhead on appropriate titles for future publication and suggests possible editors and authors for these books. Each book published under this arrangement carries the Institute’s logo. Woodhead books published in collaboration with The Textile Institute are offered to Textile Institute members at a substantial discount. These books, together with those published by The Textile Institute that are still in print, are offered on the Woodhead web site at: www.woodheadpublishing.com. Textile Institute books still in print are also available directly from the Institute’s web site at: www. textileinstitutebooks.com. A list of Woodhead books on textile science and technology, most of which have been published in collaboration with The Textile Institute, can be found on pages xi–xv.

Woodhead Publishing in Textiles: Number 80

Structure and mechanics of textile fibre assemblies Edited by P. Schwartz

Cambridge England

Published by Woodhead Publishing Limited in association with The Textile Institute Woodhead Publishing Limited, Abington Hall, Granta Park, Great Abington, Cambridge CB21 6AH, England www.woodheadpublishing.com Published in North America by CRC Press LLC, 6000 Broken Sound Parkway, NW, Suite 300, Boca Raton, FL 33487, USA First published 2008, Woodhead Publishing Limited and CRC Press LLC © Woodhead Publishing Limited, 2008 The authors have asserted their moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the authors and the publishers cannot assume responsibility for the validity of all materials. Neither the authors nor the publishers, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming and recording, or by any information storage or retrieval system, without permission in writing from Woodhead Publishing Limited. The consent of Woodhead Publishing Limited does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from Woodhead Publishing Limited for such copying. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. Library of Congress Cataloging in Publication Data A catalog record for this book is available from the Library of Congress. Woodhead Publishing ISBN 978-1-84569-135-6 (book) Woodhead Publishing ISBN 978-1-84569-523-1 (e-book) CRC Press ISBN 978-1-4200-9305-6 CRC Press order number: WP9305 The publishers’ policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp which is processed using acid-free and elementary chlorine-free practices. Furthermore, the publishers ensure that the text paper and cover board used have met acceptable environmental accreditation standards. Project managed by Macfarlane Book Production Services, Dunstable, Bedfordshire, England ([email protected]) Typeset by SNP Best-set Typesetter Ltd., Hong Kong Printed by TJ International Limited, Padstow, Cornwall, England

Contents

1 1.1 1.2 1.3 1.4 2

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13

Contributor contact details Woodhead Publishing in Textiles

ix xi

Introduction P Schwartz, Auburn University, USA Introduction: volume synopsis Future trends Sources of further information and advice References

1

Characterization and measurement of textile fabric properties A Causa and A Netravali, Cornell University, USA Introduction Tensile testing of woven fabrics Stiffness (bending) testing of fabrics Fabric shear – testing concepts Tearing strength of fabrics Test methods for fabric shear Kawabata evaluation system (KES) The FAST system: fabric assurance by simple testing Detailed study of a fabric’s compressional property Mechanisms of deformation of fabrics – summary Fibrous assemblies as reinforcement of composite structures Basic mechanics of laminates: application on testing Three-dimensional fibrous assemblies for structural composites

1 2 3 3

4 4 6 8 12 15 17 24 29 29 30 30 35 42 v

vi

Contents

2.14 2.15 2.16

Sources of further information and advice Acknowledgements References

43 45 45

3

Structure and mechanics of woven fabrics J Hu and B Xin, The Hong Kong Polytechnic University, Hong Kong Introduction Background Structural properties of woven fabrics Tensile properties of woven fabrics Bending properties of woven fabrics Shear properties of woven fabrics Characterizing the mechanical behavior of woven fabrics based on image analysis Modeling drape deformation of woven fabrics and garments Conclusions References and further reading

48

Structure and mechanics of knitted fabrics M-A Bueno, Université de Haute Alsace, France Introduction Structural properties of knitted fabrics Tensile properties of knitted fabrics Bending properties of knitted fabrics Shear properties of knitted fabrics Shear-bending comparison Modelling knitted fabric mechanics and simulation Sources of further information and advice References

84

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8

Structure and mechanics of nonwovens B Pourdeyhimi and B Maze, North Carolina State University, USA Introduction Production processes Web formation Bonding Structure property relationships Failure mechanisms Modeling nonwoven fabric mechanics: thermally bonded nonwovens References

48 48 49 56 59 62 65 75 78 79

84 85 99 105 109 110 111 112 113 116

116 117 117 119 122 130 136 139

Contents 6

6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9

Structure and mechanics of 2D and 3D textile composites C Pastore, Philadelphia University, USA and Y Gowayed, Auburn University, USA Introduction Textile reinforcements for composites Two-dimensional (2-D) fabrics Three-dimensional (3-D) fabrics Continuous stiffness/compliance variation methods Bridging model Numerical comparisons amongst models Numerical models utilizing finite element analysis (FEA) formulation Non-unit cell considerations References and further reading

vii

141

141 141 142 151 156 163 165 172 176 182

Structure and mechanics of yarns El-Mogahzy, Auburn University, USA Introduction Yarn classification Yarn structure Theoretical treatments of yarn tensile strength Strength-comfort-twist relationship Practical aspects of yarn strength Conclusions References

190

Structure and mechanics of coated textile fabrics S Adanur, Auburn University, USA Introduction Structural properties Tensile and tear properties Bending and flexibility properties Shear and shear resistance properties Modeling the mechanics of coated fabrics Recycling of coated fabrics Sources of further information and advice References

213

Index

242

190 191 193 203 204 208 211 211

213 213 221 225 226 228 230 238 239

Contributor contact details

(* = main contact)

Editor and Chapter 1

Chapter 3

Professor Peter Schwartz Department of Polymer and Fiber Engineering Samuel Ginn College of Engineering Auburn University Auburn, AL 36849-5237 USA E-mail: [email protected]

Dr J. Hu* and B. Xin The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong E-mail: [email protected]

Chapter 2

Professor Marie-Ange Bueno Ecole Nationale Supérieure d’Ingénieurs de Sud Alsace Laboratoire de Physique et Mécanique Textiles (UMR 7189 CNRS/UHA) Université de Haute Alsace – 11, rue Alfred Werner 68093 Mulhouse France E-mail: [email protected]

Dr A. N. Netravali* and Dr A. G. Causa Fiber Science Program Cornell University Ithaca, NY 14853 USA E-mail: [email protected]

Chapter 4

ix

x

Contributor contact details

Chapter 5

Chapter 7

Professor B. Pourdeyhimi* and B. Maze Nonwovens Cooperative Research Center College of Textiles North Carolina State University Raleigh, NC 27695-8301 USA E-mail: [email protected] [email protected]

Dr Yehia El-Mogahzy Professor of Polymer and Fiber Engineering and Professor of Statistics and Quality Engineering 101 Textile Building Auburn University Auburn, AL 36849 USA E-mail: [email protected]

Chapter 6

Chapter 8

Professor C. Pastore* Engineering and Design Institute Philadelphia University 4145 Station Street Philadelphia, PA 19144-5497 USA E-mail: [email protected]

Professor Sabit Adanur Department of Polymer and Fiber Engineering 101 Textile Building Auburn University Auburn, AL 36849 USA E-mail: [email protected]

Professor Yasser Gowayed Department of Polymer and Fiber Engineering Auburn University Auburn, AL 36849 USA E-mail: [email protected]

Woodhead Publishing in Textiles

1

Watson’s textile design and colour, seventh edition Edited by Z. Grosicki

2

Watson’s advanced textile design Edited by Z. Grosicki

3

Weaving, second edition P. R. Lord and M. H. Mohamed

4

Handbook of textile fibres Vol 1: Natural fibres J. Gordon Cook

5

Handbook of textile fibres Vol 2: Man-made fibres J. Gordon Cook

6

Recycling textile and plastic waste Edited by A. R. Horrocks

7

New fibers, second edition T. Hongu and G. O. Phillips

8

Atlas of fibre fracture and damage to textiles, second edition J. W. S. Hearle, B. Lomas and W. D. Cooke

9

Ecotextile ’98 Edited by A. R. Horrocks

10

Physical testing of textiles B. P. Saville

11

Geometric symmetry in patterns and tilings C. E. Horne

12

Handbook of technical textiles Edited by A. R. Horrocks and S. C. Anand

13

Textiles in automotive engineering W. Fung and J. M. Hardcastle xi

xii

Woodhead Publishing in Textiles

14

Handbook of textile design J. Wilson

15

High-performance fibres Edited by J. W. S. Hearle

16

Knitting technology, third edition D. J. Spencer

17

Medical textiles Edited by S. C. Anand

18

Regenerated cellulose fibres Edited by C. Woodings

19

Silk, mohair, cashmere and other luxury fibres Edited by R. R. Franck

20

Smart fibres, fabrics and clothing Edited by X. M. Tao

21

Yarn texturing technology J. W. S. Hearle, L. Hollick and D. K. Wilson

22

Encyclopedia of textile finishing H-K. Rouette

23

Coated and laminated textiles W. Fung

24

Fancy yarns R. H. Gong and R. M. Wright

25

Wool: Science and technology Edited by W. S. Simpson and G. Crawshaw

26

Dictionary of textile finishing H-K. Rouette

27

Environmental impact of textiles K. Slater

28

Handbook of yarn production P. R. Lord

29

Textile processing with enzymes Edited by A. Cavaco-Paulo and G. Gübitz

30

The China and Hong Kong denim industry Y. Li, L. Yao and K. W. Yeung

Woodhead Publishing in Textiles 31

The World Trade Organization and international denim trading Y. Li, Y. Shen, L. Yao and E. Newton

32

Chemical finishing of textiles W. D. Schindler and P. J. Hauser

33

Clothing appearance and fit J. Fan, W. Yu and L. Hunter

34

Handbook of fibre rope technology H. A. McKenna, J. W. S. Hearle and N. O’Hear

35

Structure and mechanics of woven fabrics J. Hu

36

Synthetic fibres: nylon, polyester, acrylic, polyolefin Edited by J. E. McIntyre

37

Woollen and worsted woven fabric design E. G. Gilligan

38

Analytical electrochemistry in textiles P. Westbroek, G. Priniotakis and P. Kiekens

39

Bast and other plant fibres R. R. Franck

40

Chemical testing of textiles Edited by Q. Fan

41

Design and manufacture of textile composites Edited by A. C. Long

42

Effect of mechanical and physical properties on fabric hand Edited by Hassan M. Behery

43

New millennium fibers T. Hongu, M. Takigami and G. O. Phillips

44

Textiles for protection Edited by R. A. Scott

45

Textiles in sport Edited by R. Shishoo

46

Wearable electronics and photonics Edited by X. M. Tao

47

Biodegradable and sustainable fibres Edited by R. S. Blackburn

xiii

xiv

Woodhead Publishing in Textiles

48

Medical textiles and biomaterials for healthcare Edited by S. C. Anand, M. Miraftab, S. Rajendran and J. F. Kennedy

49

Total colour management in textiles Edited by J. Xin

50

Recycling in textiles Edited by Y. Wang

51

Clothing biosensory engineering Y. Li and A. S. W. Wong

52

Biomechanical engineering of textiles and clothing Edited by Y. Li and D. X-Q. Dai

53

Digital printing of textiles Edited by H. Ujiie

54

Intelligent textiles and clothing Edited by H. Mattila

55

Innovation and technology of women’s intimate apparel W. Yu, J. Fan, S. C. Harlock and S. P. Ng

56

Thermal and moisture transport in fibrous materials Edited by N. Pan and P. Gibson

57

Geosynthetics in civil engineering Edited by R. W. Sarsby

58

Handbook of nonwovens Edited by S. Russell

59

Cotton: Science and technology Edited by S. Gordon and Y-L. Hsieh

60

Ecotextiles Edited by M. Miraftab and A. Horrocks

61

Composite forming technologies Edited by A. C. Long

62

Plasma technology for textiles Edited by R. Shishoo

63

Smart textiles for medicine and healthcare Edited by L. Van Langenhove

64

Sizing in clothing Edited by S. Ashdown

Woodhead Publishing in Textiles 65

Shape memory polymers and textiles J. Hu

66

Environmental aspects of textile dyeing Edited by R. Christie

67

Nanofibers and nanotechnology in textiles Edited by P. Brown and K. Stevens

68

Physical properties of textile fibres, fourth edition W. E. Morton and J. W. S. Hearle

69

Advances in apparel production Edited by C. Fairhurst

70

Advances in fire retardant materials Edited by A. R. Horrocks and D. Price

71

Polyesters and polyamides Edited by B. L. Deopora, R. Alagirusamy, M. Joshi and B. S. Gupta

72

Advances in wool Edited by N. A. G. Johnson and I. Russell (forthcoming)

73

Military textiles Edited by E. Wilusz

74

3-D fibrous assemblies: Properties, applications and modelling of three-dimensional textile structures J. Hu

75

Medical textiles 2007 Edited by J. Kennedy, A. Anand, M. Miraftab and S. Rajendran (forthcoming)

76

Fabric testing Edited by J. Hu

77

Biologically inspired textiles Edited by A. Abbott and M. Ellison

78

Friction in textiles Edited by B. S. Gupta

79

Textile advances in the automotive industry Edited by R. Shishoo

80

Structure and mechanics of textile fibre assemblies Edited by P. Schwartz

xv

1 Introduction P SCHWARTZ, Auburn University, USA

Abstract: The contents of the following volume are briefly outlined with a short description of each chapter. An attempt is made to predict future trends in the analysis of structural mechanics of fibrous assemblies. A non-exhaustive list of source materials is presented and relevant scientific meetings are identified. Key words: structural mechanics, Kawabata Evaluation System (KES), three-dimensional fibrous assemblies, woven fabric mechanics, image analysis, knitted fabrics, structural composites, spun yarns, filament yarns, coated fabrics.

1.1

Introduction: volume synopsis

In the Preface to the classic book on structural mechanics (Hearle et al., 1969), Professor Stanley Backer noted the subject of structural mechanics was a significant part of the textile literature only during the ‘last twentyfive years.’ Now, thirty-nine years later, the literature is replete with studies of the structural mechanics of fibrous assemblies but, as Professor Backer noted then, most of the work unfortunately is still to be found in the literature as individual manuscripts. This book is an attempt to collect in one place many of the developments in structural mechanics that have occurred since the 1969 publication and a companion volume (Hearle et al., 1980) that appeared eleven years later. In Chapter 2, Professors Causa and Netravali, provide an exhaustive description of the characterization and measurement of fabric properties including traditional testing methods as well as the Kawabata Evaluation System (KES) and fabric assurance by simple testing (FAST). Also included is an overview of fully three-dimensional fibrous assemblies and of fibrous assembly reinforcement for composite materials. Chapter 3, by Professors Hu and Xin, contains a thorough discussion of the structure and mechanics of woven fabrics. This chapter combines a rigorous analysis of the underlying modeling of mechanical properties with the emerging use of image analysis. Also included are experimental data that are used to validate the theoretical models. The structure and mechanics of knitted fabrics are discussed by Professor Bueno in Chapter 4. Both weft and warp knitted fabrics are included. The 1

2

Structure and mechanics of textile fibre assemblies

chapter concludes with the modeling and simulation of knitted fabric properties. Nonwoven fabrics have captured an increasing market share and most likely will continue to do so, especially in the health care product area. In Chapter 5, Professors Pourdeyhimi and Maze cover the methods of nonwovens manufacture, their structure-property relationships, failure mechanisms, and theoretical modeling. In Chapter 6, Professors Pastore and Gowayed introduce twodimensional and three-dimensional fabrics for use in structural composites. They cover the structure and mechanics of woven, knitted, and braided structures and provide a comparison of the models’ prediction with experimental data. Professor El-Mogahzy, in Chapter 7, presents both classical and more recent theories for the structure and mechanics of yarns, the building blocks of all but nonwoven fabrics. The mechanics of both spun and continuous filament yarns are covered. Coated fabrics are the subject of Chapter 8. In this chapter Professor Adanur discusses the structure and manufacture of coated fabrics. This chapter also touches upon the important properties in coated fabrics, modeling, and recycling.

1.2

Future trends

To paraphrase Professor John Hearle, fibrous assemblies pose an especially difficult problem in structural mechanics for when other engineering materials buckle they are considered to have failed, but that is precisely when most fibrous structures begin to do their intended work. With the increasing computing power on the desktop of today’s researchers, the mechanical mysteries of fibrous assemblies are beginning to become more and more lucid. Assumptions, mostly geometric, that were necessary to simplify the structural mechanics analysis of fibrous assemblies to allow for closed solutions are slowly being relaxed with the result that modeling has increasingly improved in its ability to predict mechanical behavior from the knowledge of the properties of individual fibers. Statistical methods too are an increasingly powerful tool in the analysis of fibrous assemblies themselves and end products (e.g., composite materials) incorporating them, as is image analysis. Fibrous assemblies, in the form of yarns/tows, braids, ropes, nets, felts, and fabrics – nonwoven and woven or knitted have been a part of human history since that history has been recorded, and almost surely likely before. Originally produced from natural cellulosic, protein, and mineral fibers, they now incorporate fibers regenerated from natural materials such as cellulose (e.g., rayon, acetate, lyocell), those that are truly synthetic (e.g.,

Introduction

3

nylon, polyester, acrylic, olefin), and mineral fibers (e.g., glass, graphite, and metallic fibers). The latter category allows engineers and scientists to tailor the mechanical properties of fibers for specific applications, although sometime the solution eludes us, as is the case of spider drag line silk. All in all, the field of structural mechanics of fibrous assemblies, is not, nor will ever be, closed.

1.3

Sources of further information and advice

There are many scholarly publications that contain information about the mechanics and properties of fibrous assemblies. The list below is by no means meant to be exhaustive: • • • • • • • • •

Textile Research Journal Journal of the Textile Institute Journal of Engineered Fibers and Fabrics Journal of Industrial Textiles Journal of Applied Polymer Science Polymer Science and Engineering Composites Composites Science and Technology Journal of Filtration

One would be served well by using the two texts mentioned in Section 1.4, though obtaining them may be difficult as currently they are both out of print. There are several societies that sponsor conferences where structural mechanics are discussed. The Fiber Society and the Textile Institute are probably the best known of these. Structural mechanics of fabrics are a common subject at meetings of the American Composite Manufacturers Association (ACMA). The Society for Material and Process Engineering (SAMPE), the American Chemical Society (ACS), and the Materials Research Society (MRS), often have sessions dealing with the mechanics of fibrous assemblies.

1.4

References

Hearle J W S, Grosberg P, and Backer, S (1969), Structural Mechanics of Fibers, Yarns, and Fabrics, v.1, New York, John Wiley & Sons. Hearle J W S, Thwaites, J J, and Amirbayat, J, eds, (1980), Mechanics of Flexible Fiber Assemblies, Alphen aan den Rijn, Sijthoff & Noordhoff.

2 Characterization and measurement of textile fabric properties A CAUSA and A NETRAVALI, Cornell University, USA

Abstract: In the first part of this chapter ASTM methods are discussed covering the tensile, stiffness, bending and tear testing of woven, knitted and nonwoven fabrics. Special attention is given to the following items, viz., (a) the modes of deformation in fabrics under tensile, bending and tearing loads; (b) Treloar’s pioneering research on the behavior of fabrics under shear; (c) the Trapezoid (wing tip) test that allows the measurement of the tear strength of fabrics with no substantial deviation of the tear initial direction, and (d) the Kawabata Evaluation System (KES) that covers a series of tests especially designed to study the mechanical behavior of fabrics under small strains, pertinent to apparel applications. The second part of this chapter covers the basic mechanics and predictive testing of composites reinforced with fibrous assemblies, in either stiff or soft (elastomer) matrix. The study of these composites is a very important area of materials science and engineering with a vast range of applications. In this case, in addition to the properties of the reinforcement, either two- or three-dimensional, the matrix and their interphase, the engineer must consider the critically important geometrical parameters, such as the reinforcement lay-out angles and the ply stacking sequence. Three-dimensional fibrous assemblies have been shown to improve the damage tolerance to the delamination mode of failure. This chapter demonstrates that the study of composites requires a multidisciplinary approach. Key words: fabric test methods, Kawabata Evaluation System, mechanisms of deformation of fabrics, composites reinforced by fabric assemblies (two- and three-dimensional), basic mechanics of laminates – application in predictive testing.

2.1

Introduction

In the first part of this chapter a detailed description and interpretation is provided of the ASTM test methods comprising tensile, stiffness (bending) and tear testing of woven, knitted and nonwoven fabrics. In the case of shear testing, we emphasize Treloar’s pioneering work on the effect of the testpiece dimensions on the behavior of fabrics under shear as well as reference to Hearle’s detailed analysis of the forces involved in this test. Some additional observations deserve special attention, viz., (a) the Trapezoid (wing rip) test to measure the tearing strength of fabrics featuring no deviation (or decreased deviation) of the tear direction, starting with 4

Characterization and measurement of textile fabric properties

5

the initial slit or cut made on the fabric at the start of the experiment; (b) Leaf’s equation, derived by an analytical (closed-form) solution, that opens the possibility of calculating the ‘true’ shear modulus from the bending moduli in a woven fabric described by the classical Peirce’s geometrical model, and (c) the Kawabata Evaluation System (KES) covers a series of tests especially conceived to evaluate the mechanical behavior of fabrics in the domain of small strains pertinent to apparel applications. The KES system represents an important step towards the engineering design of fabrics. The second part of the chapter deals with the fibrous assemblies as reinforcement of composite structures including testing techniques and experimental characterization. The study of composite structures reinforced by fibrous assemblies is a very important and advancing area of materials science and engineering, with extensive applications in aerospace, land and sea transportation, sporting goods, civil infrastructure and biomedical products. Within the transportation industry, there is an important and often forgotten area of fiber-reinforced composites, namely, the pneumatic tire (car, truck, aircraft, off-the-road tires) and various types of conveyor belts. A polymer matrix composite, reinforced with a fibrous assembly is commonly an anisotropic material and its response to stresses is more complex than that of an isotropic material. There are also important differences between stiff vs. soft (e.g. elastomer) matrix composites. In these composites the testing as well as the interpretation of the results is more complex. We have now to consider, besides the reinforcement and matrix properties, the reinforcement/matrix interface and interphase, and the critically important geometrical parameters, such as the reinforcement layout angles and the ply-stacking sequence. Under dynamic testing conditions it is important to indicate, besides the usual factors (temperature, oxygen concentration, humidity, etc.) whether the experiment is run under stress, strain or energy control, and the type of waveform used, that is, sinusoidal, pulse, or an arbitrary waveform derived from field experience. Laboratory built composite laminates (‘coupons’) can be effectively used to study the degradation of the composite properties under ‘real-world’ excitation, viz., mechanical, thermal and chemical loading. The measurement of damage can utilize changes in dynamic properties, spectroscopic techniques, microfractography and non-destructive evaluation techniques (X-rays, ultrasound, shearography, thermography, Moiré interferometry, electronic speckle pattern interferometry and others). In addition, laboratory studies must be integrated with the testing of the whole structure. Three-dimensional (3D) fibrous assemblies have been shown to improve the damage tolerance to the delamination mode of failure. The study of composites requires the input of many disciplines including mechanical engineering, reliability engineering, physics, fiber science and others. Both

6

Structure and mechanics of textile fibre assemblies

a deterministic approach (fracture mechanics, Arrhenius model) and a stochastic approach (S-N curves) can be successfully used. Experimental mechanics must be complemented by finite element analysis and whenever possible by closed-form, analytical solutions. Clearly, the study of composites requires a multidisciplinary approach.

2.2

Tensile testing of woven fabrics

A typical load-extension curve of a woven fabric in a tensile test is presented in Fig. 2.1. Careful examination of the generalized load-extension curve for a woven fabric reveals the presence of three distinct regions. Region 1, the initial part of the curve, is dominated by interfiber friction (usually very small), that is, the frictional resistance due to thread (yarn) bending. Region 2, a region of lower modulus, is the decrimping region resulting from the straightening of the thread set in the direction of application of the load, with the associated increase in crimp in the direction perpendicular to the thread direction. This is commonly referred to as ‘crimp interchange’. Region 3, the last part of the load-extension curve, is due to yarn extension, i.e., tensile loading of threads in the direction of stress. As the crimp is decreased, the magnitude of the loading force rises very steeply, and as a result, the fibers themselves begin to be extended. In summary, in this final region, the load-extension properties of the fabric (cloth) are basically governed by the load-extension properties of the threads or the fibers. This is clearly a region of higher modulus. During the actual test, geometrical changes in the fabric are commonly observed. Due to crimp interchange effects, length-wise loading causes a width-wise contraction. Contraction in width is greatest in the middle and

Yarn extension region

Load

3

Decrimping region 2

1 Interfiber friction effect Extension

2.1 Schematic of a typical load-extension curve for a woven fabric.

Characterization and measurement of textile fabric properties

7

decreases towards the jaws. The value of this contraction is dependent on the ratio of crimp in the warp and weft threads. In the region of the jaws the stresses in the specimen are high and could cause jaw breaks. There are two standard test methods for breaking force and elongation of textile fabrics, viz., The Strip Method, ASTM D5035-95 (re-approved 2003) and The Grab Test, ASTM D-5034-95 (re-approved 2001). The strip method covers raveled strip and cut strip test procedures for determining the breaking force and elongation of most textile fabrics. The raveled strip test is applicable to woven fabrics while the cut strip test is applicable to non-woven fabrics, felted fabrics, and dipped or coated fabrics. This test method is not recommended for knitted fabrics or other textile fabrics which have high stretch (more than 11%). In fabric testing, a ‘raveled strip test’ is a strip test in which the specimen is cut wider than the specified testing width and an approximately even number of yarns are removed from each side to obtain the required testing width. A ‘cut strip test’ is a strip test in which the specimen is cut to the specified testing width. Both types of test specimens can be used in either 25 mm (1 in) or 50 mm (2 in) widths, with a length of at least 150 mm (6 in). The longitudinal (long) dimension should be accurately parallel to the direction of testing or force application. When obtaining specimens from a roll of fabric certain precautions must be observed: (a) cut specimens with their long dimensions parallel either to the warp direction or the weft direction, or cut specimens for testing in both directions as required; (b) specimens for a given fabric direction should be spaced along a diagonal of the fabric to allow for even representation of different warp and weft yarns and (c) unless otherwise specified, take specimens no nearer to the selvedge or edge of the fabric than one-tenth of the width of the fabric. The rationale for this rule is that the fabric properties are different at the edge because of the different selvedge construction (weave) and they are no longer representative of the bulk. The tensile testing machines can be of either constant-rate-of-extension (CRE) or constant-rate-of-load (CRL) type and the values for the breaking force and elongation are frequently obtained from a computer interfaced with the testing machine. Most computers will have the necessary software to record the data and to perform calculations and run the test itself. During the execution of the test, it is critical to ensure that the specimen does not slip in the jaws, or break at the edge of or in the jaws. If these conditions cannot be eliminated by adjusting the pressure in the clamps, jaw cushions or specimen tabbing may be necessary. Verification of the total operating system (loading, extension, clamping and recording or data collection) by using specimens of standard fabrics is recommended. Comparison of results from tensile testing machines operating on different principles is not desirable. When different types of machines

8

Structure and mechanics of textile fibre assemblies

are used for comparison testing, constant time-to-break at 20 ± 3 s is the established way of producing the data. The test apparatus is designed for operation at a speed of up to 300 ± 10 mm/min (12 ± 0.5 in/min) and is capable to obtain the 20 ± 3 s time-to-break. The distance between the clamps (gauge length) is 75 ± 1 mm (3 ± 0.05 in). The grab method is quite different from the strip methods described above. The grab test uses jaw faces that are consistently narrower than the fabric specimen width, thereby avoiding the need to fray the fabric to width. Hence, this method has one major advantage over the strip method, namely, that the preparation of the specimens is simpler and faster. The specimen used is 100 mm (4 in) wide by 150 mm (6 in) long but the jaws are only 25 mm (1 in) wide. The result of this set-up is that only the central 25 mm of the fabric is submitted to the tensile stress field. However, it has been found experimentally that the stressed zone of the fabric between the jaws is somewhat reinforced by the fabric on either side. Consequently, the strength measured by this method is higher than for a 25 mm (1 in) raveled strip test. To ensure that the two jaws grip the same set of threads, a line is drawn on the fabric sample 37 mm (1.5 in) from the edge to assist in the proper alignment of the two jaws. Figure 2.1 shows a schematic of a typical load-extension curve for a woven fabric. We note that the specific shapes of these curves can be affected by the type of threads used in the fabric, fabric construction, rate of elongation, temperature and relative humidity conditions and the previous loading history of the test specimen. Standard ASTM testing conditions are 21 ± 1 °C (70 ± 2 °F) and 65 ± 2% relative humidity. Also, in most cases, conditioning of the specimens for a specific period prior to testing is necessary.

2.3

Stiffness (bending) testing of fabrics

In most applications fabrics undergo bending. One method of assessing the stiffness or flexural (bending) rigidity of a fabric is to determine the length of fabric that bends (deflects) a fixed distance under its own weight. It is an easy test to carry out and, as expected, it is called Cantilever Bending Test and described in ASTM D1388-96 (reapproved 2002) Standard Test Method for Stiffness of Fabrics and ASTM D5732-95 (reapproved 2001) Standard Test Method for Stiffness of Nonwoven Fabrics using the Cantilever Test. This cantilever test method applies to most fabrics including woven, knitted and nonwoven fabrics, either treated or untreated. However, it is not suitable for very limp fabrics or those that show a marked tendency to curl or twist at a cut edge. The basic terminology is the same as the one used in other test procedures, viz., (a) the cross-machine direction is the direction in the plane of the fabric perpendicular to the direction of the

Characterization and measurement of textile fabric properties

9

manufacture. It refers to the direction analogous to coursewise or filling (weft) direction in knitted or woven fabrics, respectively. (b) the machine direction is the direction in the plane of the fabric parallel to the direction of manufacture. It refers to the direction analogous to walewise or warp direction in knitted or woven fabrics, respectively, and (c) in nonwoven fabrics, the term machine direction is used to refer to the direction analogous to lengthwise direction in a woven fabric. In the cantilever bending test, a horizontal strip of fabric is held at one end and the rest of the strip is allowed to hang (bend) under its own weight, for a fixed distance. Peirce’s pioneering research [1, 2] produced very important results as expressed in the following equation: B = W × C3

2.1

where B is the bending (flexural) rigidity, W is the weight of the fabric and C is the bending length. Furthermore, Peirce found that when the tip of the specimen reaches a plane inclined at 41.5° below the horizontal, the overhanging length is then twice the bending length: C=

O 2

2.2

where C is the bending length in cm and O is the length of overhang in cm. Combining the two equations we get O B = W ×⎛ ⎞ ⎝ 2⎠

3

2.3

where B is the flexural rigidity, mg.cm and W is the fabric weight per unit area, mg/cm2. In the cantilever test a specimen, held at one end, is slid at a specified rate in a direction parallel to its long dimension, until its leading edge projects from the edge of a horizontal surface. The length of the overhang is measured when the tip of the specimen is depressed under its own weight to the point where the line joining the top to the edge of the platform makes a 41.5° angle with the horizontal. From this measured length, the bending length and the flexural rigidity are calculated using the above equations. A Cantilever bending tester consists of a horizontal platform that has a smooth low-friction, flat surface such as polished metal or plastic; an indicator, inclined at an angle of 41.5 ± 0.5° below the plane of the platform surface; a movable slide; a scale and reference point to measure the length of the overhang; a motorized specimen feed unit set to 120 mm/min (4.75 in/ min) ± 5%, and a cutting die to cut test specimens 25 mm by 200 mm ± 1 mm (1 in by 8 in ± 0.04 in). The long dimension of the specimen is considered as the direction of the test. The test procedure is simple. The movable slide is removed and the specimen is placed on the horizontal platform with

10

Structure and mechanics of textile fibre assemblies

the length of the specimen parallel to the platform edge. The edge of the specimen is aligned with the line scribed on the right-hand edge of the horizontal platform. The movable slide is now placed on the specimen, being careful not to change its initial position. The tester switch is turned on and the movement of the leading edge of the specimen is carefully watched. The switch is turned off the instant the edge of the specimen touches the knife edge. The overhang length is read and recorded from the linear scale to the nearest 1 mm (0.1 in). As stated earlier, the cantilever test is not suitable for very limp fabrics or those that show a tendency to curl or twist at the cut edge. For such fabrics stiffness may be measured by forming it into a loop and allowing it to hang under its own weight. In this test, a fabric strip of a certain length L has its two ends clamped together to form a loop. The undistorted length of the loop lo, from the grip to the lowest point, has been calculated in Peirce’s classical paper [1, 2] for three different loop shapes, i.e., ring, pear and heart shapes. The heart shape is the one recommended in this standard test and it is appropriately called the ‘Heart Loop Test’. If the actual length l of the loop hanging under its own weight is measured, the stiffness can be calculated from the difference between the measured and the calculated lengths d = l − lo. The test procedure includes tables that facilitate the calculations. The modes of deformation involved in woven fabric bending have been summarized very effectively in the following manner [3]. • • •

thread bending thread twisting → fabric shear thread mobility → fabric shear.

Bending (physical) ← → fabric hand (aesthetics) Stiffness is dependent on: • •

stiffness in warp and weft directions [1, 2] and quantities related to the torsional stiffness of the yarn [4].

When a fabric specimen is subjected to a bending cycle and the results are plotted in bending moment vs. curvature coordinates, the presence of a hysteresis loop is commonly noticed. Under low-curvature bending the hysteresis is attributed to the energy loss in overcoming the frictional forces. Under high-curvature bending the viscoelastic properties of the fibers (stress relaxation) must also be considered. It is interesting to relate the equation used in calculating the flexural rigidity of the fabric to the simple theory of bending applied to a cantilever beam. The fundamental bending formula is: MR = EI

2.4

Characterization and measurement of textile fabric properties

11

where M is the bending moment, R is the radius of curvature, E is the elastic modulus and I is the moment of inertia of the cross-section, also called the ‘second moment’ of the cross-section. The bending/flexural rigidity, B, is defined as the couple required to bend a structure to unit curvature, hence B = [ M ]R =1 = EI

2.5

The curvature of the bend is R−1. The sags or deflection of beams are calculated by integrating a differential equation that expresses the local deformation of a small element of the beam. Using this approach it is possible to derive the ‘differential equation of flexure of a beam’: M = EI

d2 y = EIy ′′ dx 2

2.6

where y″ is the curvature of the beam. The equation is valid only for small deformations and in reference to y-x coordinates where the neutral plane of the beam coincides with the x-axis when the beam is unloaded (unstressed). The distance along the beam (x-axis) is positive to the right side and the deflection is positive downward (y-axis). As an example, let a simple cantilever beam be subjected to an end force P under which it sags through distance δ. Within the elastic region, P is proportional to δ, and the work done by P is 1/2 Pδ which is the energy stored in the beam. The force P acts over a distance x from the end of the beam and the total length of the beam is l. Hence, the bending moment is Px and the curvature in the beam is: y ′′ =

Px EI

2.7

The stored energy, U, is given by: U=

EI l EI ⎛ P ⎞ ( y ′′ )2 dx = ∫ 2 0 2 ⎝ EI ⎠

2 l

P2l3

2 ∫ x dx = 6EI 0

2.8

The energy is now expressed in terms of the load and therefore it is in a form suitable for the application of Castigliano’s theorem: ∂U ∂ ⎛ P 2 l 3 ⎞ Pl 3 = ⎜ ⎟= ∂P ∂P ⎝ 6 EI ⎠ 3EI

2.9

which, by Castigliano, is the work-absorbing deflection under P, that is, the vertical deflection, δ, under P. It follows then that

δ=

Pl 3 Pl 3 Pl 3 , or B = = 3EI 3B 3δ

2.10

12

Structure and mechanics of textile fibre assemblies

This equation offers a rationale for the equation used in the calculation of the bending rigidity of a fabric in the cantilever bending test, where force P is the weight of the fabric and the bending distance is fixed.

2.4

Fabric shear – testing concepts

Treloar [5] published an in-depth study on the effect of the test-piece dimensions on the behavior of fabrics under shear. Previous to his work experiments were carried out almost entirely with square test pieces and two important facts were identified, viz., (a) reliable measurements of the response of fabrics under shear stresses can only be obtained as long as buckling or wrinkling of the test specimen is avoided, and (b) the strain amplitude at which wrinkling begins was shown to increase with the tensile stress applied in a direction perpendicular to the direction of shearing. Treloar’s [5] study involved woven fabrics of cotton and viscose rayon and two specimen shapes, one square and the other one rectangular, and the measurements were carried out using dead weight loading and direct microscopical observation of the fabric deformation. It was concluded that the maximum shear strain which can be applied without the occurrence of wrinkling depended not only on the applied tensile stress but also on the shape of the specimen. He also concluded that this maximum increases as the ratio of length to width of the specimen is reduced. A length : width ratio of 1 : 10 is considered to be most suitable for general measurements. In summary, the shear characteristics were found to be sensitive to the shape of the test specimen, particularly at low values of the normal tension. This sensitivity is closely related to the reduction in the amount of wrinkling with the rectangular specimen. Treloar emphasizes the importance of this reduction in the wrinkling effect in the rectangular specimen, since it allows the experimentalist to make measurements at larger strain amplitude for a given value of the normal load or alternatively, for a given amplitude, to reduce the value of the normal load. Either of these alternatives is important in practice for two reasons, viz., (a) because of the pronounced nonlinear characteristics of fabrics in shear which make extrapolation from small-strain to large strain behavior unreliable, and (b) because the behavior under small normal loads is important in the study of the fabric’s drape. We note that the expression ‘length-to-width’ ratio may be confusing and for some readers it would be preferable to use Saville’s [6] statement, i.e., ‘the errors associated with the onset of wrinkling can be reduced by the use of a narrow specimen with a reduced distance between the clamps instead of a square one. A height : width ratio of 1 : 10 is considered to be the limit for practical measurements.’

Characterization and measurement of textile fabric properties

13

Hearle [7] has done a thorough analysis of forces involved in Treloar’s shear test thereby providing an explanation for the use of an effective shear force equal to F – W tan θ. Spivak [8] adapted Treloar’s test specimen for use in a standard tester with its automatic recording capabilities. Many shear stress-strain curves over a full cycle were obtained for cotton and viscose fabrics showing, as predictable, a hysteresis loop. As mentioned before, the area within the hysteresis loop represents the energy lost in overcoming the frictional forces generated at the intersection of warp and weft. Another important parameter to measure is the ratio of the energy loss to the total work done in shearing since this ratio represents the overall response of the fabric to in-plane deformation and recovery. Spivak and Treloar [9] made an interesting study of the effect of heat setting on the shear properties of a nylon monofilament fabric of plain weave construction, with particular attention to identify the effects of two methods of heat setting, namely, with or without dimensional changes. Microscopic observations of the actual contact area at filament crossovers were used in this study. It was concluded that the properties of a nylon monofilament fabric in shear are indeed influenced by heat setting, and that the largest reduction in values of hysteresis and resistance to shearing occurs when the fabric is heat set with free contraction rather than at fixed dimensions. In the former method, due to the contraction in the dimensions of the fabric, both relaxation of internal bending stresses and change of curvature of the filaments at crossover points do occur. Associated with this change in curvature there is a considerable reduction in contact area and forces at filament crossovers. Spivak and Treloar [9] have also introduced a new dynamic method of measuring the cyclical energy loss of the fabric in shear. In this method, the fabric is mounted between two clamps, the upper one being fixed and the lower one free. If the lower clamp is displaced to produce a shear strain, and then released, a series of damped oscillations in the plane of shear will result. Mathematically, this system can be treated as a simple pendulum undergoing a damped, simple harmonic motion. The length of the pendulum is the length of the fabric between clamps, and the mass of the pendulum is the mass of the lower clamp plus any additional weights firmly attached to it. Hence, the pendulum mass is equivalent to the normal stress used in previous studies of fabric shearing. Within the context of this investigation, general agreement was found between the loss values obtained by the dynamic and the static method. However, this area deserves further study. The bending properties of the filaments were found to be unaffected by the heat setting. Spivak and Treloar [10] investigated the relation between bias extension and ‘simple shear’ for plain-woven fabrics. Bias extension refers to extension of a specimen cut at 45° to the thread directions. Their study, compris-

14

Structure and mechanics of textile fibre assemblies

ing both theory and experiments, concluded that it is not possible to obtain the complete stress-strain properties of a fabric in shear from a test in bias extension. One important factor contributing to this test result is that while the normal stress is constant during the test in simple shear, the normal component in the bias direction test is continually changing. Hence, the stresses applied in the two types of test are not identical and it is possible that this could result in some differences in the frictional restraints at crossover points which could contribute to the observed difference. On the other hand, reasonable agreement between the two tests was obtained for the parameter ‘relative energy loss’, defined, as previously mentioned in this chapter, as the ratio of the energy loss (area inside the hysteresis loop) to the total work done. Leaf and co-workers [11–14] have developed, by closed-form solutions, equations for tensile, shear and bending moduli for plain woven fabrics under small deformations. This type of research is one aspect of the efforts towards the engineering design of fabrics, that is, to design fabrics that meet specific mechanical requirements. As an example, we would like to use the following equation 2 ( l − k2 Dθ 2 )2 12 ( l1 − k1 Dθ 1 ) = + 2 G B1 B2

2.11

which relates various mechanical moduli. The notation used is that of Peirce’s [1, 2] classical model, i.e., the suffixes 1 and 2 refer to warp and weft directions, respectively; B is the flexural rigidity; G is the shear modulus; q is the ‘weave angle’, the angle that the centerline of the fabric makes with the tangent to the thread centerline; l is the actual thread length and l – kDq is the length of the straight section, or in reference to the warp, l1 − k1Dq.1 (we must keep in mind that the yarn path exemplified, let us say by the warp path, consists of straight lines and arcs of circle when it contacts the weft). D is, of course, the sum of the diameters d1 and d2 of the warp and weft threads. At this point we would like to quote Professor Leaf’s actual words during his lecture at the Mt. Fuji Textile Research Symposium – In the New Millennium [11]: This is a particularly interesting equation. So far as I am aware, we do not have a simple method for estimating experimentally the shear modulus of a fabric. The methods used by Treloar [5] and by KES equipment can be criticized on the grounds that they do not produce in the test specimen a uniform stress distribution of the kind envisaged in the definition of shear. But the KES equipment, for example, does allow us to make reasonable estimates of B1 and B2. Does this equation form the basis of a method for estimating the real shear modulus of a plain-woven fabric?

We note that KES refers to the Kawabata Evaluation System which is briefly described later in this chapter.

Characterization and measurement of textile fabric properties

2.5

15

Tearing strength of fabrics

Tearing of the fabric is the tensile failure – either sequentially, in bundles (groups) or a combination of both – of the yarn set perpendicular to the direction of the propagation of the tear [3]. The two major factors that influence the tearing behavior of woven fabrics are yarn tensile strength, and yarn mobility within the structure. Figure 2.2 gives a schematic view of a fabric tearing and Fig. 2.3 depicts a typical result of a tear test in a plot of load in the vertical axis and the jaw separation (extension) in the horizontal axis. The mechanism of tear consists of two major steps, viz., (a) ‘Del’ formation as yarns pulled through interlacing, leading to jamming and slippage (Peirce’s Model), and (b) as yarn is being pulled through the structure,

‘Del’ region

Load

2.2 Schematic view of a fabric tearing.

Jaw separation

2.3 A typical result of a tear test.

16

Structure and mechanics of textile fibre assemblies

frictional forces develop until the breaking strength of yarn is achieved. The factors affecting yarn tear strength are yarn tensile strength, fabric thread count, thread mobility and surface finishes which may affect the frictional forces. The terminology ‘del’ region or zone is based in the similarity one notices between this region where yarns fail and the well-known ‘del’ operator used in vector calculus. Scelzo et al. [15] provided a detailed description of the process of tear. When a displacement force is applied at a constant rate, the longitudinal yarns (i.e., those gripped in the jaws of the testing machine) are gradually loaded, stretched, and begin to lose their crimp. The transverse yarns (i.e., those initially perpendicular to the direction of tear) must locally align themselves with the applied load to bridge the gap from one tail to the other. As the load continues to increase, the transverse yarns that bridge the gap between the tails are pulled into the del zone; this also draws the outer edge of the fabric inward. Tension develops in the del yarns as they are pulled out of the specimen tails, a result of inter-yarn friction and the bending rigidity of the yarn. Longitudinal yarns are drawn together towards the cut line, and the transverse yarns are pulled into a nearly vertical plane; the size of the del zone increases. The resulting crowding of the longitudinal yarns necessarily forms a large number of frictional points of contact in a small area of fabric adjacent to the del. This effect, along with the jamming that takes place ahead of the del (in the region of untorn fabric), makes it extremely difficult for further slippage to take place without producing high local stresses. High localized stresses will lead to yarn break. As each break occurs, there is a sudden shift from one del structure to another that is less elongated and at a lower load than the previous del. This process provides a rationale for the shape of the tear load versus extension diagram. Accompanying yarn failure, where the transverse yarns fail either singly or as small groups, there is a contraction of the tails. Snapback of the tails may be large enough to cause the breakage of additional yarns. Tearing strength is important in both industrial and clothing fabrics. As indicated in the above paragraphs, thread mobility is an important factor affecting tear strength since it will facilitate the grouping or buckling of threads during tearing and therefore improve the tearing resistance as more than one thread has to be broken at a time. This grouping of threads is made easier if the yarns are smooth and can slip over each other. Special fabric finishes such as some crease-resistant finishes, which cause the yarns to adhere to one another, may reduce the tearing strength. The effect of the weave structure is also evident. Thus, a twill weave allows the threads to group better than a plain weave; hence, a twill weave will exhibit better resistance to tearing than a plain weave. Textured fabrics inhibit thread movement and reduce thread grouping and tear strength.

Characterization and measurement of textile fabric properties

2.6

17

Test methods for fabric shear

There are three important standard test methods to measure the tearing strength of fabrics, namely: 1. The tongue test, also known as the single rip or trouser test, ASTM D 2261-96 (re-approved 2002); 2. The trapezoid test, also known as the wing rip test, ASTM D 5587-96 (re-approved 2003) and 3. The falling-pendulum test procedure, ASTM D 1424-96. In addition, for nonwoven fabrics the following tests may be used. 1. ASTM D 5735-95, Tearing strength of Nonwoven Fabrics by the Tongue (Single rip) Procedure, (re-approved 2001). 2. ASTM D 5733-99, Tearing Strength of Nonwoven Fabrics by the Trapezoid Procedure. 3. ASTM D 5734-95 Tearing Strength of Nonwoven Fabrics by Falling Pendulum (Elmendorf Apparatus), (re-approved 2001). The major difference between these tests is in the geometry of the test specimen. Furthermore, while the tongue and trapezoid tests are conducted using a recording constant-rate-of-extension type (CRE) tensile testing machine, the falling-pendulum test requires a pendulum type ballistic tester, such as the Elmendorf tear tester. A brief discussion of these tests follows.

2.6.1 Tongue (single rip) test This test method applies to most fabrics including woven fabrics, knit fabrics, air bag fabrics, blankets, napped fabrics and pile fabrics. The fabrics may be untreated, heavily sized, coated, resin-treated, or otherwise treated. Nonwoven fabrics can also be tested by this procedure. Tear strength, as measured in this method, requires that the tear be initiated before testing. The reported value obtained is not directly related to the force required to initiate or start a tear but to propagate a tear. This test concept – notched test specimens – is quite similar to the one extensively used in experimental fracture mechanics of engineering materials, including elastomers and fiberreinforced composites. Two calculations for tongue tearing strength are provided: the single-peak force and the average of the five highest peak forces. The values stated in either SI units or inch-pound units are to be regarded as the standard. The inch-pound units may be approximate. The specimen in this method has a rectangular shape, with a cut in the center of a short edge to form a twotongued (trouser shaped) specimen (Fig. 2.4), in which one tongue of the

Structure and mechanics of textile fibre assemblies 75 mm (3 in)

Specimen cutting template

75 mm (3 in)

18

200 mm (8 in)

2.4 Template for cutting and making tongue tear test specimens (all tolerances ±0.5%).

specimen is gripped in the upper jaw and the other tongue is gripped in the lower jaw of a tensile testing machine. The rectangular test specimens 75 mm by 200 mm (3 in by 8 in) are cut using a die or a template and a cut to start the tear process is 75 mm (3 in) long, starting at the center of the 75 mm (3 in) width. From each fabric, five specimens are taken from the machine direction and five specimens from the cross-machine direction. The machine direction is defined as the direction in the plane of the fabric parallel to the direction of the manufacture. This term is used to refer to the direction analogous to lengthwise or warp direction in woven fabrics. The crossmachine direction is the direction in the plane of the fabric perpendicular to the direction of manufacture. This term is used to refer to the direction analogous to crosswise or weft (filling) direction in woven fabrics. During the test the separation of the jaws is continuously increased to apply a force to propagate the tear. At the same time, the force developed is recorded. The force to continue to propagate the tear is calculated from the classical autographic chart recorders, or in the modern laboratories from a dedicated computer provided with the required software. The tearing force is displayed in the form of peaks and valleys (see Fig. 2.3). The highest peaks are thought to reflect the strength of the yarn components (woven fabrics), fiber bonds or fiber interlocks (nonwoven fabrics), individually or in combination, needed to stop a tear in a fabric of the same construction. The peaks that are seen on the load-extension curve (N-mm) are more often from the breaking of a group of threads than from the individual ones. It is interesting to point out that a similar tear morphology is observed on the fracture surface of rubber and it is called stick-slip tear. At the start of the test, the distance between the clamps is set at 75 ± 1 mm (3 ± 0.05 in) and the testing speed can be set at either 50 ± 2 mm/min (2 ± 0.1 in/min) or 300 ± 10 mm/min (12 ± 0.5 in/min). Many experts prefer the higher speed based on the observation that in the ‘real world’ many tears do occur quite rapidly. The test specimen is secured in the clamp jaws with the slit edge of each tongue centered in such a manner that the origi-

Characterization and measurement of textile fabric properties

19

nally adjacent cut edges of the tongues form a straight line joining the centers of the clamps and the two tongues present opposite faces of the fabric to the operator. After the crosshead has moved to produce approximately 6 mm (0.25 in) of fabric tear, the single-peak force or multiple-peak forces are recorded. The crosshead motion is stopped after a total tear of 75 mm (3 in) or if the fabric has torn completely. If the fabric slips in the jaws or if 25% of the specimens break at a point within 5 mm (0.25 in) of the edge of the jaw, then the jaws must be modified to avoid these situations. If after making the modification(s), 25% or more of the specimens still break at a point within 5 mm (0.25 in) of the edge of the jaw, or if the specimens do not tear substantially lengthwise, then the fabric should be considered untearable by this test method. If the tear occurs crosswise to the direction of the applied force, this observation should be recorded. There are two options to calculate the tongue tearing force for the individual specimens. In option 1, for fabrics exhibiting five peaks or more, after the first 6 mm (0.25 in) of tear, the five highest peak forces are obtained from the data collection system to the nearest 0.1 mN (0.1 lbf). The average of these five highest peak forces is calculated and reported. In option 2, for fabrics exhibiting less than five peaks, the highest peak force is recorded as the single peak force to the nearest 0.1 mN (0.1 lbf). The tongue tearing strength is calculated as the average tearing force for each testing direction and condition for each laboratory sample. Standard deviation (SD) and coefficient of variation (CV) should be included in the report; in addition, if computer-processed data were used, it is recommended that the software be briefly described. If it is necessary to measure the tear of the wet fabric, the specimens are submerged in a container of distilled water at ambient temperature until thoroughly soaked. For fabrics that have a water-repellent finish, it is necessary to add a small amount of a nonionic wetting agent to the water bath. For wet testing, the specimen is removed from the water, and immediately mounted on the testing machine. The test must be performed within two minutes after removal of the specimen from the water. If more than two minutes elapse between taking the specimen out from the water bath and starting the test, the specimen is discarded and another one is obtained. Upon closing the discussion on the tearing strength of fabrics by the tongue test, it is important to keep in mind that depending on the direction the fabric is torn, the values obtained will be for the tearing strength of yarns perpendicular to the tear direction. If the direction to be torn is much stronger than the other direction, failure will occur by tearing across the tail so that it is not always possible to obtain both warp and weft results.

20

Structure and mechanics of textile fibre assemblies

2.6.2 Trapezoid (wing rip) test This test method covers the measurement of the tearing strength of textile fabrics by the trapezoid procedure using a constant-rate-of-extension (CRE) tensile testing machine. This test method applies to most fabrics including woven, knitted and nonwoven fabrics. It is generally conceded that the trapezoid tear produces tension along a reasonably well-defined trajectory such that the tear propagates across the width of the specimen. Consequently, this test overcomes some of the problems encountered with the tongue (single rip, trouser) test as it is capable of testing most types of fabrics without causing a transfer of tear. Cross-machine direction is the direction in the plane of the fabric perpendicular to the direction of the manufacture. This term is used to refer to the direction analogous to coursewise or filling direction in knitted or woven fabrics, respectively. Machine direction is the direction in the plane of the fabric parallel to the direction of manufacture. This term is used to refer to the direction analogous to walewise or warp direction in knitted or woven fabrics, respectively. In the case of nonwoven fabrics, the terminology used is somewhat different. A nonwoven fabric is a textile structure produced by bonding or interlocking of fibers, or both, accomplished by mechanical, chemical, thermal, or solvent means, or combination thereof. Hence, for nonwovens, an easily distinguishable pattern for orientation may not be apparent, especially if removed from the roll. Care should be taken to maintain the directionality by clearly marking the direction. For nonwoven fabrics the nomenclature used is widthwise and lengthwise directions. The widthwise direction is the direction in a machine-made fabric perpendicular to the direction of movement the fabric followed in the manufacturing machine; the lengthwise direction is the direction in a machine-made fabric parallel to the direction of movement the fabric followed in the manufacturing machine. The basic test methodology is the same for woven, knitted or nonwoven fabrics: (a) An outline of an isosceles trapezoid is marked on a rectangular specimen. The specimen is slit at the center of the smallest base of the trapezoid to start the tear. The nonparallel sides of the marked trapezoid are clamped in parallel jaws of a tensile testing machine. The separation of the jaws is increased continuously to apply a force to propagate the tear across the specimen. At the same time, the force developed is recorded. The force to continue the tear is calculated from autographic chart recorders or computer data gathering system.

Characterization and measurement of textile fabric properties

21

(b) As usual, all necessary precautions must be taken to avoid slipping of the specimen from the clamps during the test. If slippage does occur, the necessary corrective actions must be implemented. (c) Rolls or pieces of fabric are considered as the primary sampling units (lot sample). For the laboratory sample, a swatch is taken extending the width of the fabric and approximately 1 m (1 yd) along the machine direction from each roll or piece in the lot sample. For rolls of fabric a sample should exclude fabric from the outer wrap of the roll or the inner wrap around the core. From each laboratory sampling unit, five specimens are taken from the machine direction (lengthwise direction for nonwoven fabrics) and five specimens from the cross-machine direction (widthwise direction for nonwoven fabrics), for each test condition. These are the test specimens which must now be cut using the templates shown in Fig. 2.5. We note that an initial slit is made 15 mm (0.625 in) long at the center of the 25 mm (1 in) edge of the isosceles trapezoid. (d) Consider the long direction as the direction of test for the woven fabric and the short direction of test for the nonwoven fabrics. (e) For woven fabrics take the specimens to be used for the measurement of machine direction with the longer dimensions parallel to the machine direction. Take the specimen to be used for the measurement of the cross-machine direction with the longer dimensions parallel to the cross-machine direction. For nonwoven fabrics, cut the specimens to be used for the measurement of the lengthwise direction with the shorter dimension parallel to the lengthwise direction. Cut the specimens to be used for the measurement of the widthwise direction with the shorter dimension parallel to the widthwise direction. Fig. 2.6 clearly illustrates the relationship of specimen orientation with respect to the test direction. (f) At the start of the test, the distance between the clamps is set at 25 ± 1 mm (1 ± 0.05 in), and the testing speed is set to 300 ± 10 mm/min (12 ± 0.5 in/min). The test is conducted in the standard atmosphere for textiles or in the atmosphere directed by the contract order. The test

75 mm (3 in)

15 mm (0.625 in)

100 mm (4 in)

150 mm (6 in)

2.5 Templates for cutting and marking trapezoid test specimen.

22

Structure and mechanics of textile fibre assemblies Lengthwise direction of fabric

Cut the specimens to be used for the measurement of the lengthwise direction

Cut the specimens to be used for the measurement of the widthwise direction

2.6 Illustration of relationship of specimen orientation with respect to test direction – nonwoven fabrics, trapezoid test.

specimen is clamped along the nonparallel sides of the trapezoid such that the end edges of the clamps are in line with the 253 mm (1 in) side of the trapezoid and the cut is halfway between the clamps. The short edge is held taut and the remaining fabric is allowed to lie in folds. The machine is started and the tearing force is recorded (forceextension curve) and it may exhibit a simple single maximum or show several maxima and minima. (g) For other details, the reader is referred to the discussion of the tongue test.

2.6.3 Falling-pendulum test (Elmendorf apparatus) This test method covers the determination of the force required to propagate a single-rip tear starting from a cut in a fabric and using a fallingpendulum type (Elmendorf) apparatus. This test method applies to woven fabrics and many other fabrics provided the fabric does not tear in the direction crosswise to the direction of the force application during the test. This method is suitable only for the warp direction tests of warp-knit fabrics; it is not suited for the course direction of warp-knit fabrics or either direction of most other knitted fabrics. A slit is centrally precut in a test specimen held between two clamps and the specimen is torn through a fixed distance. The resistance to tearing is in part factored into the scale reading of the instrument and is computed from this reading and the pendulum capacity. The test specimen is a rectangle 100 ± 2 mm (4 ± 0.05 in) long by 63 ± 0.15 mm (2.5 ± 0.005 in) wide; the critical dimension is the distance 43.0 ± 0.15 mm (1.69 ± 0.005 in) which is to be torn during the test. This tearing distance is the distance between the end of the slit and the upper edge of the specimen when the lower edge

Characterization and measurement of textile fabric properties

23

of the 63 mm (2.5 in) wide specimen rests against the bottom of the clamp. The length of the slit is 20 mm (0.787 in). The Elmendorf tear tester is a sector-shaped pendulum carrying a clamp which is in alignment with a fixed clamp when the pendulum is in the raised starting position, where it has maximum potential energy. The specimen is fastened between the two clamps with the slit centrally located between the clamps, and the force recording mechanism is set at its zero-force position. The tester may have a pointer mounted on the same axis as the pendulum to register the tearing force on a scale, or it may have a computer and associated software for automatic collection of the data and to perform the calculations. When the pendulum is released, part of its energy is lost in tearing the fabric, hence when the pendulum is on its backward swing it will not be able to reach the same height as it started from. The difference between starting height and finishing height is proportional to the energy lost in tearing the fabric specimen. The scale attached to the pendulum can be graduated to read the tearing force directly or it may give percentage of the original potential energy. It is also evident that the work done on the fabric and hence the reading obtained is directly proportional to the length of the fabric torn. The range or capacity of the instrument can be increased by using weights to increase the mass of the pendulum. Readings obtained when the specimen slips in the jaw, or where the tear deviates more than 6 mm (0.25 in) away from the projection of the original slit, must be rejected. The operator must record if puckering occurs during the test and if the tear was cross-wise to the normal (parallel) direction of tear. It is interesting to point out that the basic principle used in the Elmendorf tear test is the same as the one used to measure the impact resistance of engineering thermoplastics, that is, the classical Charpy and Izod methods. In all these tests we are using the interconversion of potential energy and kinetic energy. In all these techniques the parameter measured is the energy absorbed from the pendulum during its oscillation. This ‘impact energy’ as it is sometimes termed, may be defined as: U=

1 I (Vo2 − Vf2 ) , 2

2.12

where I is the moment of inertia of the pendulum and Vo and Vf are the velocities of the pendulum bob just before and after striking the specimen, respectively. Assuming no windage or friction losses on the pendulum V 2o = 2gho and V 2f = ghf where ho and hf are, respectively, the initial fixed height from which the pendulum is released, then, it swings down to strike and break or tear the specimen at the bottom of the swing, and then continues its swing to a measured maximum height, hf. Then

24

Structure and mechanics of textile fibre assemblies U = gI ( ho − hf ) or, more realistically, U = K ( ho − hf )

2.13

where K is a machine constant for a given system [16]. In modern research laboratories the impact resistance of thermoplastics and composites is measured in fully computerized testing machines of horizontal design and equipped with an environmental chamber. The ruptured specimens are studied by optical and/or scanning electro microscopy (fractography). The falling pendulum (Elmendorf) apparatus can be used to measure the tearing strength of most nonwoven fabrics, provided the fabric does not tear in the direction crosswise to the direction of the force applied during the test. If the tear does not occur in the direction of the test, the fabric is considered untearable in that direction by this test method. The standard Elmendorf tear tester with interchangeable pendulum is the preferred test apparatus for determining tearing strength up to 6400 g.f. For tearing strength above this value, a high capacity test instrument is available equipped with augmenting weights to increase the capacity. The nonwoven fabrics may be treated or untreated, including heavily sized, coated or resin-treated. The test specimen is the same as described before for woven fabrics, viz., a rectangular test piece 100 ± 2 mm long by 63 ± 0.15 mm wide, with a 20 mm slit, thereby leaving 43 mm to be torn. Obviously, compared to other methods for testing tearing strength this test method has the advantage of simplicity and speed since specimens are cut with a die and results are read directly from the scale on the pendulum. Furthermore, the specimens are relatively small in area and thus, require less fabric. The reading obtained is directly proportional to the length of the material torn, therefore, it is essential that the specimen be prepared to the exact size specified.

2.7

Kawabata evaluation system (KES)

Professor Emeritus Sueo Kawabata (Kyoto and Shiga Prefecture Universities, Japan) [17] developed a comprehensive program to study fabric handle (hand) to replace the subjective assessment of fabrics by experts, with an objective, laboratory instrument-based system, capable of providing consistent and reproducible results. The KES is especially designed to study the mechanical behavior of fabrics in the domain of small strains, pertinent to apparel applications. In this case, as previously indicated, decrimping is the most important region of the load-extension curve since the load is rarely high enough for thread extension to take place. The KES has also the capability to characterize the energy loss (hysteresis loop) in the process of the

Characterization and measurement of textile fabric properties

25

mechanical deformation and recovery cycle. Some examples are briefly discussed below:

2.7.1 Tensile properties Fabric tensile properties are measured by plotting the force-extension curve from zero to a maximum force of 500 gf/cm (4.9 N/cm) as well as the recovery curve. As a result of this loading/unloading cycle, the recovery curve does not return to the origin, i.e., a residual strain remains (permanent set), which reflects the viscoelastic nature of the component fibers. The area inside the hysteresis loop denotes the energy lost during the load-unload cycle. A typical load-extension for KES showing one deformation cycle is presented in Fig. 2.7. From these curves the following values are calculated [6]: • •

•

Tensile energy WT = the area under the force-extension curve (load increasing) and represents the work done in tensile deformation WT Linearity = area triangle OAB defines the extent of non-linearity of the force-extension curve. The triangle OAB is obtained by drawing a 45 ° straight line from 0 (origin of the y-x rectangular coordinates) to point A, with a y value (ordinate) of 500 gf/cm. Point B is the corresponding value of the extension on the x axis (abscissa) [6]. area under load decreasing curve Resilience RT = × 100% WT

The relation between these parameters and the wearing performance of the fabric is the following: Load

A

O

C

B

Extension

2.7 Load-extension curves for KES showing one deformation cycle (loading-unloading). Line OA represents perfect linear elasticity.

26 • • •

Structure and mechanics of textile fibre assemblies WT, tensile energy: a lower value causes hard feeling in extension LT, linearity in extension: a higher value causes a stiff feeling RT, resilience: a lower value causes inelastic behavior.

2.7.2 Shear properties Shear properties of the fabric are measured using a rectangular specimen with a width of 20 cm and a height of 5 cm, clamped along the two long opposite edges and free on the other two edges. On this specimen, a constant tension of 10 gf/cm (98.1 mN/cm) is applied along the clamped sides of the fabric in the x direction to avoid buckling of the fabric. During the test, the fabric is subjected to shear forces on the clamped edges which undergo relative displacements along the y axis as a result of the applied shear forces. The angle θ represents the rotation of a point on the moving edge of the tested specimen. A schematic of the test is given in Fig. 2.8. The reader should also refer to Treloar’s [5] pioneering research in this area. The maximum angle of rotation in this test is 8 ° which corresponds to the wearing condition of fabrics. The following quantities are measured: •

• •

Shear modulus or modulus of rigidity G = average slope of the linear region of the hysteresis curve (shear force-shear strain curve) to ±2.5 ° shear angle. Shearing hysteresis, 2HG = average widths of the shear hysteresis loop at ±0.5 ° shear angle. Shearing hysteresis, 2HG5 = average widths of the shear hysteresis loop at ±5 ° shear angle.

Note that shearing hysteresis is also called Force hysteresis. The relation between these parameters and the wearing performance of the fabric is the following: 20 cm A

B

θ

θ

D

5 cm

C

Shear forces

x

Tensile forces y

2.8 Schematic of the KES fabric shear test.

Characterization and measurement of textile fabric properties

27

•

G, shear stiffness or rigidity: a larger value makes the fabric stiff and paper-like • 2HG, shear hysteresis at 0.5 ° shear angle: a larger value causes inelastic behavior in shearing • 2HG5, shear hysteresis at 5 ° shear angle: a larger value causes inelastic property in shearing and wrinkle problems. Hu [18] states that the KES shear tester does not produce a pure shear state deformation in the tested specimen. On the other hand, a pure shear state is indeed achieved in the conventional shear test for a stiff engineering material in which a rod of circular cross-section is subjected to torsional deformations. As previously stated, the angle θ represents the rotation of a point on the moving edge of the tested specimen, but not the shearing strain.

2.7.3 Bending properties The fabric specimen is bent between the curvatures −2.5 and 2.5 cm−1, the radius of the bend being the reciprocal of the curvature. A curve of bending moment vs. curvature is obtained by continuously monitoring the bending moment required to produce this range of curvatures. The measured bending parameters are: •

B, bending stiffness (rigidity), the average slope of the linear regions of the bending hysteresis curve between the radius of curvature of 0.5 cm−1 and 1.5 cm−1. • 2HB, bending hysteresis, the average width of the bending hysteresis loop at ±0.5 cm−1 curvature.

The relation of the obtained bending parameters with the wearing performance of the fabric is the following: • •

B, bending stiffness. A larger value makes the fabric stiff. 2HB, bending hysteresis. A larger value causes inelastic behavior in bending.

2.7.4 Compression properties Compression properties are measured by subjecting the fabric specimen, between two plates, to increasing pressure while following the change in the fabric thickness, up to a maximum pressure of 50 gf/cm2. The load is then slowly reduced and the recovery process is measured. The parameters LC, WC and RC are obtained using the same criteria as in the tensile properties.

28

Structure and mechanics of textile fibre assemblies

•

LC, linearity of the compression-thickness curve which is a measure of the deviation of the deformation curve from a straight line. Higher values of LC mean a higher initial resistance to compression. • WC, compression energy, is the work done in compression as measured by the area under the compression curve (gf.cm/cm2). • RC, compressive resilience, is the ability to recover from compression deformation and is expressed as a percentage of the work recovered to the work done under compression deformation. The relation between these parameters with the wearing performance of the fabric is the following: • • •

LC, linearity in compression. A higher value causes a hard feeling in compression. WC, compression energy. A lower value causes a hard feeling in compression. RC, resilience. A lower value causes inelastic compression property.

2.7.5 Surface properties In addition to the properties briefly discussed above, KES system includes the measurements of the fabric surface frictional coefficient and surface frictional roughness. The relation of these parameters with the wearing performance of the fabric is the following: • • •

MIU, mean frictional coefficient. Too high and too low values yield unusual surface feeling. MMD, surface frictional roughness. A higher value causes roughness; mean deviation of MIU. SMD, surface geometrical roughness. Too high and too low values make unusual feeling surface.

Additional parameters in the KES system are fabric thickness (mm) and fabric weight per unit area (mg/cm2). Instruments capable of measuring the longitudinal tensile, axial compression, transverse compression and torsional characteristics of single fiber/ filaments of an average diameter of 15 micrometres have also been developed. These parameters have become very useful in correlating mechanical properties to the fiber molecular structure and microstructure (morphology), as well as in selecting fibers or fiber assemblies as reinforcement of composite materials. In summary, Prof. Kawabata’s extensive research has provided an important contribution towards the development of a true engineered design of textile and apparel performance.

Characterization and measurement of textile fabric properties

2.8

29

The FAST system: fabric assurance by simple testing

FAST comprises test methods and instruments designed by the CSIRO division of Wool Technology, Australia, to measure the tailoring performance of the fabric and thereby identify problems that may be encountered in converting a fabric into a garment. Both KES and FAST methods are designed for measuring the low stress (or deformation) mechanical properties of fabrics, but some differences exist in the testing philosophy. Thus, while the KES bending tester uses the principle of pure bending to measure the bending property, the FAST bending tester is based on the cantilever principle. In the measurement of the shear property, the KES measures the simple shear while the FAST shear tester uses the principle of bias extension. There appears to be a consensus of opinion among the experts that the FAST system is more readily applied to industrial production, while the KES is preferred in a research laboratory environment [18].

2.9

Detailed study of a fabric’s compressional property

Matsudaira and Qin [19] developed a theoretical model for the compressional deformation of a fabric and confirmed the model experimentally. The fabric is considered as an assembly of yarns and/or fibers and with a space (air) between them. Three stages can be identified in the fabric compression and recovery curves. First stage – in the first stage the compression plate comes in contact with fibers protruding from the fabric surface (‘hairs’) and the resistance to compression comes from the bending of these fibers. Second stage – in the second stage the compression plate makes contact with the surface of the yarn, hence inter-yarn and/or inter-fiber friction provides the resistance to compression until the fibers are all in contact with one another. Third stage – in the third stage the resistance to compression comes from the lateral compression of the fibers themselves. The authors opine that the first and third stages of the compressional curve can be approximated by a linear equation of the type y = a + bx since elastic deformation predominates, while the second stage of the compressional curve can be regressed by an exponential equation of the type y = a exp(bx) + c, where y is the compressional force (gf/cm2), x is the deformation (mm) and a and b are the regression constants. In this second step frictional forces predominate.

30

Structure and mechanics of textile fibre assemblies

In the recovery curve, the first step can be approximated by the linear equation, but the second step is regressed by an exponential equation. The third step of the recovery curve is the region where instantaneous recovery is impossible. The area inside the hysteresis loop is the part of the compressional energy lost to internal friction. For the experimental confirmation of the theoretical model the KES compression tester was used. While in the KES the maximum compressive stress is 50 gf/cm2, in this study the maximum pressure was 250 gf/cm2. The fabrics used were all wool, all silk, all polyester (filament), all polyester (spun) and all cotton. The fabric thickness (mm) was obtained at the pressure of 0.5 gf/cm2 as in the KES procedure, and all the experiments were carried out at 20 ± 0.3 °C temperature and 65 ± 3% relative humidity. Very good agreement was noted between the calculated and experimental compressional and recovering curves.

2.10 Mechanisms of deformation of fabrics – summary [3] Woven

Knitted

Nonwoven

Crimp removal Fiber slippage Fiber straightening Fiber extension Yarn flattening Yarn bending Thread shearing Crimp interchange

Crimp removal Fiber slippage Fiber straightening Fiber extension Yarn flattening Yarn bending Thread shearing Change in spacing

Fiber deformation Bond deformation

2.11 Fibrous assemblies as reinforcement of composite structures The study of composite structures reinforced by fibrous assemblies is a very important area of materials science and engineering, with applications in aerospace, land and sea transportation, sporting goods, civil infrastructure and biomedical products. Of particular importance is the increased use of carbon fiber reinforced composites in structural components of large passenger airplanes. Fibers are commonly used for reinforcement of polymer, metal and ceramic matrices and the fibers themselves can be polymeric, metallic or ceramic. Reinforcing fibers can also be produced with different cross-sectional shapes and crystalline microstructure and can be engineered in the form of two-dimensional or three-dimensional architectures in order to optimize composite properties.

Characterization and measurement of textile fabric properties

31

Within the transportation industry, we must also remember an important fiber-reinforced composite, namely, the pneumatic tire (car, truck, aircraft, off-the-road tires). In the rubber industry, polymeric and metallic reinforcing fibers are predominantly utilized in the form of a cord, a plied twisted filament structure, since this type of structure can be readily varied to provide a rather wide range of alternative selections of strength, stiffness and fatigue. A simple rule of thumb is that higher twist results in better fatigue resistance at the expense of reduced stiffness and strength. From a materials science viewpoint, a pneumatic tire can be defined as a compliant, viscoelastic cord-rubber composite structure which undergoes variable periodic deformations during service. The modern radial tire features a stiff, almost inextensible belt package connected to the rim by a tough, flexible radial casing, thereby ensuring optimum traction and directional stability. Fig. 2.9 shows a schematic of the internal structure of a radial tire for a car. The tire cords are the load-carrying constituent of the tire while the rubber in the plies transmits the load to the cords via shearing stresses at the cord-rubber interface. This, of course, requires an optimum level of adhesion between the cords and the rubber matrix. Quasi-static, time dependent and dynamic mechanical properties of cord and rubber must be measured using suitable test specimens. Dynamic mechanical properties are of primary importance and comprise the measurement of elastic modulus, loss modulus, rate of heat generation (hysteresis) and fatigue as well as dependence of these properties on temperature, strain (or stress) amplitude, frequency and material microstructure. For the rubber matrix in particular, crack growth properties and network microstructures must be fully

Overlay (cap ply)

Tread

Belt (breaker) plies

Body (carcass) ply

Sidewall Beads

2.9 Schematic of the internal structure of a radial tire for a car.

32

Structure and mechanics of textile fibre assemblies

characterized. We must keep in mind that the rubber matrix itself contains non-fibrous particulate reinforcing fillers such as carbon black and silica. The properties of the rubber cord-interface are particularly difficult to study since the interface is not a simple boundary surface but it is actually an interfacial zone (‘interphase’) consisting of the surface layers of fiber (polymeric or metallic) and rubber and adhesive layer(s) between these surfaces. Why are the dynamic mechanical properties, that is, the multi-cycle fatigue strength of the cord-rubber composite so important in assessing its suitability for use in the body and belt plies of radial tires? The answer is simple if we keep in mind that 40,000 miles of passenger tire travel subjects each cord to approximately 30 million fatigue cycles! Cords in heavy duty truck tires commonly experience over one billion fatigue cycles even before retreading!

2.11.1 Fatigue of reinforced polymer composites The response of fiber reinforced, polymer composites to stress is more complex than that of an isotropic material. This is due to the fact that there are many variables that affect the composite behavior and fatigue modes. The fracture behavior of the composite is affected by the following variables: (a) type of fiber and fiber assembly construction; (b) type of matrix; (c) fiber-matrix interfacial bond strength and toughness; (d) fiber orientation and ply stacking sequence; (e) presence of flaws or discontinuities; (f) mode and rate of loading, and (g) environment (heat, moisture, chemicals). Several possible damage and failure modes can be observed in fiber reinforced polymer composites: (a) matrix fracture; (b) fiber-matrix interfacial bond failure or interfacial area failure; (c) fiber fracture; (d) crack growth from flaws or at materials and geometric discontinuities, and (e) delamination. In a multi-directional composite under complex loading one may find one or several of these damage modes, and it is sometimes difficult to identify a single dominant crack that controls the composite failure.

2.11.2 Stiff polymeric matrix composites versus elastomeric matrix composites Elastomeric matrix composites behave quite differently from stiff polymer matrix composites in the following major ways: 1. Elastomeric matrix composites have a much larger elastic deformation range than that of stiff polymer composites. Hence, the geometric changes of the configuration must be taken into account. This statement

Characterization and measurement of textile fabric properties

33

means that the stress can be defined by the force per either undeformed area (Lagrangian stress) or deformed area (Eulerian stress). 2. Elastomeric matrix composites have low shear modulus and hence exhibit large shear deformation, which allows the fibers to change their orientation under loading. 3. The stiffness of an elastomeric matrix composite (lamina or laminate) is extremely sensitive to the fiber orientation. Hence, elastomeric matrix composites are highly anisotropic. It is apparent therefore that the conventional linear elastic theory, based on the infinitesimal strain assumption for stiff polymer matrix composites is not applicable to elastomeric composites under finite deformation. Furthermore, it can be readily deduced from all of the preceding statements that although optical and scanning electron microscopy remain the key tools to pinpoint microfailure modes, in order to understand the root cause of failure, scientists and engineers must have a sound knowledge of the properties of the fiber or fiber assembly, rubber and rubber-fiber interfaces.

2.11.3 Fundamentals of predictive testing The experimental characterization of composite materials can be done on several scales, viz., micromechanical, macromechanical and structural. The testing of composite materials has three major objectives: 1. Determination of properties of the unidirectional lamina (ply) and of laminated structures. 2. Investigation and verification of predictions of mechanical behavior derived either from analytical (closed form) solutions or numerical (finite element analysis) procedures. 3. Independent experimental study of material and structural behavior for specific geometries and loading conditions [20]. The major objective of predictive testing is, as expected, to predict the lifetime of the composite structure. There are several requirements to achieve this goal: • •

sound knowledge of application understand and quantify the mechanism of failure and cumulative damage • relate to material and design • develop scaling concept in time and geometry to relate laboratory tests to actual field performance. A typical predictive accelerated testing method is the ‘step stress testing’. The engineer begins with a fairly large number of specimens and conducts

34

Structure and mechanics of textile fibre assemblies

the test for a fixed time interval starting at a low stress level. At the end of the time period, the stress is increased and the good parts remaining from the previous step are subjected to the increased stress for the same time period. The process is repeated until the onset of failure that can be caught at its initial stages using various non-destructive evaluation techniques. Stresses are applied at a constant rate or frequency and there can be a single dominant stress applied alone or in combination with other stresses depending on our knowledge of the ‘real-world’ situation. The interaction of two or more stresses has the added advantage that it may result in a a reduction in test time. If many levels of accelerated stress are employed, it becomes possible to plot a stress vs. life cycles curve (S-N curve). The S-N curve represents the mathematical model that displays the way life varies by the application of different stress levels. We will return to this topic when we describe an example of fatigue testing. Since the application of accelerated stresses may result in degradation through higher temperatures, the use of the Arrhenius model seems quite logical. This is particularly true of elastomeric matrix composites due to the viscoelastic nature of the rubber matrix. The Arrhenius model is based on the classical equation that describes the reaction rate of a chemical process, but stated in a slightly different manner. The Arrhenius approach implies that a linear relationship exists between the logarithm of the time to a certain magnitude of material property change and the reciprocal of the absolute temperature. The energy of activation is obtained from the slope of the line. Another useful technique is the Palmgren-Miner Cumulative Damage Rule. This rule states that the number of stress cycles imposed on a material or structure, expressed as a percentage of the total number of stress cycles of the same amplitude necessary to cause failure, gives the fraction of expended fatigue life. If ni is the number of cycles corresponding to the ith block of constant stress amplitude si in a sequence of m blocks, and if Nfi is the number of cycles to failure at si, then the PalmgrenMiner damage rule can be expressed mathematically in the following manner: i=m

∑

i =1

ni =1 N fi

2.13

The Palmgren-Miner’s rule has one important shortcoming; it implicitly suggests that the order in which the stress blocks of different amplitudes are imposed does not affect the fatigue life. This is not in agreement with experimental facts.

Characterization and measurement of textile fabric properties

35

2.12 Basic mechanics of laminates: application on testing Laminated composites are extensively used in engineering applications featuring, in most cases, unidirectional reinforcement. The basic mechanics of angle-ply laminates can be explained by simple graphical representations. Let us consider two separate one-ply systems, with one ply at a reinforcement angle of +θ and the other ply at −θ as shown in Fig. 2.10. If a uniform tensile stress is applied at each end of these specimens at an angle to the reinforcing fibers (off-axis loading), an in-plane shear strain will develop and the plies will undergo shear deformations of opposite signs. In fact, the deformation patterns of these plies are mirror images of each other. When the two plies are now bonded together to form a ±θ angle ply laminate, the oppositely directed in-plane shearing stresses in each ply will produce two major effects: (a) interlaminar shear stresses will develop in the matrix layer between the two plies (or laminae) and the moment produced by these stresses is equilibrated by intralaminar shear stresses within each lamina, and (b) an out-of-plane twisting of the laminates as shown in Fig. 2.11. The structure is said to exhibit in-plane to out-of-plane coupling, that is, an inplane stress causes an out-of-plane deformation. The coupling stresses arise because the laminate is not symmetrical about its center plane. When the two plies are bonded together to form a −θ/+θ angle-ply laminate, that is a laminate with reversed stacking sequence, the application of

σx (−)

σx (+)

σx T = –α

σx (+)

σx (−)

σx T=α

Ply 1 Ply 1

Ply 2

Ply 1 Ply 1

Ply 2

Ply 2

σx

σx In-plane to out-of-plane coupling caused by laminate design

σx

Ply 2

σx

σx

σx

Reversed coupling caused by reversing the stacking

2.10 Schematic of the in-plane to out-of-plane coupling of one-ply systems.

36

Structure and mechanics of textile fibre assemblies σx

+θ –θ –θ +θ

Interlaminar shear

Intralaminar shear

Direction of fiber rotation in +θ lamina σx

(a)

(b)

2.11 (a) Shear stresses resulting from tensile loading of an angle-ply (±θ) laminate and (b) laminate with no in-plane to out-of-plane coupling.

the same tensile stress will produce a twist of the same magnitude but opposite direction with respect to the ±θ laminate. It can then be readily deduced that a four-ply laminate with a stacking sequence +θ/−θ/−θ/+θ. Designated [+θ/−θ]s, will possess a plane of symmetry and will not exhibit in-plane to out-of-plane coupling. The laminate responses to unidirectional tensile stresses as described above can be demonstrated experimentally and a mathematical description is available using finite element analysis and laminate theory.

2.12.1 Application in testing The angle-ply laminate featuring metallic or polymer cords as reinforcement and an elastomer as matrix is an excellent test specimen to study the fatigue endurance of the belt structure of a radial tire. As expected, numerous investigations on this topic have been conducted and the results are available either in scientific publications or as part of patent applications. A review article is also available [21]. The fatigue studies are conducted in either an electromechanical or a servohydraulic testing machine provided with suitable data acquisition system with special software. A two-ply, +θ/−θ cord rubber laminate can be used since a device is available to allow the testing equipment to prevent the twisting of the sample. An environmental chamber and an infra-red

Characterization and measurement of textile fabric properties

37

σ

σ

Stiff

Stiff Soft

Soft A

B

A

σ1

B

C 0

C

D (a)

ε

0

ε1 (b)

ε

2.12 Stress-strain curves of stiff and soft materials tested under (a) stress and (b) strain control.

camera are needed due to the critical importance of temperature on the fatigue durability of the composite. The composite laminate must be sufficiently long so that in the region far away from the ends, end effects (due to the grips) are negligible by virtue of the Saint Venant’s principle. In addition to the environmental factors (temperature, oxygen, ozone) it is important to know the testing conditions, viz., the mode of deformation control and the type of excitation waveform used in the fatigue study. Observation of the stress-strain curves of two hypothetical compounds 1 & 2, stiff and soft, in Fig. 2.12 shows that for displacement (strain) control (b), that is, a fixed strain, the low modulus compound should be better for fatigue durability, since its strain energy density, let us call it U2 (area under its stress-strain curve) is smaller than the area U1 for the higher modulus compound. This conclusion is correct if the crack growth rate corresponding to the strain energy release rate for the U2 condition is also smaller than that which corresponds to the strain energy release rate for U1. On the other hand, if the compound is tested under load (stress) control (Fig. 2.12 (a)), we observe that the higher modulus compound will now have a lower strain energy density, U1, and therefore a longer fatigue life. This conclusion assumes that the crack growth rate corresponding to the strain energy release rate for the U1 condition is lower than that corresponding to the strain energy release rate for U2. It is also possible to run fatigue experiments under energy control [22]. Sinusoidal and pulse waveforms are commonly used in dynamic experiments, but many other waveforms can also be used. We must keep in mind that the pulse excitation has a relaxation period which is not present in the sinusoidal curve. Note that the word ‘compound’ is used in the rubber

Structure and mechanics of textile fibre assemblies

Displacement

38

Load

Cycles

Cycles

2.13 Schematic of the evolution of fatigue life of an angle-ply laminate.

industry to designate the rubber (natural or synthetic elastomer) with the addition of sulfur and an accelerator to vulcanize the rubber, plus carbon black and/or silica, and antioxidants. Figure 2.13 shows in a schematic manner the evolution of the cumulative damage, as a function of fatigue life (time), for a ±23 ° angle-ply laminate, reinforced with high tensile steel cords in a matrix of natural rubber (cis1,4-polyisoprene). The fatigue test was run under load control using a sinusoidal waveform with a frequency of 10 Hz. The width of the test piece (often called ‘coupon’) was 25.4 mm with a gauge length of 254 mm; no external heat was applied to the sample [22]. The first damage observed is in the form of small cracks in the rubber at the edge of the cords; microfractography indicates that this failure agrees with Bikerman’s concept of a weak boundary layer fracture. This edge cracking is also known as ‘socketing’ [23]. In later stages these initial cracks propagate and connect with one another not only along the length of the sample but also through the rubber layer between the two cord reinforcing layers. As predictable, the infra-red camera shows that this rubber layer is the hottest spot in the sample. The final stage shows the interply fracture, that is, the well-known delamination mode of failure. Observation of the progress of the damage in this experiment reveals an interesting difference between composites and metals. In metals much of the fatigue life is spent before cracks appear. In a composite structure much of the fatigue life is spent after the appearance of the first crack, and the cumulative damage is quite complex [24].

Stress amplitude

Characterization and measurement of textile fabric properties

39

Fatigue or endurance limit

10

102

103

104

105

106

Number of cycles to failure

2.14 Schematic representation of an S-N curve (fatigue life curve).

In addition to fracture mechanics based on the strain energy release rate, the S-N curve is another classical approach to interpret the experimental fatigue studies of composites. The fatigue life data can be conveniently presented as plots of applied stress (stress amplitude, stress range) vs. the number of cycles to failure (N), usually on a log-log scale. A schematic representation of a fatigue life curve (Woehler curve) is shown in Fig. 2.14. These plots show that the life steadily increases with decreasing stress until the horizontal asymptote is reached that defines the ‘fatigue or endurance limit’ below which the life becomes infinitely long, that is, failure does not occur on any realistic time scale. However, to define the asymptote may require lengthy experiments with increased scatter of the individual data points. Consequently, it is more appropriate to use the concept of ‘fatigue strength’, that is, the stress level at which the material will live a specified number of cycles. Stress (or strain) cyclic lifetime curves have been used for a great number of years in the study of fatigue in metals and in rigid matrix composites, and continue to be an important engineering design tool.

2.12.2 Importance of geometrical parameters Our previous statements have indicated the critical importance that geometrical parameters, such as ply stacking sequence and angles, play in the mechanical behavior of the composite structure. To emphasize this point, let us provide an example that has historical importance. Figure 2.15 shows the load-elongation behavior of two laminates with different stiffness values. The laminate which is less stiff (more compliant) has the construction we have already discussed, viz., a +/− angle-ply geometry, while the stiffer laminate has the same +/− angle-ply layout but under it lies another ply reinforced with cords lying transverse to the direction of the applied load. X-ray

40

Structure and mechanics of textile fibre assemblies Stiffness increase due to body ply cords Triangulated 90°/+q/–q laminate Pantographing

Load

+q/–q laminate

Elongation

2.15 Typical load-elongation behavior of two laminates with different stiffness values.

photographs reveal different deformation patterns for these two constructions. The less stiff laminate shows a pantographic network of criss-crossing cords which mechanically respond as deformable rhomboids, while the stiffer laminate shows a cord network made up of relatively undeforming triangles. This stiffness increase is well known to civil engineers and is called ‘triangulation’, and it was recognized in the patent filed by the Michelin Tire Company on June 4, 1946, in Paris, France, under the signature of Pierre Marcel Bourdon [25]. The reader should remember that the +/−θ angle-ply laminate represents the belt of the radial tire, while the laminate with the cords lying transverse to the direction of the applied load simulates the body ply of the tire. In a passenger tire, the former is reinforced with steel cords and the latter with polymer cords, most often, polyester. The increased stiffness resulting from triangulation provides increased rigidity to the tread and hence better treadwear, improved stability of the tire on the road and lower rolling resistance. The belt structure as defined above, that is, belt plus body plies must be characterized by its in-plane bending (flexural) rigidity and its in-plane shear stiffness (Iosipescu test method), the most important parameters controlling the cornering characteristics of the tire. The out-of-plane bending rigidity (stiffness) must also be measured since it controls the ride characteristics of the radial tire. Measurements under biaxial loading are often required. An article published in the November 2004 issue of High performance Composites provides another interesting example of the use of a geometrical parameter to obtain a specific mechanical response from a laminate structure [26]. The author states that when a laminate of the usual ‘balanced or mirrored’ construction is submitted to an axial bending force, the lami-

Characterization and measurement of textile fabric properties

41

nate will respond uniformly along its axis. On the other hand, when the laminate with an ‘unbalanced’ construction is subjected to the same axial bending force, it will shift some of the force to the off-axis direction, and the laminate will twist around its axis. This study was funded by Sandia National Laboratories, Albuquerque, NM, USA, and it was conducted by a team of companies that specialize in structural design and materials. The objective was to develop what they call an ‘adaptive wind blade’ to be used in wind turbines. As wind speed goes up (wind gust), the bending force on the blade increases, but the blade twists along its longitudinal axis thereby reducing the bending load and avoiding damage to the turbine system. ‘Adaptive blades’ are also called ‘twist coupled blades’. The blades are made of an epoxy matrix reinforced by a special carbon/glass hybrid fabric. The article emphasizes that design and materials were selected based on an extensive use of finite element analysis; therefore a prototype must be built and tested to confirm the theoretical predictions. An additional example of the importance of the ply stacking sequence in the area of elastomer matrix composites is illustrated in the patent literature, for example, US Patent No. 4,688,615, August 25, 1987 and US Patent 6,668,889, December 30, 2003, both to The Goodyear Tire and Rubber Company. In the preceding paragraphs we have discussed the elementary mechanics of the shear-deformable angle-ply laminates that function as the belt package of a radial tire. We have also covered the dynamic testing of this structure and its failure mechanism involving edge cracking and delamination. In the earlier patent mentioned above, the author states that the belt edge delamination is not altered by the constraint of the body ply. In other words, a cord-rubber composite specimen which simulates belt plies bonded to a body ply, that is a cord angle sequence of (90/+23/−23) degrees may still be prone to edge delamination between the belt plies. It was found experimentally that with this construction there is a considerable mismatch of Poisson’s ratios between the belt ply and body ply resulting in a decrease in fatigue strength. A new construction is proposed that consists in positioning a third ply between the original belt plies and, of course, bonded thereto. This third ply includes a plurality of parallel cords which form a zero degree angle with respect to the midcircumferential centerplane of the tire (also known as the ‘equatorial’ plane). The ply stacking sequence of this new construction is therefore, as a typical example, 90/+23/0/−23 °, but it is not limited to a belt angle of 23 °. This sequence of plies has been found to reduce strain gradients near the edges of the laminate and it also enables adjacent plies to have closer values of Poisson’s ratio. In addition, the positioning of a zero degree middle belt between the two adjacent but oppositely angled belts of the belt structure also strengthens the interply region between the belt plies. The overall result is a substantial improvement in

42

Structure and mechanics of textile fibre assemblies

fatigue life. The major drawback of this construction is that in many tire designs it did not produce a tire of the desired uniformity. In this patent the zero degree middle ply was made of a plurality of continuous parallel cords that were more extensible and of lower tensile strength than the cords in the conventional angled belts. In the more recent patent (Dec. 2003), the zero degree middle ply was constructed with discontinuous parallel cords resulting in the production of a uniform tire in most tire designs, with improved durability and handling properties versus a commercial control tire. In actual production it is easier to achieve improved belt edge fatigue durability and enhanced high-speed performance by positioning a ‘cap ply’ or ‘overlay’ between the belt and tread of a radial tire. The cap ply contains either continuous or discontinuous cords oriented in a circumferential direction, that is, it falls in the category of a zero degree ply as shown earlier in Fig. 2.9.

2.13 Three-dimensional fibrous assemblies for structural composites A textile structural composite is defined as a composite reinforced by textile structures (preforms) dedicated for load-bearing structural applications. The fiber preforms are produced by textile forming techniques, such as knitting, braiding, weaving and stitching and can be processed using automated techniques such as RTM (resin transfer molding). Of particular interest are the three-dimensional (3D) textile preforms, since by offering some fibers in an out-of-plane orientation, they will provide enhanced stiffness and strength in the thickness direction. This architecture will result in improved damage tolerance to delamination failure mode. In addition, 3D preforms offer the possibility of near-net-shape design and manufacturing of composite components with complex shapes at reduced cost. A study conducted by Ding and Jin at Dong Hua University in Shanghai [27] provides a good example of the importance of the architecture of the fibrous reinforcement in the fatigue behavior of composites. It also demonstrates that through-thickness reinforcement helps avoid abrupt fatigue delamination failure. In this study an 11-layer 3D woven preform was made with continuous fiberglass and an unsaturated polyester as the resin matrix. RTM was employed to inject the resin into the mold and woven composites in plate form were fabricated. Ten rectangular specimens, 70 mm × 15 mm × 2.8 mm were cut from the composite plate with the warp direction parallel to the longitudinal edge of the specimens. The fiber volume fraction of the specimens was approximately 44%. For comparison purposes, ten specimens of a unidirectional (UD) laminate were fabricated using the same fiber/resin system and conditions as the 3D woven test specimens. The fiber volume fraction of the

Characterization and measurement of textile fabric properties

43

UD-laminate was approximately 40%. As it is customary, quasi-static flexural tests were performed prior to fatigue testing in order to obtain information on failure locations and mechanisms. Flexural fatigue testing was conducted on an electro-mechanical universal testing machine using a three-point bending configuration in deflectioncontrol mode. The span was set at 16 times the thickness of the specimens (S/t ratio); the load ratio (R-ratio), that is, the ratio of minimum to maximum load, was set at 0.1, and the testing frequency was 4 Hz. The value of the frequency was selected to minimize hysteresis that would raise the temperature of the sample and decrease its fatigue life. The stiffness loss was monitored continuously by the decrease of the applied load necessary to keep the given deflection constant over the fatigue life of the test specimens. A specimen was considered to have failed when its stiffness had reduced to 70% of its initial value. Static flexural tests were conducted using a three-point bending fixture, the S/t ratio was 16, loading speed was set at 5 mm/min, and ambient temperature 20 °C and 65% relative humidity. Both the 3D woven composite and the UD laminate were tested under the same conditions. The authors in this study present the results in three plots, viz., 1. quasi-static flexural test in the form of stress (MPa) vs. strain% 2. stiffness loss E/Eo vs. N/Nf in the dynamic flexural test. The number of testing cycles has been normalized by the fatigue life, Nf and the stiffness by the initial value of Eo and 3. dD/dN, damage rate vs. N/Nf under flexural fatigue testing. The damage parameter D is defined by this simple relation: D = 1 − E Eo

2.14

where E is the stiffness which is a function of fatigue testing cycles and is calculated according to the values of applied load and resulting deflection of the test sample, and Eo is the initial stiffness of the test sample in the undamaged state, at the start of the fatigue testing. The conclusion from this study is clear, namely, that although microcracks are formed in the initial stage of the flexural fatigue test, the 3D reinforcement resists the propagation of the initial cracks and thereby prevents the onset of global delamination failure. On the other hand in the UD laminates global delamination is clearly observed in the failed specimens.

2.14 Sources of further information and advice Recommendations for further reading on this expanding field of materials science and engineering are contained in the references at the end of this chapter.

44

Structure and mechanics of textile fibre assemblies

2.14.1 List of ASTM test methods covered in this chapter Tensile testing Breaking Force and Elongation of Textile Fabrics (Strip Method), ASTM D 5035-95 (reapproved 2003). Breaking Strength and Elongation of Textile Fabrics (Grab Test), ASTM D 5034-95 (reapproved 2001). Stiffness (bending) testing Stiffness of Fabrics, ASTM D 1388-96 (reapproved 2002). Stiffness of Nonwoven Fabrics Using the Cantilever Test, ASTM D 5732-95 (reapproved 2001). Tearing strength (Same test concepts for nonwoven fabrics) Tearing Strength of Fabrics by the Tongue (Single Rip) Procedure (ConstantRate-of-Extension Tensile Testing Machine), ASTM D 2261-96 (reapproved 2002). Tearing Strength of Fabrics by Trapezoid Procedure, ASTM D 5587-96 (reapproved 2003). Tearing Strength of Fabrics by Falling-Pendulum Type (Elmendorf) Apparatus, ASTM D 1424-96. Test concepts for nonwoven fabrics Tearing Strength on Nonwoven Fabrics by the Tongue (Single Rip) Procedure (Constant-Rate-of-Extension Tensile Testing Machine), ASTM D 5735-95 (reapproved 2001). Tearing Strength of Nonwoven Fabrics by the Trapezoid Procedure, ASTM D 5733-99. Tearing Strength of Nonwoven Fabrics by Falling-Pendulum (Elmendorf Apparatus), ASTM D 5734-95 (reapproved 2001).

2.14.2 Suggested additional reading Adams, D. F., Carlsson, L. A. and Pipes, B. R., Experimental Characterization of Advanced Composite Materials, 3rd edition, CRC Press, Boca Raton, Florida, USA, 2003. Chou, T. W., Microstructural design of fiber composites, Cambridge University Press, 1992. Harrison, P. W., The tearing strength of fabrics, I., A review of the literature, Journal of Textile Institute, 51, T91, 1960.

Characterization and measurement of textile fabric properties

45

Hull, D., An Introduction to Composite Materials, Cambridge University Press, 1992. Ko, F. K. and Du, G. W., Processing of textile preforms, Chapter 5, in Advanced Composites Manufacturing, Gutowski, T. G. (ed.), John Wiley & Sons, NY, 1997. Liao, T. and Adanur, S., 3-D structural simulation of tubular braided fabrics for netshape composites, Textile Research Journal, 70, 297–303, 2000. Suresh, S., Fatigue of Materials, Cambridge University Press, 1991. Van Vuure, A. W., Ko, F. K. and Beevers, C., Net-shape knitting for complex preforms, Textile Research Journal, 73, 1–10, 2003. Weissenbach, G., Issues in the analysis and testing of textile composites with large representative volume elements, Doctoral Thesis, University of Ulster, March, 2003, Dissertation.com, Boca Raton, Florida, USA, 2004. (This discusses pioneering work by Bogdanovich, Pastore and Gowayed). Proceedings of the 30th Textile Research Symposium at Mt. Fuji in the New Millennium (2001), Fuji Educational Training Center, Shizuoka, Japan, July 30–31 and August, 1, 2001. (This contains a wealth of information from lectures delivered by experts in the area of textiles applications in both apparel and in structural composites.) Two magazines • •

High Performance Composites, Ray Publishing Inc. Journal of Advanced Materials, SAMPE (Society for Advancement of Material and Process Engineering)

2.15 Acknowledgements The authors want to thank Yuzo Yamamoto, Xiaosong Huang of Cornell University and Yao-Min Huang of Goodyear Tire and Rubber Co. for their help in the preparation of this chapter.

2.16 References 1. Peirce, F. T., The handle of cloth as a measurable quantity, Journal of the Textile Institute, 21, T377, 1930. 2. Peirce, F. T., The geometry of cloth structure, Journal of the Textile Institute, 28, T45, 1937. 3. Schwartz, P., Prof., Cornell University Notes, TXA 639, Mechanics of Fibrous Assemblies, 1992–1999. 4. Cooper, D. N. E., The stiffness of woven textiles, Journal of the Textile Institute, 51, T317, 1960. 5. Treloar, L. R. G., The effect of test-piece dimensions on the behavior of fabric is shear, Journal of the Textile Institute, 56, T533, 1965. 6. Saville, B. P., Physical Testing of Textiles, Woodhead Publishing Ltd., Cambridge, UK, 2004, pages 270 and 284–288. 7. Hearle, J. W. S., in Structural Mechanics of Fibers, Yarns, and Fabrics, Vol. 1, Chapter 12, Wiley-Interscience, 1969, page 378.

46

Structure and mechanics of textile fibre assemblies

8. Spivak, S. M., The behavior of fabrics in shear, Part I: Instrumental methods and the effect of test conditions, Textile Research Journal, 35, 1056–1063, 1966. 9. Spivak, S. M. and Treloar, L. R. G., The behavior of fabrics in shear, Part II: Heat-set nylon monofil fabrics and a new dynamic method for the measurement of fabric loss properties in shear, Textile Research Journal, 36, 1038–1049, 1967. 10. Spivak, S. M. and Treloar, L. R. G., The behavior of fabrics in shear, Part III: The relation between bias extension and simple shear, Textile Research Journal, 37, 963–971, 1968. 11. Leaf, G. A. V., Analytical woven fabrics mechanics, Invited lecture, Proceedings of the 30th Textile Research Symposium at Mount Fuji, in The New Millennium, 25–34, 2001. 12. Leaf, G. A. V. and Sheta, A. M. F., The initial shear modulus of plain woven fabrics, Journal of the Textile Institute, 75, 157–163, 1984. 13. Leaf, G. A. V., Chen, Y., and Chen, X., The initial bending behavior of plainwoven fabrics, Journal of the Textile Institute, 84, 419–427, 1993. 14. Chen, X. and Leaf, G. A. V., Engineering design of woven fabrics for specific properties, Textile Research Journal, 70, 437–442, 2000. 15. Scelzo, W. A., Backer, S. and Boyce, M. C., Mechanistic role of yarn and fabric structure in determining tear resistance of woven cloth Part I: Understanding tongue tear, Textile Research Journal, 64, 291–304, 1994. 16. Reed, P. E., Impact performance of polymers, in Developments in Polymer Fracture – 1, Andrews, E. H. (ed.) Chapter 4, Applied Science Publishers Ltc., England, 1979. 17. Kawabata, S, Niwa, M. and Yamashita, Y., Recent developments in the evaluations in the technology of fibers and textiles: Toward the engineered design of textile performance, Journal of Applied Polymer Science, 83, 687–702, 2002. 18. Hu, J., Structure and Mechanics of Woven Fabrics, Woodhead Publishing Ltd., Cambridge, UK, 2004. 19. Matsudaira, M and Qin, H., Features and mechanical parameters of a fabric’s compressional property, Journal of the Textile Institute, 86, 476–486, 1995. 20. Daniel, I. M. and Ishai, O., Engineering Mechanics of Composite Materials, Chapter 8, Oxford University Press, 1994. 21. Causa, A. G., Borowczak, M. and Huang, Y. M., Some observations on the testing methodology of cord-rubber composites: A review, in Progress in Rubber and Plastics Technology, Heath, R. J. (ed.), Vol. 15 (4), RAPRA Technology, Ltd., 1999. 22. Causa, A. G., Perspectives on testing methodology for fibers and fiber-reinforced rubber-matrix composites, Goodyear Corporate Research Division, Akron, OH, USA, Lecture delivered at the Fiber Society Fall Symposium, Ithaca, NY, October 11, 2004. 23. Breindenbach, R. F. and Lake, G. J., Rubber Chemistry Technology, 52, 96, 1979. 24. Causa, A. G., Keefe, R. L., Failure of rubber-fiber interfaces, in Fractography of Rubbery Materials, Bhowmick, A. K. and De, S. K. (eds), Chapter 7, 247–276, Elsevier Applied Science, London, 1991.

Characterization and measurement of textile fabric properties

47

25. Walter, J. D., The Firestone Tire and Rubber Co., The role of cord reinforcement in radial tires, lecture delivered at the Akron Rubber Group Meeting, October 27, 1988. 26. Mason, K. F., Composite anisotropy lowers wind-energy costs, High Performance Composites, 12, 44–46, 2004. 27. Ding, X. and Jin, H., Flexural performance of 3-D woven composites, Journal of Advanced Materials, 35, 25–28, 2003.

3 Structure and mechanics of woven fabrics J. HU and B. XIN, The Hong Kong Polytechnic University, Hong Kong

Abstract: This chapter discusses and reviews the fundamental science and technology behind fabric structure and mechanics. The chapter introduces the extent of knowledge regarding fabric deformations, such as tensile, bending and shearing, and a new kind of testing method based on image analysis to characterize fabric mechanical behavior. A general review of computer simulation techniques for woven fabrics and garments is also presented. Key words: tensile, bending, shearing, drape deformation, image analysis, computer simulation.

3.1

Introduction

Woven fabrics are produced by interlacing two sets of yarns perpendicularly to each other. The study and understanding of the structure and mechanics of woven fabrics is useful for fabric design, simulation and manufacturing. In this chapter, some of the fundamental science and technology behind fabric structure and mechanics will be introduced. The simple modes of mechanical behavior, such as tensile, bending, shearing and compression behaviors, and the complex deformation of woven fabrics will be discussed.

3.2

Background

Woven fabrics differ considerably from conventional engineering materials because they are easily deformed and stretched, heterogeneous, highly anisotropic, nonlinear and plastic even at low stress and room temperature. They possess unique characteristics, being especially suitable for accommodating movement, and permitting complicated weaving patterns that satisfy the aesthetic requirements of the wearer. The study of woven fabric mechanics dates from very early work reported by Haas in the German aerodynamic literature in 1912, at a time of worldwide interest in the development of airships. A 1937 paper by Peirce presented geometrical and mathematical mechanical models of the plain-weave structure, both of which have be used extensively and modified by researchers around the world. The main advances were included in two classic text48

Structure and mechanics of woven fabrics

49

books (Hearle et al., 1969; 1980), edited by the leading researchers Hearle, Grosberg, Backer, Thwaites, Amirbayat, Postle, and Lloyd. New developments in woven fabric mechanics can be found in a recent book (Hu, 2004) published by Woodhead Publishing Limited. Since the 1980s, the focus for research has been empirical investigations examining the relationship between the parameters obtained from the Kawabata Evaluation System (KES) (Kawabata, 1980b; Kawabata et al., 1982; Postle et al., 1983; Barker et al., 1985, 1986, 1987) and characteristics such as fabric handling and tailorability. The KES system provides five modes of tests under low-stress conditions, 17 parameters with 29 values for warp and weft, and five charts consisting of nine curves for a single fabric. This large amount of data is designed to provide a full description of the mechanical behavior of a fabric, and is useful across a wide range of research and applications. Other instruments, such as FAST, developed by the CSIRO Division of Wool Technology (Australia), scanning electron microscopy and FabricEye® have also been developed to measure the mechanical properties and appearances of fabrics. With the new developments in testing equipment and theoretical modeling of woven fabrics, textile scientists characterize the structure and mechanics of woven fabrics based on three types of model: predictive, descriptive or fitting. The predictive models, as developed by Grosberg, Hearle and Postle, predict the mechanical responses of a fabric by combining the properties of the yarn(s), inter-yarn interactions, and fabric structures, making some assumptions. The theoretical basis involves Newton’s third law, minimum energy principles and mathematical deduction of construction, and starts from physical concepts and assumptions which facilitate further deductions. Descriptive models consist of different combinations of components, such as the spring, which represents the elastic part, and the dashpot, which represents the friction element, and these are used to simulate combined responses of fabrics to applied forces. This permits the general relationships of stressstrain to be deduced. Fitting models are based on a hypothesis (a function or a statement that describes experimental results), with researchers identifying the relationship of this function to the fabric components and then subjecting it to further analysis. The theoretical background of this approach is more concerned with pure mathematics, in particular numerical methods and statistics. The ultimate aim of all these research strands is to make it possible to create virtual fabric designs, simulate the final products using a computer, and automate textile industry processes.

3.3

Structural properties of woven fabrics

The geometry of a woven fabric has a considerable effect on its mechanical behavior. Real fabrics are not regular structures capable of description in

50

Structure and mechanics of textile fibre assemblies b1 1 2

h2

b2

l1 1 2

q1

h1

p2 (a) a

f R

b

(b)

3.1 Hearle’s lenticular section geometry of plain-weave fabrics.

mathematical forms based on geometry, but it is possible to idealize their general characteristics using simple geometrical forms and physical parameters in order to arrive at mathematical deductions. Three basic geometrical models of woven fabrics have been put forward by Peirce (1937), Kemp (1958) and Hearle (Hearle and Shanahan, 1978). Peirce’s model was based on the assumption that linear and circular or elliptical yarn segments produced the desired shape; Kemp’s model has a racetrack section to modify the cross-sectional shape, so that it is much more suitable for jammed structures. Hearle’s model, as shown in Fig. 3.1, incorporated the assumptions of lenticular geometry, making it the most general model mathematically. The detailed equations governing these models and equations for deriving others can be found in Hu (2004). The models consist of two parts, the cross-sectional shape model of the yarn, and the yarn tracing or crimp model. Table 3.1 lists the basic descriptions of these models and their differences. From the research into geometric theories introduced above, four parameters can be extracted to characterize fabric geometry: yarn diameter, thickness, cover factor and crimp. The general description of each parameter is easily obtained once the cross-sectional shape and tracing style is defined based on two-dimensional geometry. Some do not require calculation but can simply be measured. In reality, woven fabric should be considered as a three-dimensional (3-D) yarn network with a certain thickness. The crosssectional shape of the yarn segment is highly dependent on fiber structure

Structure and mechanics of woven fabrics

51

Table 3.1 The comparison of three geometrical models Model type

Cross-section shape

Yarn tracing or crimp style

Features

Peirce’s model

Circular or elliptic

Valid for open fabrics

Kemp’s model

Racetrack

Hearle’s model

Lenticular

Incompressible, flexible and uniform curvature, including linear and circular or elliptic yarn segments Incompressible, flexible and uniform curvature, including linear and racetrack sections Incompressible, flexible and uniform curvature, including linear and lenticular sections

Valid for jammed fabrics Compressive treatment of flatted threads

and spinning methods. Accurately characterizing the structure of woven fabric, however, requires further investigation using advanced computer graphics and suitable modeling methods. Fabric appearance results from many small details, but these are integrated into the image seen by the human eye or recorded by a digital camera. In general, two types of related parameters should be considered in the modeling of fabric appearances, one relating to the structure of the fabric, such as yarn thickness, yarn density, yarn crimp angle and weave or knit pattern, and the other relating to the luster and color of the fabric, for example, surface reflectance ratio, color of a single yarn or the color arrangement in the weave diagram. In this section, we investigate how to establish a geometric model of a woven fabric, and characterize its surface roughness based on 3-D geometry. Modeling of fabric construction has been studied for many years. We have identified three useful studies of fabric structure above; however, our aim is to determine a mathematical method which can be used to characterize fabric appearance at yarn scale, so it has obvious differences to earlier research on the relationship between a fabric’s geometric structure and its final mechanical behavior. It is challenging to build a reasonable and simple geometric model to characterize fabric structure in a mathematical way. Our approach is to base the modeling on a set of reasonable assumptions, and to simplify the controlled parameters as much as possible. It is easy to understand that even the simplest theoretical model of yarn configuration developed by Peirce still involves transcendental functions. In this case, a simple and reasonable geometric model would not only reduce the calculation cost of validation,

52

Structure and mechanics of textile fibre assemblies

but also determine the essential relationship between these parameters and fabric properties.

3.3.1 Theoretical development Assumptions A mathematical model that permits the characterization of fabric structure and surface profile is to be developed. For simplification, here we investigate only a model for woven fabrics with basic weave patterns. This model is based on the following assumptions: 1. The yarn is circular in cross-section; no thickness variance exists along the yarn length as illustrated in Fig. 3.2. 2. The yarn is monofilament, without twist. 3. The yarn can be bent into any crimp shape without changing its crosssectional shape. 4. The surface of the yarn is smooth. 5. The crimp of the yarn is an ideal cosine or sine function as illustrated in Fig. 3.3. 6. Both warp and weft are perpendicular to each other and evenly distributed, without any distortion. Yarn modeling An ideal yarn model is used, assuming regular circular cross-sectional shape without variance along the central axis line, and that the yarn is flexible enough to be crimped into any style without cross-sectional compression. Assuming the grid origin of a 3-D coordinate system XYZ is located at the

(a) Plain weave

(b) Twill weave

3.2 Yarn cross-sectional models.

(a) Straight yarn

(b) Crimped yarn in front view

3.3 Yarn crimp models.

(c) Crimped yarn in side view

Structure and mechanics of woven fabrics z

53

z

y x

x (a) Straight yarn

y (b) Crimped yarn

3.4 Surface profile of yarn.

middle center of a straight yarn segment with a certain length L and diameter d as shown in Fig. 3.4(a), then the surface profile function of this yarn segment could be described as: x 2 + z2 = d 2 , − L 2 ≤ y ≤ L 2

3.1

Assuming the central line of one crimped yarn segment is represented as a sine or cosine function; the crimp height of yarn is H, which is the vertical distance between the top surface and bottom surface of this yarn. The grid origin of the 3-D coordinate system is located at the starting point of the yarn central line; the projective length of one yarn crimped repeat is L as shown in Fig. 3.4(b). The surface profile function of this crimped yarn segment could be described as: x2 + ⎛ z − ⎝

2 ( H − d) ⎛ y ⋅ 1 − 2 cos ⎛ ⎞ ⎞ ⎞ = d 2 ⎝ ⎝ L⎠⎠⎠ 2

3.2

We assume that the yarn segment can be rotated or translated freely to follow the yarn alignment in woven fabrics. Usually the rotation of an object can be realized through three rotating steps of the coordinate system: rotating the xy axis around the z axis in the xy plane with angle g; rotating the xz axis around the y axis in the xz plane with angle b, rotating the yz axis around the x axis in the yz plane with angle a. The coordinates of yarn surface points before and after rotation can be described by the following equation: 0 ⎡ x′ ⎤ ⎡1 ⎢ y′ ⎥ = ⎢0 cos α ⎢ ⎥ ⎢ ⎢⎣ z′ ⎥⎦ ⎢⎣0 sin α

0 ⎤ ⎡ cos β 0 sin β ⎤ ⎡ cos γ − sin α ⎥ ⎢ 0 1 0 ⎥ ⎢ − sin λ ⎥⎢ ⎥⎢ cos α ⎥⎦ ⎢⎣ − sin β 0 cos β ⎥⎦ ⎢⎣ 0

sin γ cos γ 0

0⎤ ⎡ x⎤ 0⎥ ⎢ y⎥ ⎥⎢ ⎥ 1⎥⎦ ⎢⎣ z ⎥⎦

3.3

The coordinates of the yarn surface points before and after a translation (tx, ty, tz) of yarn segment can be described by:

54

Structure and mechanics of textile fibre assemblies ⎡ x′ ⎤ ⎡1 ⎢ y′ ⎥ ⎢0 ⎢ ⎥=⎢ ⎢ z′ ⎥ ⎢ 0 ⎢ 1 ⎥ ⎢0 ⎣ ⎦ ⎣

0 1 0 0

0 tx ⎤ ⎡ x ⎤ 0 ty ⎥ ⎢ y⎥ ⎥⎢ ⎥ 1 tz ⎥ ⎢ z ⎥ 0 1 ⎥⎦ ⎢⎣ 1 ⎥⎦

3.4

In most cases of an ideal fabric model, there are only two kinds of yarn alignment: perpendicular and parallel. The alignment of two warp or weft yarns is parallel, and the alignment of warp and weft yarns is perpendicular. So once a global 3-D coordinate system with original point and coordinate direction is pre-defined, the translation is used to characterize the parallel alignment and the rotation is used to characterize the perpendicular alignment. Modeling woven fabric A plain model of woven fabric is investigated assuming ideal crimp yarn configuration: the diameter of warp and weft yarns is dp and dt respectively, and the distance between two neighbouring warp and weft yarns is tp and tt respectively. Warps and wefts are interlaced following a certain weaving configuration as illustrated in Fig. 3.5; this configuration can be described z Wp1

Wp2

Wp3

Wp4 x

W t1 Wt 2 Wt 3 Wt 4

y (a) Plain model z

Wt1 and Wt 3 Wt 2 and Wt 4

(b) Tracing profile of yarns

3.5 Yarn interlacing and tracing style.

Structure and mechanics of woven fabrics

55

Table 3.2 Yarn tracing profile Yarn no.

Tracing profile

Phase shifting

Weft

Wt1 Wt2 Wt2 Wt4 Wp1 Wp2 Wp2 Wp4

z z z z z z z z

Warp

= = = = = = = =

sin ((x sin ((x sin ((x sin ((x sin ((y sin ((y sin ((y sin ((y

+ + + + + + + +

x0)/2(dp + tp)) x0)/2(dp + tp)) x0)/2(dp + tp)) x0)/2(dp + tp)) y0)/2(dt + tt)) y0)/2(dt + tt)) y0)/2(dt + tt)) y0)/2(dt + tt))

x0 x0 x0 x0 y0 y0 y0 y0

= = = = = = = =

0 dp + tp 2(dp + tp) 3(dp + tp) 0 dt + tt 2(dt + tt) 3(dt + tt)

using a periodical function, such as sine or cosine. Two neighbouring warp and weft yarns have a certain phase shifting as listed in Table 3.2. The surface profile function at the central line of both warps and wefts can be expressed using the following equations: Wt1:

( (

))

( )

2

dt d ⎛ ⎛ x + x0 ⎞ ⎞ = t , + tt + ⎜ z − sin ⎜ ⎝ ⎝ 2 (d p + t p ) ⎟⎠ ⎟⎠ 2 2 x ∈ (0, 4t p + 4d p ), y ∈( tt , tt + dt )

y−

2

2

3.5

Wt2: y−

( (

))

y−

( (

))

( (

))

2

( )

3dt d ⎛ ⎛ x + x0 ⎞ ⎞ + 2tt + ⎜ z − sin ⎜ = t , ⎟ ⎟ ⎝ ⎝ 2 (d p + t p ) ⎠ ⎠ 2 2 x ∈ (0, 4t p + 4d p ), y ∈( 2tt + dt , 2tt + 2dt ) 2

2

3.6

Wt3: 2

( )

5dt d ⎛ ⎛ x + x0 ⎞ ⎞ = t , + 3tt + ⎜ z − sin ⎜ ⎝ ⎝ 2 (d p + t p ) ⎟⎠ ⎟⎠ 2 2 x ∈ (0, 4t p + 4d p ), y ∈( 3tt + 2dt , 3tt + 3dt ) 2

2

3.7

Wt4: 2

( )

d 7dt ⎛ ⎛ x + x0 ⎞ ⎞ = t , + 4tt + ⎜ z − sin ⎜ ⎟ ⎟ ⎝ ⎝ 2 (d p + t p ) ⎠ ⎠ 2 2 x ∈ (0, 4t p + 4d p ), y ∈( 4tt + 3dt , 4tt + 4dt )

y−

2

2

3.8

Wp1: 2

2

2

⎛ x − ⎛ d p + t ⎞ ⎞ + ⎛ z − sin ⎛ y + y0 ⎞ ⎞ = ⎛ d p ⎞ , p ⎜⎝ ⎟⎟ ⎝ ⎝ 2 ⎠ ⎠ ⎜⎝ ⎝ 2⎠ 2 ( dt + tt ) ⎠ ⎠ y ∈( 0, 4tt + 4dt ), x ∈ (t p, t p + d p )

3.9

56

Structure and mechanics of textile fibre assemblies

Wp2: 2

2

2

⎛ x − ⎛ 3d p + 2t ⎞ ⎞ + ⎛ z − sin ⎛ y + y0 ⎞ ⎞ = ⎛ d p ⎞ , p ⎟⎟ ⎜⎝ ⎝ 2⎠ ⎝ ⎝ 2 ⎠ ⎠ ⎜⎝ 2 ( dt + tt ) ⎠ ⎠ y ∈( 0, 4tt + 4dt ), x ∈ ( 2t p + d p, 2t p + 2d p )

3.10

Wp3: 2

2

2

⎛ y − ⎛ 5d p + 3t ⎞ ⎞ + ⎛ z − sin ⎛ y + y0 ⎞ ⎞ = ⎛ d p ⎞ , p ⎟⎟ ⎜⎝ ⎝ 2⎠ ⎝ ⎝ 2 ⎠ ⎠ ⎜⎝ 2 ( dt + tt ) ⎠ ⎠ y ∈( 0, 4tt + 4dt ), x ∈(3t p + 2d p, 3t p + 3d p )

3.11

Wp4: 2

2

2

⎛ y − ⎛ 7d p + 4t ⎞ ⎞ + ⎛ z − sin ⎛ y + y0 ⎞ ⎞ = ⎛ d p ⎞ , p ⎟⎟ ⎜⎝ ⎝ 2⎠ ⎝ ⎝ 2 ⎠ ⎠ ⎜⎝ 2 ( dt + tt ) ⎠ ⎠ y ∈( 0, 4tt + 4dt ), x ∈ ( 4t p + 3d p, 4t p + 4d p )

3.12

Other regions between the warps and wefts are all considered as flat surfaces with z = 0; the surface profile of the overlapping parts of warp and wefts is maximum 1. Thus, the whole surface profile can be calculated easily using the previous functions. In these profile models, both the thickness and the density of yarn are variables which can be adjusted depending on the desired application.

3.4

Tensile properties of woven fabrics

Tensile properties are one of the most important properties governing fabric performance during use. Studying tensile properties is very difficult due to the bulkiness of fabric structures and strain variation during deformation. Each piece of fabric consists of a large quantity of fibers and yarns, and hence any slight deformation of the fabric will lead to a chain of complex movements among these constituent fibers and yarns. The situation is made more complicated because both fibers and yarns behave in a non-Hookean way during deformation and show hysteresis over time (Konopasek, 1970). Figure 3.6 illustrates a typical tensile stress-strain curve for a woven fabric derived using the KES-F apparatus. For this curve, the initial region has a low slope due to decrimping and crimp-interchange. After that, the slope rises steeply until reaching its summit, which assumedly stems from fiber extensions induced by the applied forces. The magnitude of the stress-strain curve is governed by the level of yarn crimp and the relative ease of distortion of the yarn. If the fabric undergoes a cyclical loading process, it is first stretched from zero stress to a maximum (loading) and then the stress is fully released (unloading). A residual strain, eo, will be observed since textile materials

Structure and mechanics of woven fabrics

57

Strain ε

Stress δ

3.6 Tensile stress–strain curves. Stress, (gf/cm)

em

Strain, (%)

e0

3.7 Loading and unloading cycle in the tensile stress–strain curve.

are viscoelastic in nature. Due to the existence of residual strain, the recovery curve will never return to the original, as shown in Fig. 3.7. This is the hysteresis effect, which denotes the energy lost during the loading and unloading cycle. The hysteresis effect means that a deformed fabric cannot resume its original geometrical state. In Fig. 3.7, the shift to the right shown by the unloading curve depicts the magnitude of the hysteresis effect and indicates the amount of permanent set resulting from the loading history.

3.4.1 Modeling tensile stress-strain of woven fabrics Usually the tensile curve can be depicted by an exponential function with two parameters:

58

Structure and mechanics of textile fibre assemblies f =

eαε − 1 + er β

3.13

Where f is stress and e strain, a and b are unknown parameters, and er the error term. Both the SPSS nonlinear regression programme and least squares optimization can be used to fit the tested tensile curve to the proposed model. f and e can be read off tensile stress-strain curves tested on the KES system, while a and b are unknowns to be estimated.

3.4.2 Modeling the tensile anisotropy of woven fabrics The tensile behavior of a fabric results from the integration of multidirectional effects. We term the tensile properties of woven fabrics ‘anisotropy’, indicating that there is a great variation in tensile properties in fabrics with changes in direction. The highly anisotropic nature of woven fabrics means that the force needed to stretch fabrics in different directions will vary. Kilby (1963) firstly introduced the use of Young’s Modulus for any direction other than warp and weft as follows: 1 cos4 θ ⎡ 1 2σ pt ⎤ 2 sin 4 θ 2 θ θ = +⎢ − sin cos + Eθ E1 E ⎦⎥ E2 ⎣G

3.14

Where E1, E2 and Eq are the Young’s Moduli for the warp, weft and q directions respectively, G denotes the shear modulus, and spt indicates Poisson’s ratio relating the contraction in the weft direction to the strain in the warp direction. In order to simplify the calculation, the above equation is rearranged into:

or where

1 1 1 ⎤ cos4 θ ⎡ 4 sin 4 θ 2 2 = +⎢ − − θ θ + cos sin Eθ E1 E2 ⎣ E45 E1 E2 ⎥⎦ 4 2 2 4 1 cos θ cos θ sin θ sin θ + + = G′ E2 Eθ E1 1 4 1 1 = − − G′ E45 E1 E2

3.15

Equation 3.15 is very useful for predicting the full form of the polar diagram of modulus against angle, when only the values of the parameters for the warp, weft and q directions are known. The tensile behavior of woven fabric usually has a strong relationship with yarn mechanical properties and weaving structure (interlacing style, yarn crimp and density). Twill and stain woven fabrics usually demonstrate lower tensile work as compared with plain woven fabrics, due to the presence of floats, and a twill woven fabric exhibits larger elongation than plain woven fabrics due to its loose structure, despite its low yarn crimp. Another phenomenon found in woven fabrics is strain-hardening. A direct result of this

Structure and mechanics of woven fabrics

59

s e2

e1 a

d

0

b

c e

e3

e4

e

e3

3.8 Cyclic tensile stress–strain curves of textile materials.

phenomenon is that the shape of the tensile stress-strain curve of a woven fabric is usually steeper in the warp direction than that in the weft direction. This is apparently due to the repeated loading and uploading a woven fabric experiences during manufacturing and processing, as shown in Fig. 3.8.

3.5

Bending properties of woven fabrics

The bending properties of fabrics govern much of their performance, such as hang and drape, and are an essential part of complex fabric deformation analysis. In particular applications, computational models for solving largedeflexion elastic problems from theoretical models have been applied to fabric engineering and apparel industry problems, for example, predicting the robotic path for controlling the laying of fabric onto a work surface (Clapp and Peng, 1991; Brown et al., 1990). The most detailed analyses of the bending behavior of plain-weave fabrics were given by Abbott et al. (1973), de Jong and Postle (1977) and Ghosh et al. (1990a, b, c). Modeling the bending of a woven fabric requires knowledge of the relationship between fabric bending rigidity, the structural features of the fabric, and the tensile/bending properties of the constituent yarns, measured empirically or determined through the properties of constituent fibers and the yarn structure. A large number of parameters are required and it is very difficult to express bending properties in a closed form. Thus this kind of model has very limited applicability. Fabrics are very easy to bend. Their rigidity is usually less than 1/10,000 that of metal materials and about 1/100 that of tensile deformation. The bending properties of a fabric are determined by yarn-bending behavior, the weave of the fabric and the finishing treatments applied. Yarn-bending behavior,

60

Structure and mechanics of textile fibre assemblies

Bending moment

B

A

0

Curvature

3.9 Typical bending curve of woven fabrics.

in turn, is determined by the mechanical properties of the constituent fibers and the structure of the yarn. The relationships among them are highly complex. Figure 3.9 illustrates a typical bending curve for a woven fabric. For this curve, it is normally thought that there is a two-stage behavior with a hysteresis loop under low-stress deformation. Firstly, there is an initial, higher stiffness nonlinear region, OA. Within this region, the curve shows that the effective stiffness of the fabric decreases with increasing curvature from the zero-motion position, as more and more of the constituent fibers are set in motion at the contact points. Secondly, there is a close-to-linear region, AB. When all the contact points are set in motion, the stiffness of the fabric seems to be close to constant. It should be noted that when a woven fabric is bent in the direction of the warp or the weft, the curvature imposed on the individual fibers in the fabric is almost the same as the curvature imposed on the fabric as a whole. As high curvatures meet when fabrics are wrinkled, the coercive couple or hysteresis is affected by viscoelastic decay of stress in the fiber during the bending cycle (Postle et al., 1988). However, in applications where the fabric is subjected to low-curvature bending, such as in drapes, the frictional component dominates the hysteresis. Thus, if the strain in the individual fibers is sufficiently small, then the viscoelastic deformation within the fibers can be neglected. The hysteresis in Fig. 3.5 is attributed to non-recoverable work done in overcoming the frictional forces. The effect of the fibers’ viscoelasticity in this section will not be considered because the bending of fabrics on the KES tester is within the low-stress region.

3.5.1 Modeling the bending behavior of woven fabrics Bending behavior of a woven fabric can be characterized by bending rigidity (B) and bending hysteresis (2HB). Bending rigidity is the resistance of

Structure and mechanics of woven fabrics

61

a fabric to bending, which can be defined as the first derivative of the moment-curvature curve. Bending hysteresis is the energy loss within a bending cycle when a fabric is deformed and allowed to recover, denoting the difference in bending moment between the loading and the unloading curves when the bending curvature is fixed. Modeling the bending (moment-curvature) curve of woven fabrics started with the work of Peirce (1930). The bending rigidity B can be defined simply as B = wc3, where w is the weight of the fabric in grams per square cm and c is the bending length. Numerical modeling can also be based on Oloffson’s model (Oloffson, 1967), and the ‘generalized linear viscoelastic’ model proposed by Chapman. Oloffson’s model does not account for fiber viscoelastic processes which occur during fabric deformation and recovery. Chapman’s model can characterize the rheology of viscoelastic material, and the frictional couple associated with each fiber in bending is principally considered as a function of strain and absolute time (Chapman, 1974b; Grey and Leaf, 1975; Ly, 1985). Postle et al. (1988) and Hu (1994) have proved the strong relationship between bending rigidity and bending hysteresis. In particular, Postle et al. (1988) reported a very good correlation between bending and hysteresis parameters measured from fabric bending deformation recovery curves. Hu (1994) demonstrated that the correlation coefficients of bending stiffness and bending hysteresis are quite high, for instance 0.9333 for cotton fabric. For worsted and Shengosen woven fabrics, B and 2HB are also very high, at 0.7872 and 0.7596 respectively. This implies that bending stiffness and bending hysteresis are not independent, but have a linear relationship.

3.5.2 Anisotropy of woven fabric bending properties Peirce (1937) produced a formula for calculating the bending rigidity of a fabric in any direction in terms of the bending rigidity in the warp and weft directions. This was derived from the theory for homogeneous elastic material and it was found to be empirically satisfactory. This formula enabled the value for any direction to be obtained when the values in the warp and weft directions were known. 2 2 ⎡ cos θ sin θ ⎤ Bθ = ⎢ + B2 ⎥⎦ ⎣ B1

−2

3.16

where B1, B2 and Bθ are bending rigidities in warp, weft and q directions, respectively. A similar equation was considered empirically by Shinohara et al. (1980). Bθ = ( B1 cos2 θ + B2 sin 2 θ )

2

3.17

62

Structure and mechanics of textile fibre assemblies

Go et al. (1958) and Go and Shinohara (1962) also reported an equation which was derived theoretically by neglecting twist and frictional effects from Equation 3.17. Bθ = B1 cos4 θ + B2 sin 4 θ

3.18

Later, Cooper (1960) presented an equation including twist effects. The results of the twisting effect were found to be of value experimentally, and therefore Equation 3.19 was derived: Bθ = B1 cos4 θ + B2 sin 4 θ + ( J1 + J 2 ) cos2 θ sin 2 θ

3.19

where J1 and J2 are constants due to torsional moment. Chapman and Hearle (1972) also derived a similar equation by energy analysis of helical yarns as follows: BT = n1θ + η cos2 θ + n2 v2 cos2 θ ( B cos2 θ + J ) BT = n1v1 sin 2 θ ( B sin 2 θ + J y cos2 θ ) + n2 v2 cos2 θ ( B cos2 θ + J y sin 2 θ )

3.20

where BT is an expression for the bending rigidity per unit width of a thin fiber web of linearly elastic fibers and there are n1 yarns per unit length in the warp direction, each containing v1 fibers, and n2 yarns per unit length in the weft direction, each containing v2 fibers. They are assumed to comprise a two-dimensional assembly of very long straight fibers of the same type, with bending rigidity B and torsional rigidity Jy. This approach utilizes energy considerations instead of ‘force method’. Chapman and Hearles’ model involves many variables which complicate the mathematical calculations, and their approach is in fact very similar to Cooper’s, so Cooper’s model is chosen for the study.

3.6

Shear properties of woven fabrics

The shear mechanism is one of several important properties that influence the draping, pliability, and handling qualities of woven fabrics (Kawabata, 1980a; Oloffson, 1967; Lloyd et al., 1978). Shear deformation of woven fabrics also affects the bending and tensile properties of woven fabrics in directions other those of the warp and weft (Chapman, 1980; Skelton, 1976). Up to now, a general stress-strain curve for shear has been considered to have the characteristics illustrated in Fig. 3.10. If a fabric is deformed at low levels of strain, as in the OA region, the shear stiffness is initially large, and decreases with increasing strain. In this region, the shear behavior is dominated by friction mechanisms and the generally accepted model concept is that the decreasing incremental stiffness is attributed to the sequential movement of frictional elements. As soon as the stress is large enough to overcome the smallest of the frictional restraints that are acting at the intersection

Structure and mechanics of woven fabrics

63

Shear force D C

B

A 0

Shear angle

3.10 Stress–strain curve of woven fabric during shear deformation.

regions, the system starts to slip, and the incremental stiffness falls, this is the AB region. At a particular amplitude of stress, the incremental stiffness reaches a minimum level, point B, and remains almost linear over a range of amplitudes, with slopes that are thought to be controlled by the deformation of the so-called ‘elastic elements’ in the fabric. It is commonly observed that, above a relatively low level of shear strain (5 °–10 °), shear stiffness increases with increasing strain. At amplitudes greater than a certain amount C, the incremental stiffness again begins to rise, and the closed curves increase in width with increasing amplitudes of shear angle. It seems that this is due to steric hindrance between the two bent intersecting yarns, leading to transverse distortion of the yarns, or riding up of the intersection, or both.

3.6.1 Modeling the shearing behavior of woven fabrics Several authors have attempted to predict shear properties using structural analysis methods, but the conclusions reached differ in some respects, and the calculations are not presented in a form that can be readily put to practical use (Mark and Taylor, 1956; Morner and Ege-Olofsson, 1957; Postle et al., 1976; Skelton, 1976; Cusick, 1961; Behre, 1961; Lo and Hu, 2002). It is recognized that the detailed mechanisms which are operating are extremely complex and it is difficult to devise a convincing model that explains the behavior adequately. However, some authors consider shear behavior, especially in the initial region, to be controlled simultaneously by both elastic and frictional elements. The general behavior of an array of elastic and frictional components has been studied by Oloffson (1967), Skelton (1976), and Skelton and Schoppee (1976). Some of the existing literature suggests that the stressstrain behavior of a series of assemblies similar to frictional-elastic units can

64

Structure and mechanics of textile fibre assemblies

be reasonably represented in the initial, nonlinear region of shear by an expression of the form:

σ = Kε 1 2

3.21

where σ and ε are the shear stress and strain respectively. This is the simplified Olofsson formula, which is the same as the bending deformation.

3.6.2 Modeling the anisotropy of shear properties Classical elasticity theory was developed by Kilby (1963) based on the assumption that a fabric is an anisotropy lamina possessing Poisson’s effect and with two planes of symmetry at right-angles to one another. According to elasticity theory (Hu, 1994), the behavior of tensile and shear properties derived from the theoretical transformation of various compliances in the principal and bias directions can be used to yield the following equations: 1 cos4 θ ⎛ 1 2υ12 ⎞ sin 4 θ cos2 θ sin 2 θ + = +⎜ − ⎟ ⎝ G E1 ⎠ EX′ E1 E2

3.22

1 sin 4 θ ⎛ 1 2υ12 ⎞ cos4 θ cos2 θ sin 2 θ + = +⎜ − ⎟ ⎝ G E1 ⎠ EY′ E1 E2

3.23

1 1 1 2υ12 ⎞ 1 2 2 2 2 2 = 4 ⎛⎜ + + ⎟⎠ cos θ sin θ + ( cos θ − sin θ ) ⎝ GXY E1 E2 E1 G ′

3.24

where E′X, E′Y and G′XY denote the tensile modulus in the X′ and Y′ axes and shear rigidity between both principal directions respectively, with an angle q. The shear rigidity in the X′ and Y′ axes can be obtained directly from experimental tensile moduli, while u12 cannot. The theoretical treatment suggests that measurements of moduli in two directions are insufficient to define a fabric’s shear rigidity, since variation with direction is still possible for fabrics with similar E1 and E2. An investigation of the third direction is therefore necessary, and the most convenient direction is that at 45°. 1 1 2υ12 ⎞ + + Thus, the sum ⎛ may be deduced from measurements ⎝ E1 E2 E1 ⎠ in three directions by considering specimens cut along the warp, weft and 45° directions. Therefore, when considering q = 45° values, Equation 3.26 gives: 1 1 1 2υ12 ⎞ ⎛ 1 ⎞ ⎛ 1 ⎞ = 4 ⎛⎜ + + ⎟ ⎝ E1 E2 G45 E1 ⎠ ⎝ 2 ⎠ ⎝ 2 ⎠ 2

2υ12 1 1 1 = − − E1 G45 E1 E2

2

3.25 3.26

Structure and mechanics of woven fabrics

65

Substituting Equation 3.26 into 3.25, we get: 1 ⎛ 4 ⎞ 1 2 2 2 2 2 =⎜ ⎟ cos θ sin θ + ( cos θ − sin θ ) Gθ ⎝ G45 ⎠ G

3.27

Fabric shear rigidity in various directions can therefore be predicted from Equation 3.27 when its value in the warp and ±45° directions are measured. As shear rigidity provides a measure of the resistance to rotational movements between the warp and weft yarns at the intersecting points when the fabric is subjected to a small shear deformation, its relationship in both principal directions should be determined. A strong linear relationship is obtained in two principal directions by Mahar et al. (1989; 1990), and thus the measurement of fabric shear properties can be simplified and is necessary in only one principal direction. Equation 3.24 demonstrates that the shear rigidity in either the warp or weft direction with that of ±45° gives a very satisfactory result for various directions. However, if the values of shear rigidity for the warp and weft directions show large differences, the average value should be taken in both principal directions in order to calculate shear rigidity in various directions given by Equation 3.24. Shear hysteresis of a fabric can be defined as the energy loss within the shear cycle when the fabric is deformed and allowed to recover to its original position. Since a strong linear relationship between shear rigidity (G) and shear hysteresis (2HG and 2HG5) has been proved by several researchers (Collier, 1991; Jeong and Phillips, 1998; Hu, 1994), the proposed G-predicting model in different directions can be applied to shear hysteresis (2HG and 2HG5).

3.7

Characterizing the mechanical behavior of woven fabrics based on image analysis

Theoretical models of the mechanical behavior of fabrics must usually rely on a reasonable understanding of fabric properties. One direct way to investigate these properties is through experiments and observation. In previous sections, the basic theories and modeling methods for structure and mechanics have been introduced. Assumptions and predictions may simplify the complex mechanisms behind the behaviour of woven fabrics, however, the reliability of the theories should be validated through accurate and objective testing and measurement. The deformation response of woven fabric under a certain load is typically described using a stress-strain curve and polar diagram in all directions. The measurement of strain and stress using the KES or FAST system is one-dimensional and in one direction; although a polar diagram could be

66

Structure and mechanics of textile fibre assemblies

drawn to describe variations in other directions. Strictly speaking, the nature of the deformation of textiles is three-dimensional, especially for large deformation of garments, thus the strain and stress fields for textiles under a group of forces should also be three-dimensional. How to record and characterize these three-dimensional fields accurately and objectively has always been the target of testing instruments for textile materials. However, the differences between macro-scale measurement and microscale theoretical models raise some difficulties for modeling and validation. With the development of digital techniques, image analysis has become popular for both experimental measurements and industry quality control, due to the wide availability of low-cost and easy-to-use hardware and software for acquiring, recording and processing digital images. It is feasible to apply image analysis to determine the two-dimensional or three-dimensional local deformation of materials. The advantage of this technology is that it integrates a series of measurements in all directions into one measurement, rather than having to cut the sample into many strips. This nondestructive method helps to solve the problem of sample damage, where the mechanical behavior of the whole sample is not equal to the sum of the behavior of the many strips it has to be cut into for more traditional forms of measurement. In the last decade, some researchers have proposed successful non-contact optical measurements based on image correlation techniques (Peters and Ranson, 1981; Sutton et al., 1986; Zhang et al., 1999). These have been applied to measuring displacements and strains. The technique utilizes two similarly spotted images, captured by a solid state video camera, which represent the states of the object before and after deformation. Using the concept of image correlation, the displacement of each spot is determined. The computer vision-aided technique has the advantages of being simple, and permitting direct image sensing of 2-D/3-D surface deformations during stretching, bending or other, related deformation. Thus full 2-D/3-D field strain distributions of the sample surface can be determined, rather than the traditional one-dimensional strain curve recording. However, few papers have been found describing the characterization of fabric mechanical properties based on image methods. More research focused on this topic and introducing new testing techniques and concepts is needed to facilitate investigating the essential mechanism of textile materials. This section describes a testing method based on image analysis techniques used to evaluate the tensile behavior of fabrics. A digital imaging system is set up to record the image sequences of test specimens under tension, linked to a set of image analysis algorithms to calculate the strain distribution field in different directions.

Structure and mechanics of woven fabrics

67

3.7.1 Methodology System set-up Figure 3.11 illustrates a typical setup for a two-dimensional image capturing system. A digital camera (Nikon D70) is mounted on the stage of KES-FB1 (tensile measurement), and the optical axis of the camera lens is approximately perpendicular to the surface of the test specimen. The specimen is assumed to be deformed in the plane of the object’s surface, out-of-plane motion is small enough to be neglected. The digital camera acquires individual digital image sequences of the object’s surface dynamically at a certain shutter speed during the stretching process. The initial image is referred to as the ‘un-deformed image’ and each of the following images is termed a ‘deformed image’. Sample preparation A white, or light-colored, test specimen is cut into a 20 cm × 20 cm square, and 9 × 3 circular dark spots are printed on the fabric as reference points, as shown in Fig. 3.12. The diameter of each spot is 6 mm and the distance between the centers of two spots is 15 mm. Selecting a dark color and a white background gives a good contrast, and using reference points printed on the specimen is an effective way of simplifying the image analysis algorithm. Other pattern styles (such as natural textures) can also be used as reference points for experimental measurements, however, the texturematching algorithms are relatively complex. Here, we introduce the simplest image correlation technique, using dark spots on a white background.

4 3

1 2 3 4 5

KES-FB1 Specimen Digital camera Stage Computer

5 2 1

3.11 Schematic of image capturing system for in-plane tensile measurement.

68

Structure and mechanics of textile fibre assemblies

Stress direction

20 cm

15 mm

A

15 mm

B

Testing area

C 1

2 3 4 5

6 7 8

9

20 cm

3.12 Reference points printed on the specimen surface.

0 ms

5 ms

10 ms

15 ms

20 ms

25 ms

3.13 Image series captured during tension.

Deformation measurement using image analysis The specimen is mounted flat on the stage of the KES-FB1 using two chucks, and image digitization of the specimen’s surface is triggered by starting KES-FB1. Image digitization A sequence of images is recorded over the period of stretching, and then the images are analyzed to calculate the displacement of the reference points (spot centers) and the shape transformation of the spots in each frame. The visual 2-D movement of the specimen surface can be determined using these images, as illustrated in Fig. 3.13. Since the two chucks and some incomplete spots appear in the images, they must be erased by cropping the sub-image of the effective testing region, as illustrated in Fig. 3.14. Boundary detection of elliptical spots A Laplacian-Gaussian edge detection algorithm is used to identify the boundaries of dark, elliptical spots. The image pixels of elliptical spots have

Structure and mechanics of woven fabrics

69

(a) Original image

(b) Binary image (f(x, y)>t0)

(c) Boundary image g(x, y)

(d) Boundary image of ellipse disks only

3.14 Images of boundary detection.

70

Structure and mechanics of textile fibre assemblies

lower gray values compared to the white background, so a global threshold t0 can be determined to distinguish the reference points from the background based on a histogram. Let f(x,y) denote the image of the x 2 + y2 1 ⎛ x 2 + y 2 ⎞ − 2σ 2 fabric surface, and LoG ( x, y, σ ) = be a Laplacian⎜1− ⎟ ⋅e 2σ 2 ⎠ πσ 4 ⎝ Gaussian filter, where s is the spread of the Gaussian filter and controls the degree of smoothing. The boundary enhanced image of f(x,y) with LoG(x,y,s) can be expressed by the equation g(x,y) = f(x,y) ° LoG(x,y,s), where ° indicates the convolution of two functions. Parameter estimation of elliptical spots Both circular and elliptical spots can be represented parametrically in the Cartesian coordinate system by a five-parameter ellipse cell (x0,y0,a,b,q), where (x0,y0) is the center, q is the tilt of ellipse, a and b are the major and minor axes respectively. Let P(x,y) be the boundary point of an elliptical spot, then it meets the following equation: ( x cos θ + y sin θ − x0 )2 (− x sin θ + y cos θ − y0 )2 + =1 a2 b2

3.28

The five parameters of each ellipse spot printed on the specimen surface can be estimated using an ellipse identification method (Ballard, 1981). To simplify the ellipse detection algorithm, the center of ellipse (x0,y0) could n

∑ xi

, y0 = i =1 where n n (xi,yi) are boundary points. The major axis a and minor axis b can be determined by the maximum and minimum length of segment series passing through (x0,y0); q is equal to the angle (in degrees) between the x-axis and the minor axis of the ellipse. The eccentricity of ellipse is calculated using b2 e = 1 − 2 , which describes the shape deformation of the spots. a initially be estimated using the mass center: x0 =

i =1

n

∑ yi

Displacements and shape deformation measurement Assuming (x0i,y0i,ai,bi,qi) are the parameters of a spot on the specimen surface before deformation, and (x′0i,y′0i,a′i,b′i,q′i) is the ith image of the same spot during deformation, then the displacement of its center along the x axis can be calculated by ui = (x0i′ − x0i) · Sx, and the displacement of its center along the y axis is vi = (y0i′ − y0i) · Sy, where Sx, Sy is the resolution (mm/pixel) of the digital camera along the x and y axes respectively, as illustrated in Fig. 3.15. The shape deformation is then expressed by

Structure and mechanics of woven fabrics

71

x ui

f(x,y) e0=1

vi gi(xi’,yi’)

y

e’=1.2

(b)

(a)

3.15 Displacements and shape deformation measurement.

Table 3.3 Fabric basic properties Fabric ID

Thickness (mm)

Weight (g/m2)

P

0.68

4.68

T

0.86

8.07

R

0.72

5.10

Direction

Warp Weft Warp Weft Warp Weft

Tensile LT

WT

RT

EMT

0.803 0.877 0.765 0.601 0.800 0.929

2.70 3.14 3.43 2.70 3.92 3.82

54.55 50.00 37.14 52.73 41.25 44.87

5.48 5.84 7.32 7.32 6.8 6.72

ei ′ × 100% . The anisotropy of fabric tensile behavior might be ei determined by comparing displacement and deformation in different directions.

η=

3.7.2 Experiments and results Three types of fabric, white/plain/cotton/(P), green/twill/cotton/(T), and white/plain/ramie/(R), were tested using this method. All the samples were cut into 20 cm × 20 cm squares, and the mechanical properties of the samples were tested using KES, as listed in Table 3.3. Figure 3.16 illustrates the relationship between strain and stress during tension. Since the strain is determined by the one-dimensional displacement of the sliding base holding the testing sample, the two-dimensional local displacement of sample surface points is impossible to calculate and analyze using this method. Anisotropy of fabric tensile properties can also not be characterized based on this one-dimensional testing method.

72

Structure and mechanics of textile fibre assemblies 600 Sample P

Sample T

Sample R

Strain (N/m)

500 400 300 200 100 0 0

2

4

6

8

10

Strain (%)

3.16 Stress–strain curves of three samples.

Displacement in x direction (pixels)

0 –5 –10 –15 –20 –25 Point A Point B Point C

–30 –35

0

5

10

15

20 25 30 Frame number

35

40

45

50

3.17 Displacement along stress direction (pixels).

The stress-strain curves show that the three samples have very similar tensile behaviors. Sample P was chosen to illustrate the measurement of 2-D displacement and Poisson’s ratio. Figure 3.17 depicts the real-time displacements of three reference points A, B, and C, during tension along the direction of stress. It was observed that the slopes of their displacement curves were not equivalent, the slope of A was smaller than B, and the slope of B smaller than C. It was shown that the displacement of surface points increases with the distance between the surface points and the gripping points. The relationship between the displacement ui of surface points and distance di from gripping points could be determined by: ui = e · di + D, where

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4 1

Displacement in y direction (pixels)

3

2

2

3

1

4

0

5

–1

6

–2

7

–3

8

–4

9

–5 –6 0

5

10

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20 25 30 Frame number

35

40

45

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3.18 Displacement in vertical direction (pixels).

Poisson’s ratio

Point A Point B Point C 1.1

1.05

1 0

5

10

15

20 25 30 Frame number

35

40

45

50

3.19 Poisson’s ratio along stress direction.

e¯ is average strain (%) at a certain stress and D is a constant. The average strain (%) under maximum load is calculated as illustrated in Fig. 3.18: e¯ = 5.38%, this value is very close to ek = 5.48% as measured using KES. Thus strain measurement based on image analysis is as reliable and accurate as the traditional testing method. The real-time displacements of nine surface points vertical to the direction of stress were measured during tension, as illustrated in Fig. 3.19. It was

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Structure and mechanics of textile fibre assemblies

9 1 8 2 7 3 6 4 5

Poisson’s ratio

1.1

1.05

1 0

5

10

15

20 25 30 Frame number

35

40

45

50

3.20 Poisson’s ratio in vertical direction.

found that the displacement field of these points showed the anisotropy of the materials being tested. Point 5, located on the central line along the stress direction, shows almost no vertical deformation. However, other points located away from the central line show clear, large vertical displacements. The vertical displacements of symmetrical points such as point 1 and 9 are almost the same. Figure 3.20 illustrates the Poisson’s ratio of three surface points located along the stress direction at different distances from the gripping points. It was found that the Poisson’s ratio at point A was bigger than at points B and C. The Poisson’s ratio is not distributed uniformly, so might be a function depending on position. The same comparisons were made among nine surface points located symmetrically on the side of the central line in the direction of stress, as illustrated in Fig. 3.21. It was found that the Poisson’s ratio was also related to its distance from the central line. According to these observations, the surface deformation model could be estimated based on the experimental results, and the traditional theoretical mechanical models of textile materials validated much more conveniently.

3.7.3 Other applications: bending, shearing and draping Measuring the deformation of strain fields using image analysis could easily be extended to other aspects of the mechanical behavior of fabrics. Bending deformation and draping are three-dimensional, and shearing is two-dimensional, as shown in Fig. 3.22. Using image analysis methods to measure surface deformation is based on the movement of reference points on the fabric’s surface. Use of three-dimensional imaging based on stereo vision

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Displacement along stress direction (pixels)

35 30 25 20 15 10 y = 0.0538x – 8.489 5 0 250

350 450 550 Distance from gripping point (pixels)

650

3.21 Strain calculation.

3.22 Other applications of deformation measurement.

can be found in Xin and Hu (2005). The basic principle is that two digital cameras digitize separately the position of one reference point, and an accurate three-dimensional position in real world coordinates can be calculated based on previously calibrated camera geometry. Although the strain field can be measured using image analysis, measuring the stress field is still based on traditional instruments, with sensors for stresses such as stretching force and bending moment. One advantage of imaging technology is that it permits real-time measurements, so we can record and trace the movement of surface points at any time, and this could be helpful for calculating stress fields. Much more research is needed, including into the possible integration of deformation and force measurements in one instrument.

3.8

Modeling drape deformation of woven fabrics and garments

Computer simulation of the mechanical behavior of woven fabrics based on physical, numerical models is the ultimate aim of this research area. Over

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the last two decades, both computer technology and theoretical modeling have made great advances. These advances have made it possible to model complex fabric deformations, such as fabric draping, using computer simulation techniques. There have been many successes and considerable progress in this area (e.g., Hu and Teng, 1996; Ng and Grimsdale, 1996). Most early works (Weil, 1986; Dhande et al., 1993) in the area are geometrically based, with an emphasis on reproducing the cloth-like appearance of a fabric sheet on a computer. These models cannot simulate fabric behavior physically since no mechanical properties are included. Many other workers, however, have adopted various physically based models (Hu and Teng, 1996). Feynman (1986) proposed an energy-based physical model for simulating the appearance of cloth. The simulations included hanging cloth and cloth draped over a sphere. The total energy function of the model incorporates tensile strain, bending strain and gravity terms, but shear deformations are not considered. Terzopoulos et al. (1987) introduced an elastically deformable model for generalized flexible objects including fabrics. Since the model was developed for general use in computer graphics, it is not capable of directly incorporating standard engineering parameters such as Young’s modulus. The solution procedure for the equations arising from the model is also computationally intensive. Many other works (e.g., Thalmann and Yang, 1991; Thalmann and Thalmann, 1991; Carignan et al., 1992) using and extending Terzopoulos et al.’s deformable model have been reported. These works focused on the computer visualization and animation of garments. Breen et al. (1991; 1992; 1994; Breen, 1993) developed a particle-based model to simulate the draping behavior of woven cloth. In this model, the cloth is treated as a collection of particles that conceptually represent the crossing points of warp and weft threads in a plain-woven fabric. Separate empirical energy functions were proposed for yarn repelling, stretching, bending and trellising deformations. These functions were tuned empirically using KES (Kawabata, 1975) test data in their later works (Breen et al., 1992; Breen, 1993). The final position of the draped fabric was determined based on the minimization of total potential energy, which is the sum of the deformation energy terms mentioned above and the potential energy of the self weight. While the model was conceptually based on the microstructure of cloth, continuum-based macrostructure properties were used in the simulation. The particle grid of 51 × 51 used for a 1 m × 1 m cloth in the numerical examples is also far from that necessary for a microstructural or threadlevel model. In addition, the solution procedure employed a stochastic searching process and was reported to be very time-consuming. Recently Eberhardt et al. (1996) extended Breen’s particle-based model by using a different, faster technique to compute the exact particle trajectories. Some promising simulations, including cloth draped over a square table, a circular table and a sphere, were presented.

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Stylios et al. (1995; 1996) presented a physically based approach using the deformable node-bar model (Schnobrich and Pecknold, 1973) to predict complex deformations of fabrics. In their approach, the fabric sheet is assumed to be a continuum shell with homogeneous, orthotropic and linearly elastic properties. Their drape simulation was compared with results from a fabric drape testing system. The modeling of a skirt attached to a virtual female form was also described. Several other researchers employed the finite element method for the simulation of fabric draping behavior. Lloyd (1980) was probably the first to apply the finite element method to model fabrics and dealt only with inplane deformations. Collier et al. (1991) developed a large deflection/small strain analysis employing a four-node orthotropic flat shell element to predict the drape coefficient of cotton fabrics. Their results were reported to be in reasonably good agreement with experimental results. Gan et al. (1995) produced a similar analysis employing a curved shell element and presented simulation results for fabric sheets draped over square and circular pedestals. Kim (1991) described drape simulations using a geometrically exact shell theory proposed by Simo et al. (1989; 1990). Simo and Fox (1989), Deng (1994) and Eischen et al. (1996) extended the work of Kim to buckling, contact, and materially nonlinear problems. Chen and Govindaraj (1995) predicted the draping of fabrics using a shear flexible shell theory. The predicted results of a square fabric sheet draped over a flat square surface and an animation sequence were presented. Yu et al. (1993) and Kang and Yu (1995) also developed a non-linear finite-element code to simulate the draping of woven fabrics. In their study, a flat shell element model based on a convected coordinate system (Simo and Fox, 1989; Simo et al., 1989, 1990; Bathe, 1982) was used. The fabric was again assumed to be an elastic and orthotropic material. The predicted draped shapes were shown to agree reasonably well with those obtained experimentally. Ascough et al. (1996) adopted a rather simple beam element model in their cloth drape simulations, and the simulation results for a piece of fabric draped over a table corner do not appear to be close in shape to that seen in a corresponding photo. They also presented simulation results of the falling of a skirt from its initial position into contact with a human body. Their simulations were carried out as a dynamic analysis using Newmark’s method. Hu and Chung (1998) adopted the finite volume method for simulating the complex deformations of fabrics. In this method, an initially flat fabric is first subdivided into a finite number of structured small patches of finite volume (or control volumes). One control volume contains one grid node. The deformations of a typical volume can be defined using the global coordinates of its grid node and several neighbouring grid nodes surrounding it. The strains and curvatures and hence the in-plane membrane and out-

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of-plane bending strain energies of the whole fabric sheet are then calculated very easily over all control volumes, which retain their original surface areas and thicknesses. The equilibrium equations of the fabric sheet are derived employing the principle of stationary total potential energy. Geometric non-linearity and linear elastic orthotropic material properties of the fabric are considered in the formulation. This leads to a simple but rigorous way of formulating the equilibrium equations of a grossly deformed fabric sheet. As reviewed above, two main methods are used in existing approaches towards modeling fabric drape deformations: (a) the finite element or volume approach employing a shell element or a finite volume; and (b) a more empirical approach developed specifically for fabric deformation analysis, among which the particle-based model of Breen et al. (1991; 1992; 1994; Breen, 1993) is representative and the most widely quoted. The studies of Stylios et al. (1995; 1996) and Ascough et al. (1996) do not fall neatly into either of the above two approaches, but both are closely related to the first approach. The finite element approach employing a shell element has been used by a number of researchers. It has a rigorous mechanical basis and can be easily understood and further developed by the computational mechanics community. As the method was not developed using the special characteristics of fabric drape deformations, it has a number of disadvantages. First, it entails a high computational cost as high-order shape functions are used and very large displacements have to be followed in a step-by-step manner. Second, when the popular degenerated shell elements are used, the bending stiffness and the membrane stiffness of the shell surface will be coupled, and this subsequently leads to a difficulty in modeling fabric sheets due to their independent membrane and bending stiffness. Third, the method is theoretically complex, making it less easily accepted and understood by its users. On the other hand, the widely cited particle-based model of Breen and its extension (Breen et al., 1991; 1992; 1994; Breen, 1993; Eberhardt et al., 1996) contains much empiricism in the establishment of the energy functions and uses definitions of deformations that do not follow a rigorous mechanics approach. The computational cost may also be very high.

3.9

Conclusions

In this chapter, some fundamental theories for fabric structure and mechanics have been introduced, together with a review of recent research. The extent of knowledge regarding fabric deformations, such as tensile, bending and shearing, has been discussed, and a new kind of testing method based on image analysis to characterize fabric mechanical behavior described. A

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general review of computer simulation techniques for woven fabrics and garments was also presented.

3.10 References and further reading Abbott G M, Grosberg P and Leaf, G A V (1973), ‘The elastic resistance to bending of plain-woven fabrics’, J Text Inst, 64, 346–362. Ascough J, Bez H E and Bricis A M (1996), ‘A simple finite element model for cloth drape simulation’, Int J Clothing Sci and Tech, 8(3), 59–74. Ballard, D H (1981), Generalizing the Hough Transform to detect arbitrary shapes, Pattern Recognition, 13(2), 111–122. Barker R (3/1987, 2/1986, 5/1985), Reports to North Carolina State University, Kawabata Consortium, Raleigh, North Carolina 27695-8301, From School of Textiles, North Carolina State University. Bathe K J (1982), Finite element procedures in engineering analysis, New Jersey, Prentice Hall. Behre B (1961), ‘Mechanical properties of textile fabrics part I: shearing’, Textile research journal, 31(2), 87–99. Breen D E (1993), A particle-based model for simulating the draping behavior of woven cloth, NY, Doctoral dissertation, Rensselaer Polytechnic Inst. Breen D E, House D H and Getto P H (1991), A particle-based computational model of cloth draping Behavior, Scientific Visualization of Physical Phenomena (Proc. CG Inter.), Tokyo, N M Patrikalakis (ed.), 113–134. Breen D E, House D H and Getto P H (1992), ‘A particle-based particle model of woven cloth’, The visual computer, 8(5–6), 264–277. Breen D E, House D H and Wozny M J (1994), ‘A particle-based model for simulating the draping behavior of woven cloth’, Textile research journal, 64(11), 663–685. Brown P R, Buchanan D R and Clapp T G (1990), ‘Large deflection bending of woven fabric for automated material handling’, J Text Inst, 81, p1. Carignan M, Yang Y, Thalmann N M and Thalmann D (1992), ‘Dressing animated synthetic actors with complex deformable clothes’, Computer graphics (Proc. siggraph), 26(2), 99–104. Chapman B M (1974a), ‘Determination of the rheological parameters of fabric in bending’, Text Res J, 45, 137–144. Chapman B M (1974b), ‘Linear superposition of viscoelastic responses in nonequilibrium system’, J App Polym Sci, 18, 3523–3526. Chapman B M (1980), ‘Viscoelastic, frictional and structural effects in fabric wrinkling’, in Mechanics of Flexible Fibre Assembles (NATO Advanced Study Institute Series No. 38), Hearle J W S, Thwaites J J and Amirbayat J (eds), Alpen ann den Rijn, Sijhoff and Noordhoff. Chapman B M and Hearle J W S (1972),‘The bending and creasing of multicomponent visco-elastic fiber assemblies part I: general consideration of the problem’, J Tex Inst, 63, 385–403. Chen B and Govindaraj M (1995), ‘A physical based model of fabric drape using flexible shell theory’, Textile research journal, 65(6), 324–330. Clapp T G and Peng H (1991), J Text Inst, 82, 341. Collier B J (1991), ‘Measurement of fabric drape and its relation to fabric mechanical properties and subjective evaluation’, Clothing & Text Research J, 10(1), 46–52.

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Collier J R, Collier B J, O’toole G and Sargand S M (1991), Drape prediction by means of finite-element analysis, Journal of the Textile Institute, 82(1), 96–107. Cooper D N E (1960), ‘The stiffness of woven textiles’, J Tex Inst, 51, T317–335. Cusick G E (1961), ‘The resistance of fabrics to shearing forces’, J Text Inst, 52(9), T395–406. De Jong S and Postle R (1977), ‘An energy anlysis of woven-fabric mechanics by means of optical-control theory part II: pure-bending properties’, J Text Inst, 68, 62–369. Deng S (1994), Nonlinear fabric mechanics including material nonlinearity, contact, and an adaptive global solution algorithm, North Carolina State univ, Raleigh, NC, Doctoral dissertation. Dhande S G, Rao P V M and Moore C L (1993), ‘Geometric modeling of draped fabric surfaces’, Graphics, design and visualization (Proc Int Conf on computer graphics), S P Mudur and S N Pattanaik (eds), Jaico Publishing House, Bombay, 173–180. Eberhardt B, Weber A and Strasser W (1996), ‘A fast, flexible particle-system model for cloth draping’, IEEE computer graphics and applications, 16(5), 51–59. Eischen J W, Deng S and Clapp T G (1996), ‘Finite-element modeling and control of flexible fabric parts’, IEEE computer graphics and applications, 16(5), 71–80. Feynman C (1986), Modeling the appearance of cloth, Master’s dissertation, Massachusetts inst of technology, Cambridge. Gan L, Ly N G and Steven G P (1995), ‘A study of fabric deformation using nonlinear finite elements’, Textile Research Journal, 65(11), 660–668. Ghosh T K, Batra S K, and Barker R L (1990a), ‘The bending behavior of plainwoven fabrics part I: a critical review’, J Text Inst, 81(3), 245–255. Ghosh T K, Batra S K and Barker R L (1990b), ‘The bending behavior of plainwoven fabrics part II: the case of bilinear thread-bending behavior and the effect of fabric set’, J Text Inst, 81, 255–271. Ghosh T K, Batra S K, and Barker R L (1990c), ‘The bending behavior of plainwoven fabrics part III: the case of linear thread-bending behavior’, J Text Inst, 81, 273–287. Go Y and Shinohara A (1962), ‘Anisotropy of the crease recovery of textile fabrics’, J Tex Mach Soc Japan, 8, 33–38. Go Y, Shinohara A and Matsuhashi F (1957), ‘Viscoelastic studies of textile fabrics part III: on the shearing buckling of textile fabrics’, Sen-i Gakkaishi, 13, 460–165. Go Y, Shinohara A and Matsuhashi F (1958), ‘Viscoelastic studies of textile fabrics part VI: anisotropy of the stiffness of textile fabrics’, J Tex Mach Soc Japan, 14, 170–174. Grey S J and Leaf G A V (1975), ‘The nature of inter-fiber frictional effects in woven-fabric bending’, Text Res J, 45, 137–144. Grey S J and Leaf G A V (1985), ‘The nature of inter-fiber frictional effects in woven-fabric bending’, J Text Inst, 76, 314–322. Hamilton (1964), ‘A general system of woven fabric geometry, J Text Inst, T79. Hearle J W S and Shanahan J W (1978), ‘An energy method for calculations in fabric mechanics, part I: principles of the method’, J Text Inst, 69, 81–89. Hearle J W S, Grosberg P and Backer S (1969), Structural Mechanics of Fibers, Yarns, and Fabrics Vol. 1, New York, Wiley-Interscience.

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Hearle J W S, Thwaites, J J and Amirbayat J (1980), Mechanics of Flexible Fiber Assemblies (NATO Advanced Study Institute Series: E, Applied Sciences No. 38), Alpen aan den Rijn, Sijthoff & Noordhoff. Hoffman R M and Beste L F (1951), ‘Some relations of fiber properties to fabric hand’, Textile Research Journal, 21, 66. Hu J L (1994), Structure and low stress mechanics of woven fabrics, University of Manchester, PhD thesis. Hu J L (2004), Structure and Mechanics of Woven Fabrics, Cambridge, Woodhead Publishing. Hu J L and Chung S P (1998), Investigation of drape behaviour on woven fabrics with seams, Text Res J, 68(12), 913–919. Hu J L and Chen S F (2000), ‘Numerical drape behavior of circular fabric sheets over circular pedestals’, Textile Research Journal, 70(7):593–603, July. Hu J L and Newton A (1993), ‘Modeling of tensile stress-strain curves of woven fabrics’, Journal of China Textile University, 4. Hu J L and Teng J G (1996), ‘Computational fabric mechanics-present status and future trends’, Finite element in analysis and design, 21, 225–237. Jeong Y J and Philips D G (1998), ‘A study of fabric-drape behavior with image analysis part II: the effect of fabric structure and mechanical properties on fabric drape’, J Text Inst, 89(1), 70–79. Kang T J and Yu W R (1995), ‘Drape simulation of woven fabric by using the finiteelement method’, Journal of the Textile Institute, 86(4), 635–648. Kawabata S (1972), Kawabata’s Evaluation System for Fabric (KES-FB) Manual, Kato Tech Co Ltd. Kawabata S (1975), The Standardization and Analysis of Hand Evaluation, Osaka, Japan, Hand Evaluation and Standardization Committee of the Textile Machinery Society of Japan. Kawabata S (1980a), Standardization and Analysis of Hand Evaluation, 2nd edn, The Textile Machinery Society of Japan. Kawabata S (1980b), Examination of Effect of Basic Mechanical Properties of Fabric Hand in Mechanics of Flexible Fiber Assemblies, Hearle, J W S et al. (eds), Alpen aan den Rijn, Sijthoff & Noordhoff, 405. Kawabata S, Niwa M, Ito K and Nitta M (1972), ‘Application of objective measurements to clothing manufacture’, Int J Clothing Sci & Tech, 2(3/4), 8–31. Kawabata S, Postle R and Niwa M (1982), Objective Specification of Fabric Quality, Mechanical Properties and Performance, Osaka, Textile Machinery Society of Japan. Kemp A (1958), ‘An extension of Peirce’s cloth geometry to the treatment of nonlinear threads’, J Text Inst, 49, T44–48. Kilby W F (1963), ‘Planar stress-strain relationships in woven fabrics’, J Text Inst, T9–27. Kim J (1991), Fabric mechanics analysis using large deformation orthotropic shell theory, Doctoral dissertation, Raleigh, N C, North Carolina State Univ. Konopasek M (1970), Improved procedures for calculating the mechanical properties of textile structures, University of Manchester, PhD thesis. Lloyd D W (1980), The Analysis of Complex Fabric Deformations, Mechanics of Flexible Fiber Assemblies, J W S Hearle, J J Thwaites and J Amirbayat (eds), Alpen aan den Rijn, Sijthoff & Noordhoff, 311–342.

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Structure and mechanics of textile fibre assemblies

Lloyd D W, Shanahan W J and Konopasek M (1978), ‘The folding of heavy fabric sheets’, Int J Mech Sci, 20, 521–527. Lo W M and Hu J L (2002), ‘Shear properties of woven fabrics in various directions’, Text Res J, 72(5), 383–390. Ly N G (1985), ‘The role of friction in fabric bending’, in Objective Measurement: Application to Product Design and Process Control, Kawabata S, Postle R and Niwa M (eds), Osaka, Textile Machinery Society of Japan, 481–488. Mahar T J, Dhingre R C and Postle R (1989), ‘Fabric mechanical and physical properties relevant to clothing manufacture part I: fabric overfeed, formability, shear and hygral expansion during tailoring’, Int J Clothing Sci & Tech, 1(1), 12–20. Mahar T J, Dhingra R C and Postle, R (1990), ‘Measuring and interpreting low stress fabric mechanical and surface properties’, Textile Research Journal, 60, 7–17. Mark C and Taylor H M (1956), ‘Fitting of woven cloth to surfaces’, J Text Inst, 47, T477. Morner B and Ege-Olofsson T (1957), ‘Measurement of the shearing properties of fabrics’, Text Res J, 27, 611–614. Newton A and Hu J L (1992), ‘The Geometry of Cloth Structure’, Proceedings of Inaugural Conference of CSSTA (UK), 23. Ng H N and Grimsdale R L (1996), ‘Computer graphics techniques for modeling cloth’, IEEE computer graphics and applications, 16, 28–41. Oloffson B (1967), ‘A study of inelastic deformations of textile fabrics’, J Text Inst, 58, 221–241. Peirce F T (1930), ‘The handle of cloth as a measurable quantity’, J Tex Inst, T377–416. Peirce F T (1937), ‘Geometry of cloth structure’, J Text Inst, 28, T45. Peters W H and Ranson W F (1981), Digital Imaging Techniques in Experimental Stress Analysis, Optical Engineering, 21, 427–432. Postle R, Carnaby G A and de Jong S (1976), ‘Woven fabric shear and bending’, in The Mechanics of Wool Structures, Chichester, Ellis Horwood Ltd, 340–366. Postle R, Kawabata S and Niwa M (1983), Objective Evaluation of Apparel Fabrics, Osaka, Textile Machinery Society of Japan. Postle R, Carnaby G A and de Jong S (1988), ‘Surface of woven fabrics’, in The Mechanics of Wool Structures, Chichester, Ellis Horwood Ltd, 387. Schnobrich W C and Pecknold D A (1973), The Lumped-parameter or Bar-node Model Approach to Thin Shell Analysis, Numerical and Computer Methods in Structural Mechanics, F Perrone and R Schnobrich (eds), London, Academic Press, 337–402. Shinohara A, Shinohara F and Sakaebara K (1980), ‘Theoretical study on anisotropy of bending rigidity of woven fabrics, J Tex Mach Soc Japan, 26, 75–79. Simo J C and Fox D D (1989), ‘On a stress resultant geometrically exact shell model part I: formulation and parameterization’, Comp methods Appl Mech Engrg, 72, 267–304. Simo J C, Fox D D and Rifai M S (1989), ‘On a stress resultant geometrically exact shell model part II: the linear theory; computational aspects’, Comp methods Appl Mech Engrg, 73, 53–92. Simo J C, Fox D D and Rifai M S (1990), ‘On a stress resultant geometrically exact shell model, Part III, Aspects of nonlinear theory’, Comp Methods Appl Mech Engrg, 79, 21–70.

Structure and mechanics of woven fabrics

83

Skelton J S (1976), ‘Fundamentals of fabric shear’, Text Res J, 46, 862–869. Skelton J S and Schoppee M M (1976), ‘Frictional damping in multicomponent assemblies’, Text Res J, 46, 661. Stylios G K, Wan T R and Powell N J (1995), ‘Modeling the dynamic drape of fabrics on synthetic humans, A physical, lumped-parameter model’, Int J clothing Sci and Tech, 7(5), 10–25. Stylios G K, Wan T R and Powell N J (1996), ‘Modeling the dynamic drape of garments on synthetic humans in a virtual fashion show’, Int J clothing Sci and Tech, 8(3), 95–112. Sutton M A, Wolters W J, Peters W H, Ranson W F and McNeil S R (1983), ‘Determination of Displacement Using an Improved Digital Correlation Method’, Computer Vision, 1(3), 133–139. Sutton M A, Cheng M Q, Peters W H, Chao Y J and McNeil S R (1986), ‘Application of an Optimized Digital Correlation Method to Planar Deformation Analysis’, Image and Vision Computing, 4(3), 143–151. Terzopoulos D, Platt J, Barr A and Fleischer K (1987), ‘Elastically deformable models’, Computer graphics, 21(4), 205–214. Thalmann N M and Thalmann D (1991), Cloth Animation with Self-collision Detection, Modeling in Computer Graphics, T L Kunii (ed.), Berlin, SpringerVerlag, 179–187. Thalmann N M and Yang Y (1991), Techniques for Cloth Animation, New Trends in Animation and Visualization, N M Thalmann and D Thalmann (eds), Chichester, John Wiley & Sons, 243–256. Weil J (1986), ‘The synthesis of cloth object’, Computer graphics (Proc Siggraph), 20(4), 49–54. Xin B J and Hu J L (2005), ‘3D Profiling of Cloth Appearances Based on Stereo Vision Method’, Research Journal of Textile and Apparel, Vol. 9, No. 1, 13–20. Yu W R, Kang T J and Lee J K (1993), ‘Drape properties of woven fabrics’, Proc 2nd Asian textile Conf, 1, 455–459. Zhang D, Zhang X and Cheng G (1999), ‘Compression Strain Measurement by Digital Spot Correlation’, Experimental Mechanics, 39(1), 62–65.

4 Structure and mechanics of knitted fabrics M-A. BUENO, Université de Haute Alsace, France

Abstract: This chapter discusses the structure and mechanical behaviour of knitted fabrics. The two different kinds of knitted structures, warp and weft, are described. The link with their structure and their mechanical characteristics is explained in terms of tensile, bending and shear behaviours. In fact, knitted fabrics are probably the fibrous structures which offer the biggest diversity from a mechanical point of view, from 0% to more than 200% elongation. Moreover, it is possible to knit three-dimensional (3D) fabrics directly with almost any type of design, especially with the weft-knitting process. Key words: weft knit, warp knit, shear, tensile, bending.

4.1

Introduction

Knitted fabrics are generally reputed to be much more extensible than woven fabrics. This is a misperception. While some knitted structures are indeed very extensible, others are in fact less extensible than woven fabrics, independent of yarn and fibre characteristics. Knitted fabrics probably offer the greatest diversity among fibrous structures from a mechanical point of view, since the tensile elongation of knitted fabrics can range from 0% (multi-axial warp knitted fabrics) to more than 200% (rib weft knitted fabrics). This diversity has two origins. Firstly, a stitch has a 3D shape, thus during a tensile test, the stitch is deformed in all three planes of space. Secondly, a knitted structure can behave in radically different ways, depending on the role given to the stitches in the structure. From a technological point of view, many different effects exist in warp knitted fabrics, according to whether the yarn webs are inserted in one or several directions in the fabric (in machine and cross directions, for instance). If stitches are used as the foundation of the structure, the fabric can be very extensible. If stitches are used like sewing stitches, then they just keep yarn webs together and the fabric has almost no elongation due to the structure. It is possible to knit 3D fabrics directly with almost any type of design, using both weft and warp knitting processes. The most common 3D knitted products are hosiery and berets, while the most technical include turbine rotors and H-profile beams. 84

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4.2

85

Structural properties of knitted fabrics

Two different families of knitting structures exist, corresponding to warp and weft knitting processes. Often, either process can be used for the same application, since, although they have strong differences, both processes can result in similar properties, particularly for technical textile applications. Figure 4.1 shows weft (a) and warp (b) knitted fabrics. There are some basic structural and mechanical differences between the two: •

•

In weft knits, the structure is built from a unique yarn. For warp knitting, a great number of yarns (from several hundred to more than a thousand yarns per metre width) are necessary. These yarns are organised like a warp. This difference means that a weft knitted fabric can be unravelled, whereas a warp knitted fabric cannot. In weft knitted structures, the stitch is a loop in a 3D space. A yarn in a woven, warp knitted structure forms a 2D wave, i.e., in the plane perpendicular to the fabric surface. In warp knitted structures the stitch is made of a loop (overlap) as well as a float (underlap) and therefore has a small part linking these two laps. Each lap is in a plane parallel to the other, with the loop face being regarded as the front and the float face as the back.

There are a great many varieties of warp and weft knitting structures, resulting from combinations of different effects. Examples of this variety are described below for each knitting family.

(a)

(b)

4.1 (a) Weft knitted structure and (b) warp knitted structure.

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x (coursewise)

4.2 3D-loop shape for weft knitting structure.

4.2.1 Weft knitted structures The elementary entity for weft knitting is the stitch, which has a very specific 3D shape, as shown in Fig. 4.2. Looking at this shape allows us to understand two fundamental properties: • •

The fabric is made with a unique yarn, so weft knitted fabric is the result of an equilibrium of this yarn in an imposed shape. Weft knitted structures are very extensible.

A weft stitch can be separated into three parts: a head, two legs and two feet. The 3D shape of a stitch is linked to the stitches previously processed. The stitching process consists of inserting the head and legs of the new loop inside the head of the previous stitch in the same wale. The last loop in a wale only exists when the yarn is not too elastic and the inter-yarn friction force is sufficient, which implies that a weft knitted fabric represents the equilibrium between a yarn and itself. This equilibrium is very fragile when the inter-yarn friction forces are low and the stress on the fabric is high, such as in hosiery, a break in the yarn is followed by a partial unravelling of the fabric. A stitch has a totally different appearance on either side. Because of its 3D shape, from one side the visible parts are the legs in a V shape, while from the other, the head and feet are visible. When the legs are visible, the stitch is considered to be a face stitch, when they are not, it is a reverse stitch. Many weft knitted fabrics include a combination of face and/or reverse stitches. One of the three parameters that characterise weft knitted fabrics is the kind of knit. Independent of the knitting process, four basic knit structures exist: normal straight stitches, tuck stitches, racked stitches, and held or missed stitches. All knitted fabrics are manufactured using these four basic

Structure and mechanics of knitted fabrics

87

structures [39]. Normal, tuck and racked stitches can make up a fabric independently, while held or missed stitches have to be combined with normal stitches. Figure 4.1 shows a normal straight stitch. Many knitted structures are composed using only this kind of stitch. The difference between these structures is the combination of wale-wise and/or course-wise face and reverse stitches: • • • •

A fabric with only face or reverse stitches is a plain jersey fabric. A combination of face stitch wales and contiguous reverse stitch wales gives rib structures. A combination of face stitch wales in front of reverse stitch wales gives interlock structures. A combination of face stitch and reverse stitch courses only or courses and wales gives purl structures.

Some illustrations of weft-knitted structures are given in Fig. 4.3.

(a)

Feed 4

Feed 4

Feed 3

Feed 3

Feed 2

Feed 2

Feed 1

Feed 1

(b)

(c) (f)

(h)

Feed 2 Feed 4 Feed 1 Feed 3 (d)

(e)

Feed 2

Feed 2

Feed 1

Feed 1 (g)

4.3 Schematic representation of basic weft knitting structures (a) plain-jersey, (b) 1 × 1 rib, (c) 2 × 2 rib, (d) 1 × 1 interlocking rib, (e) half cardigan rib, (f) Swiss piqué, (g) French piqué and (h) Punto-di-Roma.

88

Structure and mechanics of textile fibre assemblies y x x

y z z x

4.4 Projection of a plain-jersey structure in the three space planes; arrows indicate curling directions.

The geometrical differences between these structures results mainly from the direction of the ‘accordion effect’ due to stitch curling properties. In fact, because of its 3D shape, a stitch is not balanced course-wise or wale-wise (see Fig. 4.4). Thus course-wise, plain jersey structures tend to curl to the face side. In wale-wise, the curling effect is visible on the reverse. This effect is greater in wale-wise and less prominent with stabilised fabrics. The curling effect concerns not only plain jersey fabrics, but also rib, interlock and purl structures. Balanced or unbalanced rib fabrics are flat at a macroscopic scale, and each group of similar stitch wales curls in wale-wise. This gives an accordion pleating effect in the wale-wise direction and thus these structures produce thicker fabrics than plain-jersey. For purl structures, the curling effect follows the same mechanism in the wale-wise direction. In the case of balanced interlock structures, the curling effect due to a wale group in the wale-wise direction is balanced by the wale group on the rear plane, and the fabric is therefore flat. From a geometrical point of view, these structures are similar to joined face and reverse plain-jersey structures. Another property of weft knitted fabrics lies in their ability to unravel, and in the fact that stitches can drop from the end to the beginning of the fabric. Moreover, plain-knitted fabrics can be unravelled from the beginning to the end. This is not possible with rib or interlock fabrics, since the face and reverse stitches are mutually blocked. If a wale is adjacent to another wale of the same kind of stitch (face or reverse), this wale can be dropped from the beginning to the end. This can happen for all ribs or interlock structures, except 1 × 1 rib or 1 × 1 interlock. In addition to these structural characteristics for different kinds of knit, there are other parameters which describe a knitting fabric: stitch length and yarn properties.

Structure and mechanics of knitted fabrics

89

Doyle [9] pointed out that the 3D shape of stitches depends essentially on the length of yarn per stitch. One of the characteristics of woven fabrics is the number of weft and warp yarns per unit length; for knitted fabrics the number of courses and wales depending on the fabric state [32]. In order to characterise a weft knitted fabric geometrically, stitch length and fabric state must be studied. Stitch length is almost independent of the fabric state, thus it can be considered as a constant feature of the fabric, contrary to the number of courses and wales per unit length, which changes during use or wear (socks being taken on and off, for instance). In order to characterise weft knitted fabrics from a dimensional or mechanical point of view, Munden [32] suggested considering the fabric in a reproducible state, i.e., relaxed. After deformation, the relaxed fabric almost always returns to the same dimensions, therefore has the same number of courses and wales per unit length. However, if several tensile tests are conducted on a knitted fabric without allowing for relaxation between each test, the force-elongation curves are totally different, and the mechanical behaviour is completely different. As described above, a weft knitted fabric exists due to the equilibrium between inter-yarn friction forces and yarn bending elasticity. Nevertheless, during knitting, finishing processes, or use, the fabric is subjected to wale-wise and/or course-wise tensile stresses. These stresses elongate and flatten out stitches, and thus efficient methods are required to relax the fabric effectively. Relaxation methods result in a wale-wise and/or course-wise retraction of the fabric, aimed at achieving the configuration with the lowest energy. The principle of relaxation is to react against inter-stitch friction generated by stresses. In addition to Munden, Postle [36, 37] and Knapton [27] established different relaxation processes, in dry or wet environments, and with or without external mechanical vibrations. When the relaxation procedure is more powerful, retraction is greater. Retraction is mainly due to the mechanical behaviour of the yarn in terms of bending rigidity in the elastic domain and inter-yarn friction. Retraction is achieved when inter-yarn friction and bending forces are balanced [3]. In order to illustrate this point, two fabrics made using the same knitting process are considered; the first one is manufactured with a flexible yarn, the second one with a more rigid yarn. Yarn bending rigidity is respectively Bf and Br, with Bf < Br. After relaxation, there are two possibilities relative to inter-yarn friction, Ff and Fr. When Fr < Ff, the fabric made using the more flexible yarn maintains its elongation in the wale-wise direction and also keeps its flattened-out shape. For the fabric made of rigid yarn, the result shows a retraction in the wale-wise direction and an extension in the thickness direction. Therefore, after full relaxation, the flexible yarn gives a thinner and smoother fabric than the more rigid yarn.

90

Structure and mechanics of textile fibre assemblies

In addition, the 3D loop shape of a relaxed fabric depends on the tension of the take-down system. When the yarn is more flexible and the inter-yarn friction force higher, the fabric is more sensitive to the take-down tension. When Ff < Fr, retraction after relaxation can be identical for both fabrics, and so both fabrics have the same thickness and roughness. Retraction can also be more or less significant for the fabric made of the flexible yarn. In that case, the differences between the fabrics are less significant than in the previous case and therefore, take-down tension is less influential. This effect explains the differences in geometry between fabrics knitted with different take-down system tensions [27, 28], or between presser-foot or conventional fabrics [6, 18, 21]. The results show that the loop geometry is not the same for both systems. With a take-down system, stitches are stretched during the knitting process. With a presser foot or sinkers, the stitches are pressed, and are not stressed in the wale-wise direction. The less rigid the yarn is, and the greater the inter-yarn friction coefficient, the more sensitive the relaxed fabric is to tensile stress during knitting. Furthermore, the knitting tension value is more influential on the final loop geometry and it is more difficult to obtain the fully relaxed state. Munden’s laws [32] permit the fundamental relationship between fabric geometry and stitch length to be elucidated for plain jersey fabrics. He showed that, for relaxed fabrics, the number of wales W and courses C are inversely proportional to stitch length: C=

Kc L

4.1

W=

Kw L

4.2

where Kc, Kw: constants, C: number of courses per unit length (cm), W: number of wales per unit length (cm), L: stitch length (cm). Kc, Kw have been shown to depend on yarn characteristics, including fibre (material, fineness, cross-section shape), yarn count, and yarn structure due to the knitting process [3, 27, 32, 41]. Another important parameter for the 3D shape of a stitch is fabric tightness. This can be characterised by the cover factor, which is the ratio between the projected area of yarn in the stitch and the projected area of the stitch in the fabric surface plan. In order to express the cover factor, two assumptions are made: the projected length of yarn in a stitch is equal to the real length of yarn and stitches are not interlaced, then

Structure and mechanics of knitted fabrics F=

91

L⋅ d 1 ⋅1 C W

4.3

Hence, with Equations 4.1 and 4.2: F=

d ⋅ Kc ⋅ K w L

4.4

where d: yarn diameter (cm). Yarn diameter can be expressed relative to yarn count square root, and then simple equations emerge: K=

ty L

4.5

d K′ = L where ty: yarn count (tex). F, K or K′ can be compared for the same kind of knit and the same yarn for various stitch lengths. In reality, yarn diameter is very compressive, so it is really dependent on fabric tightness (see Fig. 4.5), therefore effective yarn diameter, i.e., diameter of the yarn in the fully relaxed fabric, can be taken into account. If the fabric is knitted with several yarns in the same area (loop knitted fabrics for instance), the total cover factor is the sum of the cover factors for each yarn. In conclusion, stitch length is essential for loop configuration. Yarn morphology (fabric tightness) is less important, since yarn physical properties

1 mm

1 mm

(a)

(b)

4.5 Plain-jersey fabrics made with the same yarn (a) with a conventional cover factor (K = 15), and (b) with a low cover factor (K = 10).

92

Structure and mechanics of textile fibre assemblies

have a minor influence (both friction and bending) [33]. The kind of knit is fundamental to fabric geometry. As well as for plain jersey structures, relationships have been established between C, W and stitch length for some weft knitted structures. For balanced or unbalanced rib structures, several researchers [22, 28, 35] showed that Munden’s laws can be applied to fully relaxed fabrics. For these structures, stitch length is not the same for all stitches and the number of wales per unit length can be difficult to determine, thus stitch length and W are given as follows: Lu m+ n

4.6

W = nu ⋅ ( m + n)

4.7

L=

where Lu: length of yarn in a complete rib-repeat unit (cm), m: number of face stitch wales in a rib-repeat unit, n: number of reverse stitch wales in a rib-repeat unit, nu: number of rib-repeat units per unit length (rib-repeat unit/cm). Some complex rib structures have been studied, originally by Knapton, including with tuck stitches (half-cardigan rib) and with miss stitches (French and Swiss piqué) (see Fig. 4.3). Munden’s laws can be used for half-cardigan rib [28]. For French and Swiss piqué, Knapton proposed very simple equations where some of the parameters have to be described carefully. Firstly the fabric run-in ratio must be defined: r=

Lr Lj

4.8

where Lj: mean plain stitch length, Lr: mean rib stitch length. Secondly, the cell unit stitch length is defined as: Lu = 2 ⋅ Lj + 6 ⋅ Lc

4.9

Further, the number of wale and course units per centimetre, respectively Wu and Cu, must be measured. Cu is the number of cell units course-wise per centimetre, where a unit needs four machine feeds for both French and Swiss piqué; and Wu is the number of cell units wale-wise, where a unit has four needles (two for each needle bed). Then, for a given run-in ratio [26], relations between Cu, Wu and Lu are similar to Equations 4.1 and 4.2 [25]. For these kinds of structures, the cover factor is defined as:

Structure and mechanics of knitted fabrics K′ =

ty ⋅ ntu Lu

93

4.10

where ntu: number of needles forming loops in the cell unit (eight for both piqué), Lu/nu is the mean stitch length. For balanced interlock structures, the number of courses per unit length is proportional to 1/L; but it seems to be more elaborate for the number of wales per centimetre. Indeed, the relationship between W and 1/L seems to depend strongly on the yarn. This relationship can be proportional for wool [22, 35], or linear for acrylic and cotton [22]. For complex interlock structures, such as Punto di Roma (Fig. 4.3), the case is close to piqué because Munden’s laws can be used for a given run-in ratio, but with the following cell unit stitch length: Lu = 4 ⋅ Lj + 4 ⋅ Lc

4.11

Some values of Kc, Kw are given for different structures in Tables 4.1 and 4.2. For basic structures, fabric thickness can be evaluated qualitatively for a large range of cover factors by using the following assumption: ratio of fabric thickness t and yarn effective diameter depends essentially of the kind of knit [31, 35] (see Table 4.1). Munden’s laws for plain knitted structures and their expansion to other weft knitted structures allow the calculation of the fabric grammage M in a very simple way: M=

K c ⋅ K w ⋅ ty 10 ⋅ L

4.12

For regular interlock structures, if Kc, Kw are given for the number of wales and courses/cm in one face, the value of M obtained using Equation 4.12 has to be doubled. Figure 4.6 shows the approximate evolution of fabric grammage relative to the kind of knit for given yarn count and stitch length.

4.2.2 Warp knitted structures Similarly to weft knitted structures, the basic unit of a warp knitted structure is the stitch. But in the warp knitting process, the stitch is composed of two distinct parts, a loop (overlap) and a float (underlap), with a small part that links these two laps. These two parts are not in the same plane and so they give two layers. Two kinds of stitches exist: open and closed. If the overlap and underlap are in the same direction, the stitch is open; if the

94

Structure and mechanics of textile fibre assemblies

Table 4.1 Range for Kc and Kw for some weft knitted structures after full relaxation. These values are experimental1 or simulated2 and are taken from the literature. Ratio of fabric thickness and yarn diameter t/d values from [35]3. In the literature, the way in order to calculate Kw and Kc is not always the same, some authors consider L in stitches/cm and some others in unit cells/cm, and the number of wales or courses/cm or number of unit wales or courses/cm. Here, the values correspond to the number of wales and courses/cm in one face

Plain jersey 1X1 rib 2X2 rib 3X3 rib 4X4 rib 5X5 rib 1X2 rib 1X3 rib 1X4 rib 1X5 rib 1X6 rib 2X3 rib 2X4 rib 2X5 rib 2X6 rib 3X4 rib 3X5 rib 3X6 rib 1X1 interlock

Kw

Kc

Reference

4.0–4.1 6.1–6.8 7.4–8.2 8.9–11.4 10.9–17.0 34.0 5.4 4.9 4.7 4.5 4.4 7.0 6.4 6.1 5.8 10.3 9.7 9.2 4.2–5.2 (wool)3

5.3–5.7 4.5–5.2 4.8–5.8 4.9–5.8 5.0–5.6 5.0 4.7 4.8 4.9 4.9 4.9 4.9 4.9 4.9 5.0 4.9 5.0 5.0 4.4–5.43

[22, [22, [22, [22, [22, [22, [22, [22, [22, [22, [22, [22, [22, [22, [22, [22, [22, [22, [22,

34]1,2 28, 35]1,2 35]1,2 35]1,2 35]1,2 35]2 35]2 35]2 35]2 35]2 35]2 35]2 35]2 35]2 35]2 35]2 35]2 35]2 30, 35]1,2

t/d 2.6 4.4 6.5 9.4

4.4 4.4 4.4 4.4 7.5 8.4 9.4 10.9 12.4 4.1

Table 4.2 Range for Kc and Kw for some complex knitted structures after full relaxation and for various run-in ratios. These values are experimental and are taken from the literature [26]

French piqué Swiss piqué Punto-di-Roma

Kw

Kc

15.5–16.5 16–17 16–17

23–28 21–23 21–24

overlap and underlap are in opposite directions, the stitch is closed. Closed stitches are most commonly used, but in some cases, open stitches are better from a process point of view. In contrast to weft knitted fabrics, warp knitting has a number of parameters:

Structure and mechanics of knitted fabrics

95

500

Fabric grammage (g/m2)

450 400 350 300 250 200 150 100 50 3×n Rib 2×n structures 1×n

0 0 1 Plain-je rsey Numbe

2 r of rev

3 erse wa

4 les in a

5

6

repeat

4.6 Representation of fabric grammage relative to the kind of knit (plain jersey and 1 × n rib structures) for given yarn count and stitch length.

• • • • •

the the the the the

number of guide bars position of each guide bar on the machine threading diagram for each guide bar knitting movement of each guide bar stitch length, i.e., the run-in, of each guide bar.

Warp knitting technology can offer products with a very great variety of mechanical characteristics, from very extensible structures (for instance nets) to non-elongating structures (multi-axial warp knit fabrics), as well as a great variety of aspects (e.g. lace). Since the purpose of this book is to concentrate on mechanical behaviour, laces and fabrics with tuck stitches (fall-plate or special presser bar fabrics) are not described here. From a basic point of view, since the guide bars are fully threaded, different kinds of structures can be considered. The fabric mechanical properties are a combination of the properties of structures from each guide bar, influenced by their position on the machine (front, middle, back, etc). When guide bars are fully threaded, each bar generally has a basic evolution. There are three families of basic evolutions and for each one, the length of overlap is a needle space. The first family has only one member: pillar or chain stitch (see Fig. 4.7). Usually, this structure is made up of open stitches.

96

Structure and mechanics of textile fibre assemblies

(a)

(d)

(b)

(f)

(g)

(c)

(e)

(h)

4.7 Schematic representation of basic warp knitting structures (a) pillar stitch with open loops, (b) 1-and-1, (c) 2-and-1, (d) 4-and-1, (e) atlas and (f) locknit, (g) reverse locknit and (h) Queen’s cord from the technical back.

With a full threading diagram, this evolution does not give a surface but a succession of chains, therefore it is used in combination with other structures. The second family, which is the n-and-1 reciprocating structure family, consists of a stitch (an overlap of one needle and an underlap of n needle spaces) followed by the same stitch along vertical symmetry (see Fig. 4.7). Increasing underlap length n has some consequences for fabric mor-

Structure and mechanics of knitted fabrics

97

1 and 1

2 and 1

3 and 1

4 and 1

5 and 1

4.8 Schematic representation of technical back of some n and 1 reciprocating structures.

phology. When n changes, the difference between fabrics is only in underlap and overlap can be considered as identical. Figure 4.8 illustrates the reverse sides of some n-and-1 reciprocating structures. As for weft knits, warp knitted fabrics must be characterised in the relaxed state. For synthetic fibres, if the fabric dimensions are fixed for when the fabric is used with a thermal process, then the fabric must be studied in this state. Stitch length can be expressed as the sum of overlap and underlap lengths, hence: L ( n) = Lo + c 2 + n2 ⋅ w 2

4.13

where Lo: overlap length (cm), n: length of underlap (needle space), c: course length (cm), where c = 1/C, w: wale width (cm), where w = 1/W. Therefore, stitch length is almost proportional to n [23]. Most models hold with this expression for underlap length whatever the guide bar position on the machine, but differ in expression of overlap length. For all authors [12, 38, 40], the expression of overlap length is a function of course spacing and yarn diameter, and is influenced by guide bar position. For example, Grosberg’s model proposes: Lo = 2.55c + λd

4.14

where l: constant depending on guide bar position and fabric state (dimensionless); its value is between 2.6 and 7.2.

98

Structure and mechanics of textile fibre assemblies

The definition of the cover factor K due to a guide bar is the same as for weft knit fabrics (see Equation 4.3), the application to warp knitted structures is:

(

) c ⋅tw

K ( n) = Lo + c 2 + n2 w 2 ⋅

y

4.14

Moreover, fabric grammage due to a guide bar can be expressed as follows:

(

) 10 ⋅tc ⋅ w

M ( n) = Lo + c 2 + n2 w 2 ⋅

y

4.15

K and M increase with n. For several guide bars, the cover factors and the grammages from the different bars are summed. Equations 4.14 and 4.15 highlight the relation between cover factor and fabric grammage. For the same yarn, with the same number of wales and courses per centimetre, fabric grammage evolution relative to n is illustrated in Fig. 4.9. The third family of basic warp knitting structures is the atlas family. With this structure, the underlap and overlap directions are the same over a few courses and after direction reverses (see Fig. 4.7). For fully threaded warp knitted fabrics, the longer the underlaps on the reverse, the smoother this side is. However, the roughness of the face does not change with n. For a fabric made with a single guide bar and a single needle bed machine, the face is made of loops and the back contains only floats. For a number m of guide bars fully threaded, the fabric contains m − 1 successive layers with a face constituted of only overlaps and other layers made from under-

Fabric grammage (g/m2)

140 120 100 80 60 40 20 0 1

2

3

4

5

Underlap length (needle space)

4.9 Fabric grammage evolution relative to underlap length (in needle space).

Structure and mechanics of knitted fabrics

99

laps. Underlaps made by the front bar appear on the reverse. Looking at the reverse, the underlaps from the following bar appear just behind the previous bar underlaps, and so on, till the front bar underlaps touch the overlaps. For instance, two guide bar fabrics are constituted of three layers; viewed from the face, the first layer is made by overlaps, thus contains only loops, the second layer comprises underlaps from the back guide bar and the last layer is built up from underlaps from the front guide bar. This kind of fabric is a multi-layered structure, and such fabrics offer many interesting design possibilities to accommodate various needs. Run-in for the same guide bar lapping movement is higher for the front guide bar than for the back guide bar, and this effect increases with underlap length. This difference arises from the manufacturing process. During the underlap movement, the back bar yarns slide on needles, whereas the front bar yarns slide on the back bar yarns. The inter-yarn friction coefficient is higher than the steel-yarn friction coefficient, therefore front bar yarns tend to stick to back bar yarns [23]. For instance, locknit, i.e., 1-and-1 evolution on the back bar and 2-and-1 on the front bar, is smoother and needs longer yarn than reverse locknit, i.e., 2-and-1 evolution on the back bar and 1-and-1 on the front bar (see Fig. 4.7).

4.3

Tensile properties of knitted fabrics

The mechanisms involved in a uniaxial tensile test are quite different for warp and weft knitted structures. In the case of warp knits, rotation and friction are involved, whereas for weft knits, it is bending and friction.

4.3.1 Weft knitted fabrics The structure of a plain jersey fabric incorporates face or reverse stitches. During a tensile test on a weft knitted fabric, the loops are strained in three steps whatever the tensile direction, wale-wise or course-wise: • •

Decrease of stitch bending in the thickness direction: bending forces are involved, The legs of the loop (for wale-wise tension) or the head and feet (for course-wise tension) come closer: yarn to yarn friction forces.

These two first steps build up the structure rearrangement (the beginning of the ‘J’ load-extension curve), and are followed by yarn compression and traction (the end of the ‘J’ load-extension curve). A rib structure has similar behaviour to that described above in the walewise direction. Both experimental and simulated results (see Table 4.1) show the same order of magnitude of Kc (from 4.5 to 5.8) for all balanced or unbalanced rib fabrics. In the course-wise direction, another scale occurs:

100

Structure and mechanics of textile fibre assemblies

the rib scale, which is coarser than the stitch scale. In fact, a rib is made of one or several columns of face stitches adjacent to one or several columns of reverse stitches. The effect in the course direction is a combination of the curling effect from columns of face stitch groups against the same effect but in the opposite direction from columns of reverse stitch groups. The result is a fabric without curling at the macroscopic level and an ‘accordion effect’ in the course-wise direction. The wider each group of columns, the higher this effect, and the more the fabric stretches in the course-wise direction. During tensile stress, four mechanisms occur in sequence: •

• •

The first two mechanisms interfere, and are rotation of the float between two stitches of different types (face and reverse), and uncurling, i.e., unbending, of each wale group of the same type of stitches. The longer the rib-repeat, the larger and earlier the uncurling phase. Subsequently, stitch elongation occurs, with bending and inter-yarn friction. Finally, yarn tensile stress starts.

The transition between these four steps is of varying visibility, depending on the kind of knit, yarn bending rigidity, and inter-yarn friction. For plain jersey structures, the first two mechanisms do not occur, which is why plain jersey elongation in the course-wise direction is lower than in rib knits. It is possible to make a rough comparison of wale-wise elongation for plain jersey and rib structures regarding the Kw values (see Table 4.1). Some assumptions have to be considered: • •

The theoretical maximum length course-wise is equal to a total uncrimping of yarn, less a fraction due to yarn interlacing. The fraction of stitch length due to yarn interlacing has the same value for plain jersey and rib structures.

The theoretical maximum course-wise extension can be evaluated roughly as follows, without considering yarn extension: ε c = K w ( 1 − a) − 1

4.16

where a: fraction of stitch length due to yarn interlacing that limits extension (depending on yarn diameter under compression and stitch length, therefore depending on tightness). εc: maximum course-wise extension. εc is not always obtained because the fabric breaks when the applied stress is higher than the yarn breaking stress at the inter-yarn contact area. Yarn breaking stress depends on yarn, but the corresponding fabric breaking stress also depends on fabric tightness.

Structure and mechanics of knitted fabrics

101

The theoretical maximum wale-wise extension can be evaluated allowing for the following assumptions: • •

The theoretical maximum wale-wise length is equal to half the total length of uncrimped yarn, less a fraction due to yarn interlacing. The fraction of stitch length due to yarn interlacing has the same value for plain-jersey and rib structures.

Hence: 1 ε w = Kc ⎛ − b⎞ − 1 ⎝2 ⎠

4.17

Where: b: fraction of stitch length due to yarn interlacing that limits extension (depending on yarn diameter under compression and stitch length, therefore depending on tightness), εw: maximum wale-wise extension. Thus the maximum elongation for different structures can be compared from a qualitative point of view (see Fig. 4.10). Purl structures also present an ‘accordion effect’ in the wale-wise direction. A held stitch can exist only if there is a miss stitch, which then gives a float. Both held stitches and floats have an effect on tensile properties but not in the same directions: held stitches block wale-wise extension and floats have no elongation, consequently they lock the structure in the course-wise direction. A tuck stitch has an effect on the mechanical properties similar to that of held stitches in the wale direction. Nevertheless, a tuck presents an elongation in the course direction, not as significant as a stitch but more so than a float, and this elongation can be expressed with a maximum value. A tuck has a reverse V shape with 1/C in width and 1/W in height, hence: 2

W 1 εc = 2 ⋅ ⎛ ⎞ + − 1 ⎝C⎠ 4

4.18

From a mechanical point of view, 1 × 1 interlock fabric is similar to joined face and reverse plain jersey fabrics. Hence, its theoretical maximum expansion is approximately the same as that for plain jersey, but at higher stresses [35].

4.3.2 Warp knitted fabrics We begin with two basic structures: pillar stitch and 1 and 1 lapping structures. A pillar stitch is not a surface; therefore it does not have any

Maximum extension in wale-wise direction (%)

Structure and mechanics of textile fibre assemblies

70% 60% 50% 40% 30% 20% 10% 3×n 2×n Rib 1 × n structures

0% 0 Plain-je

1 rsey

2

Numbe

r of rev

3

4

erse wa

les in a

5

6

repeat

(a) Maximum extension in course-wise direction (%)

102

600% 500% 400% 300% 200% 100% 3×n 2×n Rib 1 × n structures

0% 0 Plain-je

1 rsey Numbe ro

2

3

f revers

e wales

4

5

6

in a rep

eat

(b)

4.10 Theoretical maximum elongation for diverse weft knitting structures (a) wale-wise and (b) course-wise.

Structure and mechanics of knitted fabrics

103

properties course-wise, but this structure is very interesting in the wale-wise direction. Indeed, a pillar stitch does not underlap any needle, thus its float (underlap) is in the wale direction. During a tensile test in this direction, the loop can be elongated (the linear parts of the loop become closer together and longer) but this structural arrangement is small because the structure is locked by floats. For 1 and 1 lapping structures, the angle between the wale direction and the float (underlap) is approximately 45°. A tensile test with this kind of structure in either wale or course directions will orientate the float as close as possible to the direction of tension, i.e., via a rotation of the float. Therefore, elongations in the wale and course directions have the same order of magnitude. The longer the underlap, the higher the elongation is in the wale direction and the lower it is in the course direction. In this situation, the elongation due to overlap must also be considered, but it is approximately constant with a change in underlap length, so the maximum elongation can be considered to be due to underlap. Without considering yarn properties, it can be expressed in the wale direction as: εw = 1 +

n2 ⋅ w2 − 1 + ε w (overlap) c2

4.17

where εw(overlap): elongation of the underlap due to yarn slipping from overlap to underlap, during wale-wise stress. In the course direction, the maximum elongation is given by: εc = 1 +

c2 − 1 + ε c(overlap) n ⋅w2 2

4.18

where εc(overlap): elongation of the underlap due to yarn slipping from overlap to underlap, during course-wise stress. An illustration of elongation in wale-wise and course-wise directions is given in Fig. 4.11. It is possible to combine these basic, fully threaded structures in order to combine some of their properties. The most common combination involves two guide bars, i.e., two structures. In this case, the maximum elongation in each direction is the lowest elongation of each guide bar structure for that direction. The mechanism occurring during tensile tests comprises not only rotation of the underlaps but also friction between underlaps from adjacent guide

104

Structure and mechanics of textile fibre assemblies Elongation in wale-wise direction (%)

700 600 500 400 300 200 100 0 1

2 3 4 Underlap length (needle space)

5

Elongation in course-wise direction (%)

(a) 30 25 20 15 10 5 0 1

2 3 4 Underlap length (needle space)

5

(b)

4.11 Theoretical maximum elongation for diverse warp knitting structures (a) wale-wise and (b) course-wise.

bars. With two guide bars, for example, the middle layer is constituted of back guide bar underlaps and is limited by the other layers. It is subjected to important friction forces from both the underlap front guide bar layer and the overlap layer. This mechanism explains the difference in properties between two fabrics made with the same number of guide bars and the same guide bar lapping movements but with a change in guide bar position. In this case, the lower the interlayer friction, the easier it is to elongate the fabric. Interlayer friction shows the same trend as middle layer underlap length, so the most stable structure is that with the longest underlaps in the middle layer. The consequence is not a decrease in maximum elongation,

Structure and mechanics of knitted fabrics

105

but an increase in the load needed in order to reach that elongation, thus the slope at the beginning of the ‘J’ curve increases. Considering the above, it is possible to design the least extensible structure using two guide bars, namely Queen’s cord (see Fig. 4.7). This structure has a pillar stitch on the front bar and a reciprocating n-and-1 movement on the back bar, with n at least equal to 3. As mentioned previously, yarn slipping mechanisms permit the overlap to undergo elongation during stress. In order to reduce elongation to zero, one guide bar in a two-guidebar structure can produce no overlap, by laying-in. The best solution remains insertion of weft yarn perpendicular to the wales in order to reduce or eliminate course-wise elongation, resulting in the development of weft inserted warp knitted fabrics.

4.4

Bending properties of knitted fabrics

Very different mechanisms are involved in the bending behaviour of warp and weft knitted fabrics. For weft knitted fabrics, the most influential mechanism is due to stitch curling properties, whereas for warp knitting fabrics, the multi-layer structure is the critical factor. The instantaneous parameter measured in a bending test is the moment applied to the fabric relative to the curvature. For a blade or a beam it can be expressed as: M = E⋅I ⋅K M = B⋅ K

4.19

where M: bending moment (N.cm), E: Young’s modulus of the material (N.cm−2), I: moment of inertia of the cross-section (cm−4), K: curvature (cm−1), B: flexural rigidity (N.cm2). E represents the influence of the material, I the cross-sectional shape and dimensions, and K the blade bending length and the strain. For knitted fabrics, the relationship between bending moment and curvature is not linear. Moreover, bending rigidity is not constant, and increases with increasing curvature due to the increasing yarn compression forces at inter-yarn contact points. E is not constant with strain, since it is a fibre assembly with inter-yarn friction and yarn compression forces. However, Equation 4.19 can be used comparatively, and E is then considered as the instantaneous slope of the force-extension curve. For the same fabric, I is considered as a constant. A convention used by several authors is that curvature is positive when the face of the fabric is to the outside. In the opposite configuration, curvature is negative.

106

Structure and mechanics of textile fibre assemblies Bending moment 15 (10-3 N.mm/mm)

e

10

op Sl

B1

5 +0.28

–0.28 2M° 0

Curvature k (mm–1)

–5

–10 e

op Sl

B2

–15

4.12 Example of bending hysteresis curve with bending parameters for Punto-di-Roma fabric (from [15]).

The parameters used to characterise fabric bending properties are bending rigidity, which represents the elastic component of the resistance to deformation, and frictional bending moment, which is a measure of the degree of hysteresis or the inter-fiber friction within the fabric during deformation [11]. Bending rigidity is measured as the slope of the linear region of the hysteresis curve (see Fig. 4.12) for positive and negative curvatures, while frictional moment is defined as half the width of the hysteresis at zero deformation. For weft knitted fabrics, the relationship between bending rigidity and frictional bending moment is linear. For warp knitted fabrics, this relationship is not so obvious [11].

4.4.1 Weft knitted fabrics It was mentioned previously that the intensity of the curling effect depends on the state of the fabric, i.e., how stabilised or relaxed it is. As a consequence, fabric bending properties are influenced by fabric state. With the help of Section 4.3 and Equation 4.19, it can be deduced that, for the same stress, the course-wise elongation is higher than the wale-wise elongation for plain jersey fabrics. Hence the slope of the force-extension curve is always lower for course-wise elongation and, for plain jersey fabric, bending rigidity is therefore lower since the courses are bent [1, 14, 34].

Structure and mechanics of knitted fabrics

107

Due to the curling effect in both wale and course directions, flexural rigidity is lower for positive curvature since the courses are bent, and for negative curvature, since the wales are bent [14, 34]. Moreover, because the curling effect is greater in the wale-wise direction, flexural rigidity for positive curvature and for course bending is lower than that for negative curvature, where the wales are bent [14]. The mechanism involved in the direction of low flexural rigidity is unbending of the yarn and rotation of the stitch. The mechanisms involved in directions where flexural rigidity is high are inter-yarn compression, i.e., jamming, and inter-yarn friction. For a given stitch length, the higher the cover factor, the higher the fabric flexural rigidity [1, 5, 14, 34]. It has been shown that fabric bending properties also vary with yarn parameters [1, 14]. Fabric bending rigidity Bf increases with yarn bending rigidity By. The ratio Bf/By lies between 0.1 to 1.5 [34], therefore it can be much easier or slightly more difficult to bend a knitted fabric than the equivalent number of component yarns. On the other hand, fabric bending properties are strongly dependent on fabric state, i.e., relaxed or unrelaxed [14, 34]. Indeed, the influence of cover factor and bending direction is more significant for unrelaxed fabrics in terms of flexural rigidity and frictional bending moment measured with bending hysteresis. For fully relaxed fabrics, the curling couple should be zero [14], and the frictional bending moment is clearly lower than for unrelaxed fabrics. In the case of balanced structures, bending rigidity is similar for positive and negative curvatures and fabric state has a very low influence compared with its influence on unbalanced structures. Bending rigidity is higher for rib structures than for plain knitted fabrics, particularly since the wales are bent [1, 2]. For plain jersey, ribs and interlocks, flexural rigidity is lower for course bending than for wale bending [5]. In fact, during course bending, bending occurs between wales and the mechanism is close to a rotation, while in wale bending, the stitches are bent. However, interlock fabrics, i.e., double knitted, are less flexible than rib fabrics, i.e., single knits, both in wale and course directions [5]. As for tensile behaviour, miss stitches block structure in bending, therefore ribs or interlock fabrics with miss stitches are more difficult to bend [5].

4.4.2 Warp knitted fabrics The bending behaviour of warp knitted fabrics has been studied less than that of weft knitted fabrics, but some basic principles can be extracted nevertheless. Warp knitted fabrics have different bending properties relative to the sign of the curvature, positive or negative, and whatever bending is occurring in the wale or course directions [10, 11]. This fact is quite obvious and derives from the multi-layer morphology of this kind of fabric. Figure

108

Structure and mechanics of textile fibre assemblies y x Underlap to next course Underlap to previous course

y z Previous loop

Next loop z

Underlap

x

4.13 Projection of a 1-and-1 reciprocating warp-knitted structure in the three space planes (from [10]); arrows indicate lowest bending rigidity for both wale and course bending.

4.13 shows that when wales are bent in positive curvature yarn, contacts, or jamming, occur and lock the structure. This mechanism does not exist for negative curvature [10]. Hence, during wale bending, bending rigidity is higher for positive than for negative curvature. When the courses are bent in negative curvature, the loops are in contact because of underlap bending. This is not the case with a positive curvature. Hence, during course bending, flexural rigidity is lower for positive than for negative curvature. In order to compare wale and course bending, the lowest bending rigidity is for wale bending in negative curvature and the highest is for course bending in negative curvature. In addition, the bending frictional moment and bending rigidity are higher when the courses are bent. When courses are bent in single bar n-and-1 structures, the longer the underlap, the higher the bending rigidity. In fact, the number of yarns which are bending increases with n. This mechanism can be expanded to fabrics with two or more guide bars [10]. For a single guide bar structure and during wale-wise bending, the evolution of bending rigidity depends on the friction between loops and underlaps and on the bending resistance of the loops. During wale-wise bending, the loops are bent and this mechanism needs lower force than to bend the floats between wales in course-wise bending. Some experimental results underline this interpretation [11]. For double guide bar structures, bending properties in both directions are influenced by each guide bar evolution and by guide bar position. When courses are bent, flexural rigidity is higher when the back guide bar gives longer underlaps, because inter-yarn friction forces are stronger.

Structure and mechanics of knitted fabrics

109

When the wales are bent, for laying-in warp knitted fabrics, flexural rigidity is higher for positive curvature. However, bending rigidity and the frictional bending moment are higher when the courses are bent [10]. As for weft knitted fabrics, the frictional bending moment is clearly lower after relaxation.

4.5

Shear properties of knitted fabrics

The instantaneous parameter measured in a shear test is the shear stress applied to the fabric relative to the shear angle. For small deformations, the shear modulus can given by: G=

E 2 ⋅ (1 + ν )

4.20

where G: shear modulus (N·cm−2), E: Young’s modulus of the material (N·cm−2), ν: Poisson ratio (dimensionless). The fabric shear stress relative to the angle is not linear and thus the shear modulus is not constant. The parameters used to characterise fabric shear properties are shear rigidity, which represents the elastic component of the resistance to deformation, and frictional shear stress, which is a measure of the degree of hysteresis or the inter-fibre friction within the fabric during deformation [11]. Shear rigidity is measured as the slope of the linear region of the hysteresis curve (see Fig. 4.14) in both shear directions. Frictional moment is defined as half the width of the hysteresis at zero deformation. The shear mechanism for weft knitted structures is stitch shear with inclination of stitches, which induces jamming, i.e., inter-yarn compression. Therefore, for warp knitted fabrics, the main mechanism is underlap rotation and buckling. In contrast to bending parameters, there is no relationship between shear rigidity and frictional shear stress [11], moreover, shear curves are symmetrical relative to shear angle sign [11]. It should be noticed that during shear tests, tension must be applied to the fabric in order to minimise its tendency to buckle [15].

4.5.1 Weft knitted fabrics Shear rigidity increases with yarn count [15] and cover factor [4, 5], these trends being obvious. Frictional stress increases with yarn count [15] and can be constant [4], or can increase [5] because the cover factor increases. These parameters are higher for shear in the wale direction [5, 15]. In fact,

110

Structure and mechanics of textile fibre assemblies Shear 10 stress (10–3 N/mm)

e

lop

G1

S 5

+0.15

–0.15 2σ° 0

Shear strain

–5

e

op Sl

G2 –10

4.14 Example of shear hysteresis curve for Punto-di-Roma fabric with shear parameters (from [15]).

loop shape shows a better ability to be inclined parallel to course direction than to wale direction. Shear stiffness values are higher in the wale direction [5], except for interlock structures [4]. Interlock structures present a higher shear rigidity than rib and plainknitted structures [4, 5]. In the interlock structure, the floats between stitches restrict deformation. Structures with miss or tuck stitches are more difficult to shear, because these stitches lock structure whatever the stress type, whether it is tensile, bending or shear.

4.5.2 Warp knitted fabrics The longer the underlap, the higher the shear rigidity [8], while frictional shear stress keeps almost constant. Both frictional shear stress and shear rigidity are lower for laid-in warp knitted fabrics than for ordinary warp knitted structures [8]. During shear tests, fabric buckling occurs more easily for warp knits than for weft knitted fabrics [11].

4.6

Shear-bending comparison

Frictional shear stress or bending moments are more sensitive to changes in fibre material, yarn and type of knit than elastic rigidity parameters [11]. A representation of frictional shear stress relative to frictional bending moment provides a classification of fabric structures (see Fig. 4.15).

Structure and mechanics of knitted fabrics

Finished fabrics Woven fabrics Wool double-knits Polyester double knits Warp knits Plain knits

5

Frictional shear stress σ (10–2 N/cm)

111

Warp knits 4

3

Polyester double knits

2

Plain knits

Wool double-knits

1 Woven fabrics 0 0

50

100

150

200

250

300

350

Frictional bending moment Mo,weft or Mo,courses (10–3N.cm/cm)

4.15 Representation of frictional shear stress relative to frictional bending moment for 87 fabrics (from [11]).

4.7

Modelling knitted fabric mechanics and simulation

As is clear from this chapter, the majority of modelling and simulation works have been done on weft knitted fabrics. For weft knitted fabrics, most of the work focuses on plain knitted fabrics, with a few studies on rib structures, interlock, and complex structures like French and Swiss piqués and Punto-Di-Roma. For warp knitted fabrics, research mainly concerns 1-and-1 and n-and-1 lapping structures. Most of these models are geometrical, as for instance the Munden [32] and Knapton [25, 26, 27, 28, 29, 30] models for weft knitted fabrics and the Grosberg model for warp knitted fabrics [12, 13]. For weft knitted structures, some models take into account internal forces or energy, such as that of Hepworth for weft knitted structures [17, 18, 19, 20], and Postle [4, 11, 14, 15, 34, 35, 41]. Hepworth’s model can predict the relaxed geometry of basic weft knitted fabrics and tensile behaviour. The most versatile method is that of Postle, since it can simulate fabric geometry, tensile, bending and shear behaviour, and curling effect. It can also be applied to many structures. For warp knitted structures, Postle’s energy approach is the most thorough [8, 10, 16]. Nevertheless, other models are of interest in specific cases,

112

Structure and mechanics of textile fibre assemblies

for instance for the geometrical characteristics of weft-inserted warp knitted fabrics [42, 43], and for the bending behaviour of plain and rib knitted fabrics [1], or multiaxial warp knitted fabrics [24]. This list is not exhaustive.

4.8

Sources of further information and advice

The knitting process has two major advantages for a lot of applications: •

•

Complex shapes: the possibility of knitting complex shapes not only has apparel applications, but also technical applications, such as medical, composite reinforcements, civil engineering, etc. Extremely low elongation: warp knitting provides the possibility of having almost zero elongation of the structure, as in the case of multiaxial warp knitted fabrics. This has applications in, for instance, composite reinforcements for aerospace.

Most complex, 3D shapes are achieved with weft knitting [7]. Some shapes can be obtained by warp knitting, but this is more difficult and requires special equipment (vascular prostheses, for instance). 3D shapes have been knitted on weft knitting machines for a long time, such as berets, pantyhose and socks. Over the last few years, this fabulous property of the weft knitting process has became of interest to those working in technical textiles (composite reinforcements, car upholstery) and the clothing industry, which is looking at the possibility of knitting a one-piece, complete garment. A stitch is extensible but it is possible to limit its extensibility by introducing straight and non-extensible yarns in one or several directions, known as weft insertion knitting technology. In the weft knitting process, weft insertion has been used in production for a long time. This technology can produce fabric that is very rigid course-wise, in the warp knitting process often being combined with pillar stitch to ensure low wale-wise extensibility as well. It is possible to increase rigidity in several directions by inserting yarn web at different angles to the machine direction, creating multiaxial warp kintted fabrics. Stitches are only necessary for fitting the different layers of yarns together during handling. This concept is used with weft knitting technology by the Institute of Textile and Clothing Technology, Dresden, Germany. However, there is a major difference between multiaxial warp and weft structures; with weft technology, the inlay yarns do not move from one side to the other side of fabric therefore the effect concerns only a limited fabric width, contrary to weft insertion warp knitting technology. The main advantage is the possibility of using standard flat knitting machines with special yarn feeders. This technique can be used concurrently with multiaxial warp knitting technology for small pieces. The most interesting challenge here is to combine knitting processes for 3D shapes with a multiaxial effects.

Structure and mechanics of knitted fabrics

4.9

113

References

1. Alimaa, D., Matsuo, T., Nakajima, M. and Takahashi, M., Effect of Yarn Bending and Fabric Structure on the Bending Properties of Plan and Rib Knitted Fabrics, Textile Research Journal 70, 783–794 (2000). 2. Alimaa, D., Matsuo, T., Nakajima, M. and Takahashi, M., Sensory Measurement of the Main Mechanical Parameters o Knitted Fabrics, Textile Research Journal 70, 985–990 (2000). 3. Bueno, M.A., Renner, M. and Nicoletti, N., Influence of Fiber Morphology and Yarn Spinning Process on the 3D Loop Shape of Weft Knitted Fabrics, Textile Research Journal 74, 297–304 (2004). 4. Carnaby, G.A. and Postle, R., The Shear Properties of Wool Weft-knitted Structures, Journal of the Textile Institute 65, T87–T101 (1974). 5. Choi, M.-S. and Ashdown, S.P., Effect of Changes in Knit Structure and Density on the Mechanical and Hand Properties of Weft-Knitted Fabrics for Outerwear, Textile Research Journal 70, 1033–1045 (2000). 6. Cooke, W.D., The Geometry of Presser-foot Fabrics, Journal of the Textile Institute, 90–93 (1981). 7. de Araujo, M., Hong, H. and Fangueiro, R., Production of shaped 3D reinforcing fabrics by knitting shape, Melliand Textilberichte, 307–308/E66–E67 (1996). 8. Dhingra, R.C. and Postle, R., Shear Properties of Warp-Knitted Outerwear Fabrics, Textile Research Journal 49, 526–529 (1979). 9. Doyle, P.J., Fundamental aspects of the design of knitted fabrics, Journal of the Textile Institute 44, P561–P578 (1953). 10. Gibson, V.L., Dhingra, R.C. and Postle, R., Bending Properties of Warp-Knitted Outerwear Fabrics, Textile Research Journal 49, 50–58 (1979). 11. Gibson, V.L. and Postle, R., An Analysis of the Bending and Shear Properties of Woven, Double-knitted, and Warp-Knitted Outerwear Fabrics, Textile Research Journal 48, 14–27 (1978). 12. Grosberg, P., The Geometry of Warp-Knitted Fabrics, Journal of the Textile Institute 51, T39–T48 (1960). 13. Grosberg, P., The Geometrical Properties of Simple Warp-Knit Fabrics, Journal of the Textile Institute 55, T18–T30 (1964). 14. Hamilton, R.J. and Postle, R., Bending and Recovery of Wool Plain-Knitted Fabrics, Textile Research Journal 44, 336–343 (1974). 15. Hamilton, R.J. and Postle, R., The Bending and Shear Properties of Wool Punto-Di-Roma Double-Knitted Fabrics, Journal of the Textile Institute 68, 5– 11 (1977). 16. Hart, K., de Jong, S. and Postle, R., Anaysis of the Single Bar Warp Knitted Structure Using and Energy Minimization Technique, Textile Research Journal 55, 489–497 (1985). 17. Hepworth, B., The biaxial load-extension behaviour of a model of plain weftknitting. Part 1, Journal of the Textile Institute 69, 101–107 (1978). 18. Hepworth, B., The dimensional properties of 1 × 1 rib fabrics, Melliand Textilberichte 70, 837–840/E360–E361 (1989). 19. Hepworth, B., Spirality in knitted fabrics caused by twist-lively yarns: a theoretical investigation, Melliand Textilberichte 74, 515–520/E212–E213 (1993).

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20. Hepworth, B. and Leaf, G.A.V., The mechanics of an idealized weft-knitted structure, Journal of the Textile Institute 67, 241–248 (1976). 21. ITF-Maille, Ch. J, Etude fondamentale de la Jet 2F, in Géométrie des Tricots: application à la mise en fabrication, ITF-Maille, 85–95 (1976). 22. ITF-Maille, Géométrie des tricots: application à la mise en fabrication, ITFMaille, Troyes, 1976. 23. ITF-Maille, Géométrie des tricots à mailles jetées, Bulletin Scientifique de l’Institut Textile de France 7, 189–230 (1978). 24. Jiang, Y. and Lu, J., Characterizing and Modeling Bending Properties of Multiaxial Warp Knitted Fabrics, Textile Research Journal 69, 691–697 (1999). 25. Knapton, J.J.F., Geometry of complex knittted structures, Textile Research Journal 39, 889–892 (1969). 26. Knapton, J.J.F., Factors affecting the stable dimensions of double-jersey structures, Journal of the Textile Institute 32, 293–299 (1974). 27. Knapton, J.J.F., Ahrens, F.J., Ingenthron, W.W. and Fong, W., The dimensional properties of knitted wool fabrics. Part 1: The plain-knitted structure., Textile Research Journal 38, 999–1012 (1968). 28. Knapton, J.J.F., Ahrens, F.J., Ingenthron, W.W. and Fong, W., The dimensional properties of knitted wool fabrics. Part 2: 1 × 1, 2 × 2 rib, and half-cardigan structures., Textile Research Journal 38, 1013–1026 (1968). 29. Knapton, J.J.F. and Fong, W., The dimensional properties of knitted wool fabrics. Part 4: 1 × 1, 2 × 2 rib, and half-cardigan structures in machine-washing and tumble-drying., Textile Research Journal 40, 1095–1105 (1970). 30. Knapton, J.J.F. and Fong, W., The dimensional properties of knitted wool fabrics. Part 5: Interlock and Swiss double-piqué structures fully-relaxed and in machine-washing and tumble-drying., Textile Research Journal 41, 158–166 (1971). 31. Knapton, J.J.F., Truter, E.V. and Aziz, A.K.M.A., The geometry, dimensional properties and stabilization of the cotton plain-jersey structure, Journal of the Textile Institute 12, 413–419 (1975). 32. Munden, D.L., The geometry and dimensional properties of plain-knit fabrics, Journal of the Textile Institute 50, T448–T471 (1959). 33. Munden, D.L., Objective measurement of knitted fabric parameters – Its importance to control of knitting process, The Textile Machinery Society of Japan, 39–44 (1985). 34. Postle, R., Carnaby, G.A. and de Jong, S., Chapter 10: The plain-knitted structure, in The mechanics of wool structures, Ellis Horwood Limited, 227–273 (1988). 35. Postle, R., Carnaby, G.A. and de Jong, S., Chapter 11: Complex knitting-fabric structures, in The mechanics of wool structures, Ellis Horwood Limited, 274– 306 (1988). 36. Postle, R. and Munden, D.L., Analysis of the dry-relaxed knitted-loop configuration. Part I: Two-dimensional analysis, Journal of the Textile Institute 58, T329–T351 (1967). 37. Postle, R. and Munden, D.L., Analysis of the dry-relaxed knitted-loop configuration. Part II: Three-dimensional analysis, Journal of the Textile Institute 58, T352–T365 (1967). 38. Raz, S., Chapter 32: Warp Knitted Fabric Geometry, in Warp Knitting Production, Bamberg, M., Heidelberger Verlagsanstalt und Druckerei GmbH, (1987).

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39. Raz, S., Flat Knitting Technology, C. F. Rees GmbH, Heidenheim, 1993. 40. Reisfeld, A., Chapter 23: Fabric Calculations and Parameters, in Warp Knit Engineering, National Knitted Outerwear Association, (1966). 41. Shanahan, W.J. and Postle, R., A Theoretical Analysis of the Plain-Knitted Structure, Textile Research Journal 40, 656–665 (1970). 42. Zhuo, N.J., Leaf, G.A.V. and Harlock, S.C., The geometry of weft-inserted warpknitted fabrics. Part 1: Models of the structures., Journal of the Textile Institute 82, 361–371 (1991). 43. Zhuo, N.J., Leaf, G.A.V. and Harlock, S.C., The geometry of weft-inserted warpknitted fabrics. Part 2: Experimental validation of the theroetical models., Journal of the Textile Institute 82, 373–379 (1991).

5 Structure and mechanics of nonwovens B POURDEYHIMI and B MAZE, North Carolina State University, USA

Abstract: Nonwovens are complex fiber assemblies whose mechanical properties depend on numerous and often random factors. This chapter first discusses nonwoven production processes and how they relate to key properties like ODF and mass uniformity. The second part focuses on the different approaches used to model the mechanical behavior of nonwovens. Key words: nonwovens, fiber orientation distribution function (ODF), mass uniformity, mechanical modeling.

5.1

Introduction

Webster’s Dictionary defines a nonwoven as follows: ‘non-woven is made without weaving, especially having textile fibers bonded together by adhesive resins, rubber, or plastic or felted together under pressure 〈∼fabrics〉’ [1].

This definition is both simplistic and incomplete. More recently, INDA1 defined a nonwoven as ‘a sheet, web, or batt of natural and/or man-made fibers or filaments, excluding paper, that is bonded by any of several means.’ EDANA2 defines a nonwoven as ‘A manufactured sheet, web or batt of directionally or randomly oriented fibers, bonded by friction, and/or cohesion and /or adhesion, excluding paper and products, which are woven, knitted, tufted, stitch-bonded incorporating binding yarns or filaments, or felted by wet-milling, whether or not additionally needles.’ The definition of nonwovens is much more complicated. The term nonwoven refers to web-like assemblages of fibers wherein fiber to fiber bonding replaces twisting and interlacing. We define a nonwoven as an engineered fabric structure that may contain fibrous and non-fibrous elements and that is often manufactured directly from fibers or filaments and may incorporate other types of fabrics. The difference primarily between a nonwoven and

1

INDA – The Association of the Nonwoven Fabrics Industry located in Cary, North Carolina, USA. 2 EDANA – The European Disposables and Nonwovens Association located in Brussels, Belgium.

116

Structure and mechanics of nonwovens

117

its more traditional counterparts (woven, knitted and braided structures) is the structure. The fibers or filaments in a nonwoven are not interlaced or inter-looped and are somewhat random layered assemblies of fibers held together by a variety of different means. The structure of a nonwoven is defined therefore as its fiber orientation distribution function (ODF). Another important structural aspect to consider is the basis weight (mass per unit area – g/m2 or more commonly referred to as gsm) and its uniformity. While ODF may dictate behavior, basis weight uniformity dictates failure. The structure-property relationships in a nonwoven cannot be decoupled from the process utilized to form the nonwoven. Therefore, below, we present a short review of the processes employed in the making of nonwovens followed by a discussion of the structure-process-property relationships and will make an attempt to describe the mechanical properties of one class of nonwovens.

5.2

Production processes

The first question which comes to mind when asked about nonwoven mechanical properties is: what process was used to make it? After all, one of the definitions just mentions a ‘manufactured sheet, web or batt of directionally or randomly oriented fibers’. Nonwovens production is usually split into two steps: web formation and web consolidation (or bonding). We will describe some of the most common web formation and bonding processes which will be used as illustrations in the remainder of this chapter.

5.3

Web formation

5.3.1 Carding and cross-lapping As the fibers from the fleece at the exit of a card are essentially parallel, cross-lapping is necessary to give some strength in the lateral direction. The fiber fleece delivered by the card is laid zigzag by the cross-lapper onto a transport belt, situated at 90° angle to the transport direction of the fleece (Fig. 5.1). The ratio of the feed speed and delivery speed will determine the angle of lapping and thus the resulting ODF. The lapping process will also increase the basis weight. This process, albeit slow, is still in use as it allows easy blending of fibers and high basis weight.

5.3.2 Air laid In order to overcome the anisotropy generated by a cross-lapper, an alternative is the air laid process (Fig. 5.2). Fibers are first opened, then suspended in an air flow and finally deposited on a forming surface (belt or

118

Structure and mechanics of textile fibre assemblies Fleece

Fiber feed Card

Delivery belt

Cross-lapper

Fibrous web

5.1 Cross-lapper schematic.

Fibers in

2

1

5

Web To bonding

4 Air in

3

1 – Combined feed system 2 – Taker-in roller with metallic clothes 3 – Screen drum with cover to control web thickness

Dirty air out 4 – Fiber web delivery conveyor 5 – Gauge level control

5.2 Air-laid schematic.

drum). The main advantage is an almost perfectly random ODF. Basis weight uniformity is also very good.

5.3.3 Spunbond In the spunbond process, the initial material is not fibers but raw polymer pellets. Those are melted, extruded, spun, drawn and collected on a belt (Fig. 5.3). The resulting web is made of continuous filaments. Uniformity can be an issue, especially at low basis weight. The ODF is slightly MD oriented.

5.3.4 Meltblown The meltblown process (Fig. 5.4) is similar in principle to the spunbond. The main difference is at the spinneret exit, where supersonic air is blown. This will fragment and greatly draw the polymer flow. As a result, the web is made of very fine fibers.

Structure and mechanics of nonwovens

119

1 2 1 – Polymer pellets 2 – Extruder 3 – Spinnerets 4 – Cooling/drawing 5 – Collection screen 6 – Web

3 4 6

5

5.3 Spunbond schematic.

Air manifold Meltblown nonwoven

Polymer pellets Extruder

Winder

Gear pump

Collector Die

5.4 Meltblown schematic.

5.4

Bonding

5.4.1 Calendering The web to be bonded is passed through the nip of two rolls (cylinders) pressed against each other, one or both of which are heated internally. In many cases, the fabric wraps around two ‘chill rolls’ in sequence, under one and over the other (capstan fashion), after exiting the heated roll nip. If the nip rolls are smooth, the heat is transferred from hot surface of the roll(s) into the fabric. Under these circumstances, every fiber crossover point in the web can be, potentially, bonded. This type of bonding is called area bonding. The fabrics so bonded are made highly dense and thin; while they may be strong, often they tend to be stiff (both in extension and bending or shear). The level of bonding (that is the density and strength of bonds) is determined by the temperature(s) of the roll(s), the ‘nip pressure’ (or ‘load’) and throughput speed, in addition to the web parameters (basis weight, fiber type, fiber mass linear density and blend levels). The nip pressure is defined as the sum of forces applied at two ends of the rolls (Fig. 5.5) divided by the length of contact between rolls and the fabric; the units may be N/m or

120

Structure and mechanics of textile fibre assemblies

Nip width

Input web

Point bonded web

5.5 Calendering schematic.

lbs/in, etc. The throughput speed, for a given diameter rolls, determines the ‘residence time’ in the nip, which in turn determines whether all fibers, in the nip and through the fabric thickness, get heated to the desired ultimate temperature level. In calender bonding machines, the calender rolls are usually followed by one or two ‘chill rolls’. The chill rolls have cool water flowing through them, axially. The idea is to draw the heat out of the fabric as soon as it comes out of the nip rolls. This should help solidify bonds at fiber junctions in the fabric before it is called upon to sustain the tension inherent in the subsequent (additional) cooling and wind-up processes. The chill rolls do play an important role in guidance of the web downstream. Whether their ‘chilling effect’ is beneficial to final properties of the fabric is not clear. Opinions in the literature differ on this point. To counteract stiffness of the area bonded fabrics, point bonding (sometimes called embossing) is employed. In point bonding, the heat is applied through conduction in selected areas of the web; the selected areas are usually arranged in a uniformly repetitive array (pattern). The fibers in the web between the selected bond sites, also called bridging fibers, receive some heat through convection and radiation. As such, secondary bonds may form between the bridging fibers. Usually, the secondary bonds are mechanically broken in subsequent web handling or processing, either deliberately or as a matter of course, leaving the bridging fibers free to move within the fabric structure. This enables the fabric to remain flexible, while retaining optimal strength. Point bonding is achieved in one of two ways. In one case, one of the rolls carries an engraved pattern of embossing sites upon its surface, as shown in Fig. 5.6. The engraved patterns have repeats as shown. The heat is con-

Structure and mechanics of nonwovens

121

5.6 Bond pattern for embossing.

ducted through land sites, which in the fabric becomes bond sites. In this method, bond sites can have different shapes and repeat (simple or complex) patterns. The second, mating, roll serves as the anvil which supports the web in the nip. The face of the resulting fabric shows areas of blooming fibers in between pressed-in, flat bond sites, whereas its back looks relatively uniform and ‘smooth.’ The fraction of land area (bond area) in a repeat determines the degree to which the structure is bonded, which, in turn, determines the strength and stiffness of the structure. As a rule of thumb, the strength and stiffness of the fabric increases with increasing fractional bond area. Both in area bonding and point bonding, the roll surfaces are heated from inside by direct electrical heat (resistive or inductive), or through the use of heated oil. Heated oil is much preferred because it leads to much more uniform temperature distribution along the nip. In some configuration a fixed quantity of oil is sealed inside the roll and it is heated electrically. Thermal inertia of internally heated systems with or without oil is generally high. As a result heating by circulating oil systems is much preferred.

5.4.2 Hydroentangling Hydroentangling (Fig. 5.7) is a mechanical bonding process that uses highspeed waterjets originating from a series of cone-capillary nozzles with a typical capillary diameter of 100 to 130 microns. It is also called spunlacing or water needling. The hydroentangling system consists of several manifold and nozzle strip assemblies, with multiple nozzles arranged in row or rows, a conveying belt (or mesh), to carry the web, and vacuum units, to remove the process water from the web. The water in the manifold is pushed through the nozzles in the strip to produce a curtain of waterjets. The nozzle strips run the width of the machine and can measure several metres. Usually, the first curtain of jets that the web encounters in a machine is used for

122

Structure and mechanics of textile fibre assemblies Manifolds

Waterjets

To drying and winding

Forming surface

Vacuum

5.7 Hydroentangling schematic.

pre-wetting the web before hitting it with high-pressure jets in the subsequent manifolds.

5.5

Structure property relationships

Clearly, the properties of a nonwoven fabric will depend on the nature of the component fibers as well as the way in which the fibres are arranged and bonded [2–7]. Nonwovens, regardless of the process utilized, are assemblies of fibers bonded together by chemical, mechanical or thermal means. In most nonwovens, the overwhelming majority of fibers are planar x, y stacks of fibers having little or no orientation through the plane (z direction). Some loft air laid processes make an attempt to create a third dimension in the orientation of webs they produce. It may be argued that needle punching and perhaps hydroentangling also result in some fibers lying in the z direction. It must be noted, however, that the ratio of fibers in the z direction is a small fraction of the total number of fibers and that the planar x-y orientation is still responsible for the performance of the nonwoven. It may be argued therefore, that the x, y planar fiber orientation is the most important structural characteristic in any nonwoven. Modelling and predicting the performance of nonwovens cannot be separated from the fiber orientation distribution and the structure anisotropy it brings about.

5.5.1 Fiber orientation distribution function (ODF) The definition offered below is due to Folgar and Tucker [2] and best describes the fiber orientation distribution function (ODF) in a nonwoven. The orientation distribution function [ODF] y is a function of the angle a. The integral of the function y from an angle a1 to a2 is equal to the probabil-

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123

ity that a fiber will have an orientation between the angles a1 and a2. The function y must additionally satisfy the following conditions:

ψ (α + π ) = ψ (α ) π

5.1

∫ ψ (α ) dα = 1 0

¯ given by [3]: The peak direction mean is at an angle a N

α=

1 tan −1 2

∑ f ( α i ) sin 2α i i =1 N

5.2

∑ f ( α i ) cos 2α i i =1

while the standard deviation about this mean is given by [3]: 1 σ (α ) = ⎡ ⎢⎣ 2 N

∑ f ( α i ) (1 − cos 2 (α i − α ))⎤⎥⎦ N

12

5.3

i =1

Anisotropy is often described by the ratio of the maximum to the minimum frequency of the ODF. For uni-modal distributions, in the range 0 to 180, the degree of anisotropy can also be characterized by the width of the orientation distribution peak given above. These definitions have to be reinterpreted for bimodal distributions in the range 0 to 180 such as are obtained from cross-lapped webs or for crimped fiber webs viewed at short segment lengths. A more general approach would be to use the so-called cos2 anisotropy parameter, Ht, given by [8] H t = 2 cos2 φ − 1

5.4

where cos2 φ =

π 2

2 ∫ ft (φ ) cos (φ ) dφ

−π 2

The average cos2 anisotropy parameters can range between −1 and 1. A value of 1 indicates a perfect alignment of the fibers parallel to a reference direction and a value of −1 indicates a perfect perpendicular alignment to that direction. A uniform ODF (random ODF) would yield a zero value. It would be customary to set the reference direction to machine direction. More appropriately, the peak direction should be used as the reference instead of the machine direction.

5.5.2 The influence of the production method on anisotropy The different web formation processes will impart different initial ODF, which might be further modified by the bonding process. Most thermally

124

Structure and mechanics of textile fibre assemblies

bonded nonwoven fabrics are made by hot calendering a carded web of short staple fibers. The opening and carding processes have a significant impact on the orientation of the resultant web. The carding process, by nature, imparts a high degree of orientation to the fibers in the machine direction. The main cylinder and the workers in the card align the fibers parallel to the machine direction. Inadequate opening of the fibers creates a blotchy, nonuniform fabric that has a tendency to break easily during processing. A fabric formed from a web with fibers mostly aligned in the machine direction will be expected to have high strength in the machine direction and relatively low strength in the cross direction. Other properties follow the same pattern. To improve the cross direction strength requires the rearrangement of the fibres so as to have a higher degree of orientation in the cross direction. This can be achieved by several mechanical methods. One method involves stretching the web in the cross direction prior to the consolidation or bonding step. When the web is stretched in the cross direction, fibres are pulled away from the machine direction and realigned in the cross direction. Of course, the web must be cohesive enough to prevent too much fibre slippage, which could tear the web. The second method of imparting cross direction orientation to fibers involves a randomising doff mechanism at the exit of the card. This randomising is accomplished by buckling the web as it is doffed. Another method commonly employed is a cross-lapper that takes a card feed and cross-laps it into a uniform batt before consolidation or bonding. Most cross-lapped webs have a bimodal fibre orientation distribution. The ODF in the wet lay process also has a machine direction dependency. Here, the ODF can be adjusted by controlling the throughput and the speed of the belt. Unlike the systems above, most air-lay systems have a tendency of creating a more randomized web. The spunbonded and meltblown variety of webs also often have a machine direction dependency. Some spunbonded products also have a bimodal distribution. Here, the aspirator and the laydown system are responsible for the lay-down of the webs. In conclusion, most nonwovens are anisotropic, with a machine direction dependency and that anisotropy typically increases with machine (belt) speed. This also implies that the properties of most nonwovens are also anisotropic. Also significant is that the ODF is typically symmetrical around the machine of cross directions. The symmetry is lost at any other direction.

5.5.3 The role of ODF on mechanical performance When a simple tensile deformation is applied along a direction around which the initial orientation distribution is symmetric, it will remain sym-

Structure and mechanics of nonwovens

125

metric through the deformation process. However, if it is applied along a different direction, the symmetry could be lost with respect to the initial symmetry direction, but develop progressively with regard to the test direction. The changes in ODF that occur as a result of fabric strain can be followed through the following three average anisotropy parameters and an asymmetry parameter. We already have the overall average anisotropy parameter, Ht, given above. We define a left-quadrant average anisotropy parameter, HLt, as H tL = 2 cos2 φ

L

−1

5.5

where 0

cos2 φ

L

=

2 ∫ ft (φ ) cos (φ ) dφ

−π 2

0

∫ ft (φ ) dφ

−π 2

and a right-quadrant average anisotropy parameter, HRt, as: H tR = 2 cos2 φ

R

−1

5.6

where π 2

cos φ 2

R

=

2 ∫ ft (φ ) cos (φ ) dφ 0

π 2

∫ ft (φ ) dφ 0

We can therefore define an asymmetry parameter, A(m) t , as: ⎡⎛ At(m) = 4 ⎢⎜ ⎣⎝

π 2

⎛

⎞

⎤

⎞ 2 2 2 2 ∫ ft (φ ) dφ ⎟⎠ cos φ sin φ R − ⎜⎝ ∫ ft (φ ) dφ ⎟⎠ cos φ sin φ L ⎥ 0 −π 2 0

⎦

5.7

Each of the average anisotropy parameters can range between −1 and 1. A value of 1 indicates a perfect alignment of the fibers parallel to a reference direction and a value of −1 indicates a perfect perpendicular alignment to that direction. A uniform ODF (random ODF) would yield a zero value. The asymmetry parameter, A(m) t , will govern the magnitude of the moment that can arise around the tensile test direction and also its direction, with A < 0 and A > 0 leading to clockwise and anticlockwise moments, respectively. The factor, 4, has been introduced in the definition of A(m) only to t limit its range from −1 to 1. These limiting values represent conditions that would lead, respectively, to maximum clockwise and anti-clockwise moments when a tensile stress is applied along the reference (test) direction.

126

Structure and mechanics of textile fibre assemblies a = 0.50 mm b = 1.01 mm c = 2.26 mm d = 1.51 mm q = 34° 58 spots/cm2

Machine direction

Unit cell height, c

She ar a ngle

0°

θ

90°

Bond height, a

Unit cell width, d

Bond width, b

5.8 Unit cell.

Let us examine the behavior of a carded, calendered nonwoven in tension at various directions. Tensile testing was performed at 0° (machine direction), ±34° (bond pattern stagger angles), and 90° (cross direction). The choice of these three specific test directions was based on the goal of exploring the anisotropic mechanical properties of the fabric and the requirement that the repeating unit of the bond pattern is easily identifiable with respect to the test direction. The nonwoven sample strips, 25.4 mm (1 in) wide, were tested at a gauge length of 101.6 mm (4 in). The tensile tests were carried out at 100%/min extension rate. Five strips were tested at each angle; the average values are used in the plots. From the images digitized during tensile testing at 0°, +34°, 90°, and −34° directions, the fiber orientation distribution function (ODF) and the shear deformation angle of the unit cell were measured. The deformation parameters are described Fig. 5.8. Figure 5.9 shows a typical sequence of the images captured during tensile testing, in this case at the 90° direction (cross direction). The ODF was measured from a series of such images captured at regular intervals of deformation at each test direction. The ODF results are summarized in Figs 5.10(a)–(d). The loading direction is defined with respect to the sample axis (i.e., orientation angle). As can be noted from Fig. 5.10(a), when the samples are tested in the cross direction (90°), the fibers reorient significantly and the dominant orientation angle changes from its initially preferred machine direction towards the loading direction. In the case of samples tested in the machine direction (0°), where the initially preferred orientation coincides with the loading direction, the deformation-induced effect is, as expected,

Structure and mechanics of nonwovens

127

1 mm

25 %

0%

50 %

5.9 Images at 0, 25% and 50% strain.

primarily to increase this preference of fibers (Fig. 5.10(b)). Because of the anisotropy of the initial structure, it is expected that, when the samples are tested in different directions, the relative contributions to the total deformation from structural reorientations and fiber deformations would be different. The reorientations due to the test deformations imposed at 34° and −34° also show similar changes in the dominant orientation angle (Figs 5.10(c) and (d)), but of a much smaller magnitude than that obtained at 90°. When the samples are tested in the cross direction, the nonwoven structure undergoes significant reorientation before the fibers themselves are strained. This is reflected in a high failure strain. In this case, reorientation is due to bending of fibers at their interfaces with the bonds. This would obviously lead to highly localized stress concentrations and high shear stresses at the fiber-bond interface, leading to a relatively low failure stress. In contrast, if the samples are tested in the machine direction, which is the direction of initial preferred orientation, there can only be a limited extent of fiberreorientation facilitated deformation of the nonwoven material. This is

Structure and mechanics of textile fibre assemblies

Load direction Machine direction

12 9

(c) +34 direction

ra

–60 –30 0 30 60 90 0 Orienta tion an gle

in

15 12 9 3

)

6

50 40 30 20 10 (%

(%

)

50 40 30 20 10

Frequency (%)

12

St

Frequency (%)

Load direction Machine direction

15

3

0 30 60 90 0 tion an gle

(b) Machine direction

Load direction Machine direction

6

(%

Orienta

(a) Cross direction

9

–60 –30

ra in

3

)

6

50 40 30 20 10

–60 –30

in

–60 –30 0 30 60 90 0 Orienta tion an gle

ra in (%

3

)

6

50 40 30 20 10

0 30 60 90 0 tion an gle

ra

9

15

St

12

Frequency (%)

15

St

Frequency (%)

Load direction Machine direction

St

128

Orienta

(d) –34 direction

5.10 Re-orientation with different testing directions.

reflected in a low strain, but high stress, at failure, occurring predominantly due to tensile failure of the fibers. If the bonding is optimal, failure can be initiated at the fiber-bond interface, or any other position in the path of the fibers that traverse between bonds. As can be seen in Fig. 5.11, the samples tested at 34° and −34° directions fall between the two cases of ‘low stress–high strain’ and ‘high stress– low strain’ failure along the cross and machine directions, respectively. Also, the failures are dominated by shear when the fabrics are tested at 34° and −34°. The fracture edges are shown for each case in Fig. 5.11. As expected, failure tends to propagate along the dominant orientation angle. The propensity for shear deformation along the direction of preferred fiber orientation is clearly manifested in these tests. The unit-cell shear deformation results are shown in Fig. 5.12. It is clear that application of a macroscopic tensile strain produces a significant shear deformation along the initially preferred direction in fiber ODF, except when the two directions are either parallel or normal to each other. The degree of asymmetry in the structure is shown in Fig. 5.13. As may be noted, the moments are

Structure and mechanics of nonwovens

30 0° 25

Load (N)

20 –34° 34°

15 10

90° 5 0 0

20

40

60

80

100

120

Extension (%)

5.11 Stress strain behaviour and fracture surfaces.

150

0° 56°

Shear angle (°)

100

90° 146°

50 0 –50 –100 0

10

20

30

40

Fabric strain (%)

5.12 Shear angle as a function of strain.

50

60

129

130

Structure and mechanics of textile fibre assemblies 0.10 0 Asymmetry parameter

34 0.05

–34 90

0.00

–0.05

–0.10

0

10

20

30

40

50

60

Fabric strain (%)

5.13 Asymmetry parameter as a function of strain.

greatest when the test is performed in directions other than the two principal directions (machine and cross). It has been shown clearly that the fabric performance is a function of its structure or the manner in which the fibers are arranged within the structure. It has also been revealed that, while failure can follow different modes, it is likely to be dictated, under most conditions, by shear along the preferred direction of fiber orientation. Regardless of bonding conditions (a most important processing parameter), the structural changes brought about in the structure and the microscopic deformations are driven by the initial orientation distribution function (ODF) of the fibers and are similar for all structures with the same initial ODF. The bonding conditions only dictate the point of failure. The magnitude of the moment during the deformation process that can arise around the tensile test direction and also its direction can be determined by the asymmetry parameter. It is confirmed that from the asymmetry parameter values the moments are greatest when the test is performed in directions other than the two principal directions (machine and cross).

5.6

Failure mechanisms

As is usual, the main source of failure in nonwovens is defects. Those defects can be split into two categories: non-uniformities, mostly originating from the web formation, and over/under bonding. As it has been shown previously, once failure is initiated, its propagation is essentially ruled by the ODF.

Structure and mechanics of nonwovens

131

The foremost factor in this category is the so-called basis weight uniformity of a nonwoven. This refers to the degree of mass variation in a nonwoven normally measured over a certain scale. Local variation of the mass results in unattractive appearance, but more importantly will lead to, and potentially dictate the failure point of a nonwoven. For example, tensile failure may be initiated and propagated first in areas that are fiber-poor (region with low mass), or barrier properties are lost because of the existence of fiber-poor regions in the fabric. Variation of mass (basis weight) in webs, paper and nonwovens has historically been used as an index of uniformity in nonwovens [9]. The method employed often involves the direct measurement of the coefficient of variation of the weight of numerous samples of a given size. A major difficulty in determining the basis weight uniformity lies in the fact that the measurement is often size dependent. That is, the variations occurring at a given size will not be the same as those at another size. There have been a number of attempts reported in the literature dealing with the development of appropriate sensor strategies for automating this process [10–12]. Boeckerman provides an excellent review of the sensor requirements for basis weight measurements [13]. Of significance however, is the work employing image analysis methods. The use of image analysis for determining basis weight uniformity on the basis of the variations of the optical density is not a new concept. For a review of the relationship between optical density and basis weight, refer to reference 9. Mass variations in an image result in the formation of spatial details and specific textures. In other words, the mass variation, when properly illuminated, appears as slowly (spatially) varying signals superimposed by high frequency texture. Since a texture is an image property, its parameters are determined as much by the viewing perspective and resolution of the imaging system as the physical surface it represents. Apropos of this, we are ultimately interested in both how an automated system may process texture information and what features are most important to the eye-brain system of the consumer. Heuristically, one may ask whether the position of a given unit is predictive of other such units in its vicinity. If the probability of finding another unit is high, the units are said to be clumped or aggregated, if low, their distribution is uniform, and if position is not predictive, the units are distributed in a random fashion. In a nonwoven, it is rather impractical to define a ‘unit’ or an ‘object’. The area being examined must be sufficiently large to be representative of the overall fabric structure. An image of a large section of the fabric will lack spatial resolution and the details of the structure cannot be resolved to define appropriate units. However, since any mass non-uniformity will be reflected in variations in local image intensity, one can resort to methods that determine uniformity for a given area.

132

Structure and mechanics of textile fibre assemblies

It is in fact, common in industry to have sensors sample and determine basis weight for areas 1 cm2 or smaller. The problem with this methodology is that the data may not be comparable to that measured say, over a 4-cm2 area. This issue was partly treated by Xuan and Bresee for nonwovens [9] where they measured the mean image intensity and coefficient of variation (CV) of the image brightness for a range of window sizes to create ‘nonuniformity spectra’. This type of methodology is not new however, and is referred to in the literature as the ‘quadrant method’ (see Wiegert, 1962 [14]). Quadrant based methods have been used by Ecologists for many years to identify an appropriate ‘window size’ for determining uniformity of spatial distributions of plants and animals. It has been suggested in the literature [8] that CV values are high for areas measuring 4 mm2 and that they become insensitive to size beyond cell areas greater than 4 mm2. While this may be true for one specific set of samples, the conclusion may not hold for other samples. The sensitivity to size is indeed a structure property that should vary with the degree of uniformity of the sample. That is, if the sample has little or no variation, then it will be expected that there would be little or no variation in the CV regardless of the size and as a function of size. On the other hand, as the sample becomes more non-uniform, then it should be expected that the CV will increase as a function of size. Regardless of the system used, the issues with the number of samples required and their location have to be dealt with as well. Typical density variations range in different spatial dimensions. For a full description of the strategies for the measurement of basis weight refer to references 15 and 16. The variation in basis weight is a critical attribute that controls both the appearance and the failure characteristic of a nonwoven. This is especially important in light weight nonwovens where the blotchiness can be readily seen. Most nonwovens would not have to be as heavy as they are if it were not for covering their blotchiness. An important implication is that better uniformity can lead to lower weights and concomitantly significant cost savings. It must be noted that an index of basis weight uniformity if measured over a certain area does not necessarily relate to an index measured over another area. For example, the uniformity measured over an area measuring 1 cm2 may be significantly different from one measured at say, 10 cm2 when the nonwoven is nonuniform. On the other hand, the indices would be little or no different if the nonwoven was perfectly uniform. An ideal method would be invariant to size and would employ this characteristic to measure the uniformity [16]. Another characteristic of a nonwoven may be the extent to which the fiber diameter varies in a nonwoven. This is particularly important in spunbonded and meltblown structures where the fiber diameter variation may

Structure and mechanics of nonwovens

133

come about as a result of roping (fibers sticking together to form bundles) or because of the process leading to thin and thick fibers. This becomes significant at the micro scale and can lead to failure in a similar manner to the variations in basis weight. In calender and thru-air bonding, it is quite easy to obtain under-bonded or over-bonded structures. Under-bonding occurs when there are an insufficient number of chain ends in the molten state at the interface between the two crossing fibers or there is insufficient time for them to diffuse across the interface to entangle with the free ends of the chains in the other fiber. Thus, only a few tie chains exist and the bonds can be easily pulled out or ruptured under load. The formation of a bond requires partial melting of the crystals to permit chain relaxation and diffusion. In the case of underbonding, insufficient melting has occurred or too little time for diffusion was allowed prior to cooling. Over-bonding occurs when many chains have diffused across the interface and a solid, strong bond has been formed. The fibers within the bond spot have lost their orientation and their strength, but the bond spot itself represents a more rigid and larger area compared to the fibers entering the bond spot. The fibers entering the bond have also lost some of their molecular orientation (and strength) at the fiber bond interface. They may have also become flat and irregular in shape. The bond site edge becomes a stress concentration point where now the weaker fibers enter. In a fabric under load, this mechanical mismatch results in the premature failure of the fibers at the bond periphery. Over-bonding occurs when too much melting has occurred. Figure 5.14 shows images of under-bonded and over-bonded bond spots. Note, in the under-bonded case, the fibers in the bond still maintain their shape and definition; significant melting has not occurred. In the overbonded bond spot however, significant melting (and shrinkage) has occurred and fibers begin to or have lost definition. The mechanical properties of the resultant fabrics can be influenced significantly by a difference of only a few degrees in the bonding temperature.

5.14 Under-bonded (left) and over-bonded (right) bond spots.

134

Structure and mechanics of textile fibre assemblies 50 40

Load (N)

160 °C

150 °C

30 20

180 °C 140 °C

10 170 °C 0

0

20

40

60 80 Extension (mm)

100

12

5.15 Typical load-extension behavior as a function of bonding temperature.

Typically, for a given set of processing conditions, there is an acceptable bonding temperature window for optimal bonding. Temperatures below this window will lead to under-bonded and temperature above this limit will yield over-bonded, stiff structures. Furthermore, it is commonly believed that the bond spots are rigid. Recent experimental evidence [17] suggests that this is not always true. Indeed, the bond area domains can undergo substantial deformation in many testing configurations. It is generally true that the strength of the structure improves with bonding temperature, reaches a maximum, and then declines rapidly because of over-bonding and premature failure of the fibers at the fiber bond interface. However, the structure stiffness (tensile modulus, bending rigidity and shear modulus) continues to increase with bonding temperature. Figure 5.15 shows a typical load-extension behavior for a polypropylene carded calendered nonwoven. Note that the structure is under-bonded at 140 degrees C and becomes over-bonded at temperatures above 170 degrees C. The optimal properties lie between 150 and 160 degrees C. Where temperature was the parameter used to gauge bonding previously, the amount of energy transferred to the web is used in the case of hydroentangling. The hydroentangling energy calculation is based on Bernoulli equation that ignores viscous losses throughout the system. Having the manifold’s pressure, P1, the jet velocity is: V1 = 2 P1 ρ

5.8

Where r = 998.2 kg/m is the density of water at room temperature, P1 is the pressure in Pa, and V1 is in m/s. Note that 1 bar is equal to 105 Pa. The rate of energy transferred by waterjet is calculated as follows: 3

Structure and mechanics of nonwovens

135

π E = ρd 2Cd V 3 8

5.9

where d is diameter of the orifice of the capillary section in .metres (0.127 mm in the system used), Cd is the discharge coefficient, and E is energy rate in J/s. Specific energy is calculated based on the following formula: ⎡ J ⎤ E SE ⎢ 5.10 ⎥=  ⎣ kg fabric ⎦ M . where M is the mass flow rate of the fabric in kg/s and is calculated as follows:  = Samplewidth [ m ] × Basisweight [kg m 2 ] × Beltspeed [ m s] M

5.11

Therefore, SE will be obtained in Joules per kg of fabric. This can also be expressed as Watts per kg of fabric. Two sets composed of a total of ten fabrics were prepared with the following processing parameters from nylon and polyester staple fibers measuring 3 cm in length. The linear densities were 1.8 and 1.5 deniers respectively for nylon and polyester. Webs were prepared by carding. All web characteristics (web structure and density) were kept constant. The samples in each set were submitted to increasing specific energy. As can be seen from Fig. 5.16, both appear to show an increase in their tensile properties with energy until reaching a peak at the same critical energy and then declining rapidly.

12

Maximum tensile stress (N/mm)

10

Nylon Polyester

8 6 4 2 0

0.0

0.5

1.0

1.5

2.0

2.5

Energy (kw/kg)

5.16 Peak tensile failure stress for polyester and nylon samples.

136

Structure and mechanics of textile fibre assemblies

5.7

Modeling nonwoven fabric mechanics: thermally bonded nonwovens

Thermally bonded nonwovens are probably the easiest to simulate amongst the variety of structures nonwovens can have. They are usually thin and light-weight so, for most purposes, they can be considered as bidimensional. Additionally, in the case of point-bonded nonwovens, the pattern of the bonds provides some order of unit cell. There are two main approaches to represent the structure of a nonwoven: a macroscopic one, which uses a bulk equivalent material, or a microscopic one, which details each and every fiber in the web.

5.7.1 Macroscopic scale The web is considered as a flat sheet and meshed for the purpose of a finite element analysis. The fiber orientation function and local fiber density can be used to generate the rigidity matrix of each element. A good example for this approach is given by Liao et al. [18–19]. The results are somewhat insufficient for a standalone nonwoven simulation but very useful when the nonwoven is part of a larger structure, like a composite.

5.7.2 Microscopic scale A number of pioneering researches have been done for two-dimensional fiber assemblies. Cox [20] was the first to offer a fiberweb theory to discuss the effect of fiber orientation distribution function (ODF) on the stiffness of a fibrous web. The earliest publications directly related to the mechanics of nonwoven fabrics are due to Petterson and Backer [21–22]. They also developed a fiberweb theory for dense, well-bonded thin fiberwebs, similar to that of Cox. Hearle and Stevenson [23] generalized Petterson’s fiberweb theory to include the effect of fiber curl. Allan and his co-researchers [24] studied spot-resin-bonded nonwoven structures. The characterization of the fiber-binder contacts, the bonded and the free lengths of fibers in the web, and the nearest neighbor distance of a spot were discussed. In the early 1980s, Britton et al. [25–27] demonstrated the feasibility of computer simulation of the behavior of a network generated mathematically. Grindstaff and Hansen [28] on the other hand developed a computer simulation for stress-strain curve of point-bonded fabrics, but their results have limited applicability, because several important effects, such as bond pattern, bond area fraction, shape of bond site, fabric strength mechanism and even fiber orientation distribution function (ODF) were not included. This type of simulation can be split in three stages: web generation, bonding and mechanical simulation.

Structure and mechanics of nonwovens

L/2

137

α

α L/2

d

P

O

5.17 μ and I randomness.

5.7.3 Web simulation There are two ways to approach it: generate a representative web or an equivalent web. For the first case, Pourdeyhimi et al. [29] developed two techniques, the use of which depends on the fiber type: μ-randomness for continuous fibers and I-randomness for staple fibers. These methods have been fully detailed and their use justified in [29–32]. They can be summed up as follows (Fig. 5.17). m-randomness A line is defined by the perpendicular distance d from the center of the sample and the angular position of the perpendicular α. The distance d is sampled from a random distribution and the slope α from 90° minus a value from the ODF. A line is then drawn perpendicular to the α direction, distance d away from the center. In order to get a uniformly random web, the sample size must be increased by a factor 2 before the generation process and then cropped back to its original size. The sample must be square or momentarily expanded into a square. I-randomness A point P is chosen at random by its coordinates such that it lies in a surface larger than the original sample size by length l. This ensures that edges of the sample are intersected by appropriate fibers of length l having their center of mass outside the sample. Next, a slope α is selected from the ODF and a segment of length l with slope α and with the point P as its middle is created. The sample is cropped to its original size and can be rectangular. For generating an equivalent web, Mueller et al. [33] used a star shape pattern (Fig. 5.18) in which the lines represent bundles of fibers. The basis

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5.18 Orientation of link elements representing unbonded fibers in the base cell.

weight is obtained from the total number of fibers and the ODF from the repartition of these fibers among the bundles.

5.7.4 Bonds The key here is of course to respect the pattern and shape of the bonds. For their mechanical behavior, they can be considered as without deformation or following the isotropic material behavior. However, the delicate part is the interface between the bonds and the fibers, where it is usually safe to assume a behavior similar to degraded fibers. This degradation can be modeled by various means: reduced modulus, reduced breaking load and extension or a scaled down version of the fiber stress strain curve.

5.7.5 Deformation simulation In the case of a finite element based model, the solving of the mechanical equations is taken care of by a computational finite element solver, like ANSYS. The main limitation is that the geometry cannot be altered on the fly and thus the progressive breakdown of the web due to fibers failing can not be shown. For the other model, a force network approach must be used. The web is deformed by small steps and for each of those, the forces exerted by the fibers on the bonds must be balanced. In order to reach this balance, the bonds are moved and rotated in small increments. Once balance is reached, the fibers which have gone beyond their breaking point are removed and the web must be balanced again. This a very time consuming

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process but it has the advantage of showing both the necking and complete failure of the fabric.

5.8

References

1. Webster’s Dictionary. 2. Folgar, F. and C. Tucker III, J. of Reinforced Plastics and Composites, 3, 98–119, (1984). 3. Kim, H. S., Deshpande, A., Pourdeyhimi, B., Abhiraman, A. S. and P. Desai, ‘Characterizing Structural Changes in Point-Bonded Nonwoven Fabrics during Load-Deformation Experiments’, Textile Research Journal, 71(2), 157–164, (2001). 4. Kim, H. S., Pourdeyhimi, B., Abhiraman, A. S. and P. Desai, ‘Angular Mechanical Properties in Thermally Point-Bonded Nonwovens, Part I: Experimental Observations’, Textile Research Journal, to appear. 5. Lee, S. M. and A. S. Argon, ‘The Mechanics of the Bending of Nonwoven Fabrics, Part I: Spunbonded Fabric (Cerex)’, Journal of the Textile Institute, No. 1, 1–11, (1983). 6. Lee, S. M. and A. S. Argon, ‘The Mechanics of the Bending of Nonwoven Fabrics, Part II: Spunbonded Fabric with Spot Bonds (Fibretex)’, Journal of the Textile Institute, No. 1, 12–18, (1983). 7. Lee, S. M. and A. S. Argon, ‘The Mechanics of the Bending of Nonwoven Fabrics, Part III: Print-Bonded Fabric (Masslinn)’, Journal of the Textile Institute, No. 1, 19–30, (1983). 8. Pourdeyhimi, B., Dent, R., Jerbi, A., Tanaka, S. and A. Deshpande, ‘Measuring Fibre Orientation in Nonwovens, Part V: Real Fabrics’, Textile Research Journal, 69, 185–192, (1999). 9. Xuan-chao, H. and R. Bresee, ‘Characterizing Nonwoven Web Structure Using Image Analysis Techniques, Part III: Web Uniformity Analysis’, INDA Journal of Nonwovens Research, 5(3), 28–38, (1994). 10. Drouin, B., Gagnon, R., Cheam, C. and J. Silvy, ‘A New Way for Testing Paper Sheet Formation’, Composites Science and Technology, 61, 389–393, (2001). 11. Kallmes, O. J., ‘Techniques for Determining the Fiber Orientation Distribution Throughout the Thickness of a Sheet’, Tappi, 52, 482, (1969). 12. Kallmes, O. J. and H. Corte, ‘Formation and Structure of Paper, 1, Technical section’, British Paper and Board Maker’s Association, William Clowes & Sons, Ltd., London, 13–46, (1962). 13. Boeckerman, P., ‘Meeting the Special Requirements for on-line Basis Weight Measurement of Lightweight Nonwoven Fabrics’, Tappi, 166–172, (1992). 14. Weigert, R. G., ‘The Selection of an Optimum Quadrant Size for Sampling the Standard Crop of Grasses and Forbes’, Ecology, 43, 125–129, (1962). 15. Pourdeyhimi, B. and L. Kohel, ‘Area Based Strategy For Determining Web Uniformity’, Textile Research Journal, 72(12), 1065–1072, (2002). 16. http://www.allasso-industries.com 17. Kim, H. S. and B. Pourdeyhimi, ‘The Role of Structure on Mechanical Properties of Point-Bonded Nonwovens’, International Nonwovens Journal, Volume 10, (2), (2001).

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18. Liao, T., Adanur, S. and J.-Y. Drean, ‘Predicting the mechanical properties of nonwoven geotextiles with the finite element method’, Textile Research Journal, 67, 753–760, (1997). 19. Liao, T. and S. Adanur, ‘Computer simulation of mechanical properties of nonwoven geotextiles in soil-fabric interaction’, Textile Research Journal, 68, 155–162, (1998). 20. Cox, H. L., ‘The Elasticity and Strength of Paper and Other Fibrous Materials’, British Journal of Applied Physics, 3, March 1952, p. 72–79. 21. Petterson, D. R., ‘On the Mechanics of Nonwoven Fabrics’, D. Sc. Thesis, M.I.T., August 1958. 22. Petterson, D. R. and S. Baker, ‘Relationships Between the Structural Geometry of a Fabric and Its Physical Properties, Part VII: Mechanics of Nonwovens: Orthotropic Behavior’, Text. Res. J., 33, 809–816, (1963). 23. Hearle, J. W. S. and P. J. Stevenson, ‘Studies in Nonwoven Fabrics, Part IV: Prediction of Tensile Properties’, Text. Res. J., 34, 181–191, (1964). 24. Allan, G. G., Ong, C. L. and E. M. Passot, ‘Fundamentals of Fiber Assemblages, VI. Spot-Bonded Nonwoven Structures’, Cellulose Chem. & Tech., 18, 223–243, (1984). 25. Britton, P. N., Sampson, A. J., Elliott, C. F. Jr., Graben, H. W. and W. E. Gettys, ‘Computer Simulation of the Mechanical Properties of Nonwoven Fabrics, Part I: The Method’, Text. Res. J., 53, 363–374, (1983). 26. Britton, P. N., Sampson, A. J., and W. E. Gettys, ‘Computer Simulation of the Mechanical Properties of Nonwoven Fabrics, Part II: Bond Breaking’, Text. Res. J., 54, 1–5, (1984). 27. Britton, P. N., Sampson, A. J., and W. E. Gettys, ‘Computer Simulation of the Mechanical Properties of Nonwoven Fabrics, Part III: Fabric Failure’, Textile Research Journal, 54, 425–428, (1983). 28. Grindstaff, T. H. and S. M. Hansen, ‘Computer Model for Predicting PointBonded Nonwoven Fabric Strength, Part I’, Textile Research Journal, 56, 383– 388, (1986). 29. Pourdeyhimi, B., Ramanathan, R. and R. Dent, ‘Measurement of Fiber Orientation in Nonwovens, Part 1, Simulation’, Textile Research Journal, 66(11), 713–722, (1996). 30. Pourdeyhimi, B., Ramanathan, R. and R. Dent, ‘Measurement of Fiber Orientation in Nonwovens, Part 2: Direct Tracking’, Textile Research Journal, 66(12), 747–753, (1996). 31. Pourdeyhimi, B., Dent, R. and H. Davis, ‘Measuring Fiber Orientation in Nonwovens, Part III: Fourier Transform’, Textile Research Journal, 67, 143–151, (1997). 32. Pourdeyhimi, B., Dent, R., Jerbi, A., Tanaka, S. and A. Deshpande, ‘Measuring Fiber Orientation in Nonwovens, Part V: Real Webs’, Textile Research Journal, 67, 143–151, (1997). 33. Mueller, D. and M. Kochmann, ‘Numerical Modeling of Thermobonded Nonwovens’, International Nonwovens Journal, Spring 2004.

6 Structure and mechanics of 2D and 3D textile composites C PASTORE, Philadelphia University, USA, and Y GOWAYED, Auburn University, USA

Abstract: This chapter introduces the reader to the basic technology and nomenclature associated with textile reinforced composites and presents various theoretical methodologies for the elastic characterization of textile reinforced composites. Key words: textile reinforced composites, woven, knitted, braided.

6.1

Introduction

The objectives of this chapter are to introduce the reader to the basic technology and nomenclature associated with textile reinforced composites and to present various theoretical methodologies for the elastic characterization of textile reinforced composites. These theoretical methods are supported with experimental data to demonstrate the applicability and accuracy of the methods.

6.2

Textile reinforcements for composites

Textile reinforced composites are fiber reinforced composites whose unit reinforcement structures are characterized by more than one fiber orientation. These materials are typically formed from hierarchical systems built from fibers, yarns, and fabric structures. Figure 6.1 shows a schematic illustration of the hierarchical nature of textile materials. As illustrated, the fiber is the basic unit from which textile materials are formed. Additionally it is possible to join various sub-assemblies together to form even more complex structures. Fibers can be converted into yarns, or direct formed fabrics1. Yarns can then be converted into a variety of fabric structures. Some brief descriptions of each of these material forms are presented below. A glossary of textile terms applicable for composites can be found in Pastore (1993b). A brief 1

Frequently in the literature, fabrics formed directly from fibers are (unfortunately) called nonwovens.

141

142

Structure and mechanics of textile fibre assemblies Unidirectional tape

Slit tape

Woven fabric Fiber

Yarn

Braided fabric Knitted fabric Orthogonal cross-lapped

Direct formed fabric

6.1 Schematic illustration of the hierarchy of fibers, yarns, and fabrics in textile processes.

glossary is also included in the Composites volume of the ASM Engineered Materials Handbook (1987).

6.3

Two-dimensional (2-D) fabrics

Fabrics are made using yarns or fibers as the basic manufacturing unit. Direct formed fabrics are made directly from fibers. Woven, knitted, and braided fabrics are made from yarns. These four classes represent the vast majority of fabrics used in composite materials. In the textile nomenclature, woven fabrics are formed by interlacing yarns, knitted by interlooping yarns, braided by intertwining yarns, and direct formed fabrics by interlocking fibers. A comparative discussion of fabrics for composites can be found in Clarke and Morales (1990) or Ko and Pastore (1987). Some detail is presented below. Because of the high width to thickness ratio2 of these fabrics, and the fact that they are typically layered to form a thick structure, they are called3 ‘two-dimensional’ or 2-D fabrics. This distinguishes them from 3-D fabrics, which possess a much greater inherent thickness. 2

As will be seen below, these fabrics typically have thicknesses no greater than three yarn diameters, but widths on the order of a few metres. 3 In the composites industry only.

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6.3.1 Direct formed fabrics Direct formed fabrics, as indicated above, are created directly from fibers without a yarn processing step involved. Furthermore there is no interlacing, intertwining, or interlooping of fibers within the structure. Thus these fabrics are called nonwovens in much of the literature, despite the obvious inadequacy of this term. According to ASTM. a nonwoven is . . . a textile structure produced by bonding or interlocking of fibers, or both, accomplished by mechanical, chemical, thermal, or solvent means and combinations thereof.

Generally there are two steps in the direct forming process. First a web is constructed of fibers. The web formation process dictates the distribution of in-plane fiber orientation. Next the web is densified to create a handleable material. Densification typically involves some through thickness entanglement or bonding. Interested readers are directed to Buresh (1962), or Krcma (1971), as an example, for specifics on the manufacturing process.

6.3.2 Woven fabrics Woven fabrics are by far the most commonly used textile system for composite applications. The woven structure is characterized by the orthogonal interlacing of two sets of yarns, called warp and weft yarns. The warp yarns are aligned with the direction of the fabric leaving the loom, which is also called the warp direction. A warp yarn may also be called an end. The weft yarns run perpendicular to the warp direction, and are sometimes called fill yarns or pick yarns. Interested readers are directed to Lord and Mohamed (1982) for details on the weaving process. The woven structure is realized through a loom, which fundamentally consists of five components: a yarn supply (either a creel or a warp beam), harnesses, a filling insertion mechanism, a combing mechanism, and a takeup mechanism. A simplified loom is illustrated in Fig. 6.2. There may be additional mechanisms in a modern loom to optimize performance, but these five are essential in even the most primitive loom. Some of the most basic 2-D weave structures are illustrated in Fig. 6.3. In this figure, the three most common weave structures, plain weave, twill weave, and satin weave are shown. Each of the warp and weft yarn elements can be considered to be either inclined (as it passes from top to bottom of the fabric) or straight (as is passes over or under another yarn). In the case of a plain weave fabric, the entire yarn length (for both warp and fill) is inclined as the yarn is continuously moving from the top to the bottom of the fabric. In the case of a satin

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Fill

Structure and mechanics of textile fibre assemblies

Hamess frame

Warp

Shuttle

Fill Warp yarns

z

Warp

Heddle

Harnesses Filling yarn Filling insertion

Yarn supply

Combing

Tensioning system

Take-up z Warp

6.2 Schematic illustration of a primitive loom.

weave, the yarns maintain some in-plane linear segment before sinking or floating to the bottom (or top) of the fabric. The length of the in-plane linear segment in a n-harness satin is the distance required to traverse n-number of yarns, as shown in Fig. 6.3. Thus, in a simplistic manner a plain weave can be considered as a two-harness satin weave. It should be noted that this nomenclature is not used in the textile industry, and is introduced here for generalization purposes only. Of interest is the crimp associated with the yarns. The crimp is defined as one less than the ratio of the yarn’s actual length to the length of fabric it traverses. Crimp levels influence fiber volume fraction, thickness of fabric, and mechanical performance of fabric.

6.3.3 Weft knitted fabrics There are two basic types of knitting, weft knitting and warp knitting. Although both are loop making processes, they are distinguished by the direction in which the loops are formed. Weft knitting, the most common type of knitting in the apparel industry, forms loops when yarns are moving in the weft direction, or perpendicular to the direction of fabric formation.

Structure and mechanics of 2D and 3D textile composites

Plain weave

2/1 Twill

Crowfoot twill

2/2 Twill

5 Harness satin

145

2/2 Basket

8 Harness satin

2/1 Twill

Plain weave

5 Harness satin weave

2/2 Basket weave

6.3 Schematic illustration of various weave structures.

This is also called the course direction. The direction in which the fabric is formed is called the machine direction, warp direction, or wale direction. There are many excellent texts describing the details of weft knitting, such as Chamberlain and Quilter (1924), Reichman et al. (1967), or Thomas (1976). The simplest weft knit structure is the jersey weft knit, sketched in Fig. 6.4. The repeating unit loop structure is called a ‘knit.’ This type of structure is used in many undergarments, scarves, and other apparel applications. The geometry of the jersey knit is measured by the density of courses (courses per inch or cpi) and the density of wales (wales per inch, or wpi).

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Structure and mechanics of textile fibre assemblies 1/wpi

1/cpi

Warp

Weft (course)

6.4 Schematic illustration of jersey knit.

The weft knitted structure is inherently bulky due to the high curvature of the yarn and the interlooping structure. The ‘natural’ thickness of a jersey knit fabric is roughly three times the thickness of the constituent yarns, resulting in yarn packing factors of 20–25%. Combining the fiberyarn packing factor (typically around 60–75%) results in 15–20% fiber volume fractions in the undeformed state. One feature of weft knitted fabrics useful for composites applications is their high extensibility (up to 100% strain to failure) that allows complex shape formation capabilities. There are many variations to the weft knitted fabric that can be realized. One of interest to composites applications is the use of rib knitted structures. The basic rib knit is illustrated in Fig. 6.5, which consists of sequences of knits and purls4. In a rib knit structure it is possible to incorporate large yarns in the course (weft) direction to create a weft inserted rib knit. In such way a ‘unidirectional’ preform can be constructed. However, as shown by Ramakrishna and Hull (1994), it is difficult to achieve fiber volume fractions greater than 30% in these structures due to the inherent bulkiness of the fabric. 4

A purl can be considered as a ‘knit’ which has been reflected through the plane of the fabric.

Structure and mechanics of 2D and 3D textile composites Rib knit

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Rib knit with weft inserts

Warp

Weft (course)

6.5 Schematic illustration of rib knit and weft inserted rib knit.

6.3.4 Warp knitted fabrics Warp knitting differs from weft knitting in that multiple yarns are interlooped simultaneously. A set of yarns are supplied from a creel or warp beam and interlooped in the cross (course) direction. Of particular interest for the composite technology is the use of warp knitting for the production of weft inserted warp knits (WIWK), Multi-bar weft inserted warp knits (MBWIWK), and multiaxial warp knits (MWK). Details of warp knitting can be found in Thomas, for example. The WIWK and MBWIWK are warp knitted fabrics with large load bearing yarns incorporated into the fabric structure in the machine (wale) direction. In the WIWK, the load bearing yarns are locked into the structure through the knitting process (Fig. 6.6), not unlike a 90° rotation of the warp inserted weft knits described previously (for example, see Ko et al. (1980) or Scardino (1989)). In the case of MBWIWK, yarns are introduced in the weft and warp direction simultaneously. To keep the warp yarns interlocked with the fabric, the supply of warp yarns moves in the weft direction during insertion to create a quasi-sinusoidal path with respect to the warp direction (Fig. 6.6), see Ko et al. (1985), or Pastore et al. (1986). MWK allow the placement of warp, weft, and off-axis materials directly into the fabric structure; see Ko et al. (1986) for example. There are two basic types of warp knit structures, those which impale (such as the Liba system, Kaufmann (1991)) and those which do not impale (such as the Mayer system, Raz (1989)). Liba type systems can incorporate materials other than yarns into the knitting structure and use the knitting process as a form of stitching to combine multiple layers of fabric together. The Mayer type system needs yarns as input. The yarn passes between the knitting

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Structure and mechanics of textile fibre assemblies

WIWK Basic tricot warp knit stitch

MBWIWK Warp

MWK

Weft

6.6 Schematic illustration of WIWK, MBWIWK, and MWK warp knit fabric structures.

needles. This is capable of placing the off-axis (bias) yarns at angles ranging from roughly 20° to 80° with respect to the warp axis. MWK fabrics are currently of more interest than the WIWK or MBWIWK due to the increased flexibility in yarn placement (Raz (1987)). One of the most attractive features of this type of fabric is the ability to combine multiple layers of oriented yarn in a single structure. However there are limitations to the processing, depending on the particular technique (Liba or Mayer) in use. In the case of Mayer type systems, a four layer fabric is always produced as [90/0/θ/-θ]. This means that symmetric stacks can only be achieved through introduction or removal of individual layers of yarn.

Structure and mechanics of 2D and 3D textile composites

Diamond braid (1/1)

Regular braid (2/2)

149

Hercules braid (3/3)

6.7 Schematic illustration of diamond, regular, and Hercules braided fabric structures.

6.3.5 Braided fabrics The intertwining of yarns about each other creates braided fabrics. Details of braided fabrics can be found from a variety of sources, such as Krumme (1927), Brunschweiller (1953), Douglass (1964), and Ko et al. (1989). Braided fabrics are available in three typical structures: diamond braid, regular braid, and Hercules braid. The machine dictates the particular braid pattern. The diamond braid has an intertwine pattern characterized by any given yarn passing over one opposing yarn, then under one opposing yarn, and repeating this pattern. This is designated as 1/1. In this nomenclature, regular braids are 2/2, and Hercules braids are 3/3. Figure 6.7 illustrates the basic geometric nature of these fabrics. The regular braid constitutes the vast majority of all braided fabrics made. It should be noted that the Hercules braid is a very rare construction, and it is very difficult to find machines capable for producing these fabrics. On the other hand, diamond braids can be made using a regular braid machine. Generally tubular in form, the biaxial braided fabrics may incorporate a longitudinal yarn within the fabric structure, creating a triaxial braid. Figure 6.8 shows a triaxial regular braid, showing how the longitudinal (sometimes called ‘triaxial’) yarns are entrapped in the fabric structure. The braided fabric is characterized mainly by the braid angle, θ, (which can vary from about 10° to about 80°, depending on yarn size and existence and size of longitudinal yarns, if a triaxial braid), cover factor (the fraction of yarn projected surface area per unit area), and percent longitudinals (the ratio of volume of longitudinal yarns to volume of all yarns in a unit volume).

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Structure and mechanics of textile fibre assemblies

x

θ y

6.8 Triaxial regular braid.

Because the braided fabric is formed in a tubular form, it is frequently compared with filament winding in terms of manufacturing, and has been shown to be cost competitive (see Sanders (1977) or Morales (1992)). The braided fabric is flexible before formation, and thus the fabric can conform to various shapes. The braided fabric may be formed around a mandrel, and rather complex shapes can be formed (see Ko and Pastore (1990) or Johnson et al. (1993) for example).

6.3.6 Assembled fabrics In some cases different fabric systems are assembled together through various processes such as sewing or stitching, needle punching, or knitting. This is generally accomplished to increase the overall thickness of the preform before infiltration with a liquid resin. Additionally, depending on the type of assembly employed, the through thickness performance characteristics may be enhanced. There has been a great deal of interest in stitched woven and braided fabrics, wherein a series of fabrics are stacked upon each other until some desired thickness and stacking sequence is attained. This assembly is then sewn through the thickness using a load bearing yarn. In addition to debulking the fabric assembly before placing it in a mold, the stitching yarn provides some through thickness strength and stiffness properties but may cause stress concentration due to yarn breakage. Depending on the yarn size and frequency of stitching, the effect of this vertical reinforcement varies. However it appears that there may be some significant resistance to

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delamination, and subsequently compression after impact strength due to this reinforcement approach. Another mechanism for assembling fabrics is to pass them through a needle punch process (see above) to provide some layer-to-layer entanglement through broken fibers. The needles puncture the fabric layers, break filaments from the yarns, and the broken filaments are directed through the thickness of the fabric to provide some z-directional properties.

6.4

Three-dimensional (3-D) fabrics

Three-dimensional fabrics are so called because they can be formed to near net shape with substantial thickness. There is no need for layering to create a part, thus a single fabric provides the full three-dimensional reinforcement. These 3-D fabrics are based on centuries old technology in both weaving (see Lord and Mohamed (1982)) and braiding, (see Pastore (1988) or Dexter et al. (1985)). Since the late 1960s, emphasis on designing these fabrics for composite reinforcement created a technological drive which resulted in the creation of new mechanisms for the production of 3-D woven fabrics (e.g., Bluck (1969), Maistre (1978), Dow and Ramnath (1985) and Malek and Pastore (2000)) and 3-D braided fabrics (see Stover et al. (1971), Florentine (1982), Weller (1985), Brown (1986), Brookstein et al. (1996), and Mungalov and Bogdanovich (2002) for example).

6.4.1 Three-dimensional woven fabrics Three-dimensional weaving is a variant on the two-dimensional weaving wherein more than two yarns are in the thickness direction. An extension of ancient technology for forming double and triple cloth (see Lord and Mohamed (1982)), three-dimensional weaving allows the production of fabrics up to 10 cm in thickness. Figure 6.9 shows a schematic cross-sectional view of the yarn path in a 3-D woven fabric. The weaver or web yarn takes a path through the thickness and along the length. Three-dimensional woven reinforcements were considered in the early 1970s as reinforcement for brittle matrix composites (e.g. Roze et al. (1970)). Since then the technology has made these materials much more cost effective and they are under consideration for polymer matrix reinforcements, as was shown in Tolks et al. (1986), Morales and Pastore (1990) and Smith and Dexter (1991), for example. One of the attractive features of 3-D weaving is the ability to taper the shape in all three directions during the weaving process, producing near net shape fabrics, which can be placed directly in a mold with no additional touch labor. It should be noted that in the case of fully tapered 3-D woven fabrics there are some cut-ends that are necessarily formed. The fundamen-

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Structure and mechanics of textile fibre assemblies Z-yarns Fill Warp

6.9 Three-dimensional layer-to-layer weave showing the warpthickness plane of the structure.

tal nature of 3-D weaving is the orthogonal placement of yarns in the warp and weft (typically x and y) directions – thus shaped structures which can be made with 2.5-D fabrication techniques can also be formed with 3-D weaving. The details of creating the actual woven structure and making a good weave to hold the material together is currently primarily a matter of craft. Although algorithms have been developed to numerically describe the weaving process (see Morales and Pastore (1990)), these algorithms do not consider the range of possible weave structures and their effects on the integrity and weavability of the final structure. There are a variety of ways to create the 3-D woven structure. Generally speaking, the family of 3-D weaves is classified as layer-to-layer (Fig. 6.9), through the thickness (Fig. 6.10) and XYZ weaving Fig. 6.11. Recently a technique has been developed by Malek and Pastore (2000) to create a doubly stiffened panel using the 3-D weaving process. The skin and the stiffeners are formed as a single piece of fabric and the yarns from each section of the material interact with each other. At the intersections of the stiffeners there is little to no yarn crimp. Such capabilities to form complex shaped fabrics provide additional cost savings for composite products. There are no layups necessary thus the labor cost of the part is dramatically reduced. The weaving process is particularly effective at producing long (virtually continuous) lengths of material with widths up to about 1.5 metres. It is possible to make wider looms, but they have not yet been applied to composites formation. Three-dimensional woven fabric can provide good in-plane tensile response in the warp and fill direction. Fiber volume fractions of over 65% have been achieved. There is z-directional reinforcing fiber in the structure that leads to good damage tolerance.

Structure and mechanics of 2D and 3D textile composites

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Z-yarns Fill Warp

6.10 Through-the-thickness 3-D woven fabric showing yarn orientation in warp-thickness plane.

Z-yarns Fill Warp

6.11 XYZ woven fabric showing yarn orientations in the warpthickness plane.

However the basic woven structure has only fibers in the principal x and y directions in the plane, leading to poor shear performance.

6.4.2 Three-dimensional braided fabrics Three-dimensional braided fabrics can be considered as a variant on the spinnets produced by sailors in the 16th century, but were developed for reinforcement of brittle matrix systems in the late 1960s. Although Bluck (1969) holds an early patent related to 3-D braiding, probably the first published document establishing the basis for current 3-D braiding technology was by Stover et al. (1971), considering 3-D braiding (under the name

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Structure and mechanics of textile fibre assemblies

Omniweave) as a carbon-carbon reinforcement. Since then the technology has been further developed by Florentine (1982), Brown (1986), Li and ElSheikh (1988), Ko and Pastore (1990), Du and Ko (1991), and Mungalov and Bogdanovich (2002). A brief review of the history of 3-D braiding technology can be found in Thaxton et al. (1991). Some variations of the 3-D braiding process, such as the so-called ‘two step braid’ (McConnell and Popper, (1988)) and the AYPEX (Adjacent Yarn Position EXchange, Weller (1985)) have been developed, but these have been shown by Pastore (1988) to be topologically and geometrically equivalent to the general 3-D braid established as Omniweave. The basic principle of 3-D braiding is the mutual intertwining (or twisting) of yarns. A set of yarns are arranged in a grid (rectangular, annular or cylindrical) and the ends of each yarn are joined together at a point some distance perpendicular to the plane of yarn carrier placement (Fig. 6.12). Through motions of the yarn carriers, a ‘knotting’ of the yarns takes place and a fabric is formed. Proper movement of the yarn carriers can result in the formation of various shapes. The process is conceptually like extrusion in that a constant cross-sectional shape with virtually infinite length can be produced. However with proper manipulation it is possible to change the cross-section of the fabric as a function of length to produce very complex shaped parts (Pastore 1993a). Three-dimensional braiding is most well suited to relatively small, prismatic type reinforcement structures. They have been developed for pipes and rods, stiffening elements (I, T, J shapes), and other slender composite applications. In other cases 3-D braiding has been employed for very complex structures such as fully near-net-shape turbine rotors. Advantages of 3-D braiding are the ability to provide significant shear modulus and high levels of through the thickness reinforcement. Difficulties

Rectangular

6.12 Schematic illustration of 3-D braiding setup in rectangular form.

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155

are related to the size of the machine necessary to form large parts. Generally speaking, 3-D braiding is most suited for cylindrical objects of complex cross-sectional shape. Recently, Bogdanovich and Mungalov (2002) developed a method for creating engine valves using a 3-D braiding system allowing for an integrated reinforcement to a carbon-carbon system. Machinery developments in 3-D braiding are still limited and consequently the cost of these products is quite high compared to 3-D weaving.

6.4.3 Orthogonally cross-lapped fabrics Orthogonally cross-lapped fabrics are formed by the placement of yarns at right-angles to each other, typically in either rectangular or cylindrical space. Generally the starting point is the preparation of a ‘porcupine’, or a billet with rigidized yarns inserted perpendicular to the surface. This billet may be either flat (for rectangular) or cylindrical (e.g. Mullen and Roy (1972)). Yarns are alternately laid between these ‘quills’ in the other two orthogonal directions to create a thick structure. There is no interlacing or other form of entanglement to hold the structure together (see, for example, Lachman et al. (1978), or Fowser and Wilson (1985)). This type of preform is generally used for brittle matrix reinforcements. The ‘Euclidean’ version of the orthogonally cross-lapped fabric, called an XYZ fabric, is shown in Fig. 6.13. The ‘polar’ version, called RQZ is used for construction of thick cylindrical shapes.

6.13 XYZ orthogonally cross-lapped fabric.

156

Structure and mechanics of textile fibre assemblies

6.5

Continuous stiffness/compliance variation methods

Stiffness/compliance averaging was used to build numerical models for textile composites in lieu of the laminate theory developed for laminated composites. The basic idea is based on the premise that the elastic properties of composite materials can be calculated as the added contribution of the stiffness/compliance of each of their constituents averaged over their relative volume fractions. Many approaches were developed to account for the added geometric complexity of the textile composites as compared to laminated composites. Some of these models are listed in the ensuing sections.

6.5.1 Modified matrix method The modified matrix method (Tarnopol’skii et al. (1973) was developed to predict the elastic response of orthogonally XYZ type composites. The concept behind this method is to reduce the complexity of the problem by solving each system of reinforcement, x, y, and z separately. For example, the yarns in the z direction may be combined with the matrix material to create an effective medium in the sense of unidirectional micromechanics. The structure is now considered to be composed of x and y oriented fibers embedded in this modified matrix. This process may be repeated to eliminate an additional system of fibers. Two variants, ‘Modified Matrix Method 1’ and ‘Modified Matrix Method 2’ were introduced and are described below. Modified matrix method 1 In this approach (Tarnopol’skii et al. (1973)) two reinforcing systems (x and y, for example) are consecutively averaged with the matrix to form a mechanically equivalent homogeneous anisotropic matrix, following the approach of Abolinsh (1966). An additional step is applied such that the composite material can then be represented as a unidirectional composite with an anisotropic matrix reinforced with isotropic fibers in the remaining direction (z, in our example). In the first step, the elements of the compliance matrix for the matrix reinforced with i directional fibers are given as:

[ν (fi)Vi + nioν m ( 1 − Vi )][1 + ( nio − 1) Vi ] + [nioν m − ν (fi) ] =−

2

S (jki)

(1 − Vi ) Vi

[1 + ( n − 1) ] 2 [Vi + nio (1 − Vi )][1 + ( nio − 1) Vi ] − [nioν m − v(fi) ] (1 − Vi ) Vi (i) Skk = [1 + ( nio − 1) Vi ] E(fi) o i

Vi E (fi)

6.1

Structure and mechanics of 2D and 3D textile composites

157

For i, j and k ∈ {1, 2, 3} in which i ≠ j, j ≠ k, and i ≠ k. Here n (i) f is the Poisson’s ratio of the fiber oriented in the i direction, νm is the Poisson’s ratio of the 5 matrix material, E (i) f is the tensile modulus of the fiber oriented in the i (i ) Ef direction, nio = , Em is the tensile modulus of the matrix, and Vi is the Em relative reinforcement fraction in the ith direction. The elements of the compliance matrix for the above modified matrix (reinforced with i fibers), which are subsequently reinforced with j fibers, S(klj,i) are given as:

[Vj + n ji ( 1 − Vj )][1 + (n ji − 1) Vj ] + [S(jki) E (fi) + v(f j) ] (1 − Vj ) Vj [1 + (n ji − 1) Vj ] E (f j) (i) ( 1 − Vj ) S(jkj) − v(f j)Vi Skk Slk( j ,i) = 1 + ( n ji − 1) Vj ( j ,i) Skk =−

6.2 For i, j and k ∈ {1, 2, 3} in which i ≠ j, j ≠ k, and i ≠ k, and nji = Ef(j)/Ej(i). The elements of the compliance matrix for k fibers reinforcing the modified matrix (which contains i and j fibers) are given as: Sll =

Sll( j ,i) 1 + ( nk − 1) Vk

Slm =

( i, j ) ( 1 − Vk ) Slm − ν f Sll(i, j )Vk 1 + (ν k − 1) Vk

6.3

Where i, j, and k ∈ {1, 2, 3}; i ≠ j; j ≠ k; and i ≠ k; nk = Ef(k)/Ek(j,i). The shear modulus can be described by: ⎛ mkj ( 1 + Vk ) + 1 − Vk ⎞ ( j,i) Gkj = ⎜ G ⎝ mkj ( 1 − Vk ) + 1 + Vk ⎟⎠ kj

6.4

( j,i) ⎛ mkj ( 1 + Vj ) + 1 − Vj ⎞ (i) Gkj Gkj( j,i) = ⎜ ( j,i) ⎝ mkj ( 1 − Vj ) + 1 + Vj ⎟⎠

6.5

where

and Gkj(i) = and mkj( j, i) =

2 [(1 + ν (fi) ) Vi + uio ( 1 + ν m ) ( 1 − Vi )]

G(f j )

Gkj(i) direction fiber. 5

E (fi)

; mkj =

G(fk ) Gkj( j, i)

6.6

and G(k) is the shear modulus of the kth f

Fibers are assumed to be isotropic in this analysis.

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Structure and mechanics of textile fibre assemblies

Modified matrix method 2 Although Modified Matrix Method 1 provided a direct calculation procedure for the prediction of elastic properties of XYZ reinforced composites, an algorithmically simplified version was presented by Tarnopol’skii et al. (1973). Modified Matrix Method 2 was derived by considering the numerical simplifications under the assumption that Ef >> Em. In this approach the three-dimensional structure was reduced to a two-dimensional structure. Bolotin’s approach (1966) was then used to calculate the elastic constants of this two-dimensional material. The difference from Bolotin’s approach is that the third fiber direction, orthogonal to the plane of calculated constants, is averaged together with the matrix to form a transversely isotropic modified matrix before applying the approach. This methods yields the following equations to determine the elastic and shear moduli for a composite with Ef >> Em: Em (1 + Vk ) ⎡⎣(1 − Vi − Vj ) Vi + ( 1 + Vi + Vj ) Vj ⎤⎦ 2

Ei = Vi E f + Gij =

(1 + Vk ) (1 − Vi − Vj ) (Vi + Vj )

Gm (1 + Vi + Vj ) (1 − Vi − Vj ) ( 1 − Vk )

6.7

Where i, j and k ∈ {1, 2, 3} in which i ≠ j ≠ k. The Poisson’s ratio for the modified matrix, in this method, was primarily proposed to be calculated from E = 2G(1 + n) due to an assumption of isotropy. However, when compared to experimental results, the predicted values were very high. Subsequently Tarnopol’skii et al. (1973) proposed that the Poisson’s ratio of the composite be given as that of the fibers in the i and the j directions respectively.

6.5.2 Curved Fibers Model In order to generalize the analytical tools from strictly XYZ type fabrics to include woven and 3-D woven reinforcements, Roze and Zhigun (1970) introduced their model for curved fibers and employed the Modified Matrix Method for solution. In the Curved Fibers Model, it was assumed that the reinforcement consisted of linear yarns in the y direction, and curved yarns in the x-z plane. These yarns were assumed to be located in equidistant planes (y = constant). The path of these yarns alternated in two steps. The yarns located in odd layers are assumed to have paths described by: z1( x ) = Af ( x ) = Af ( x + l ) = − Af ( x + 1 2)

6.8

and for even layers as: z2 ( x ) = − Af ( x ) = − Af ( x + l ) = Af ( x + 1 2)

6.9

Structure and mechanics of 2D and 3D textile composites

159

where z1 and z2 are the deviation of the fibers in the z direction from its average position. The angle (q) of the fibers curvature can be represented as: ⎛ ⎜ 1 θ = − cos−1 ⎜ ⎜ df ⎜⎝ 1 + A dx

( )

2

⎞ ⎟ ⎟ ⎟ ⎟⎠

6.10

The following equations give the compliance coefficients for a single element dx of the reinforcement: o * = S11 S11 − ΔS o sin 2 θ − ΔS o ′ sin 2 2θ o * = S33 S33 + ΔS o sin 2 θ − ΔS o ′ sin 2 2θ o * = S55 S55 + 4 ΔS o ′ sin 2 2θ o * = S13 S13 + ΔS o ′ sin 2 2θ * = − 1 ΔS o sin 2θ − ΔS o ′ sin 4θ S15 2 * = − 1 ΔS o sin 2θ + ΔS o ′ sin 4θ S35 2

6.11

where Sij° are the compliance coefficients for composite with straight fibers, o o ΔS o = S11 − S33 1 o o o o ΔS o ′ = [ S11 + S33 − 2S13 − S55 ] 4

6.12

The compliance coefficients of the composite Sij affected by the fibers curvature in the warp direction can be expressed as: 1  ∫ Sij*dx  0 i, j = 1, 3, 5. Sij =

6.13

Assumptions for linearity, homogeneity and isotropy of fibers and matrix as well as elasticity equations were employed in the modified matrix model and the curved fibers model. Yarn crimp, processing degradation effects, yarn interlacing effects, interfacial bond between fibers and matrix, and matrix voids and defects were not considered in this solution.

6.5.3 Stiffness averaging method The stiffness averaging method for textile reinforced composites was initially presented by Kregers and Melbardis (1978). The stiffness averaging method attempts to incorporate effects of geometrical characteristics of the reinforcement. A comprehensive discussion of this technique and its appli-

160

Structure and mechanics of textile fibre assemblies

cation to XYZ, 3-D woven, and other textile reinforced materials can be found in Lagzdin et al. (1989). One attractive feature of stiffness averaging is that although continuity of internal stresses is violated, continuity of strains (and thus displacements) is maintained. Intuitively, from the mechanics point of view, less error should be realized when maintaining continuity of displacements only than when maintaining continuity of stresses only. The stiffness averaging method consists of subdividing the reinforcement system into distinct sets of rods (yarns). Each yarn sub-system is considered to be a unidirectional composite with some spatial orientation. The individual yarn sub-systems are assumed not to interact with each other, and the composite body as a whole is assumed to be subject to a constant strain state. The sequence used to derive the global stiffness matrix can be divided into the following steps •

• • •

•

Define the elastic properties for a unidirectional rod (presenting a yarn and an equal volume fraction of matrix around it) using any acceptable micromechanics approach. Construct the local unidirectional compliance matrix S(i) from a micromechanical model. −1 Calculate the local stiffness matrix C(i) = S(i) Transform the unidirectional rod to account for individual yarn orientation in the global stiffness Cg(i):       6.14 C(gi) = QT ( r1(i) , r2(i) , r3(i) ) C(i) Q ( r1(i) , r2(i) , r3(i) )  (i)  (i)  (i)  (i) where Q( r 1 , r 2 , r 3 ) is the strain transformation matrix, and r j is the unit vector describing the local axis j of the yarn sub-system i in terms of the global coordinate system. Average the stiffness matrix of all unidirectional elements volumetrically to obtain the total stiffness matrix n

Ct = ∑ ki Cig

6.15

i =1

where ki is the relative volumetric proportion of the ith yarn sub-system. From this approach, there are two issues that strongly influence the response of the system: (i) the calculation of unidirectional properties for each yarn sub-system, and (ii) quantification of the number (and geometric properties) of yarn sub-systems. For the case of unidirectional rod properties, by comparing with experimental data, Kregers and Teters (1979a) showed that it is reasonable to assume that each sub-system is characterized by the same fiber volume fraction, which is the global fiber volume fraction of the composite as a whole. Quantification of the geometry is more complex, and needs some special treatment, as will be done later. The outcome of the geometrical model required to apply the stiffness averaging approach is the number of sub-

Structure and mechanics of 2D and 3D textile composites

161

systems, the volumetric ratio of each sub-system6, and the strain transformation matrix for each sub-system. The formation of the strain transformation matrices depend exclusively on the orientation vectors. These may be viewed as the unit vectors associated with the principal axes of the fibrous reinforcement. At this point it is worth noting that for materials reinforced with curvilinear fibers, each curved yarn sub-system can be divided into some arbitrary number of assumed piece-wise linear elements as an approximation and the approach can be applied in the presented form. In the limit, equation (6.15) can be replaced with the following modification (from the method of Roze and Zhigun (1970)) and can be used to determine the stiffness element value for the whole fiber system (see Kregers and Tekers (1979b)): n       ds L(i ) Ct − ∑ ki ∫0 QT ( r1(i) ( s) , r2(i) ( s) , r3(i) ( s)) C(i) Q ( r1(i) ( s) , r2(i) ( s) , r3(i) ( s)) (i) L i =1 6.16 where L(i) is the arc length of yarn sub-system i, and the direction vectors  r j(i)(s) are the instantaneous orientation vectors for sub-system i at any point s along the yarn path.

6.5.4 Compliance averaging method A complementary variant on the stiffness averaging technique is the compliance averaging technique. In this case it is assumed that all components of the material system are under constant stress. It is important to recall that such a model, while satisfying continuity of internal stresses, violates continuity of displacements between the phases. The algorithmic approach is the same as in stiffness averaging, except that the final result is Ct = ⎛∑ ki Sig ⎝i = 1 n

)

−1

6.17

where Sgi is the compliance matrix of yarn sub-system i transformed to the global coordinate system, given as the inverse of Cgi .

6.5.5 Stiffness-compliance blending As was seen in the case of unidirectional composite materials, neither isostrain (stiffness averaging) nor iso-stress (compliance averaging) satisfy the physical assumptions of the material. Furthermore, any averaging system implicitly assumes a dilute mixture. However, in the case of textile reinforced materials, the inherent interlacing of yarns makes the assumption of iso-strain more attractive than in the case of unidirectional composites. It must be recognized that such a blending approach violates both continuity of internal displacements and stresses. 6

Subject to the constraint that the total fiber volume fraction is equal to one.

162

Structure and mechanics of textile fibre assemblies

Jaranson et al. (1993) and Singletary (1993) have suggested that predictions of triaxially braided composites can be improved by combining elements of stiffness averaging and compliance averaging. Pochiraju et al. (1993) developed a finite element type of analysis to combine stiffness and compliance averaging for the analysis of a plain weave unit cell, based on the mosaic model of Ishikawa and Chou (1982b), but it requires substantial algorithmic treatment. A simplified approach is to blend elements of the stiffness averaged compliance vector with elements of the compliance averaged compliance vector:

)

n  n   Sb = Y ( ξ1 , ξ2 , ξ3 ) ⎛∑ S (i) + ( I − Y (ξ1(i) , ξ2(i) , ξ3(i) )) ⎛∑ C (i) ⎝i = 1 ⎝i = 1

)

−1

6.18

where Ψ(ξ1, ξ2, ξ3) is called the ‘blending matrix’ (21 × 21) for this model, I is the 21 × 21 identity matrix, and the three parameters ξ1, ξ2, and ξ3 determine the specific elements of these matrices. The stiffness vectors are constructed from the stiffness matrix. The blending matrix is purely diagonal, and is proposed as: ⎛ ξ1 ⎞ ⎜ ξ12 + ξ22 ⎟ ⎜ 2 ⎟ 2 ⎜ ξ1 + ξ3 ⎟ ⎜ ξ2 ⎟ ⎜ 1 ⎟ ⎜ ξ12 ⎟ ⎜ ⎟ 2 ⎜ ξ1 ⎟ ⎜ ξ22 ⎟ ⎜ 2 ⎟ 2 ⎜ ξ2 + ξ3 ⎟ ⎜ ξ22 ⎟ ⎜ ⎟ ⎜ ξ22 ⎟ Fii = ⎜ ξ22 ⎟ ⎜ ⎟ ⎜ ξ32 ⎟ ⎜ ⎟ 2 ⎜ ξ3 ⎟ ⎜ ξ32 ⎟ ⎜ ⎟ 2 ⎜ ξ3 ⎟ ⎜ 0 ⎟ ⎜ ⎟ ⎜ 0 ⎟ ⎜ ⎟ ⎜ 0 ⎟ ⎜ 0 ⎟ ⎜ ⎟ ⎜ 0 ⎟ ⎜⎝ ⎟ 0 ⎠ 2

6.19

Structure and mechanics of 2D and 3D textile composites

163

If we consider a ‘degenerate’ case in which there are two sub-systems, one solely matrix and the other solely fiber, and ki equal to the fiber volume fraction, the model ideally should yield a unidirectional elastic property prediction. When blending was applied to unidirectional composites a two parameter model was employed such that when ζ1 = 1 and ζ2 = 1 the result was very close to rule of mixtures predictions. Note that in equation 6.19 substituting (1,0,0) for (ξ1, ξ2, ξ3) will yield the same results. Note further that using (0,1,0) and (0,0,1) gives the same result for a fiber oriented in the 2 and 3 directions respectively. A similarity between (ξ1, ξ2, ξ3) and ξ, exists. This similarity will be exploited to assume that in general,

ξc = (ξ1 , ξ2 , ξ3 )

6.20

where ξc is some characteristic vector describing the reinforcement geometry.

6.6

Bridging Model

The Bridging Model of Ishikawa and Chou (1982b) is a combination of the ‘Crimp Model’ and the ‘Mosaic Model’ specifically focused on satin weave composites. The unit cell of the composite is presented in five ‘bricks’, as shown in Fig. 6.14. Brick III represents an interlacing in the structure, while bricks I, II, IV, and V are considered equivalent to [0/90] laminates. The mechanical properties of brick III are calculated using an analogy to the ‘Curved Fibers Model’, and the properties of the other bricks through a reduced stiffness averaging approach, following the tradition of laminated plate theory. It should be noted that this model is only appropriate for predicting in-plane properties. The model is pursued in a two-step process. The following presentation of the model only included the matrix A used to determine engineering z y x

II I

III IV

III p1

I,V

V p1√nH

p1(√nH−2)/2 p1√nH

p1(√nH−2)/2

2 p1

II , IV

6.14 Schematic illustration of RVE representation of a satin weave for the Bridging Model of Ishikawa and Chou (1982).

164

Structure and mechanics of textile fibre assemblies

constants. The B and D matrices were treated in a similar manner by Ishikawa and Chou (1982b). First, bricks II, III and IV are considered to be joined in iso-strain, yielding the result: AA =

kII + kIV kIII A II + A III kII + kIII + kIV kII + kIII + kIV

6.21

Where Aε is the reduced stiffness matrix for brick ε7 and AA is the reduced stiffness matrix of the assemblage of bricks II, III, and IV. The reduced stiffness matrix is given as: E1ε ⎛ ε ε ⎜ ν 12ν 21 ⎜ ε ε ν E A ε = ⎜ 12 ε 2 ε ⎜ 1 − ν 12ν 21 ⎜ 0 ⎜ ⎜⎝

ε ν 12 E2ε ε ε 1 − ν 12 ν 21 E2ε ε ν 12ν 2ε1 0

⎞ ⎟ ⎟ 0 ⎟ ⎟ ⎟ ε G12 ⎟ ⎟⎠ 0

6.22

where, E1ε and E2ε are the in-plane tensile moduli of the material in brick ε, ε ε G12 is the shear modulus of the material, and n 12 and n ε21 are the Poisson’s ratios. ki is the volumetric ratio of brick i to the total volume of all of the bricks, given as: kI = 1 −

2 nH nH

nH − 1 nH 2 kIII = nH kIV = kII kV = kI kII =

6.23

Where nH is the number of harnesses defining the woven fabric structure. Note that if nH is less than 4, kI is negative, thus Ishikawa and Chou caution that the model is only applicable for 4-harness satins8 and greater. This assemblage of II, III, and IV will be considered as replaced by a single brick, ‘A’, of mechanically equivalent material with mechanical prop7

It is important to note that in Ishikawa and Chou (1982b) they suggest that the local fiber volume fraction for brick III be determined distinctly from the local fiber volume fraction of the other four bricks. Thus the global fiber volume fraction of the composite is the volumetric average of the volume fractions of each brick. 8 Recall that a 4-harness satin is a 3/1 twill.

Structure and mechanics of 2D and 3D textile composites

165

erties given by CA. Next, bricks I, A, and V are considered to be smeared through an iso-stress assumption, yielding the result: At−1 = ( kI + kV ) AI−1 + ( kII + kIII + kIV ) AA−1

6.24

Where A−1 t is the inverse of the reduced stiffness matrix for the entire RVE, −1 A−1 I is the inverse of the reduced stiffness matrix of brick I, and AA is the inverse of the reduced stiffness matrix of the effective brick A. These models can be extended to consider hybrid materials (see Ishikawa and Chou (1982b)) by introducing additional bricks in the RVE, which belong to one or the other reinforcement system. A full discussion of the variations applied to this model can be found in Chou (1992).

6.7

Numerical comparisons amongst models

In the following, comparisons amongst the various models and with experimental data are presented. Analytical comparisons amongst models are made to indicate the trends and behavior of the various models. Comparisons with experiments are made to indicate the validity and usefulness of the models for predicting elastic properties of various material systems.

6.7.1 Comparison with experimental data for XYZ composites Zhigun et al. (1973) studied the effect of fiber spacing and arrangement on the elastic constants of 3-D orthogonal GRP(Ef = 73.1 GPa, Em = 3.3 GPa, νf = 0.25 and νm = 0.35). The reinforcements in this study were XYZ type orthogonally cross-lapped fabrics, wherein the spacing of the Z direction fibers was varied. Table 6.1 illustrates the fiber volume fraction and spacing of the materials considered. Table 6.2 illustrates the results obtained from the experimental data compared with predictions from the applicable models for material system Type I. All experimental data are from Zhigun et al. (1973). For the case of lapped-lapped XYZ type fabrics, the modified matrix methods are applicaTable 6.1 Reinforcement characteristics of glass reinforced XYZ fabrics I.D.

I II

Volume ratio

Fabric thickness (mm)

Vf

Vx

Vy

Vz

59.0 63.0

39.8 43.0

54.9 47.3

5.25 9.68

9 7.5

Fiber spacing (mm) x−z

y−z

4.5 4.5

9 4.5

166

Structure and mechanics of textile fibre assemblies

Table 6.2 Experimental and analytical results for XYZ Type I composites Type I Value

Experimental

MMM-1

MMM-2

Stiffness

Compliance

Blending

E1 (GPa) E2 (GPa) E3 (GPa) n12 n13 n23 G12 (GPa) G13 (GPa) G23 (GPa)

22.0 29.0 14.0 0.13 0.14 0.13 3.86 3.60 3.50

21.1 26.7 8.5 – – – 3.97 3.04 3.26

25.0 29.8 12.8 – – – 3.56 3.62 3.68

21.7 26.5 10.8 0.10 0.23 0.28 3.36 3.51 3.47

13.0 15.6 9.4 0.11 0.22 0.23 3.36 3.51 3.46

15.0 18.1 9.8 0.09 0.19 0.20 3.36 3.51 3.46

Table 6.3 Experimental and analytical results for XYZ Type II composites Type II Value

Experimental

MMM-1

MMM-2

Stiffness

Compliance

Blending

E1 (GPa) E2 (GPa) E3 (GPa) n12 n13 n23 G12 (GPa) G13 (GPa) G23 (GPa)

23.0 28.0 17.0 0.16 0.14 0.12 4.80 3.80 4.00

23.4 25.0 10.5 – – – 4.17 3.41 3.48

27.7 28.9 15.1 – – – 4.70 3.46 3.52

24.3 25.7 13.2 0.11 0.20 0.21 3.69 3.84 3.83

14.7 15.4 10.6 0.12 0.20 0.20 3.69 3.83 3.82

16.9 17.8 11.3 0.10 0.17 0.17 3.69 3.83 3.82

ble. Additionally, stiffness averaging, compliance averaging and blending are compared. Table 6.3 shows the same comparison applied to the experimental results for Type II composites. Again the experimental data are from Zhigun et al. (1973). Compliance averaging and blending do not predict modulus properties well, although the blending model seems to predict ν13 and ν23 slightly better than the others. Modified Matrix Method 2 provides the best predictions of E2, G12 and E3. Modified Matrix Method 1 and stiffness averaging methods both predict E1 rather well, and stiffness averaging provides the best predictions of ν12, G13 and G23. Stiffness averaging provides the least total error across all nine constants.

6.7.2 Comparison with experimental data for 2-D woven fabrics For the prediction of elastic properties of a generalized n harness satin weave, there are four models to consider: (i) stiffness averaging, (ii) bridging model, (iii) compliance averaging and (iv) blending model. For the purposes

Structure and mechanics of 2D and 3D textile composites

167

h R Lenticular shape

4h p1 0.5p1

6.15 Schematic illustration of example n harness satin.

of comparing the response of these models, a comparison of their predictions on satin weave fabrics with harness counts ranging from 4 to 12 are presented. The general geometry of the fabric under analytical consideration is illustrated in Fig. 6.15. The yarn cross-section is assumed to be lenticular, and is characterized by the radius R of the circles and the arc of intersection φ. The center-to-center spacing of the warp yarns, p1 is assumed to be constant. The thickness of the fabric is varied by reducing the yarns in the thickness direction while maintaining a constant cross-sectional area of the yarn, Ay, given as: Ay =

1 2 R (φ sin φ ) 2

6.25

Then the total length of warp yarn, Lw, in a unit cell can be determined by: Lw = ( nH − 2) p1 + 2 ( R + h) φ

6.26

Where nH is the number of harnesses under consideration and h is the halfthickness of a single yarn. Then the crimp in a single yarn can be given by: C = 1−

Lw nH p1

6.27

The fabric will be assumed to be ‘balanced’ in the textile sense; the warp and fill yarns are identical, have the same center-to-center spacing, and have the same crimp. The total volume of yarn, Ωy within a unit cell is given as: Ω y = 2 nH Ay Lw

6.28

due to symmetry. Thus the total fiber volume fraction can be given as Vf =

Ωy 4 hnH2 p12

6.29

168

Structure and mechanics of textile fibre assemblies 0.40

8HS

Fiber volume fraction

0.35

4HS

0.30

0.25

0.20

0.15 0.4

0.5

0.6 0.7 Unitless fabric thickness

0.8

6.16 Dependency of fiber volume fraction on fabric thickness for Example 4 and 8 harness satin weaves.

where the thickness is given as 4h, or four half yarn thicknesses. Because p1 is treated as a constant, increasing the thickness of the yarn (thus fabric) will decrease the fiber volume fraction due to the yarn width decrease. The relationship between fabric thickness and fiber volume fraction is presented in Fig. 6.16, for 4-harness and 8-harness satin weave with p1 = 2 (2 Ay ) . The thickness is given without units, where a value of 1 would be equal to 4H (as above). Similarly, the total crimp in the yarn, C decreases with increasing thickness because the relative length of the floats increases more rapidly than the local curvature around the yarn, as shown in Fig. 6.17. In the following comparisons it is important to recognize that the change in fabric thickness corresponds with the aforementioned changes in fiber volume fraction and yarn crimp. Thus increasing thickness decreases fiber volume fraction (reduces in-plane elastic properties) and decreases yarn crimp (increases in-plane properties, decreases out-of-plane properties). The woven fabrics are considered to have been formed from isotropic fiberglass yarns (Ef = 73.1 GPa, νf = 0.25) with an epoxy matrix (Em = 3.3 GPa, νm = 0.35). For each fabric thickness, fiber volume fraction is calculated and the micromechanics model of Vanyin (1966) is employed to predict the elastic properties of the unidirectional composite sub-system. Stiffness averaging, compliance averaging, the bridging model, and the blending model were applied for each fabric thickness. Figure 6.18 shows a

Structure and mechanics of 2D and 3D textile composites

169

0.4 8HS 4HS

Total crimp

0.3

0.2

0.1

0.0 0.4

0.5

0.6 Fabric thickness

0.7

0.8

6.17 Dependency of total yarn crimp on fabric thickness for Example 4 and 8 harness satin weaves.

In-plane tensile modulus (GPa)

30

20

10

Stiffness averaging Bridging Compliance averaging Blending

0 0.4

0.5

0.6 0.7 Unitless fabric thickness

0.8

6.18 Comparison of predictions of in-plane tensile modulus as a function of fabric thickness for Example 8 harness satin weaves.

170

Structure and mechanics of textile fibre assemblies

In-plane shear modulus (GPa)

2.4

2.2

2.0

1.8

0 0.4

0.5

0.6 0.7 Unitless fabric thickness

0.8

6.19 Predictions of in-plane shear modulus as a function of fabric thickness for Example 8 harness satin weaves.

comparison of the predictions of in-plane tensile modulus9 as a function of fabric thickness. As can be seen, stiffness averaging and compliance averaging bound the bridging and blending models. The differences between the models are relatively small across the entire range of fabric thicknesses, and the blending model tends towards the stiffness averaged predictions for such a high harness count. Since the woven fabric has only yarns with orientations in the x and y projected directions, there is no difference in the predictions of G12 for the various models. For the sake of completeness, the predictions of G12 are shown in Fig. 6.19. Poisson’s ratio is a more complex property to model. For the 8-harness satin weave, a comparison of the in-plane Poisson’s ratio predictions, ν12, is presented in Fig. 6.20. These predictions are quite distinct from each other, some increasing with fabric thickness, some decreasing. Notably, the bridging model shows little sensitivity to the change in thickness (and associated changes in fiber volume fraction and yarn crimp). In the case of fewer floats, the relative comparisons change. For the case of a 4-harness satin, predictions of E1 indicate that the bridging model and blending model approach each other, as shown in Fig. 6.21. Shear modulus predictions are identical for all four models and are not presented. Again Poisson’s ratios predictions are quite distinct from each 9

Because the fabric is balanced moduli in warp and weft directions are equal.

Structure and mechanics of 2D and 3D textile composites 0.6

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0.5

Stiffness averaging Bridging Compliance averaging Blending

0.4

0.3

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0.0 0.4

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6.20 Comparison of predictions of in-plane Poisson’s ratios as a function of fabric thickness for Example 8 harness satin weaves.

In-plane tensile modulus (GPa)

30

20

10

Stiffness averaging Bridging Compliance averaging Blending

0 0.4

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0.6 0.7 Unitless fabric thickness

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6.21 Predictions of in-plane tensile modulus as a function of fabric thickness for Example 4 harness satin weaves.

171

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Stiffness averaging Bridging Compliance averaging Blending

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6.22 Predictions of in-plane Poisson’s ratio as a function of fabric thickness for Example 4 harness satin weaves.

other as can be seen in Fig. 6.22. The general trend is similar to that observed for the 8-harness satin, but the bridging model has a somewhat higher slope. It can be concluded that all three models provide reasonable response for the prediction of in-plane elastic properties of n-harness satin weaves. The Bridging Model is only applicable for in-plane predictions, whereas the averaging methods are not restricted.

6.8

Numerical models utilizing finite element analysis (FEA) formulation

6.8.1 Traditional finite element analysis Many researchers have been exploring the possibility of using traditional finite element approaches to understand the mechanical response of textile composite RVE’s. This type of approach provides the opportunity to examine detailed stress fields throughout the RVE, potentially providing the information necessary for failure analysis and damage propagation studies. This type of approach is acceptable only when the solution technique satisfies all of the appropriate internal compatibility conditions, which is generally not the case in commercial FEA packages. Early work by Kabelka (1984) suggested a methodology to evaluate the elastic and thermal properties of plain weave composites using a 2-D model, which accounted for the crimp in both the warp and weft directions. Some

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2-D analyses of plain weave composites were presented by Woo and Whitcomb (1993) (using Macro Elements) and Sankar and Marrey (1993). In both works, the solution is realized through the implicit assumption of a plane strain state. Although this approach is applicable to laminated systems, in a textile composite, which has variation of geometry in all three spatial directions, this assumption is not valid and there is no way to extend these solutions to correctly model a textile composite. Three-dimensional models employing conventional finite elements have also been presented by Yoshino and Ohtsuka (1982), Whitcomb (1989), Dasgupta et al. (1992), Naik and Ganesh (1992), Lene and Paumelle (1992), Blacketter et al. (1993) and Glaesgen et al. (1995). In all of these cases, the finite element models have been developed specifically for plain weave fabric composites. Hill et al. (1994) developed finite element methodologies for 3-D woven composites, and Naik (1994) developed an approach for the prediction of elastic properties of triaxially braided composites, which also employs numerical techniques. One of the great difficulties encountered when using any of the 3-D models of the reinforcement is the difficulty in correctly quantifying the reinforcement geometry. Typically the yarns are described as circular, polygonal or lenticular in cross-section and the yarn path is described through some trigonometric relationship. Using such simplified, albeit mathematically elegant, representations of the yarn shape and path inevitably result in under prediction of fiber volume fraction. Using lenticular cross-sections and sinusoidal yarn paths typically results in maximum fiber volume fractions of 25–30%, compared with actual materials containing up to 65% fiber. Thus there has been work carried out in improving the geometric description of the reinforcement. Notably, Naik and Ganesh (1992) have developed more complex yarn path descriptions, yet still keep trigonometric functions to describe the path. They are able to achieve maximum theoretical fiber volume fractions of 37% for individual layers of fabric. Glaesgen et al. (1995) used both experimentally determined reinforcement geometries and B-spline based geometries to define the yarn paths and shapes within their model. Using the B-spline based model in accordance with Pastore et al. (1990), they were able to achieve maximum theoretical fiber volume fractions of 42%, still much lower than necessary. A unique application of FEA in modeling of textile composites, the Finite Cell Model, was developed by Lei et al. (1988b) in which the composite preform was modeled as a space truss structure. The truss consists of yarn elements and matrix ‘sticks’ on the edge of the cell (Fig. 6.23). When modeling a 3-D braid, the yarns are assumed to be the diagonals of a unit cell and the matrix is represented by a truss member, connecting two ends of each pair of yarns. Hence, the matrix plays a role in restricting the movement of the yarns giving it only three degrees of freedom in translation. An experi-

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Structure and mechanics of textile fibre assemblies Yarns Matrix

6.23 Schematic representation of yarns and matrix in the Finite Cell Model.

mental and analytical study was performed on 3-D braided systems under compressive loading.

6.8.2 Hybrid finite element analysis Using traditional FEA to mesh yarns as they move through space and touch each other, as well as meshing matrix pockets between yarns, causes singularities and problems in the numerical solution. Hybrid FEA was used by Gowayed et al. (1996) in their model Graphical Integrated Numerical Analysis (pcGINA) in an attempt to reduce the number of elements needed to mesh the yarns and the matrix and reduce the possibilities of numerical singularities. pcGINA is a two-part approach that is used to model the mechanical and thermal properties of textile composites. First a geometrical model is used to construct the textile preform and characterize the relative volume fractions and spatial orientation of each yarn in the composite space (Fig. 6.24). Data acquired from the geometrical analysis is used by a hybrid finite element approach to model the composite mechanical and thermal behavior. The geometrical model used in pcGINA starts by modeling the preform forming process – weaving or braiding. An ideal fabric geometrical representation is constructed by calculating the location of a set of spatial points, ‘knots’, that can identify the yarn center-line path within the preform space. A B-spline function is utilized to approximate a smooth yarn centerline path relative to the identified knots. The B-spline function is chosen as the approximation function due to its ability to minimize the radius of curvature along its path and its C2 continuity. The final step in this model is carried out by constructing a 3-D object (i.e. yarn) by sweeping a cross-section along the smooth centerline forming the yarn surface. A repeat unit cell of the modeled preform is identified from the geometric model and used to represent a complete yarn or tow pattern. A hybrid

Structure and mechanics of 2D and 3D textile composites Z X Y

175

X Y

6.24 Orthogonal fabric (left) and compressed plain weave fabric (right) as modeled by pcGINA.

Subcell

Subcell assembly

Homogenize properties around each integration point Unit cell

6.25 Finite element divisions of a unit cell and micro-level homogenization for pcGINA.

finite element approach is used to divide the unit cell into smaller subcells. Each subcell is a hexahedral brick element with fibers and matrix around each integration point. A virtual work technique is applied in the FE solution to calculate the properties of the repeat unit cell. The unit cell properties are considered to be representative of the composite properties. The heterogeneous solution, although successful in cutting down the number of elements, has a limitation. This limitation is bounded by the difference in the fiber and matrix properties the can cause instabilities in the numerical solution. To overcome such limitation a homogenization operation is carried out at the micro-scale level. This is done around each integration point in the FE mesh. Figure 6.25 shows a schematic presentation of the finite element division scheme and the micro-level homogenization. Currently, pcGINA can predict, with a good level of accuracy, the elastic properties, thermal conductivities, thermal expansion coefficients for textile

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composite materials for 2-D fabrics (e.g., plain weaves and n-HS), biaxial and triaxial braids, angle and layers interlock weaves, and orthogonal 3-D weaves.

6.9

Non-unit cell considerations

The traditional approach, as presented previously, to understanding the mechanical properties of complex inhomogeneous materials is based upon the concept of the unit cell or repeating volume element. The unit cell is considered to fill the volume of the material under investigation with an (effectively) infinite number of elements in each direction. When considering textile composites, it is appropriate initially to address two issues: (i) What is a unit cell? and (ii) Is unit cell based analysis appropriate for these materials? The definition of a unit cell must be based on the application. In general, a unit cell is the smallest sub-volume of the material that can reconstruct the whole through juxtaposed tessellation involving translation only. Generally this is approached as a geometry problem. However when the problem at hand is the prediction of mechanical properties, then it would make sense to consider the unit cell as the smallest sub-volume whose mechanical response epitomizes the mechanical response of the entire material. It is reasonable to accept that the geometric unit cell can serve as a mechanical unit cell, but it is not intuitively obvious if this is the smallest such cell. There may be a volumetric element that does not function as a geometric unit cell, but will function effectively as a mechanical unit cell. In the case of such doubt, the geometric unit cell can be employed without loss of accuracy. The unit cell coincides with our previous definition of a representative volume element (RVE). The decision regarding the suitability of unit cell based analysis depends on the details of the system under investigation. The unit cell approach is based upon the premise that there are a large number of unit cells in the structure and the gradients of stress and strain are small enough to be considered negligible within the unit cell. Our objective is the characterization of elastic constants, thus the only ‘structures’ we consider are materials subject to uniform stress/strain states. Thus the question becomes ‘is there a sufficiently large number of unit cells to justify the use of unit cell based analysis?’ This can be answered philosophically or phenomenologically. Let us consider the latter. To evaluate the quality and correctness of a theoretical model, the predictions can be compared with experimental results. For example, consider the measurement of uniaxial tensile modulus, E1. This is typically carried out with a simple tensile coupon, approximately 3–5 cm in width and 0.2–0.4 cm in thickness. Depending on the textile reinforcement under consideration,

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the number of unit cells contained within such a coupon will vary. In high braid angle triaxially braided composites formed from 24 K carbon yarns, it is not unusual to observe unit cells with dimensions 1–2 cm in width, 0.25–0.5 cm in height, and 0.1–0.2 cm in thickness. Thus a tensile coupon could contain as few as four unit cells in its cross-section. Clearly this is not a large number. However, for finer structures, such as 3 K woven laminates, the number of unit cells in the width may be 50 or more. Even when there are a large number of unit cells in the cross-section, the actual strain state is inhomogeneous, and care must be taken in making measurements of response. The experimental techniques developed for fine structured materials, such as bulk metals and polymers, were established with the understanding that the crystal structure is very small. However when we consider textile reinforced composites this assumption is not true. For example, for a triaxial braided carbon/epoxy composite, Fig. 6.26 shows a segment of the Moiré interferometry displacement field in the applied load direction (longitudinal) from Masters et al. (1992b). Masters et al. added the schematic of the underlying yarns to emphasize the location of the strain gradients. In Fig. 6.26, the boundaries between adjacent yarns are outlined, and it can be seen that shear deformation occurs at interfaces between adjacent yarns. It can also be clearly seen that the axial strain varies significantly within the unit cell (as shown by the non-uniform fringe spacing). The ratio of maximum to minimum strain is about 2 : 1. In a standard test, a strain gage will be placed on the surface of this part and will record the average displacement associated with the area of that gage. Thus, the measured response from a small gage will be highly sensitive to the exact location of the gage with respect to the underlying material. It is expected that enough readings with random placement of gages will provide an average value that is correct. To consider this effect, Minguet et al. (1994) carried out an effect of strain gage study on braided and 3-D woven composites. Figure 6.27 shows the

6.26 Vertical displacement field from Moirè interferometry of triaxially braided composite subject to vertical tensile load (from Masters et al. (1992)) with sketch of underlying braid structure superimposed.

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1.3

1.1

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0.5 0

2

4 6 Gage area / unit cell area

8

6.27 Variation of measured elastic modulus as a function of gage area for triaxially braided composites.

distribution of normalized measured E*1 values for a series of three different carbon/epoxy triaxially braided composites against the normalized area of the strain gage. In this case E*1 is normalized by the mean value of measured tensile modulus for the particular reinforcement scheme and the gage area is normalized by the dimensions of the unit cell of the material which is under the gage. Figure 6.27 confirms the notion that a larger gage results in less variation in measured strains (thus less variation in calculated tensile modulus), but does not provide any clear guidance except that the gage should be at least 2.5 times the area of the unit cell to get less than 10% error in measurements. Consider the area under the gage as an arbitrary sub-volume with no correlation to the unit cell. By quantifying the geometry of this subvolume, analytical techniques such as stiffness averaging can be applied to the arbitrary material and prediction of local elastic properties can be carried out. To illustrate this concept, a triaxially braided composite will be considered (as experimental data is readily available from Minguet et al.) Figure 6.28 shows a schematic illustration of a field of unit cells with a test cell superimposed upon it. The test cell represents a strain gage that may be placed on the surface of a specimen during testing. The location of this cell is effectively random with respect to the locations of the unit cell. If we try to match the upper left corner of the test cell with the upper left corner of a unit cell, there will be some horizontal and vertical offset. Similarly, the

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a

b

Unit cell

hy Test cell

y1

y hx

x1

x

6.28 Location of test cell with respect to underlying unit cells in a triaxially braided composite.

size of the test cell is not correlated to the unit cell. Thus the test cell can be characterized by four parameters: hy and hx are the off-set parameters that measure the distance from the upper left corner of the test cell to the upper left corner of the nearest unit cell. Note that 0 ≤ hy < b and 0 ≤ hx < a where a is the width of the unit cell and b is the height of the unit cell. The parameters x1 and y1 are the width and thickness respectively of the test cell. If the test cell is moved around to all possible positions, it is expected that different elastic properties will be predicted. To evaluate this hypothesis, a small test cell will be considered as it will show the greatest variation. This test cell will have dimension y1 = b (one unit cell tall), and x1 = 4.1a. This is roughly comparable to a standard strain gage size, and it is important to not have an integer number of unit cells under the gage or else the unit cell properties will result in every position. The vertical off-set, hy will be kept at 0, and the horizontal off-set will be varied from 0 to a (due to periodicity of the underlying unit cell grid). Thus we are effectively moving the test cell across the surface horizontally. At each value of hx, the internal geometry is calculated and a stiffness averaging procedure is applied to the reinforcement scheme following the methods presented in Section 6.2. A numerical example on a 60° triaxial braid formed from 12 K AS-4 yarns

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Normalized tensile modulus

1.06 E1 E2 E3

1.05 1.04 1.03 1.02 1.01 1.00 0.99 0.98 0.97 0.96

0.2a

0.4a 0.6a Horizontal off-set

0.8a

a

6.29 Predicted variation of tensile moduli for a 60° triaxially braided AS-4/epoxy composite test cell with dimensions y1 = b and x1 = 4.1a.

and epoxy matrix was carried out. The elastic properties of the test cell were extracted and plotted as a function of hx in Fig. 6.29. As can be seen in this figure, passing over a longitudinal yarn increases the prediction of E*1 as expected. Furthermore, E*2 and E*3 increase slightly due to the increase in local fiber volume fraction when including an extra longitudinal yarn. By considering every possible value of hx, maximum and minimum values of measured tensile modulus can be determined. These upper and lower bounds can be determined for any particular size of test cell. To understand the measured response reported by Minguet et al., each braided composite system was considered independently, rather than all at once as in Fig. 6.27. For each particular braided system the upper and lower bounds as a function of test cell width x1 were calculated for a test cell of height y1 = b using all possible values of hx and hy. The predicted upper and lower bounds from these analyses are compared with measured values from Minguet et al. in the following figures. Figure 6.30 shows the comparison for a 45° braid with 12% longitudinal yarns. Figure 6.31 shows the comparison with a 45° braid angle and 46% longitudinal yarns. Figure 6.32 compares predictions and experimental values for a 70° braid angle composite with 46% longitudinals. It can be seen in these figures that the upper and lower bounds coincide at integer number of gage width/unit cell width values, as expected. The amplitude of variation decreases within increasing gage (test cell) width, generally falling within 10% when the gage has width equal to three unit cells or more. Curiously, this value of three unit cell widths resulting in less than 10% variation in measured elastic modulus also showed up in experimental studies of 3-D woven composites by LaMattina (1993).

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1.3 Experimental Upper Lower

Normalized tensile modulus

1.2

1.1

1.0

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2 Gage width / UC width

4

6.30 Comparison of predicted and experimental variation of measured tensile modulus of a triaxially braided AS-4/epoxy composite with 45° braid angle and 12% longitudinal yarns. 1.3 Experimental Upper Lower

Normalized tensile modulus

1.2

1.1

1.0

0.9

0.8

0.7 0

2 Gage width / UC width

4

6.31 Comparison of predicted and experimental variation of measured tensile modulus of a triaxially braided AS-4/epoxy composite with 45° braid angle and 46% longitudinal yarns.

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Structure and mechanics of textile fibre assemblies 1.3 Experimental Upper Lower

Normalized tensile modulus

1.2

1.1

1.0

0.9

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0.7 0

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4 6 Gage width / UC width

8

6.32 Comparison of predicted and experimental variation of measured tensile modulus of a triaxially braided AS-4/epoxy composite with 70° braid angle and 46% longitudinal yarns.

It should be pointed out that through this discussion, the limitations of the unit cell based approach become apparent. Unit cell approaches are acceptable when the material is homogeneous on the scale of the test cell under consideration (all test cells contain similar reinforcement) and the test cell contains a sufficient number of unit cells so that convergence of properties is achieved. The unit cell approach is not acceptable when the material is inhomogeneous on the meso-volume level, or when the test cell contains a ‘small’ number of unit cells. When the test cell contains less than one unit cell, clearly the unit cell approach is not acceptable.

6.10 References and further reading Abolinsh, D. S., (1965) ‘Compliance Tensor for an elastic material reinforced in one direction’, Polymer Mechanics, 1 (4), pp. 52–59 (In Russian. English translation by Consultants Bureau, New York, London. Translation pages 28–32). Abolinsh, D. S., (1966) ‘Compliance tensor for an elastic material reinforced in two directions’, Polymer Mechanics, 2 (3), pp. 372–379 (In Russian. English translation by Consultants Bureau, New York, London. Translation pages 233–237).

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Blacketter, D. M., Walrath, D. E. and Hansen, A. E., (1993) ‘Modelling Damage in Plain Weave Fabric Reinforced Composite Materials’, Journal of Composites Technology and Research 15 (2), pp. 136–142. Bluck, R. M., (1969) High Speed Bias Weaving and Braiding, US Patent 3,426,804, February 1969. Bogdanovich, A. and Mungalov, D., (2002) 3-D Braided Composite Valve Structure, US Patent 6,345,598, February 2002. Bogdanovich, A. E. and Pastore, C. M., (1995) Mechanics of Textile and Laminated Composites, Chapman and Hall, London. Bogdanovich, A. E., Pastore, C. M. and Birger, A. B., (1993) ‘Three Dimensional Deformation and Failure Analysis of Textile Reinforced Composite Structures’, Proceedings of the Ninth International Conference on Composite Materials, ICCM, Woodhead Publishing Limited, Madrid, pp. 495–501. Bolotin, V. V., (1966) ‘Theory of Reinforced Layered Medium with Random Initial Irregularities’, Polymer Mechanics, 2 (1), pp. 11–19 (In Russian. Translated by Consultants Bureau, New York, London. Translation pages 7–11). Brookstein, D., Rose, D., Dent, R., Dent, J. and Skelton, J., (1996) Apparatus for Making a Braid Structure, US Patent 5,501,133, March 1996. Brown, R. T., (1986) Method for sequenced braider motion for multi-ply braiding apparatus, US Patent 4,621,560, November 1986. Brunschweiller, D., (1953) ‘Braids and Braiding’, Journal of the Textile Institute, 44, pp. 666–686. Buresh, F., (1962) Nonwoven Fabrics, Reinhold, 1962. Carter, W. C., Cox, B. N., Dadkhah, M. S. and Morris, W. L., (1995) ‘An Engineering Model of Composites Based on Micromechanics’, Acta Metallurgica. Chamberlain, J. and Quilter, J., (1924) Knitted Fabrics, Sir Isaac Pitman and Sons, 1924. Chou, T. W., (1992) Microstructural Design of Fiber Composites, Press Syndicate of the University of Cambridge, Cambridge, England. Chou, T. W., Yang, J. M. and Ma., C. L., (1986) ‘Fiber Inclination Model of Three Dimensional Textile Structural Composite’, Journal of Composite Materials, 20 Oct., pp. 472–484. Clarke, S. and Morales, A., (1990) A Comparative Assessment of Textile Preforming Techniques, in Fiber-Tex 90, NASA Langley Research Center, pp. 125–134. Cox, B. N. and Dadkhah, M., (1995) ‘The Macroscopic Elasticity of 3D Woven Composites’, Journal of Composite Materials, 29, pp. 795–819. Cox, B. N. and Flanagan, G., (1997) Handbook of Analytical Methods for Textile Composites, NASA CR-4750, March 1997. Dasgupta, A., Bhandarkar, S., Pecht, M. and Barker, D., (1992) ‘Thermoelastic Properties of Woven Fabric Composites Using Homogenization Techniques’, Journal of Composites Technology and Research, 6 (8), pp. 593–602. Dexter, H. B., Camponeschi, E. T. and Peebles, L., (1985) 3-D Composite Materials, NASA Conference Publication 2420, NASA, Hampton, VA. Douglass, W., (1964) Braiding and Braiding Machinery, Centrex Publishing Company, 1964. Dow, N. and Ramnath, V., (1985) ‘Evaluations and Criteria for 3-D Composites’, in 3-D Composite Materials, NASA Conference Publication 2420, NASA, 1985. Dow, N. and Ramnath, V., (1987) Analysis of Woven Fabrics for Reinforced Composite Materials, NASA Report, April 1987.

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Du, G. W. and Ko, F. K., (1991) ‘Unit Cell Geometry of 3-D Braided Structure’, in Proceedings of the American Society for Composites, Sixth Technical Conference, Technomic, American Society for Composites, pp. 788–797. Engineered Materials Handbook, (1987) Vol. 1 Composites, ASM, pp. 206–217. Florentine, R. A., (1982) Apparatus for Weaving a Three Dimensional Article, US Patent 4,312,261, January 1982. Fowser, S. and Wilson, D., (1985) ‘Analytical and Experimental Investigation of 3-D Orthogonal Graphite/Epoxy Composites’, in 3-D Composite Materials, NASA Conference Publication 2420, NASA, NASA Langley Research Center, pp. 91–108, November 1985. Foye, R. L., (1991) ‘Improved Inhomogeneous Finite Elements for Fabric Reinforced Composite Mechanics Analysis’, in Proceedings of FIBER-TEX 1991, NASA Langley Research Center, pp. 171–183, 1991. CP 3176. Foye, R. L., (1992) ‘Finite Element Analysis of Unit Cells’, Fiber Tex ’90, ed. J. Buckley, NASA Langley Research Center, Hampton, VA, May, pp. 45–53. Fujita, A., Maekawa, Z., Hamada, H. and Yokoyama, A., (1992) ‘Mechanical Behavior and Fracture Mechanism in Flat Braided Composites. Part 1: Braided Flat Bar’, Journal of Reinforced Plastics and Composites, 11 (6), pp. 600–617. Glaesgen, E. H., Pastore, C. M., Griffin, O. H. and Birger, A. B., (1995) ‘Geometrical and Finite Element Modeling of Textile Composites’, Composites Engineering. Gowayed, Y. A., (1992) ‘An Integrated Approach to the Mechanical and Geometrical Modeling of Textile Structural Composites’, Ph.D. Thesis, North Carolina State University, Raleigh, NC. Gowayed, Y., Pastore, C. and Howarth, C., (1996) ‘Modification and application of unit cell continuum model to predict the elastic properties of textile composites’, Composites Part A – Applied Science and Manufacturing, 27A, pp. 149–155. Hill, B. J., McIlhagger, R. and Harper, C. M., (1994) ‘Woven integrated multilayered structures for engineering preforms’, Composites Manufacturing, 5 (1), pp. 25–33. Howarth, C. S., (1991) Characterization of the Torsional Properties of Triaxially Braided Composites, M.S. Thesis, Drexel University, Fladelfa, PA. Ishikawa, T. and Chou, T. W., (1982a) ‘Stiffness and Strength Behavior of Woven Fabric Composites’, Journal of Materials Science, 17, pp. 3211–3220. Ishikawa, T. and Chou, T. W., (1982b) ‘Elastic Behavior of Woven Hybrid Composites’, Journal of Materials Science, 16 (1), pp. 2–19. Ishikawa, T. and Chou, T. W., (1983a) ‘One Dimensional Analysis of Woven Fabric Composites’, AIAA Journal, 21, p. 1714. Ishikawa, T. and Chou, T. W., (1983b) ‘Nonlinear Behavior of Woven Fabric Composites’, Journal of Composite Materials, 9, pp. 399–413. Jaranson, J., Pastore, C. M., Singletary, J. N., Field, S., Kharod, A. M., Kniveton, T. and Rushing, H., (1993) ‘Elastic Properties of Triaxially Braided Glass/Urethane Composites’, Advanced Composites Technologies Conference Proceedings, Engineering Society of Detroit, Dearborn, MI, pp. 379–398. Johnson, N. L., Browne, A. L., Watling, P. J. and Peterson, D. G., (1993) ‘Parameter Effects on the Dynamic Performance of Braided “Hourglass” Cross Section Composite Tubes’, in Advanced Composites Technologies, ESD, Engineering Society of Detroit, pp. 403–420, November 1993. Jortner, Julius, (1984) ‘A Model for Predicting Thermal and Elastic Constants of Wrinkled Regions in Composite Materials’, ASTM 836: Effects of Defects in Composite Materials, ASTM, Philadelphia, PA, pp. 217–236.

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Kabelka, J., (1984) ‘Prediction of the thermal properties of fibre-resin composites’, Developments in Reinforced Plastics – 3, Elsevier Applied Science Publishers, London, ed. G. Pritchard, pp. 167–202. Kaufmann, J., (1991) ‘Industrial Applications of Multiaxial Warp Knit Composites’, Proceedings of FIBER-TEX 91, NASA Langley Research Center, pp. 77–86. Ko, F. K. and Pastore, C., (1987) ‘Design of Complex Shaped Structures’, Textiles: Product Design and Marketing, The Textile Institute, pp. 123–135, May 1987. Ko, F. K. and Pastore, C. M., (1989) ‘Fabric Geometry and Finite Cell Models for Three Dimensional Composites’, Proceedings of the First US/USSR Conference on Composite Materials, Riga, Latvia. Ko, F. K. and Pastore, C. M., (1990) ‘CIM of Braided Preforms for Composites’, Computer Aided Design in Composite Materials Technology, Springer Verlag, pp. 134–151, 1990 (A). Ko, F., Bruner, J., Pastore, A. and Scardino, F., (1980) ‘Development of Multi-bar Weft Insertion Warp Knit Fabrics for Industrial Applications’, Journal of Engineering for Industry, 102 (4), pp. 333–341, November 1980. Ko, F., Fang, P. and Pastore, C., (1985) ‘Structure and Properties of Multiaxial Multibar Weft Inserted Warp Knits’, Journal of Industrial Fabrics, 4 (2), pp. 4–12, December 1985. Ko, F., Pastore, C., Yang, J. and Chou, T.-W., (1986) ‘Structure and Properties of Multi-layer Multidimensional Warp Knit Fabric Reinforced Composites’, in Proceedings of the Third U.S./Japan Conference on Composites, U.S./Japan Conference on Composites, 1986. Ko, F. K., Pastore, C. M., Lei, C. and Whyte, D. W., (1987) ‘A Fabric Geometry Model for 3-D Braid Reinforced FP/Al-Li Composites’, in 1987 International SAMPE Metals Conference: Competitive Advances in Metals/Metal Processing, ASTM, American Society for Testing and Materials, Aug. 1987. Ko, F. K., Pastore, C. M. and Head, A., (1989) Atkins and Pearce Handbook of Industrial Braiding, Atkins and Pearce, Covington, KY. Krcma, R., (1971) Manual of Nonwovens, Textile Trade Press, 1971. Kregers, A. F., (1981) ‘Determination of the Deformation Properties of Composite Materials Reinforced with a Sterically curvilinear reinforcement’, Mechanics of Composite Materials, 15 (5), pp. 790–793 (In Russian. Translation by Consultants Bureau, New York, London. Translation pages 512–515). Kregers, A. F. and Melbardis, Yu. G., (1978) ‘Determination of the Deformability of Three-Dimensionally Reinforced Composites by the Stiffness Averaging Method’, Polymer Mechanics, 14 (1), pp. 3–8 (In Russian. Translation by Consultants Bureau, New York, London. Translation pages 1–5). Kregers, A. F. and Teters, G. A., (1979a) ‘Use of Averaging Methods to Determine the Viscoplastic Properties of Spatially Reinforced Composites’, Mechanics of Composite Materials, 15 (4), pp. 617–624 (In Russian. Translation by Consultants Bureau, New York, London. Translation pages 377–383). Kregers, A. F. and Teters, G. A., (1979b) ‘Optimization of the Structure of Spatially Reinforced Composites by the Method of Stiffness Averaging’, Mechanics of Composite Materials, 1, pp. 79–85. Kregers, A. F. and Teters, G. A., (1981) ‘Determination of the Elastoplastic Properties of Spatially Reinforced Composites by the Averaging Method’, Mechanics of Composite Materials, 17 (1), pp. 30–36 (In Russian. Translation by Consultants Bureau, New York, London. Translation pages 25–31).

186

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Krumme, W., (1927) ‘Maschinen Flechten und Maschinen Klöppeln’, Technologie der Textil Fasern, R. O. Herzog, Band II, p. 313, 1927. In German. Lachman, W. L., Crawford, J. A. and McAllister, L. E., (1978) ‘Multidirectionally Reinforced Carbon-Carbon Composites’, in Proceedings of the International Conference on Composites Materials, Metallurgical Society of the American Institute of Mining, Metallurgical, and Petroleum Engineers, pp. 1302–1319. Lagzdin, A. Z., Tamuzh, V. P., Teters, G. A. and Kregers, A. F., (1989) Method of Orientation Averaging for Mechanics of Materials, Zinatne, Riga, Latvia. LaMattina, B., (1993) Preforming, RTM Processing and Textile Characterization of 3-D Angle Interlock Carbon/Epoxy Composites, PhD Thesis, University of Delaware, May 1993. Lei, C. and Ko, F., (1990) ‘Fracture Behavior of 3-D Braided Hybrid SiC/Al Composites’, FiberTex ’90, NASA publication, Greenville SC., Aug. 14. Lei, C. and Whyte, D. W., (1987) ‘A Fabric Geometry Model for 3-D Braid Reinforced FP/Al-Li Composites’, 1987 International SAMPE Metals Conference: Competitive Advances in Metals/Metal Processing, Aug., ASTM. Lei, C., Cai, Y. J. and Ko, F. K., (1988a) ‘Finite Element Analysis of 3-D Braided Composites’, Advances in Engineering Software, ASME 14, p. 187. Lei, C., Wang, A. S. and Ko, F., (1988b) ‘A Finite Cell Model for 3-D Braided Composites’, ASME Winter Annual Meeting, Chicago. Lene, F. and Paumelle, P., (1992) ‘Micromechanics of Damage in Woven Composites’, Composite Material Technology, ASME, PD-45, pp. 97–105. Lennox-Kerr, P., (1972) Needle Felted Fabrics, Textile Trade Press, 1972. Li, W. and El-Sheikh, A., (1988) ‘The Effect of Processes and Processing Parameters on 3-D Braided Preforms for Composites’, in Proceedings of the 33rd International SAMPE Symposium, SAMPE. Lord, P. and Mohamed, M., (1982) Weaving: Conversion of Yarn to Fabric, Merrow Technical Library, 1982. Maistre, M. A., (1978) Three Dimensional Structure for Reinforcement, US Patent 4,168,337, 1979. Maistre, M. A., (1979) Three Dimensional Structure for Reinforcement, US Patent 4,168,337, 1979. McConnell, R. and Popper, P., (1988) Complex Shaped Braided Structures, January 1988. Malek, A. and Pastore, C., (2000) Automated Three Dimensional Method for Making Integrally Stiffened Skin Panels, US Patent 6,019,138, February 2000. Masters, John E., Ifju, Peter G. and Fedro, Mark J., (1992a) ‘Development of Test Methods for Textile Composites’, Proceedings of FIBER-TEX 92, NASA Langley Research Center, Hampton, VA, CP 3211, ed. John Buckley, pp. 249–269. Masters, John E., Fedro, Mark J. and Ifju, Peter G., (1992b) ‘Experimental and Analytical Characterization of Triaxially Braided Textile Composites’, Proceedings of the Third NASA Advanced Composites Technology Conference, NASA, pp. 263–287, ed. John Buckley. Masters, J. E., Foye, R. L., Pastore, C. M. and Gowayed, Y. A., (1992c) ‘Mechanical Properties of Triaxially Braided Composites: Experimental and Analytical Results’, NASA CR 189572, Hampton, VA. Masters, J. E., Gowayed, Y. A., Pastore, C. M. and Foye, R. L., (1993) ‘Mechanical Properties of Triaxially Braided Composites: Experimental and Theoretical

Structure and mechanics of 2D and 3D textile composites

187

Results’, Journal of Composites Technology and Research, 15 (2) Summer, pp. 112–122. Minguet, P. J., Fedro, M. J. and Gunther, C. J., (1994) Test Methods for Textile Composites, NASA Contractor Report 4609, Hampton, VA. Morales, A., (1992) ‘Design and Cost Drivers in 2-D Braiding’, FIBER-TEX 92, NASA Langley Research Center, pp. 69–78, 1992. CP 3211. Morales, A. and Pastore, C., (1990) ‘Computer Aided Design Methodology for Three Dimensional Woven Fabrics’, in FIBER-TEX 90, NASA Langley Research Center, pp. 85–96, 1990. CP 3128. Mullen, C. K. and Roy, P. J., (1972) ‘Fabrication and Properties of AVCO 3-D Carbon-Carbon Cylinder Materials’, in Proceedings of the 17th National SAMPE Symposium, SAMPE, p. III A-2, 1972. Mungalov, D. and Bogdanovich, A., (2002) Automated 3-D Braiding Machine and Method, US Patent 6,439,096, August, 2002. Naik, R. A., (1994) TEXCAD-Textile Composite Analysis for Design, NASA Contractor Report 4639, Hampton, VA. Naik, N. K. and Ganesh, V. K., (1992) ‘Prediction of On-Axes Elastic Properties of Plain Weave Fabric Composites’, Composites Science and Technology, 45, pp. 135–152. Nosarev, A. V., (1967) ‘Effect of Curvature of the Fibers on the Elastic Properties of Unidirectionally Reinforced Plastics’, Polymer Mechanics, 3 (5), pp. 858–863 (In Russian. Translated from Russian by Consultants Bureau, New York, London. Translation pages 567–570). Pastore, C. M., (1988) ‘A Processing Science Model of Three Dimensional Braiding’, Ph.D. Thesis, Drexel University, March 1988. Pastore, C. M., (1993a) ‘Quantification of Processing Artifacts in Textile Composites’, Composites Manufacturing, 4 (4), pp. 87–112. Pastore, C. M., (1993b) Illustrated Glossary of Textile Terms for Composites, NASA Langley, October. Pastore, C. M., (1993c) ‘Quantification of Processing Artifacts in Textile Composites’, Composites Manufacturing, 4 (4), pp. 87–112. Pastore, C. M. and Gowayed, Y. A., (1994) ‘A Self-Consistent Fabric Geometry Model: Modification and Application of a Fabric Geometry Model to Predict the Elastic Properties of Textile Composites’, Journal of Composites Technology and Research, 16, pp. 32–36. Pastore, C., Whyte, D., Soebroto, H. and Ko, F., (1986) ‘Design and Analysis of Multiaxial Warp Knit Fabrics for Composites’, Journal of Industrial Fabrics, 5 (1), pp. 4–17, September 1986. Pastore, C. M., Gowayed, Y. A. and Cai, Y. J., (1990) ‘Applications of Computer Aided Geometric Modelling for Textile Structural Composites’, in Computer Aided Design in Composite Material Technology, Computational Mechanics Publications, pp. 45–53. Pastore, C. M., Bogdanovich, A. E. and Masters, J. E., (1992) ‘The Effects of Specimen Width on Tensile Properties of Braided Laminates’, 3rd Advanced Composites Technology Symposium, NASA/DoD, Long Beach, CA. Pierce, F. T., (1937) ‘The Geometry of Cloth Structures’, Journal of the Textile Institute, 28, pp. T45–T96. Pochiraju, K., Parvizi-Majidi, A. and Chou, T. W., (1993) ‘Process-MicrostructurePerformance Relationships of 3-D Braided and Woven Textile Structural

188

Structure and mechanics of textile fibre assemblies

Composites’, Quarterly Report, NASA Advanced Composites Technology Mechanics of Textile Composites Work Group, NASA Langley, Hampton, VA. Raju, I. S., Foye, R. L. and Avva, V. S., (1990) ‘A Review of Analytical Methods for Fabric and Textile Composites’, Proceedings of Indo-US Workshop on Composite Materials for Aerospace Applications. Ramakrishna, S. and Hull, D., (1994) ‘Tensile Behaviour of Knitted Carbon-Fibre Fabric/Epoxy Laminates – Part I: Experimental’, Composites Science and Technology, 50, pp. 237–247. Raz, S., (1987) ‘Bi-Axial and Multi-Axial Warp Knitting Technology’, Kettenwirk Praxis, March, pp. 11–16. Raz, S., (1989) ‘The Karl Mayer Guide to Technical Textiles’, Kettenwirk Praxis, Jan/Feb, pp. 60–94. Reichman, C., Lancashire, J. B. and Darlington, K. D., (1967) Knitted Fabric Primer, National Knitted Outerwear Association, 1967. Roze, A. V. and Zhigun, I. G., (1970) ‘Three-Dimensional Reinforced Fabric Materials 1: Calculation Model’, Polymer Mechanics, 6 (2), pp. 311–318 (In Russian. Translated from Russian by Consultants Bureau, New York, London. Translation pages 272–278). Roze, A. V., Zhigun, I. G. and Dushin, M. I., (1970) ‘Three-Dimensionally Reinforced Woven Materials, 2: Experimental study’, Polymer Mechanics, 6 (3), pp. 471–476 (In Russian Translated from Russian by Consultants Bureau, New York, London. Translation pages 404–409). Sanders, L. R., (1977) ‘Braiding – a Mechanical Means of Composite Fabrication’, SAMPE Quarterly, pp. 38–44, January 1977. Sankar, B. V. and Marrey, R. V., (1993) ‘A Unit-Cell Model of Textile Composite Beams for Predicting Stiffness Properties’, Composites Science and Technology, 49 (1), pp. 61–69. Scardino, F., (1989) ‘Warp Knit Fabrics for Composites’, in Textile Structural Composites, 3, Elsevier, 1989. Sendeckyj, G. P., (1970) ‘Longitudinal Shear Modulus of Filamentary Composite Containing Curvilinear Fibers’, Fibre Science and Technology, 2, pp. 211–222. Singletary, J. N., (1993) Characterization Of The Elastic Properties Of Triaxially Braided {E}-Glass/Urethane Composites, MS Thesis, North Carolina State University. Singletary, J. N., (1994) Characterization Of The Elastic Properties Of Triaxially Braided E-Glass/Urethane Composites, MS Thesis, North Carolina State University. Smith, D. L. and Benson Dexter, H., (1991) ‘Woven Fabric Composites with Improved Fracture Toughness and Damage Tolerance’, in Proceedings of Fiber Tex 91, NASA, pp. 75–89, 1991. CP 3038. Smith, L. V. and Swanson, S. R., (1993) ‘Stiffness and Strength of Braided Specimens in Biaxial Compression’, Quarterly Report, June–Sept., NASA Advanced Composites Technology Mechanics of Textile Composites Work Group, Langley, VA. Stover, E. R., Mark, W. C., Marfowitz, I. and Mueller, W., (1971) ‘Preparation of an Omniweave Reinforced Carbon-Carbon Cylinder as a Candidate for Evaluation’, in the Advanced Heat Shield Screening Program, NASA Langley, March 1971. Tarnopol’skii, Yu. M., Portnov, G. G. and Zhigun, I. G., (1967) ‘Effect of Fiber Curvature on the Modulus of Elasticity for Unidirectional Glass-Reinforced

Structure and mechanics of 2D and 3D textile composites

189

Plastics in Tension’, Polymer Mechanics, 3 (2), pp. 243–249 (In Russian. Translated from Russian by Consultants Bureau, New York, London. Translation pages 161–166). Tarnopol’skii, Yu. M., Polyakov, V. A. and Zhigun, I. G., (1973) ‘Composite Materials Reinforced with a system of Three Straight, Mutually Orthogonal Fibers, 1: Calculation of Elastic Characteristics’, Polymer Mechanics, 9 (5), pp. 853–860 (In Russian. Translated from Russian by Consultants Bureau, New York, London. Translation pages 754–759). Thaxton, C., Rona Reid and Aly El-Sheik, (1991) ‘Advances in 3-Dimensional Braiding’, in Proceedings of FIBER-TEX 1991, NASA Langley Research Center, pp. 43–66, 1991. CP 3176. Thomas, D. G. B., (1976) Introduction to Warp Knitting, Merrow Publishers, 1976. Tolks, A. M., Repelis, I. A., Gailite, M. P. and Kantsevich, V. A., (1986) ‘Carcasses for Three-Dimensional Reinforcement Woven in One Piece’, Mechanics of Composite Materials, 22 (5), pp. 795–799 (In Russian Translated from Russian by Consultants Bureau, New York, London. Translation pages 541–545). Tsiang, T.-H., Brookstein, D. and Dent, J., (1984) ‘Mechanical Characterization of Braided Graphite/Epoxy Cylinders’, Proceedings of the 29th National SAMPE Symposium. Vanyin, G. A., (1966) ‘Elastic Constants and State of Stress of Glass-Reinforced Strip’, Polymer Mechanics, 2 (4) July–August, pp. 593–602 (In Russian. Translated from Russian by Consultants Bureau, New York, London. Translation pages 368–372). Weller, R. D., (1985) Three Dimensional Interbraiding of Composite Reinforcements by AYPEX, US Navy Report, 1985. Whitcomb, J. D., (1989) ‘Three Dimensional Stress Analysis of Plain Weave Composites’, 3rd Symposium on Composite Materials: Fatigue and Fracture, American Society for Testing and Materials, Philadelphia, PA. Whyte, D., (1986) On the Structure and Properties of 3-D Braided Composites, Ph.D. Thesis, Drexel University, Philadelphia, PA. Woo, K. and Whitcomb, J. D., (1993) ‘Global/Local Finite Element Analysis for Textile Composites’, 34th AIAA/ASME/ASCE/AHS/ACS Structures, Structural Dynamics and Materials Conference, AIAA/ASME/ASCE/AHS/ACS, La Jolla, CA, pp. 1721–1731. Yoshino, T. and Ohtsuka, T., (1982) ‘Inner Stress Analysis of Plain Woven Fiber Reinforced Plastic Laminates’, Bulletin of the JASME, 25 (202), pp. 485–492. Zhigun, I. G., Dushin, M. I., Polyakov, V. A. and Yakushin, V. A., (1973) ‘Composites Reinforced with a system of Three Straight, Mutually Orthogonal Fibers, 2: Experimental Study’, Polymer Mechanics, 9 (6), pp. 1011–1018 (Translated from Russian by Consultants Bureau, New York, London. Translation pages 895–900).

7 Structure and mechanics of yarns Y EL-MOGAHZY, Auburn University, USA

Abstract: Yarn, being the building block of many diverse fabrics, should be designed and manufactured in such a way that it can meet the performance characteristics of these end products. The driving forces in the design and manufacturing of yarns are twofold: structure and mechanics. As a result, these two aspects have represented the main focus of yarn research over the years. This chapter provides an overview of some of the key structural aspects of yarns. These include fiber compactness, fiber arrangement in the yarn, and the extent of fiber mobility in the outer and inner layers of yarn. These aspects vary with fiber type, spinning system, and other parameters uniquely defined for each spinning system (e.g., yarn twist, fiber wrapping, fiber migration, etc.). The chapter also discusses the importance of utilizing yarn mechanics not only for the purpose of gaining strength, as required for most woven structures, but also for providing flexibility and yarn porosity as required for most knit structures. In this regard, the concept of ‘strength-comfort-twist relationship’ is introduced. Finally, the chapter discusses some of the practical aspects of yarn strength and key technological and analytical challenges associated with modeling yarn strength. Key words: continuous-filament yarn, spun yarn, textured yarn, plied yarn, cabled (multi-folded) yarn, carded yarn, combed yarn, woolen yarn, worsted yarn, ring-spun yarn, open-end spun yarn, air-jet spun yarn, compact yarn, friction-spun yarn, fiber compactness, bulk density, specific volume, open-packed yarn, hexagonally closed-packed yarn, packing fraction, fiber migration, yarn hairiness, strength, modulus, coefficient of friction, migration period, twist, comfort.

7.1

Introduction

In classic terms, a yarn is defined as a long, fine structure capable of being assembled or interlaced into such textile products as woven and knitted fabrics, braids, ropes, and cords1. With few exceptions (ropes and cables), a yarn is essentially an intermediate product that must be converted into a fabric to reflect its usefulness. Since fabrics can be used in numerous end products from knit apparels to woven clothing, from towels to sheets, and from carpets to industrial fabrics, yarn being the building block of these diverse fabrics must be designed and manufactured in such a way that can meet the performance characteristics of these end products. As a result, it is often difficult to determine what constitutes a desired yarn performance. 190

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Indeed, different textile manufacturers often express different views of desired yarn performance depending on the particular end product produced and the type of downstream processing used2. For example, a spinner may describe a good yarn performance as an index of appearance, strength, uniformity, and level of imperfections. However, the spinner is much more concerned about how the yarn user views yarn performance. A knitter may have more detailed criteria for yarn performance. These may include: •

A yarn that can unwind smoothly and conform readily to bending and looping while running through the needles and sinkers of the knitting machine. This translates to flexibility and pliability. • A yarn that sheds low fly in and around the knitting machine. This translates to low hairiness and low fiber fragment content. • A yarn that leads to a fabric of soft hand and comfortable feeling. This translates to low twist, low bending stiffness, and yarn fluffiness or bulkiness. • A yarn that has better pilling resistance. This translates to good surface integrity. The weaver, on the other hand, may have a different set of yarn performance criteria: •

• •

A yarn that can withstand stresses and potential deformation imposed by the weaving process. This translates to strength, flexibility, and low strength irregularity. A yarn that has a good surface integrity. This translates to low hairiness and high abrasion resistance. A yarn that can produce defect-free fabric. This translates to high evenness, low imperfection, and minimum contamination.

In light of these different, and often conflicting, views of performance, a yarn should be designed to meet the desired criteria of end products. This is primarily achieved using the appropriate yarn structure. In addition, yarn integrity is a key aspect in all applications. This requires understanding of some of the basic concepts of yarn mechanics and the challenges facing the task of exploring and predicting yarn failure. These two issues are the subjects of this chapter. Before proceeding with the discussion of these two subjects, it will be important to provide the reader with a brief classification of different yarn types.

7.2

Yarn classification

As indicated above, a yarn is generally defined as a long fine fiber strand consisting of either twisted staple fibers or parallel continuous filaments

192

Structure and mechanics of textile fibre assemblies Continuous monofilament yarn (e.g. nylon, rayon, polyester)

Polymer

Continuous multifilament yarn (e.g. nylon, rayon, polyester)

Spinneret Texturized yarns

Bulked yarn Stretch yarn (a) Continuous filament yarns

•Opening Spun yarn (or staple-fiber yarn) •Natural staple fibers •Drawing (e.g. cotton, wool, flax) •Consolidation •Man-made staple fibers •Natural/man-made blends •Twisting & winding (b) Spun yarns (or staple-fiber yarns )

7.1 Continuous filament yarns and spun (staple-fiber) yarns.

that is capable of being interlaced into a woven structure, intermeshed into a knit structure, or inter-twisted into braids, ropes, or cords. This definition implies that there are two main types of yarn: continuous filament yarns and spun yarns. A continuous filament yarn represents a simple structure in which multiple filaments are laid side by side in parallel arrangement. This type of yarn is typically made by extruding polymer liquid through a spinneret to form liquid filaments that are solidified into a continuous fiber strand. As shown in Fig. 7.1, a continuous filament yarn is commonly called a monofilament yarn when it consists of a single filament; or a multifilament yarn when it consists of many filaments. Continuous filaments can also be converted into other structural derivatives via deliberate entanglement or geometrical reconfiguration, using a process called texturizing for the purpose of producing stretchy or bulky yarns2–4. Spun yarns, on the other hand are produced from staple fibers of natural or synthetic sources using a number of consecutive processes such as blending, cleaning, opening, drawing and spinning to align the fibers and consolidate them into a yarn via twisting or other means2. Yarns can also be classified based on their structural complexity into single yarns, plied yarns, and cabled yarns as shown in Table 7.1; based on the method of fiber preparation into carded, combed, worsted, and woolen yarns as shown in Table 7.2; and based on the method of spinning into ring-spun, rotor-spun, air-jet, and friction-spun yarn as shown in Table 7.3.

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Table 7.1 Yarn types: by structural complexity1–3 Yarn type

General features

Single yarn

• A single yarn can be made from continuous filaments, monofilaments, or staple fibers. • Continuous filament yarn basically consists of a monofilament or multifilament arrangement. • Staple-fiber (or spun) yarns are made by twisting fibers, or by a false-twist technique in which other forms of binding fibers such as wrapping can be used.

Plied yarn

• Plied yarn commonly consists of two single yarns twisted together to form a thicker yarn. • A ply yarn may be twisted in the same direction as the single yarn or in opposite direction to add visual and appearance effects.

Cabled (multi-folded) yarn

• Several plied yarns can be twisted together to form cabled yarns. • Cabled yarns are typically used for heavy-duty industrial applications such as mooring and heavy weight lifting.

7.3

Yarn structure

The subject of yarn structure has been covered in numerous publications, for example, refs 1–4 and 7–11. Therefore, it is somewhat difficult to add much, if anything, to what has been published in this area. Perhaps, some clarification of the meaning of yarn structure, particularly from a practical viewpoint, may be considered as an addition. In general, yarn, being the building block of fabric, contributes to end product performance through three key structural aspects: (i) fiber compactness, (ii) fiber arrangement, and (iii) fiber mobility.

7.3.1 Fiber compactness The integrity of a yarn structure is maintained partially by some form of compactness of fibers or filaments in the yarn. In case of a continuous

194

Structure and mechanics of textile fibre assemblies

Table 7.2 Yarn types: by preparation1–3,5,6 Yarn type

General features

Carded yarn

• A carded yarn is a single yarn made using cotton processing equipment in which fibers are opened, cleaned, carded, and drawn prior to spinning. • It may be considered as an economy-yarn as a result of its lower manufacturing cost than a combed yarn (presented below). • The yarn lacks good fiber orientation, has possible moderate to high trash content (when made from cotton), and relatively high neps. • It is typically used for coarse to medium yarn counts that can be woven or knitted to a wide range of apparel from heavy denim to shirts and blouses.

Combed yarn

• A combed yarn is a single yarn made using the same cotton processing equipment for carded yarn, but with the addition of the so-called combing process. • The combing process substantially upgrades the fiber quality and consequently, the quality of the yarn produced. • Combing removes short fibers (≤ 0.5 inch), remove neps, and reduced trash content to nearly zero. It also results in a superior fiber orientation in the yarn, leading to smoother and softer yarns. • Combed yarns are typically upper medium to fine count yarns. They are also more expensive than carded yarns. • Combed yarns are typically used for high-fashion apparel with comfort and durability representing a unique performance combination.

Woolen yarn

• Woolen yarns are made on the so-called woolen system using basic steps such as fiber selection, dusting, scouring, drying, carding and spinning. • Products produced from woolen yarns include blankets, carpets, woven rags, knitted rags, hand-knitting yarn, and tweed cloth.

Worsted yarn

• This is a high quality yarn made on a series of operations to yield stronger and finer wool yarn quality than that of woolen yarns. • Operations involved in worsted yarn include sorting, blending, dusting, scouring, drying-oiling, carding, combing, gilling operations, and drawing. • Products produced from worsted yarns include highquality fashionable wool apparel.

Table 7.3 Yarn types: by spinning system1–3,5,6 Yarn type

General features

Ring-spun yarns

• Yarns made on the ring-spinning system. • Can be carded or combed. • Fibers in the yarn exhibit largely true twist and take a helical path crossing the yarn layers. • Some fiber points can be in the core of the yarn and others can be in intermediate or outer layers due to the phenomenon of fiber migration. • It can be made of a wide range of yarn count and twist. • The strongest yarn of all spun yarns. • It can exhibit high hairiness and high mass variation. • The most diverse yarn type as it can be used in all types of fabric from knit to woven.

Carded Combed

Compact-spun yarn

• Yarns made on compact spinning which is a modified ring-spinning system in which fibers are aerodynamically condensed to reduce hairiness and improve yarn strength. • It is commonly used for fine yarns and highquality apparel.

Rotor (open-end) spun yarns

• Yarns made on rotor spinning. • Can be carded or combed. • Three-layer structure: truly twisted core fibers, partially twisted outer layer, and belt fibers. • It is limited to coarse-to-medium yarn count, and it requires higher twist than ring-spun. • Relatively weaker than ring-spun yarns but has lower mass variation. • It can be used for many knit or woven apparels, but its greatest market niche is denim fabrics.

Belt fibers

Partially twisted outer layer

Truly twisted core fibers

Air-jet spun yarn

Wrapping fibers Core parallel fibers

Friction-spun yarn

Fiber loops

• Yarns made on air-jet spinning, the fastest spinning system. • It consists of two layers, core-parallel fibers and wrapping fibers. • The yarns exhibit no twist, and the source of strength is the wrapping fibers. • Used for many apparel and home products particularly sheets and bed products. • Yarns made on friction spinning. • The yarn exhibits true twisted fibers but a great many fiber loops are present. • It can be made only in very coarse yarn counts used for industrial applications. • Largely used for making industrial yarns of different structures including core/sheath yarns. • It can be made from a blend of raw fibers and waste fibers.

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Structure and mechanics of textile fibre assemblies

filament yarn, filaments adhere together, by virtue of their large number and the long inter-filament contact under lateral forces imposed by the outer filaments pressing against the inner ones. This produces the highest compactness level as virtually no air is allowed to penetrate between the filaments. When filament yarns are converted into textured yarn, a great deal of inter-filament space is created leading to lower compactness. In case of spun yarns, fibers are compacted together by lateral forces imposed by the twist inserted to form the yarn. The discrete nature of the fibers provides for variable compactness with plenty of air pockets inside the yarn structure filling in the inter-fiber spaces. The importance of fiber compactness stems from two important points that should be realized in the design of fibrous products. For a given fiber type, high fiber compactness is likely to result in low yarn compressibility (or low softness), high strength, low yarn flexibility, low yarn porosity, and more moisture wicking along the yarn surface than along the fibers in the yarn. On the other hand, low fiber compactness is likely to result in high yarn compressibility (or high softness), high flexibility, high porosity, and more moisture wicking along the fibers in the yarn. Between these two situations, yarns of different levels of fiber compactness can be produced to meet key fabric performance characteristics such as strength, hand, drape, moisture management, and comfort. Furthermore, fiber compactness is a key factor in determining the yarn dimensional stability; a yarn can be considered dimensionally stable if the fiber compactness is the same in the relaxed state and under low levels of stress4. The extent of fiber or filament compactness in a yarn structure can be expressed by two key factors: (i) the yarn bulk density (g/cm3) or more precisely the specific volume, vy, of yarn (cm3/g), and (ii) the volume of still air inside the yarn. One can imagine a three-dimensional yarn structure consisting of fiber material and air pockets that are created by virtue of the discontinuities of fiber flow along the yarn axis in case of spun yarns or separations between filaments in case of continuous-filament yarn or texturized yarn. Accordingly, a yarn is essentially a porous structure. Based on the analysis of the ideal yarn model (Fig. 7.2(a)) by Hearle et al.1, the specific volume (cm3/g) of yarn can be expressed by the following equation: ⎛ πR ⎞ vy = ⎜ × 10 5 ⎝ Tt ⎟⎠ 2

7.1

where R is the yarn radius, Tt is yarn tex. This equation suggests that the density of packing of fibers in the yarn remains constant throughout the model. This idealization resulted in further theoretical analysis in which idealized fiber packing forms in the yarn were suggested. These include: the open-packed yarn, and the hexagonally close-

Structure and mechanics of yarns

r

l

h

h

θ

L

A fiber inside the yarn

Yarn

α

R

197

2πr θ

l

h

α

h

L

2πR

(a) Idealized twisted yarn structure

Open-packed structure

Close-packed structure

(b) Idealized packing

7.2 Twist in idealized yarn structure1.

packed yarn shown in Fig. 7.2(b). The effect of twist on the specific volume of yarn can be realized from the following equation1: ⎛ tan 2 α ⎞ vy = ⎜ × 10 5 ⎝ 4π Tt T 2 ⎟⎠

7.2

where T is the twist level (turns per unit length), and α is the surface twist angle. The above relationship indicates that for a given yarn count, Tt, the effect of twist on yarn specific volume is primarily a function of the variation in yarn circumference caused by twisting. Accordingly, if the yarn has a constant diameter, as suggested by the idealized model, the specific volume will also be constant. In a real yarn, variation in yarn diameter is highly expected. An increase in yarn circumference, or yarn diameter, due to twisting will result in a quadratic increase in its specific volume, or a quadratic reduction in bulk density. This situation can only hold if the increase in yarn diameter is achieved at a constant mass per unit length, Tt, or constant yarn count. Another relationship developed by Neckar12 indicates that yarn volumetric density has approximately linear relationship with the product (twist.tex1/4) of spun yarn. The true specific volume of yarn will depend on the volume occupied by the fibers and by the amount of inter-fiber space which is filled with air. This leads to a useful term called ‘packing fraction, φ’1:

φ=

v fiber v fiber = vyarn v fiber + vair

7.3

Structure and mechanics of textile fibre assemblies

0.45 0.44 0.43 0.42 0.41 0.40 0.39 0.38

0.42 Ring-combed

Ring-carded

Density (g/cm3)

Density (g/cm3)

198

0.40 0.36 0.34 0.30 4

8

10

12

Yarn count (Ne)

(a)

(b)

Compact-combed-weave Ring-combed-weave

Ring-combed-knit 50

6

Yarn count (Ne)

60

70 80

90 100

Density (g/cm3)

Density (g/cm3)

Rotor-carded

0.32

15 20 25 30 35 40 45

0.58 0.56 0.54 0.52 0.5 0.48 0.46 0.44 40

Ring-carded

0.38

0.43 0.42 0.42 0.41 0.41 0.40 0.40 0.39 0.39 0.38

14

16

14

16

Ring-carded-weave

Ring-carded-knit 4

6

8

10

12

Yarn count (Ne)

Yarn count (Ne)

(c)

(d)

7.3 Uster® yarn density at different preparations and different spinning methods 13.

At the time the above equations were developed, ways to measure yarn density did not exist. In recent years, measures of yarn density were made possible by Uster® Technologies13. These measures make use of a combination of capacitive techniques to measure the yarn mass and optical techniques to measure the yarn thickness2. Figure 7.3 shows values of density for some different spun yarns. Some of the interesting points that can be revealed from this figure are as follows: •

•

Most traditional spun yarns exhibit volumetric density ranging approximately from 0.30 to 0.6 g/cm3. This is a wide range from a yarnperformance viewpoint as it implies a significant range of yarn bulkiness, which could have a high impact on fabric performance characteristics such as compressibility, softness, porosity, and stiffness. Corresponding data for continuous-filament yarns are not available, but one can expect them to be significantly higher than those for spun yarns. Textured yarns can have a wide range of bulkiness depending on the method of texturizing used. Combed yarns are denser than carded yarns (see Fig. 7.3(a)). This is expected on the ground that the combing process results in better fiber

Structure and mechanics of yarns

199

alignment and better evenness in fiber length via the removal of short fibers and fiber hooks2,3. • Ring-spun yarns have substantially higher density than rotor-spun yarns (Fig. 7.3(b)). This difference is directly attributed to the structural difference between the two yarn types summarized in Table 7.3. • Compact yarn has the highest density of all traditional spun yarns (see Fig. 7.3(c)). This is a direct result of the deliberate compactness of fibers in the yarn3, making it a denser yarn (see Table 7.3). • Yarns made for woven fabrics are denser than those made for knit fabrics (see Figs 7.3(c) and (d)). This is a direct result of the higher twist used for the former than the latter. Yarns made for woven fabrics are typically stronger than those made for knit fabrics and this requires higher twist for a given fiber type and a given set of fiber characteristics. On the other hand, yarns made for knit products are typically softer and more flexible; this requires low levels of twist. In light of the above discussion, the key factors influencing fiber compactness in the yarn are spinning preparation (e.g. carded vs. combed), spinning method (or yarn type), and yarn twist. Although the results in Fig. 7.3 show values of yarn density at different yarn counts, they should not be used as indications of the effects of yarn count on density. This is due to the fact that these results are obtained from the Uster® Statistics data which is typically taken from various mills using various spinning equipment. In addition to the above factors, fiber compactness in the yarn can be altered or controlled using many fiber-related parameters for a given yarn type and yarn count. These include: fiber density, fiber length, fiber fineness, fiber crimp, fiber cross-sectional shape, and the number of fibers that can be accommodated in the yarn cross section. For example, fine and long fibers will normally result in higher yarn density than coarse and short fibers. In addition, fibers of circular cross-sectional shape are likely to form yarns of higher bulk density than those of triangular or trilobal shapes.

7.3.2 Fiber arrangement The way fibers are arranged in the yarn structure can have a great impact on a number of yarn and fabric performance characteristics such as yarn liveliness, yarn appearance, yarn strength, fabric dimensional stability, and fabric cover. As illustrated in Fig. 7.1 and described in Tables 7.2 and 7.3, different yarn types exhibit different forms of fiber arrangement. Obviously, the simplest fiber arrangement is that of a continuous-filament yarn where fibers (or continuous filaments) are typically arranged in parallel and straight form. Deviations from this arrangement can be caused by slightly twisting the filaments or through a deliberate distortion in filament orienta-

200

Structure and mechanics of textile fibre assemblies

tion as in the texturizing process. In spun yarns, fiber arrangement is quite different from the simple arrangement of continuous-filament yarns. The discrete nature of staple fibers makes it difficult to fully control the fiber flow in such a way that can produce a well-defined fiber arrangement. As a result, the analysis of fiber arrangement in spun yarns typically begins with an idealized twisted yarn structure1 and then seeks ways to interpret or evaluate the deviation from this structure as discussed earlier. The idealized twisted yarn structure can be useful in exploring some of the important relationships between different yarn structural parameters. However, it does not fully describe the fiber arrangement in actual spun yarn. Indeed, a yarn following this idealized arrangement will neither be practically feasible nor useful. For example, the assumption that a yarn is composed of a series of concentric cylinders of differing radii and that each fiber follows a uniform helical path around one of the concentric cylinders, implies that the outer cylinders are held firmly by some cohesive forces without fiber interference. Obviously, this is not true as the fibers on the surface would be merely wrapped around and not gripped at all. In a real spun yarn, twisted fibers will still take some form of helical shape but they can migrate from one layer of the yarn to another with some points on one fiber being on the outer layer and others being in the intermediate layers or at the center of the yarn. This creates a self-locking structure that provides the necessary integrity to the yarn. This phenomenon, called ‘fiber migration’, was the subject of extensive research for many years1,2,10,11. Some yarn types may even have a greater deviation from the idealized twisted structure. For example, air-jet spun yarn exhibits no true twist with fibers in the core being largely parallel and outer fibers forming random wrapping around the core fibers. Thus, yarn structural integrity and fiber packing is largely a result of the continuity in the core fibers and the lateral pressure imposed by the wrap fibers.

7.3.3 Fiber mobility Fiber mobility is a key design aspect of yarn as it determines the dimensional stability of both the yarn and the fabric woven or knitted from it. In case of continuous filament yarn, there is a small tendency of fiber movement in the yarn except for the tendency of filaments to split apart under buckling effects imposed by processing factors or end use factors. In case of textured yarns, bulkiness or stretchability are both induced by some distortion in the filaments after which heat setting or self-locking of filament loops (as in air texturing) assist in providing dimensional stability to the yarn. Obviously, when such conditions are partially removed (e.g. by wearing, washing and drying), the filaments will have a greater tendency to mobilize.

Structure and mechanics of yarns

201

In the case of spun yarns, the discrete nature of staple fibers can result in many modes of fiber mobility depending on the external effects encountered. Under minimum yarn strain, fibers will tend to settle down and cohere. If the yarn is relaxed or slack, the fibers will likely be in a bending mode; if the yarn is tensioned, the fibers will follow the path of minimum length or a straight line between fiber ends; if the yarn is twisted, the fibers may be buckled or tend to snarl; and when a yarn end is set free, the fibers will tend to untwist. The point is that most spun yarns exhibit a great deal of fiber mobility that in one way or another can influence yarn performance during the conversion of yarn into fabrics and during the use of fabric in various applications. Perhaps no greater fiber mobility is observed in a yarn than that of the fiber segments or filaments near the yarn surface. In an untwisted continuous filament yarn, filaments in the outer layer will tend to snag or come loose, particularly under external rubbing conditions. For this reason, it is sometimes recommended to insert slight twist in this type of yarn to avoid snagging as mentioned earlier. In spun yarns, an inevitable phenomenon is the existence of fiber segments protruding from the yarn body. This is called ‘yarn hairiness’ and it is measured by the number of hairs projecting from the yarn and their lengths. Typically, short hairs (less than two millimetres) adhered to the yarn body are acceptable as they provide a nice fuzzy feeling in apparel fabrics against the skin. This is particularly true when the protruding hairs are flexible so that they can bend easily against the skin. They may also create an opportunity to create tiny fiber pockets that can entrap air for good thermal insulation. On the other hand, long hairs protruding from the yarn body can be of major adverse effect on yarn performance. During the conversion of yarns to fabrics, long hairs of different yarns will tend to entangle together creating fiber bridges that hinder a smooth flow of the yarn during processing. This phenomenon is frequently observed in the denim manufacturing process particularly in the stage of rope beaming. One way to minimize or eliminate long hair is by using the singeing process in which projecting fibers are carefully burned away. The level of hairiness in spun yarns will largely depend on a number of factors including yarn size, yarn twist, spinning preparation, and spinning method. Figure 7.4 shows values of hairiness for different spun yarns obtained from Uster statistics. In this case, yarn hairiness is measured by the so-called hairiness index, H, which is the length of hair per unit length of 1 cm. Thus, a hairiness index of 4 will simply mean that the accumulated length of hair of a certain yarn is 4 cm per unit length of 1 cm. Some of the interesting points that can be revealed from this figure are as follows: •

Most traditional spun yarns exhibit hairiness ranging approximately from 2.0 to 12. This is a wide range from a yarn-performance viewpoint

202

Structure and mechanics of textile fibre assemblies 11.00

6.5

Yarn hairiness (H)

Yarn hairiness (H)

7 Ring-carded

6 5.5 5

Ring-combed

4.5 4 15

20

25 30 35 Yarn count (C)

40

10.00 8.00 7.00 6.00

Rotor-carded

5.00 4.00

45

Ring-carded

9.00

4

6.5 6 Ring-combed-weave 5.5 5 4.5 4 Ring-combed-knit 3.5 3 Compact-combed-weave 2.5 2 10 15 20 25 30 35 40 45 50 Yarn count (C) (c)

Yarn hairiness (H)

Yarn hairiness (H)

(a) 11.00 10.50 10.00 9.50 9.00 8.50 8.00 7.50 7.00 6.50 6.00

6 8 10 12 14 16 Yarn count (C) (b)

Ring-carded-knit

Ring-carded-weave 4

6

8

10 12 14

16

Yarn count (C) (d)

7.4 Uster® yarn hairiness at different preparations and different spinning methods 13.

•

• •

as it can have a wide impact on fabric performance characteristics such as fabric texture, fabric hand or feel, and fabric dimensional stability. In general, the finer the yarn, the lower the degree of hairiness. This is generally attributed to two reasons. The first reason is a statistical one as finer fibers normally have lower number of fibers per yarn crosssection leading to lower chance of creating hairiness. The second reason is that fine yarns are typically made from long fibers or combed slivers with lower percent of short fibers. Most hairiness is created by short fibers. In line with the above point, combed yarns exhibit lower hairiness than carded yarns (see Fig. 7.4(a)). Ring-spun yarns have substantially higher hairiness than rotor-spun yarns (Fig. 7.4(b)). This is a result of the differences in the principles of the two spinning methods. In ring-spinning, the phenomenon of fiber migration forces a great deal of short fibers to be positioned near the yarn surface resulting in potential hairiness2. In addition, the ringtraveler system in ring spinning stimulates the hairs through the rubbing

Structure and mechanics of yarns

•

•

203

effect. In rotor spinning, the back doubling effect and the low fiber migration rate result in lower hairiness2,3. Compact yarn has the lowest hairiness level of all traditional spun yarns (see Fig. 7.4(c)). This is a direct result of the deliberate compactness of fibers in the yarn, making it a less hairy (see Table 7.3). The difference between hairiness of yarns made for woven fabrics and that of yarns made for knit fabrics is not so large (Figs 7.4(c) and (d)).

In addition to yarn hairiness, other fiber structural irregularities such as belt fibers in case of rotor-spun yarns or loose wrapping fibers in case of air-jet yarns are easily movable under the effect of rubbing against other yarns or other surfaces. This can influence the abrasion resistance and the propensity for pilling of fabrics made from these yarns.

7.4

Theoretical treatments of yarn tensile strength

No subject has received more attention in textile research than yarn mechanics, thanks to top scientists beginning with Gégauff in 1907 followed by Platt in the late 1940s, then the work by Hearle and co-workers in the 1950s and 1960s. These contributions focused primarily on the mechanical behavior of yarn and the structural features that influence this behavior. Engineers and technologists involved in the design of yarn should read the book titled Structural Mechanics of Fibers, Yarns, and Fabrics published in 1969 and coauthored by Hearle, Grosberg, and Backer1. This book provides an excellent review of these major contributions. Another excellent book by Zurek, titled The Structure of Yarn, translated from Polish to English in 1975, provided a critical dimension of yarn structure, which is the nature of variability in fiber arrangement in different fiber strands7. Again, in order to add to the great contributions made by previous studies, one must first learn from these great efforts in order to avoid reinventing the wheel, or recycling research. In addition, one must take new approaches of handling the mechanics of yarns via utilization of the simulation and modeling powers introduced by today’s computer software capabilities. Indeed, any further progress in this area would not be possible via classic ‘research’, but rather via innovative and creative ‘search’. In light of learning from the outstanding efforts made by these scientists, one should keep in mind that the idealized model of a twisted yarn structure largely stemmed its success from its close resemblance of the straightforward continuous filament yarn structure. It also largely approximates the conventional ring-spun yarn in which fibers are largely truly twisted with relatively minimum fiber disturbance. This structure results from fibers being consolidated into the yarn under tension and in a controlled mechanical media where drafting, twisting, and winding are harmonized in such a

204

Structure and mechanics of textile fibre assemblies

way that makes fiber behavior in the yarn highly predictable and easily explored. One of the classic theoretical treatments that have great merits in exploring yarn mechanics was that made by Hearle et al.1 for continuous filament yarns. This analysis was extended to accommodate the more complex spun yarns through analytical and empirical adjustment for the reduction in tension in the surface layers of the yarn as a result of using discontinuous fiber segments or staple fibers. This analysis yielded the class equation of yarn to fiber modulus ratio: Yarn strength ( or modulus ) Ey = = cos2 α [1 − k cos ec α ] Fiber strength ( or modulus ) E f

7.4

where Ey is yarn modulus, Ef is fiber modulus, α is the twist angle, and k is expressed by the following equation: k=

2 ⎛ aQ ⎞ ⎟ ⎜ 3L f ⎝ μ ⎠

12

7.5

where L is the fiber length, a is the fiber radius, Q is the migration period, and m is the coefficient of friction. The above equation indicates that there are two basic components determining yarn strength-twist relationship for a given fiber strength14: the cos2 α (which is the only component needed in case of continuous filament yarn) and the (1–k cosec α) required to adjust for spun yarn structure. The former component yields a decreasing strength with the increase in twist angle and the latter yields an increasing strength with twist, which is largely dependent on the k value (higher k values will result in lower strength ratios). Fiber properties reflected in this equation are fiber length, fiber fineness (or fiber diameter). As fiber length increases k decreases, leading to higher yarn strength; as the fiber diameter, a, increases k increases, leading to lower yarn strength. The equation also indicates that the increase in friction results in a decrease in k value, or an increase in yarn strength. This point is highly questionable as friction is typically associated with a trade-off between too slippery and too tight contact from preparation to fiber consolidation. As admitted by the developer, the above equation is associated with a great deal of approximation. Nevertheless, it clearly explores the key parameters constituting yarn structure (discussed earlier) and the factors influencing yarn mechanics, namely: yarn twist (or fiber compactness), fiber migration (fiber mobility and arrangement), and basic fiber properties such as fiber length, fiber fineness, and fiber cohesion.

7.5

Strength-comfort-twist relationship

In meeting the strength requirements of yarn, it is important to also consider other performance criteria, particularly those that may come in con-

Yarn strength

Structure and mechanics of yarns

205

•Fibers are inclined w.r.t. the yarn axis

•Fibers are aligned with the yarn axis

•Less fiber contribution along the yarn axis

•But no cohesion

Optimum twist

Twist factor

7.5 Effect of twist on spun-yarn strength.

flict with yarn integrity. To explain this point, the familiar strength-twist relationship described theoretically by equation 7.4 should be considered. This relationship is shown in Fig. 7.5. Initially, as the twist level (number of turns per unit length) increases, yarn strength will also increase. This effect holds only up to a certain point beyond which further increase in twist causes the yarn to become weaker. Thus, one should expect a point of twist at which yarn strength is at its maximum value. This point is known as the ‘optimum twist’. In practical terms, the strength-twist relationship may be explained on the ground that at zero twist, fibers are more or less oriented along the yarn axis but without any binding forces (except their interfacial contact). As twist slightly increases, the contact between fibers will increase due to the increase in traverse pressure, and the force required to stretch the yarn must first overcome the inter-fiber friction. Further increase in twist will result in further binding between fibers and an increase in the self-locking effect imposed by more cross-linking points between fibers. This provides an opportunity for many fibers to be held at some points along their axis by other fibers. When this happens, the fiber strength begins to play a role in resisting the force required to stretch or rupture the yarn. Eventually, fiber strength will play a greater role than inter-fiber friction in tensile resistance. However, the discrete nature of fibers will always necessitate inter-fiber cohesion. The trend of increasing strength with twist will continue until some points where the fibers become so inclined away from the yarn axis that the contribution of fiber strength will decrease. This will result in a reduction of yarn strength with the increase in twist. In light of the above interpretation, one can see that there are two effects governing the strength-twist relationship. The first effect is an increase in

206

Structure and mechanics of textile fibre assemblies

Resistance to slip (1– k cosec α).

A r c s tw oh is es t ion

FibFibe As er r o twi co bliq st ntr ui ibu ty tio n

Fi be

Yarn strength

Resistance to fiber breakage cos2 α

All fibers break

All fibers slip Optimum twist

Twist level

7.6 Interpretation of strength-twist relationship.

yarn strength with twist resulting from the increase in the cohesion of fibers as the twist is increased. The second effect is a decrease in yarn strength with twist resulting from a decrease in the effective contribution to the axial loading of the yarn due to fiber obliquity. Thus, the curve shown in Fig. 7.5 may be divided into two sections (Fig. 7.6): (i) a low twist region in which the effect of fiber cohesion outweighs that of obliquity, giving rise to an increase in strength, and (ii) a high twist region in which further increase in cohesion no longer produces an increase in strength because of the overwhelming effect of fiber obliquity. The twist level used can influence a number of fabric characteristics. These include: fabric hand, and skew. High or low levels of twist may be required depending on the type of fabric produced and its desirable characteristics. Highly twisted yarns are ‘lively’ and tend to untwist (or snarl). Consequently, fabrics made from these yarns will possess a lively handle. This effect is utilized in producing crepe yarns (TM = 5.5–9.0), which are used to produce crepe surface cloth. When soft fabrics are desirable (e.g. knit shirts), a low level of twist is required. Low twist level is also required to minimize fabric skew. As the level of twist increases in the yarn the tendency for the knit fabric to skew or torque increases. For most spun yarns, the desire to increase strength via twisting may come at the expense of yarn softness or fluffiness, which is a desirable characteristic in most knit fabrics. This means that an optimum twist with respect to strength may not be desired for yarn softness or fabric comfort. The effect of twist on yarn softness and ultimately on fabric hand and comfort was

Performance index

Structure and mechanics of yarns (B) Comfort-twist relationship

1

207

(A) Strength-twist relationship

0.8 0.6 0.4 0.2

(C) Strength-comfort curve

0 0

1

2 3 Optimum twist for comfort-strength

4 5 Optimum twist for strength

6 Twist index

7.7 Performance-twist/performance-cost characteristic curves.

studied by the present author15,16. The conclusion of this study was that the optimum twist for knit yarns should be selected in the context of both yarn softness and yarn strength. This point is illustrated in Fig. 7.7 in which the strength-twist relationship discussed above is superimposed with another relationship in which a comfort index is the dependent variable. This relationship reflects the effect of twist on yarn stiffness and fiber compactness in the yarn. According to this relationship, excessive twist can lead to stiffer and low-porosity yarn, which can result in high discomfort to the wearer of the fabric made from this yarn. Note that the optimum twist level is determined by the intersection of two curves: curve A, the strength-twist curve and curve B, the comfort-twist curve. For simplicity, in both curves the performance parameter is expressed by an index so that both parameters can be superimposed. In case of the comfort-twist curve, the index ranges from 0 to 1, with 0 indicating high discomfort, and 1.0 indicating the highest possible comfort level. In case of the strength-twist curve, the strength index implies the ratio between the actual strength produced at a certain twist level and the maximum strength that can be obtained from the spinning system used and the fiber characteristics utilized. The net curve (C) representing these two performance parameters, is called the strength-comfort characteristic curve. In light of the above discussion, the twist level in the spun yarn should be large enough to provide maximum yarn strength, yet as small as possible to provide yarn flexibility and optimum fiber compactness, or good yarn porosity. One of the main approaches to reduce twist and, at the same time, maintain high strength and optimum comfort is to select appropriate fiber material and certain values of fiber characteristics. In general, the choice of long, strong, and fine fibers can result in lower optimum twist levels (see Fig. 7.8). Since only expensive fibers can exhibit these levels of fiber

208

Structure and mechanics of textile fibre assemblies

Performance index

Long/strong/fine fibers 1

Short/weak/coarse fibers Manufacturing cost

Fiber cost Fiber value

0.8 0.6

(C) Strength-comfort curves

0.4 0.2 0 0

1

2

3

4

5

6 Twist index

7.8 Effects of fiber properties on optimum twist.

characteristics, a trade-off should be achieved between the cost of material and the economical gains resulting from using lower twist levels.

7.6

Practical aspects of yarn strength

The theoretical treatments of yarn tensile strength primarily aim at exploring the various effects of the critical parameters influencing yarn strength. In practice, yarn mechanics is a desirable subject in the context of two key aspects: (i) estimating yarn strength, and (ii) predicting yarn strength. These two aspects are typically handled using empirical models in which yarn strength is related to some processing parameters or fiber properties. These models are useful for the particular processes they are developed for, but they can not be generalized to accommodate all processes. In order to develop fiber-to-yarn models, two basic challenges should be addressed. These are: (i) technological challenges, and (ii) analytical challenges. The natures of these challenges are discussed below.

7.6.1 Technological challenges The critical technological challenge associated with fiber-to-yarn modeling is ‘what fiber parameters should be included in the models’? This challenge stems from the fact that some fiber properties are physically interrelated (or correlated) by virtue of their breeding and growing nature. In some varieties, longer fibers are also fine fibers; in other varieties, finer fibers may also be immature. In addition, impurities such as trash, dust, and nep content can indeed influence other fiber parameters such as fiber fineness and maturity (by virtue of the testing technique used). Furthermore, critical

Structure and mechanics of yarns

209

color parameters such as Rd (color reflection) and +b (yellowness) often reflect the sample color, not the fiber color; a cotton sample with high trash content will likely yield a low Rd value and samples that come from bales that have been stored improperly (excessive sun and rain) can exhibit high yellowness values. This, in turn, can affect fiber strength leading to a high correlation between yellowness and strength. All these issues must be dealt with in developing a good database of fiber properties suitable for fiber-toyarn models. In recent years, revolutionary developments have been made in cotton fiber testing (e.g. High Volume Instrument, HVI, and Advanced Fiber Information System, AFIS). Accordingly, the models developed can rely on the parameters generated by these systems as model inputs and on standard yarn or fabric quality parameters as model outputs or response variables. Other technological challenges stem from the need for more fiber parameters to fully model the impact of fiber quality on yarn or fabric quality. For example, when the strength of yarn or fabric is in question, the two critical parameters are fiber strength and fiber elongation. Fiber strength is measured by the HVI in a beard form. Fiber elongation has not been considered as a standard fiber quality value; it is not reported in the USDA data and questions regarding its reliability have been raised. Fundamentally, it is well known that the yarn breaks at the points of low-elongation fibers. This suggests that fiber elongation is a key factor in determining yarn and fabric strength. In addition, yarn flexibility, particularly for knit products, is largely influenced by fiber elongation as yarn elongation is directly affected by fiber elongation. Another key fiber parameter that is not measured by current testing systems is a measure of the surface integrity and the surface nature of fibers. Examples of this category of parameters may include: fiber friction, and surface morphology (convolution rate and micro-orientation). These parameters are assumed to be constant for most cotton types. Obviously, this is a gross assumption as evident by the differences in fiber performances (processibility, nep-forming propensity, and fiber breakage, etc.) for fibers that exhibit the same values of standard fiber properties. In addition, surface integrity has a great impact on yarn and fabric quality (strength, feel, and comfort). Indeed, the touch and feel of cotton stem from the tapered shape of the fiber and the nature of surface layers along the tapered length; yet, none of these parameters is measured on routine basis. Another technological challenge facing fiber-to-yarn modeling is the realization of the true physical effects of fiber properties on yarn and fabric properties. This realization lies in the heart of establishing a true value of cotton. It is a challenging issue since a good model should be based on understanding these physical effects; yet empirical models do not necessarily follow the physical effects in value or direction of trend.

210

Structure and mechanics of textile fibre assemblies

7.6.2 Analytical challenges The analytical challenges facing empirical fiber-to-yarn modeling stem from the difficulty in performing this approach in practice. Some of the common features of empirical models are as follows2: •

•

•

•

•

The model primarily derives its reliability from the database from which it is developed. In other words, it should ideally be used for processes using the same data. Substantial changes in the process leading to significant alteration of the data values or levels may require the development of new empirical models or adjusting of the existing ones. Although it is preferable, the model does not need to be physically correct as it relies on input and output data representing different parameters, or regressors. Empirical models developed from statistical analyses (e.g. regression models) are typically un-exploratory. In other words, they cannot be used to reveal causes and effects associated with the response variable. Linear empirical models are more predictive than non-linear models as linear trends are easier to extrapolate. Yet, the relationship between yarn strength and fiber properties is hardly linear. Unlike theoretical models, empirical models account for the variability in the parameters used depending on the extent of this variability in the database.

As indicated earlier, the most commonly used approaches of empirical modeling is regression analysis using the familiar least-squares method. In order to perform regression analysis, a number of regression assumptions must be made and used. Violations of these assumptions result in unreliable models. Two critical assumptions are: (i) wide range of values, and (ii) minimum or no collinearity between the independent variables in the model. These criteria are often difficult to meet in practical environment as mills tend to use a consistent mix of fibers of more or less equal values of fiber properties from one mix to another. In a recent work by Subramanian17, an effort was made to estimate spun yarn tenacity using a phenomenological model. The structural equation proposed by the author is in the following form: CS = Z × R × F1 × F2 × F3 × F4

7.6

where CS is yarn tenacity in terms of the count (Ne) × strength (lbs) product, Z is the fiber bundle tenacity at zero gauge length (g/tex), R is a numerical conversion factor to adjust for the units in use in expressing fiber-bundle tenacity and yarn tenacity, as well as for differences in testing procedures, F1 is the number of fibers available at the place of break

Structure and mechanics of yarns

211

expressed as a fraction of the average number of fibers corresponding to yarn count, F2 is the fraction of fibers at the place of break which break themselves as against the remaining which slip when yarn breaks in tensile testing, F3 is the fraction of zero-gauge fiber bundle tenacity available at the gauge length at which fiber bundles themselves break when yarn breaks in tensile testing, and F4 is the fraction for obliquity correction for the angle made by fibers to the direction of tensile loading in yarn testing. Using numerical values of the various terms represented by the above equation, the author was able to provide some estimates of yarn strength. Obviously, as one can see from this equation most the parameters represented in the equation cannot be estimated easily in a practical environment making it nearly impossible to estimate yarn strength as each of these parameters must be estimated as well. However, the equation is reported here to simply demonstrate the magnitude of difficulty of reaching a reliable way of estimating or predicting yarn strength.

7.7

Conclusions

In this chapter, a review of the key structural features of yarn was presented. These features should be emphasized in future studies in which yarn structure is treated as an integral aspect of end product design. Few points on yarn mechanics were also mentioned for the sake of illustrating the challenges associated with estimating or predicting yarn failure. Fortunately, once a yarn is woven or knitted into a fabric structure, factors such as yarn assistance and network assembly provide a great help in maintaining good fabric integrity.

7.8

References

1. J.W.S. Hearle, P. Grosberg and S. Backer, Structural Mechanics of Fibers, Yarns, and Fabrics, Wiley-Interscience, New York, 1969. 2. Yehia El-Mogahzy, and Charles Chewning, Jr., ‘Fiber To Yarn Manufacturing Technology’, Cotton Incorporated, Cary, NC, U.S.A, 2001. 3. Yehia El-Mogahzy, Yarn Engineering, Indian Journal of Fiber & Textile Research, Special Issue on Emerging Trends in Polymers & Textiles, Vol. 31, No. 1, PP 150–160, 2006. 4. B.C. Goswami, J.G. Martindale and F.L. Scardino, Textile Yarns, Technology, Structure and Applications, Wiley-Interscience Publication, John Wiley & Sons, NY, London, Sydney, Toronto, 1977. 5. K.L. Hatch, Textile Science, West Publishing Company, Minneapolis, NY, 1999. 6. Peter R. Lord, Handbook of Yarn Production, Technology, Science, and Economics, The Textile Institute, CRC Press, Woodhead Publishing Limited, Cambridge, England, 2003.

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Structure and mechanics of textile fibre assemblies

7. Yehia El-Mogahzy, Yarn types: compound and fancy yarns, video-lecture, Quality-Business Consulting (QBC), http://www.qualitybc.com/, 2005. 8. Manuela Ferreira, Serge Bourbigot, Xavier Flambard, Bernard Vermeulen, ‘Interest of a compound yarn to improve fabric performance’, AUTEX Research Journal, Vol. 4, No1, March 2004. 9. W. Zurek, The Structure of Yarn, Translated from Polish, published by the USDA and the National Science Foundation, 1975. 10. F.T. Pierce, J. Text. Inst., 1926, 17, T355. 11. W.E. Morton, Text. Res. J., 1956, 26, 325. 12. B. Neckar, Yarn Fineness, Diameter, and Twist, a paper presented in TEXSCI ’98, Liberec, Czech Republic May 25–27, 1998. 13. UsterTM Technologies Technical Data, http://www.uster.com/ 14. J.W.S. Hearle, ‘Engineering design of textiles’, Indian Journal of Fiber and Textile Research, Special Issue on Emerging Trends in Polymers & Textiles, Vol. 31, No. 1, PP 135–141, 2006. 15. Y.E. El-Mogahzy, Understanding Fabric Comfort, Human Survey, Textile Science 93 International Conference Proceedings, Vol. 1, Technical University of Liberec, Czech Republic, 1993. 16. Yehia El-Mogahzy, Fatma Selcen Kilinc, and Monir Hassan, Developments in Measurements and Evaluation of Fabric Hand, Chapter 3, ‘Effect of Mechanical and Physical Properties on fabric hand’, Hassan Behery, Editor, Woodhead Publishing, pp 45–65, 2004. 17. T.A. Subramanian, ‘A Solution for Testing Cotton Yarn Tenacity’, International Textile Bulletin (ITB), 4, pp 36–38. 2004.

8 Structure and mechanics of coated textile fabrics S ADANUR, Auburn University USA

Abstract: Coated fabrics are an important family of textile structures and have a wide range of applications. Geometry and manufacturing methods of coated fabrics along with fibers and fabrics used in the reinforcement structures are explained. Polymers and additives used in coated fabrics are included. Adhesion between coatings and fabrics is critical for the high performance expected of coated fabrics. The behavior of coated fabrics in tensile, tear, bending and shear loading is analyzed. Models to simulate the mechanics of coated fabrics are discussed. Recycling techniques of coated fabrics are included. Key words: coated fabrics, polymers, additives, mechanical behavior, modeling, recycling.

8.1

Introduction

A coated fabric is a composite structure that consists of at least two components: base fabric and coating. The base fabric is usually woven, knit or nonwoven; braided structures are rarely used for coating. Coating is a manmade or natural polymer. The fabric can be coated on one side or both sides. Sometimes, coating is sandwiched between two fabric layers as in the case of life vests (Fig. 8.1). The main purpose of the base fabric is to provide strength and dimensional stability to the coated fabric structure. Coating protects the base fabric against the outside effects while making the structure air and water proof. Coated fabrics are used in many industrial applications such as architecture, construction, transportation, safety and protective systems [1]. Since a coated fabric is a composite made of two components, its behavior is different from any of its components or the sum of its components.

8.2

Structural properties

8.2.1 Geometry and manufacturing methods of coated fabrics Woven, knit, tufted and nonwoven fabrics are used in coating. A woven fabric can be of plain, twill or satin construction. The knitted fabrics can 213

214

Structure and mechanics of textile fibre assemblies

8.1 Possible structures of coated fabrics.

be warp knits or tubular knits finished and slitted. Cut edges are treated with resin to prevent stitch running. The nonwoven fabrics could be stitch bonded, spun bonded or needle punched constructions. Tufted fabrics are also back coated to prevent unraveling of tufts and to impart dimensional stability. Coating methods There are several methods and machinery presently available for applying polymeric coating compounds to textile substrates. Although a great deal of cloth is coated without preliminary treatment, for some, precoating preparation of the fabric is often necessary. Once coated, the fabric is passed through an oven where the excess solvent, if present, is evaporated, and the resin is cured. In calendering, the plastic is calendered directly onto the fabric or an unsupported film is formed which is subsequently laminated to the cloth in a separate laminating operation. A compound containing resin, plasticizer, stabilizer, and pigments is fed to a preblender, where it is blended to a free flowing powder. This powder is then charged to a mixer, in which it is fused into a plastic state. The hot plastic is then fed to the calender, where the film is formed. In the case of calender coating, the hot viscous resin is deposited on the two top rolls of the calender. The resin is picked up by an intermediate roller which transfers it to the fabric at the pressure nip between the fabric feed roller and the intermediate roller. Two calender coaters are shown diagrammatically in Fig. 8.2. In knife or spread coating operation the viscous coating material is spread onto the fabric surface, which is then passed under a closely set metal edge

Structure and mechanics of coated textile fabrics

215

Inverted ‘L’ calender

+

+

+ Fabric in +

‘Z’ type calender Fabric in +

+

+

+

8.2 Schematics of calender coating.

called a coating knife. The knife serves to spread the coating uniformly across the entire width of the substrate fabric, simultaneously controlling the weight of coating material applied. There are different types of coating methods such as knife-over-roll coating and floating knife coating. Figure 8.3 shows the schematic of different knife coating techniques. Knife-overroll coating is suitable for applying thin coatings of high viscosity materials onto fairly closely woven fabric. The simplest type of coating device is the roll coater where a roller, rather than a knife, applies the coating compound to the fabric. A two-roll reverse roll coater utilizes a smaller diameter back-up roll and doctor knife to exert some measure of control upon the thickness of the applied coating. Low viscosity coating materials can be speedily applied to fabrics using nip coating (Fig. 8.4). As the fabric passes through the nip formed between the two rolls, the coating is forced into the fabric. Dip coaters are used when complete saturation impregnation of the base fabric is required. If the coating is to be applied without the application of pressure, a reverse roll metering action is executed. One advantage of this technique is that both the face and back of the fabric can be coated in one pass through the coating machine. The cast coater combines both the coating and curing operation into one process as a method of producing a high gloss coating upon a fabric web.

216

Structure and mechanics of textile fibre assemblies Coating knife Coating compound Backing roll

+

Knife-over-roll

Coating compound

Coating knife

Endless rubber blanket

Driver roll

Knife-over-blanket Coating compound

Coating knife +

Support roll

Support channel Floating knife

8.3 Knife coating.

A +

+ Fabric +

B

+

8.4 Nip coating.

C

Coating material

Structure and mechanics of coated textile fabrics Coated fabric

Stripping roll

217

Sheeting die Hot resin + Chill roll

+ Rubber pressure roll

8.5 Hot extrusion coater.

While the curing operation may not be quite complete, it is sufficient to create the exceptionally smooth coating surface. Vinyls, polyethylenes, and polystyrenes can be successfully coated to substrate fabrics by using a hot extrusion coater, illustrated in Fig. 8.5. In this process, the coating material is extruded as a soft sheet into the nip formed between the chill roll and the rubber pressure roll. In the spray coating method, the latex coating formulation, at a lower viscosity than conventional coating compounds, is sprayed through a series of nozzles uniformly on the traveling fabric web. The fabric is then dried and cured as in other coating methods. The method is widely used for backcoating of upholstery fabrics where the fabric weights, construction or yarns do not allow conventional knife or roller coatings. The foam back coatings are generally used to stabilize the coated base fabric, to impart opacity (prevent see-through), for bulkiness, for softness (hand) and for desired aesthetics depending on end use. Foam coated fabrics are produced for textile applications by the crushed foam coating method, uncrushed foam coating or by flocked foam coating techniques. Typically additives in a back coating foam contains latex, filler, foaming agent, auxiliary foaming agents, thickeners and alkali such as ammonium hydroxide to adjust required pH range. UV-curable coating systems can be used for vinyl coated fabrics. Vinyl coated wall coverings have poor soil resistance. A typical UV-curable top coat system based on polyurethane contains the urethane oligomer with acrylate end groups, reactive acrylate monomer, multifunctional acrylate cross linker and photosensitizer. The UV top coats are considered superior to conventional coated fabrics in resisting ball point ink stains, and other soiling materials [2]. Powder coating using thermosetting epoxy resins, cross-linkable polyester resins, or acrylic resins are used for coating fabrics, wire, pipes and for bottle coatings [3]. Electrostatic application, spray method or screen methods are commonly used. Powder coating methods can also be used for applying the laminating adhesive or thermoplastic resins to fabric surface.

218

Structure and mechanics of textile fibre assemblies

8.2.2 Fibers and fabrics used in the reinforcement structure The choice of fiber, size of the yarn and type of reinforcement structure for coated fabrics determine the fabric properties. The yarn and fabric construction influences the durability of coating. The fiber selection is critical as to the bonding of polymer compound since mechanical adhesion and chemical bonding vary from fiber to fiber. If the fiber is synthetic, spun yarn construction compared to filament yarn give different mechanical properties to the coated fabric. Fabrics made of cotton were the traditional base material used in coating. This trend has declined due to the availability of synthetics which give improved strength characteristics as compared to cotton. Nylon is widely used for lighter weight coated fabrics as it imparts higher strength, toughness, flexibility, waterproofness and durability. Coated nylon fabrics are used for survival rafts, inflatable medical products, personal floating devices, truck tarpaulins, machinery covers, tents, swimming pool covers, liners and irrigation tubing. Since lighter weight fabrics can be coated, they are easier to transport. Filament nylon fabrics can be coated as gray fabric. A pretreatment called the tie coat, which is usually solvent based, is applied to fabric prior to coating for improving adhesion of coating compound. Due to environmental reasons the solvent based pretreatment is replaced with a water based system. Spun nylon/cotton blends of 200– 300 g/m2, camouflage printed, fire retardant treated and waterproof coated are used for military tents. Use of polyester in coating applications is increasing. Although the abrasion resistance is somewhat lower than nylon, it gives flexible, tough coatings similar to nylon and has high tensile and tear strength. The improved priming methods and improved yarn manufacturing give better adhesion of coating compound to polyester and improved dimensional stability. As in the case of nylon the polyester filament yarns can be used for coating in the gray stage. For coated lighter weight sheetings, polyester is often blended with cotton. Nonwoven polyester coated for stability and waterproof treated is extensively used in the outdoor furniture market. Polypropylene has excellent mechanical properties under normal conditions but has poor thermal stability. Polypropylene has high stress decay and poor coating adhesion which limits its use. Polypropylene fabric is widely used in the carpet industry replacing jute backing. Polypropylene fabric tufted with nylon or polyester yarns producing carpets, is normally back coated for dimensional stability. Glass, Nomex® aramid, Kevlar® aramid and graphite fibers are used in coating where high performance composites are needed. These fibers possess inherent flame retardancy and have merit in certain applications.

Structure and mechanics of coated textile fabrics

219

Polyester or nylon coated with fire retardant compounds, limits the use of costly high performance fibers in coating. Nonwoven fabrics of stitch bonded, spun bonded or needle punched constructions are used as the base fabric for coating and film laminating. Various fiber combinations and binders are selected, depending upon end use requirements. Certain nonwoven fabrics have a random fiber distribution, assuring balanced strength and elongation. These base materials provide good tear strength, flexibility, and smooth surfaces for embossing, with no ‘show through’ of weave pattern. They also provide high thicknessto-weight ratios at reasonable cost, and can be calendered, laminated, or electronically heat sealed to vinyl film. Polyester nonwoven fabrics, back coated for stability and coated on face with water and stain repellents, are used for the outdoor furniture market. Only small usage of rayon and acrylic fabrics is found in the coating market. The mechanical properties of the modified acrylics limit its application in the coating field.

8.2.3 Polymers and additives used as coating The base polymer for coating can be natural or synthetic rubber or rubber like polymers. High polymeric materials such as cellulose ester and ethers, polyamides, polyesters, acrylics, vinyl chloride, vinylidene chloride, polyurethanes and natural and synthetic elastomers and rubbers are used in compounding [4]. The mixing operation of various chemicals to produce the coating compound is commonly known as the compounding operation. The compounding can be within a coating plant or can be bought from a supplier as a compounded product. The choice of compounding chemicals and fillers is governed by the end product requirements. Besides polymers, resins and fillers, other additives such as fire retardants, thickener and coloring agents may be included in coating formulations. The following polymeric materials are used in coating: • • • • • • • • • • • •

natural rubber balata gum acrylic polymers polybutadiene styrene-butadiene rubber (SBR) and copolymers butadiene-acrylonitrile copolymers (nitrile rubber) polyisobutylene butyl rubber polysulfide rubber chloroprene rubber (neoprene) chlorosulfonated polyethylene (Hypalon®) silicone rubber

220 •

• • • • • •

Structure and mechanics of textile fibre assemblies

fluorinated polymers – polytetrafluoroethylene; CF2=CF2 (Teflon® from DuPont); – polytrifluoro-monochloroethylene; CClF=CF2 (Kel F from 3M Co.) – trifluorochloroethylene and vinylidene chloride co-polymer; (Kel F 3700 and 5500 from 3M Co.) – polyfluoropropylene and vinylidene fluoride co-polymer (Viton A from DuPont and Kel F 2140 from 3M Co.). – Scotchgard® brand of polymers from 3M and Teflon® from DuPont polyurethane foam urethane coating resins vinyl resins pyroxylin starch cellulose.

Fillers The amount and type of fillers used in a coating compound depends on the end product. Fillers are classified as active or inactive fillers. The common fillers are inactive and their use can alter physical properties such as tear and tensile strength and abrasion resistance. The inactive fillers include, talc, carbon black, kaolin, calcium carbonate, barium sulfate, magnesium carbonate and zinc oxide. Pure silica (SiO2) is considered as an active filler whereas calcium silicate is a semi-active filler. The inorganic and organic fire retardant additives are also considered as fillers in a compound. Pigments Both inorganic and organic pigments are used in coating compounds if a color is needed. A commonly used white pigment is titanium dioxide. Iron oxide is a typical example of an inorganic pigment. There are environmental problems in using chromium and cadmium based inorganic pigments. Organic pigments are based on azo dyes and phthalocyanine dyes. Brilliant colors are obtained with azo pigments and they are widely used. Generally certain blues and green colors are based on phthalocyanine dyes which are metal complexed organic pigments.

8.2.4 Adhesion between coatings and fabrics Studies on the effect of coating methods showed that certain coating techniques changed the porosity of the coating and therefore caused an increase in tear strength of coats [5]. Mewes reported that adhesion affects tear

Structure and mechanics of coated textile fabrics

221

40 35

Peeling force N/cm

30 25 20 15 10 5 0

0%

T1 PES-knit

2.5% Bonding agent add-on T2 PA-knit

T3 PES-knit

5%

PES-weave

8.6 Peeling force versus bonding agent content for knit and woven fabrics. T1: 1100 dtex PES, 7 × 7, 180 g/m2. T2: 940 dtex PA 6, 6, 8.8 × 6, 160 g/m2. T3: 100 dtex PES, 4.7 × 4.7, 120 g/m2 [8] (copyright Sage Publications).

resistance only under very specific conditions. Increasing adhesion in a plain woven fabric of 1000 denier from 100 N/5 cm to 200 N/5 cm decreased the tear propagation by 25% [6]. Haddad and Black studied parameters that affect the coating adhesion of fabrics [7]. Their results showed that air textured multifilament yarns and open-end (rotor) yarns had better mechanical adhesion. False twist textured multifilament yarns had lower adhesion than air textured yarns but better adhesion than flat multifilament yarns. Dartman and Shishoo studied the adhesion mechanism of PVC coatings and textile substrates [8]. They suggested that moisture content and environmental conditions during the coating process affects the bonds between the PVC coating and fabric substrates. As a result of shear and peel tests, they concluded that bond strength depends on mechanical and chemical mechanisms in the structure. They investigated the effect of fabric construction on coating adhesion by measuring the peeling force of PVC coated knit and woven fabrics (Fig. 8.6). They found out that the most important parameter for adhesion is the fabric cover factor. However, use of bonding agent reduces this effect.

8.3

Tensile and tear properties

Abbott et al. studied the influence of fabric construction on tensile and tearing of coated cotton fabrics [9]. They coated various plain, twill and

222

Structure and mechanics of textile fibre assemblies

basket woven fabrics with polyvinylchloride plastisol using knife-overblanket technique. They reported that breaking load was increased by coating for all the fabrics tested. Breaking elongation was increased as well except in the direction of slack mercerized and compacted yarns. They could not find any relation between the tensile properties and fabric construction. The increase in tensile strength of coated fabrics was attributed to the fiberto-fiber adhesion. The tear test results of uncoated fabrics showed that, cover factor being the same, the tear strength was decreased from basket to twill to plain weave due to decrease in the deformability of the structure. Coating of these fabrics did not change the order of tear strength but lowered it for all. After coating, the plain designs lost 25%, twills 60% and baskets 70% of their uncoated tear strengths. It was also reported that twills and baskets made of plied yarns have lower tear resistance than those with single yarns. In another study, they investigated the effect of coating characteristics on tear and flexural strength of some of these cotton fabrics with different coats [10]. They concluded that the effect of coating on tear resistance is purely mechanical; in other words, the chemistry of the coating does not play a role, provided that the chemistry of the coating does not deteriorate the strength of the fibers. Farboodmanesh et al. investigated the effect of coating penetration on tensile behavior of coated fabrics [11]. As the penetration depth increased, the tensile strength also increased slightly as shown in Fig. 8.7. They reported that as the coating penetration increases, the fibers are held together better to bear the load until an optimum depth. The tensile strength decreased for complete penetration which was attributed to the lack of redistribution of stress applied to the fabric. Breaking load vs. penetration depth Sample A z = 22 μm

Load (N)

1150

Sample D z = 58 μm Sample C z = 39 μm

1050 950 Uncoated 850 750 0

20

40

100 60 80 Penetration depth (μm)

8.7 Effect of coating penetration depth on tensile load [11] (copyright Sage Publications).

Structure and mechanics of coated textile fabrics

223

Eichert investigated the residual tensile and tear strength of coated plain woven polyester industrial fabrics after weathering tests [12]. The fabrics were made of Diolen 174S 1100 dtex Z60 with 9 yarns/cm in warp and filling with white pigmented coating. The weight and coating thickness of the fabrics were 540 g/m2 (coating thickness 20 μm), 600 g/m2 (coating thickness 50 μm), and 900 g/m2 (coating thickness 230 μm). The results are shown in Fig. 8.8 and 8.9 for tensile and tear strengths, respectively. In Fig. 8.8, the fabric with the thinnest coating had only 22% residual strength at the end of ten years. The drop in warp strength was slower; one reason for this is that the warp yarns were protected better in the structure for all coating thicknesses. The tear residual strength results also showed that the damage in the warp direction was less than the damage in the filling direction. The

USA Miami 0.5% UV-absorber

% Residual tensile strength 100

1 1 2 1

80

540 g/m2 600 g/m2 900 g/m2

60 40

2 2

20

0

1 = Warp 2 = Filling

2

4

6

8

10 Years

8.8 Residual tensile strength of coated fabrics after weathering tests [12] (copyright Sage Publications).

% Residual tensile strength

1 = Tearing through warp USA Miami 0.5% UV-absorber 2 = Tearing through filling

100 80 60 40

RLD = Rectangular leg destruction 540 g/m2 600 g/m2 RLD 900 g/m2 ? RLD RLD ? RLD

1 1 2 2

20

0

1 2

2

4

6

8

10 Years

8.9 Residual tear strength of coated fabrics after weathering tests [12] (copyright Sage Publications).

224

Structure and mechanics of textile fibre assemblies 55 Dacron-neoprene Fabric N337A15 (pr = 150 1b/in if  = 0) 2r = 5.33 in. 2r = 8.0 in 2r = 12.0 in 40.6 pr =   .65 (1 + .76 r )

50

Critical hoop tension, pr, 1b/in.

45 40 35 30 25 20 15 10 5 0 0

0.1

0.2

0.3

0.4 0.5 0.6 0.7 0.8  = Slit length r Cylinder radius

0.9

1.0

8.10 Hoop strength of a single ply slit polyester-neoprene cylindrical fabric structure [13] (copyright Sage Publications).

RLD is the ‘rectangular leg destruction’ which is the tear propogated in the direction vertical to the slit in the fabric during the tongue tear testing (ASTM D3949). Topping measured the burst resistance of neoprene coated cylindrical fabric structures with a slit and compared his experimental results to four different theories [13]. Figure 8.10 shows the hoop strength of a plain weave 49 × 49 count and 220 × 220 denier cylindrical coated polyester fabric structure. He found that burst strength is independent of the width of the slit and the cylinder length. Slits at an angle to the natural axes of the fabric are not as critical as those of equal length parallel to a natural axis. He concluded that none of the theories is completely satisfactory for predicting burst resistance of neoprene coated cylindrical fabric structures with a slit. Szostkiewicz and Hamelin analyzed failure mechanisms of ripped coated samples with uniaxial and biaxial tests [14]. They noticed that in a coated fabric the matrix transfers the energy caused by the breaking yarns directly to the other yarns. As a result, crack propagation becomes easier and tear strength is reduced as shown in Fig. 8.11(a). Figure 8.11(b) shows the sample geometry for biaxial tests. Many similarities were observed between uniax-

Force (kN)

Structure and mechanics of coated textile fabrics 16 14 12 10 8 6 4 2 0

2a = 20 and 60 mm, V = 0.1mm/S Uncoated - 20 mm Coated - 20 mm Uncoated - 60 mm Coated - 60 mm

225

Warp

2a ϕ

Weft

0 200 400 600 800 1000 1200 1400 1600 1800 Time (s) (a)

(b)

8.11 (a) Uniaxial tear strength of coated and uncoated fabrics. 2a is the slit length in the fabric and V is the tearing speed, (b) Sample shape for biaxial tear [14] (copyright Sage Publications).

ial and biaxial failure mechanisms. Two failure modes were noticed, progressive and brutal. They noted that the failure mode and crack propagation direction depend on the crack length and orientation, applied loading ratio, warp and weft yarn mechanical properties and weaving design. They also modeled biaxial tests with a finite element analysis software. They concluded that biaxial tests are more reliable to characterize coated fabrics for material orthotropy, yarn crimps and matrix softness. Woven fabric design has a significant effect on tear resistance. The higher original tear strength of a basket weave, as compared with a plain weave, may not be retained when such fabrics are coated. The increased openness (i.e., lower cover factor) of the basket weave causes greater resin coating ‘strike through’ into the fabric structure. Yarns may thus become immobile and be incapable of bunching together to reinforce each other. The yarns then break individually rather than in groups, and the tear strength is thus severely lowered.

8.4

Bending and flexibility properties

Abbott et al., studied the influence of fabric construction on flexural rigidity of woven cotton fabrics that are coated on one side only [9]. As expected, coating increased the flexural rigidity of the plain, twill and basket designs drastically in that order since coating penetration was more with more open structures. Due to one sided coating, the results depended on the direction that the fabrics were bent. If the coating is on the outside of the bend, its effect becomes less. Farboodmanesh et al. investigated the effect of coating penetration on bending behavior of coated fabrics [11]. As the coating penetration

226

Structure and mechanics of textile fibre assemblies Flexural rigidity vs. penetration depth Flexural rigidty (gm × cm)

1500

Sample D z = 58 μm

1250

Sample C z = 39 μm

1000 Sample A z = 22 μm 750

Sample B z = 26 μm

Series1

500 0

10

20

30

40 50 60 Penetration depth (μm)

8.12 Effect of coating penetration depth on flexural rigidity [11] (copyright Sage Publications).

Wrinkling

Load

Locking angle/ compaction limit Initial state

Shearing / compaction

Shear angle (θ)

8.13 Schematic of shear deformation in woven fabrics [15].

increased, the flexural rigidity also increased as shown in Fig. 8.12. This is because the yarns were prevented from rotation which stiffened the fabric.

8.5

Shear and shear resistance properties

Figure 8.13 shows the mechanism of shear deformation in a typical uncoated woven fabric [15]. Under shear loading, the yarns may rotate and slip first, then compaction takes place and finally the shear angle is locked. Coating restricts the movement of the yarns in the fabric structure and therefore increases shear resistance. Testa and Yu [16] used bias extension method shear angles of below ten degrees and observed that the shear stress-strain

Structure and mechanics of coated textile fabrics

227

400

Load (N)

300

200

100

0

0

10 20 30 40 Shear angle (degrees)

50

Single-coat Uncoated

8.14 Shear behavior of neoprene coated and uncoated polyester fabrics. Fabric characteristics: 4 harness, warp: 2 ply/150 denier, filling: 220 denier, yarn spacing: 15 × 16/cm, weight: 0.01 g/cm2, number of crossovers: 60 [11] (copyright Sage Publications).

curve is linear-elastic. However, using a trellis frame and higher shear angles (40–50 degrees), other researchers observed a nonlinear behavior in shear response of coated fabrics [17,18,19]. Farboodmanesh et al. investigated the shear behavior of single rubber coated fabrics and compared the results to those of uncoated fabrics and pure rubber sheet [15]. The fabric is fixed in a trellis frame with the yarns parallel and perpendicular to the four sides. As the machine crosshead moved, the fabric was subjected to pure shearing. They observed a significant increase in shear load for coated fabrics as well as a change in the curve shape. Figure 8.14 shows the nonlinear curve of the coated fabric versus uncoated fabric. The uncoated fabric curve is concave; the curve of the coated fabric starts with a convex shape and then changes to a concave shape. The shear angle of this transition is between 20–30 degrees, and it depends on the weave pattern and yarn sizes. They found that the shear behavior of the coated fabric is affected by the rubber at low shear angles and by the fabric parameters at high shear angles, depending on the coating’s ability to restrict yarn movement. Fabric construction and yarn sizes affect the shear response of coated fabric. They concluded that yarn mobility is critical for the shear behavior of the fabric. Farboodmanesh et al. later investigated the effect of coating thickness and penetration on shear behavior of neoprene coated fabrics [11]. They coated a polyester plain woven fabric with multiple coats. It was noticed that the thickness of the composite did not increase as much as the coating mass added, which indicates that most of the earlier coating mass penetrated into the yarns rather than increasing the thickness. The shear

228

Structure and mechanics of textile fibre assemblies 800

Load (N)

600

400

200

0

0

10

20 30 40 Shear angle (degrees)

Uncoated Single-coat Double-coat Triple-coat

50

8.15 Effect of multi-coating on shear resistance of the fabrics (copyright Sage Publications).

z Blade L

Flowing fluid y

h(x)

h1 v

u

Moving boundary

h2 P(x,0)

x

U0

8.16 Schematic of the model by Farboodmanesh et al., for knife coating [11] (copyright Sage Publications).

resistance of the coated fabrics is shown in Fig. 8.15. As the number of coatings increased, the load-shear angle curves became more linear. As expected, triple coated fabric exhibited the highest shear load.

8.6

Modeling the mechanics of coated fabrics

Farboodmanesh et al. modeled the coating penetration for the knife-roll coating process using Darcy’s law for flow through porous media and lubrication theory for the pressure applied on the substrate material [11]. Figure 8.16 shows the schematic of their model. In the model, u and v are the velocity components in the x and z directions, respectively. At the rigid boundary surface (coating blade), u = 0, and on the fabric, u = U, where U

Structure and mechanics of coated textile fabrics

229

Pressure profile vs. gap

Pressure (Pa)

116000 112000 108000 104000 100000 0 P1

0.5 P2

1

1.5

P3

2

2.5

Blade width (mm)

8.17 Pressure profiles for different gap distances, where Po = 101325 Pa, L = 2.6 mm, U = 3 m/min. Gap 1 (G1): pressure is P1, h1 = 0.2786 mm, h2 = 0.2286 mm, Gap 2 (G2): pressure is P2, h1 = 0.3802 mm, h2 = 0.3302 mm, and Gap 3 (G3): pressure is P3 and h1 = 0.4564 mm, h2 = 0.4064 mm [11] (copyright Sage Publications).

is the coating speed. Using the appropriate modified dimensionless forms of the Navier-Stokes equations in the model, they showed that the pressure under the blade is a function of x only, i.e., P = P(x). The volumetric flow rate, Q, is given by: Q=

Uh1 h2 h1 + h2

8.1

and the pressure under the plate is given by: P ( x ) = P0 + 6 μUL

( h1 − h ( x )) ( h2 − h ( x )) ( h2 2 − h12 ) h ( x)2

8.2

where P0 is the atmospheric pressure, and m is the coating viscosity. This pressure is the maximum possible pressure that can push the coating through the porous media. The pressure profile for different gap distances is given in Fig. 8.17. The blade width depends on the coated fabric width. They gave the following formula for the maximum possible penetration: z ( x ) = 12

KL L ∫ f ( x )dx φ 0

8.3

( h1 − h ( x )) ( h2 − h ( x )) , K is the permeability, and f is the ( h22 − h12 ) h2 ( x) porosity. They showed that coating penetration has a significant effect on the mechanical properties of coated fabrics, however, the relation between coating thickness and mechanical response is not linear. At a certain level of penetration, the fabric reinforcement loses its freedom of movement and where f ( x ) =

230

Structure and mechanics of textile fibre assemblies 8 Hedgepeth

7 6

3.0

SCFt

5

5.0

4

8.0

3

12.0

2 1

a

Fabric samples: b c d e f

g

0 0

10

20 30 40 50 Slit length (# breaks)

60

70

8.18 Analytical (curves) and experimental (symbol) values of stress concentration factor (SCF) versus slit length for various fabrics. The numbers next to the curves denote a parameter as a measure of slitdamage tolerance [20].

acts as a rigid, embedded reinforcement. At higher penetration levels, the tensile strength of the fabric is also reduced because of this rigidity since redistribution of stress concentrations is not allowed. Their model predicted the following: • • •

Pressure is increased by increasing application speed and reducing gap distance. Decreasing gap distance increases penetration depth. Penetration depth is independent of coating speed and viscosity.

Godfrey et al. developed a micromechanical model to predict the onset of tearing at slit like damages in biaxially loaded coated plain woven fabrics and compared it with experiments [20]. They defined a ‘stress concentration factor’ (SCF) as the ratio of the maximum tension in the first intact yarn at the tip of the slit to the remote applied load. Figure 8.18 shows their experimental and analytical results for several fabrics which are shown in Table 8.1. Their study showed that the treatment of inelastic deformation involving yielding or separation of the coating and relative displacement between the interlaced yarns near the slit tip is critical.

8.7

Recycling of coated fabrics

Coated fabrics have been widely used as engineering textiles in many fields, occupying a dominant position in the production and application of indus-

Structure and mechanics of coated textile fabrics

231

Table 8.1 Fabrics used by Godfrey et al. [20] Sample

Coating

Base fabric

Construction (warp/cm, weft/cm)

a b c d e f g

One sided urethane Double sided urethane Double sided PVC One sided urethane Double sided heatset urethane Double sided PVC One sided tent liner fabric

Nylon Nylon Polyester Kevlar® Aramid Nylon Polyester –

26 × 20 16 × 16 7.4 × 8.7 14 × 14 31 × 23 18 × 13 27 × 20

trial fabrics. The post-consumption disposal of coated fabrics as solid textile waste is an environmental pollution source and is becoming a serious problem recognized by society and governments. The manufacturers and the consumers of coated fabrics have suffered from the development of this serious problem. The environmental awareness of the public and the issuance of federal regulations has forced manufacturers to seek solutions. Recycling of coated fabrics is one solution that decreases exhaustion of raw materials and energy and eliminates or lessens the amount of waste. Recycling is becoming increasingly attractive because it obviates the need for landfill sites; it avoids the need for incineration plants where toxic or noxious fumes may be emitted; and it husbands resources by lessening the demand for primary materials [21]. Usually plastic recycling systems can be divided into four categories as follows [22]: 1. Primary recycling is the processing of scrap plastic into the same or similar types of product from which it has been generated, using standard plastics processing methods. 2. Secondary recycling is the reprocessing of scrap plastic into plastic products with less demanding properties. 3. Tertiary recycling is the recovery of chemicals from waste plastics. 4. Quaternary recycling is the recovery of energy from waste plastics. The distinction between different recycling processes is often quite arbitrary; sometimes several processes coexist at the same time. But as the intended treatment, any process is considered as one type of recycling process. In some cases, it depends on the economic and technological conditions prevailing at a given time. The approaches for recycling of PVC coated fabrics, i.e., grinding at room temperature, or low temperature, and processing using solvents, were reported in the literature [23]. PVC coated fabrics can be ground up in a commercially available granulator, yielding a bulk blend of very low bulk

232

Structure and mechanics of textile fibre assemblies

density. The PVC is not separated from the fabric. A reground material that has been produced in this way can be used as a ‘filler’ in standard types of plasticized PVC compounds. Their mechanical properties, however, deteriorate rapidly as the added quantity of the regrind increases. At temperatures as low as the nitrogen liquefaction temperature (−196 °C), plastics become so brittle that they can be very easily pulverized. The powder produced by this method is used as a filler in PVC plastisols. This is a technically feasible process, though the high cost would appear to rule it out for use on an industrial scale. PVC dissolves well in a variety of solvents, some of which are known to be carcinogenic. The most suitable solvent is tetrahydrofuran (THF). The PVC component in the coated fabric is dissolved in THF to form a viscous solution (dope) while PET fabric is not soluble and suspends in the solution. The PVC solution can be separated by filtration and reused directly to cast film by adjusting concentration or composition. However, the remained PET fabrics are stained with PVC solution. If precipitated directly by water, PET fabrics and coagulating PVC form bulky sediments which are useless. If the PET fabric or fiber is needed to be recovered from PVC, a large amount of solvent must be used to wash it by removal of attached PVC. In another method waste PVC coated fabrics are combusted to yield energy and hydrochloric acid. But incineration of some plastics destroys resources, creates a serious health hazard and unwanted and highly toxic by-products, such as dioxin [24]. Therefore incineration will become more difficult in the future as well, because the originator of waste will be required to show conclusive proof of the impossibility of recycling before the material will be released for disposal by incineration. In a method developed by Adanur et al., the polyester in the base fabrics (PET) and the polyvinyl chloride coating (PVC), along with plasticizers and adhesive/glue were separated from a commercial coated fabric by a scheme of chopping, grinding and extracting with a selected preferred aqueous MEK solution [25,26]. A recovering method called the swelling method was introduced to separate and reuse waste PVC coated PET fabrics as shown in Fig. 8.19. In comparison with other recycling techniques, the swelling method is a simple procedure with minimal environmental impact. The selection of the swelling agent of methyl ethyl ketone (MEK) was made after an analysis of the physical and chemical properties of several chemicals. Phase separation was found in the MEK/water system which serves as swelling bath. The two phases exist over a wide concentration range. Both methyl ethyl ketone and water are polar molecules to a certain extent so that they can mix with each other. However, they can not mix intimately at the entire concentration range. As shown in Fig. 8.20(a), methyl ethyl ketone and water are miscible at high and low volume fractions to form a uniform single phase. In the middle region they are not compatible

Structure and mechanics of coated textile fabrics

233

Belt shape PVC coated PET fabrics

Chop to small pieces

Digest in MEK

Grind to separate PVC and PET

Separation

PVC and MEK mixture

Separate MEK from PVC

MEK

PET fabrics and fiber

Wash with water

PVC

Dry

Wash with water

PET fabrics and fiber

Dry PVC

8.19 Schematic of the recovering process by swelling [25, 26] (copyright by Sage Publications].

and separate into two phases between which there is a clear, stable interface. Because the specific gravity of water is greater than that of methyl ethyl ketone, the MEK-rich phase usually floats above the water-rich phase. These two phases are in equilibrium until the volume fraction is less than a certain value, which is the saturation point. These two phases are more stable and do not dissolve each other regardless of the mixing. With agitation, the phase of a small amount is easily broken into smaller beads (small isolated domains). The small beads usually are much greater in dimension than the wavelength of light. The bead surface scatters light reflections and the blend becomes opaque or translucent.

Structure and mechanics of textile fibre assemblies

Refractive index

1.38 1.37 1.36 1.35 1.34

0

0.25

0.5

0.75

1

Solubility parameter (cal/cm3)1/2

234

25 20 15 10 5

MEK volume fraction

0

0.25 0.5 0.75 MEK volume fraction

(a)

(b)

1

8.20 Phase separation of MEK/water system [25, 26].

From the thermodynamic standpoint, it is merely mechanically mixed but it is not in a stable or equilibrium state. Therefore, it will return to the initial two-phase layers after settling for a certain time. This is because during this process Gibbs free energy ΔG became positive which indicated that the process was not spontaneous. Whenever the external factors making ΔG positive are released, the process will tend to turn to a direction that ΔG decreased to zero or less than zero. As shown in Fig. 8.20(b), the plot is not continuous and two interruption points exist which are evidence that the phase properties changed unsteadily. The two interruption points are at about 0.315 and 0.89 of volume fraction. The blend is one phase either below 0.315 or above 0.89, and consisted of two phases in the middle region. The behavior of the swelling system, and the swelling properties of recovered components were investigated by parameters such as refractive index, swelling degree, and the average particle size of recovered PVC. The MEK/ water system was partially heterogeneous, which would influence its solubility properties. According to the thermodynamic equation, the solubility parameters of mixture solvents are attributed to the individual components based on their amount: δ Blend = fi δ i + f2 δ 2 + . . . . . . + fn δ n

8.4

where δBlend is the solubility parameter of the blend, fi is the volume fraction of the pure component i, and δi is the solubility parameter of the pure component i. The solubility parameter of the component can be predicted by using a quantity known as the cohesive energy density Ecoh, which is the energy per unit volume V required to separate the molecules completely in a system. δ = ( Ecoh V )

12

= [( H o vap − RT ) V o ]

12

8.5

Structure and mechanics of coated textile fabrics

235

In this equation, Hovap and V o are the molar enthalpy of vaporization and molar volume. R is the gas constant and T is the absolute temperature. Assuming that the volume of the additives did not change during the mixing process, the solubility parameters of a methyl ethyl ketone/water system with different weight ratios could be calculated on the basis of the aforementioned equations as shown in Fig. 8.20(b). The contour of the curve in Fig. 8.20(b) is similar to that of Fig. 8.20(a) in that two interruption points exist. A variety of analytical methods were used to characterize the separation solvent, the amount and removeability of the glue, the changes in the chemical and physical properties of the PVC and PET polymers during the processes, and the extent of recovery of the plasticizer. Initial recovery PET fabrics (scraps) were further treated with removal of glue from the fabric surface in a dimethyl formamide (DMF) solution. The final product was the recycled PET fiber (staple). The structure and performance of recovered PET fiber were examined by several testing techniques, such as, DSC, WAXD, birefringence, acoustics emission and tensile testing. Experimental results were evaluated and analyzed to draw optimal parameters which would make mass production feasible. The PVC component and PET fabrics were separated and sorted. Their properties are very important because they determine the application and economics of the recycling process. PVC coating consists of polyvinyl chloride, plasticizers, and pigments, in which PVC and plasticizer are the main components. Their compositions are listed in Table 8.2. The chemical structure of plasticizer was examined by the Fourier transform infra-red spectroscopy (FTIR). In the IR spectra carbonyl band and benzene band appear at 1726 and 1276 cm−1. From experience, it is probably dioctyl phthalate (DOP), which is widely employed in the plastic industry. Compared with the standard reference IR spectra of DOP [27], it is conformed as dioctyl phthalate. Table 8.2 indicates that some plasticizer is lost during the process because it can dissolve and mix with MEK. It is assumed that, except for the amount of plasticizers, the composition of the PVC component was the same as the virgin form. By dissolving recycled PVC components in a proper solvent with a certain amount of Table 8.2 Composition of PVC coated polyester fabrics [26] PVC

New fabric Recovered

34.4 ± 2.8% 34.4 ± 2.8%

Polyester fiber 24.7 ± 3.2% 24.7 ± 3.2%

Glue

13.3 ± 3.4% 13.3 ± 3.4%

Plasticizer in PVC

Loss

27.6 ± 2.8% 13.8 ± 2.9%

0 13.8 ± 2.9%

236

Structure and mechanics of textile fibre assemblies

(a)

(b)

8.21 Optical micrograph of (a) recovered polyester fabric covered with glue and (b) polyester fabric treated in dimethyl formamide bath at 110 °C [26].

plasticizers, they can be mixed with virgin PVC to cast film on coated fabrics, and their reclamation would not affect the performance of the product end-use. Another component is PET fabric which serves as a framework in coated fabrics. Because it is not a solvent to polyethylene terephthalate, MEK can not penetrate into PET bulk or influence the chemical and physical properties of it. Therefore, polyester fabric scraps were preserved with their initial physical and chemical properties. At this time, polyester fabric was still covered by glue as shown in Fig. 8.21(a). The glue, composed of polyvinylidene chloride and isocyanate, was applied during finishing for modification of the surface performance of polyester fabrics and is fixed to the fibrous structure. In general, PET fabrics used in coated fabrics are woven or knitted using high tenacity polyester fibers (continuous filaments). They are more expensive and useful than average polyester fiber. Glue covering recycled polyester fabric scraps might limit their usefulness. For this reason, the polyester fabric scraps with glue were further treated to remove the glue, and pure polyester staple fibers were obtained. Dimethyl formamide (DMF) was selected to remove the glue on the fabric surface. Table 8.3 shows the properties of glue-free PET fiber. With an increase of DMF bath temperature, the decrease of orientation of whole chain led the fiber strength to decline. This is because fiber strength is determined by the orientation of the molecules in the fiber axis direction. When the polymer molecules are longitudinally oriented, the applied stress along the fiber axis is resisted by both covalent bonds and intermolecular forces within the

Table 8.3 Effect of treatment temperature in dimethyl formamide on mechanical properties of the recovered polyester fiber [26] Temperature (°C)

Untreated

25

40

55

70

85

95

110

120

Tenacity (g/d) Elongation (%) Sonic modulus (N/Tex)

8.2 ± 1.03 24.9 ± 7.26 13.2 ± 0.22

8.3 ± 0.81 24.4 ± 7.53 6.41 ± 0.12

8.2 ± 0.78 24.5 ± 6.8 5.29 ± 0.12

8.3 ± 1.2 26.4 ± 7.0 6.17 ± 0.10

8.1 ± 1.07 27.2 ± 6.23 2.97 ± 0.17

7.8 ± 1.06 29.3 ± 4.85 3.77 ± 0.12

7.7 ± 1.04 31.9 ± 8.20 2.09 ± 0.12

7.5 ± 1.33 33.0 ± 7.1 2.23 ± 0.12

7.5 ± 1.35 35.1 ± 5.9

238

Structure and mechanics of textile fibre assemblies

Table 8.4 Properties of recovered polyester fabric reinforced epoxy composite [26] Resin

3 parts of epoxy resin 811-163 1 part of epoxy hardener 811-165 Fabric PET fabric covered with glue Fabric/resin ratio (g/g) 12/33 4.47 ± 0.85 Stress of midspan (×107 N/m2) Total energy absorbed of impact loading (J ) 14.25 ± 2.76

structure. If the molecules’ lengths are oriented perpendicular to the applied stress, the initial primary resistance to the applied stress is presented by intermolecular force only which is much weaker than covalent bond. As shown in Table 8.3, fiber elongation at break increased. The sonic modulus of recycled PET fibers decreased with an increase of DMF bath temperature. Recycled PET fabric scraps with glue were used as substrate to reinforce epoxy composites. Glue-free PET staple fibers were used to make needlepunched nonwoven fabrics. Initially, recycled PET scraps covered by a coat of glue on the fabric surface were not affected by the swelling agent, chemically or physically. They can be used as filler to reinforce some structures. Recycled PET scraps with glue were used to make composites. The scraps were mixed with a resin which was composed of epoxy resin and amine hardener. The mixture was poured in the mold and compressed under a proper pressure, while epoxy resin cured at a certain temperature (50– 80 °C) for a required time (2.5 to 3.5 hours). The glue on the surface should make epoxy resin have intimate contact with the fabric scraps and reinforce the composite structure. The flexural and impact resistances of the resulting composite samples are listed in Table 8.4. Glue-free PET staple fibers were still of high strength with lower shrinkage than normal high tenacity fiber. They were used to make needle punched nonwoven fabrics. Length of recycled fiber was not uniform which depended on cutting of coated fabric scraps. They were firstly opened and combed by fiber opener to form a uniform density layer. Then the loose layers were needle-punched to yield a dense nonwoven fabric [26].

8.8

Sources of further information and advice

Badger, J. H. and Rosin, M. L. Polyurethane coatings; Chemistry and Consumer, AATCC Coated Fabrics Conference Book of Papers, March 1973. Coated Fabrics Technology, Symposium Book of Papers, American Association of Textile chemists and Colorists (AATCC), March 28–29, 1973.

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239

Coated Fabrics Update, AATCC Conference Book of Papers, April 1976. Coated fabrics Update, Symposium Book of Papers, American Association of Textile Chemists and Colorists (AATCC), March 31–April 1, 1976. Developments in Coating and Laminating, Papers Presented at the Shirley Institute Conference, Publication S41, March 27, 1981. Eirich, F. R., Science and Technology of Rubber, Academic Press Inc., New York, 1978. Gohlke, D. J. and Tanner, J. C., Gore-Tex® Waterproof Breathable Laminates, AATCC Coated Fabric Update Conference Book of Papers, April 1976. Industrial Coatings: Conference proceedings, ASM/ESD Conference, Chicago, November 1992. Lerner, A., Polyesters in Urethane Fabric Coating, AATCC Coated Fabric Update Conference Book of Papers, April 1976. Nettles, J. E., Handbook of Chemical Specialties, John Wiley and Sons, 1983. Progress in Textile Coating and Laminating, Papers Presented at the British Textile Technology Group (BTTG) Conference, July 2–3, 1990. Schmuck, G., ‘Textile Coating Techniques’, Review, Ciba-Geigy, 1974/4. Tanis, P., Developments in Mechanical Foaming Applied to Coating, BTTG Conference Book of Papers, July 2–3, 1990. Van Mol T. and Nijkamp, A., Latest Developments in Coating and Finishing, BTTG Conference Book of Papers, July, 1990. Woodruff, F. A., Some Developments in Coating Machinery and Processes, Shirley Institute Publication S41, March 1981.

8.9

References

1. Adanur, S., Wellington Sears Handbook of Industrial Textiles, Technomic Publishing Co., Inc., 1995. 2. Koch, S. D. and Price, J. M., ‘UV-Cured Coatings for Vinyl Coated Fabrics’, Coated Fabrics Technology – Vol. 2, Technomic Publishing Co., Inc., Westport, CT, 1979. 3. Powder Coatings – Recent developments, Noyes Data Corporation, Park Ridge, New Jersey, 1981. 4. Hofmann, W., Rubber Technology Handbook, Hanser Publishers, Oxford Press, N.Y, 1989. 5. Abbott, N. J., Lannefeld, T. E., Barish, L. and Brysson, R. J., ‘A Study of Tearing in Coated Cotton Fabrics, Part II: The Influence of Coating Application Techniques’, Journal of Coated Fibrous Materials, Vol. 1, Jan. 1972, pp. 130–149. 6. Mewes, H., ‘Adhesion and Tear Resistance of Coated Fabrics from Polyester and Nylon’, Journal of Coated Fabrics, Vol. 19, Oct. 1989, pp. 112–128. 7. Haddad, R. H. and Black, J. D., ‘Mechanical Parameters Influencing Coating Adhesion of Fabrics’, Journal of Coated Fabrics, Vol. 16, Oct. 1986, pp. 123–138.

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8. Dartman, T. and Shishoo, R., ‘Studies of Adhesion Mechanisms Between PVC Coatings and Different Textile Substrates’, Journal of Coated Fabrics, Vol. 22, April 1993, pp. 317–333. 9. Abbott, N. J., Lannefeld, T. E., Barish, L. and Brysson, R. J., ‘A Study of Tearing in Coated Cotton Fabrics, Part I: The Influence of Fabric Construction’, Journal of Coated Fibrous Materials, Vol. 1, July 1971, pp. 4–17. 10. Abbott, N. J., Lannefeld, T. E., Barish, L. and Brysson, R. J., ‘A Study of Tearing in Coated Cotton Fabrics, Part II: The Influence of Coating Characteristics’, Journal of Coated Fibrous Materials, Vol. 1, Oct. 1971, pp. 64–84. 11. Farboodmanesh, S., Chen, J., Mead, J. L., White, K., Yesilalan, E., Laoulache, R. and Warner, S. B., ‘Effect of Coating Thickness and Penetration on Shear Behavior of Coated Fabrics’, Journal of Elastomers and Plastics, Vol. 37, No. 3, 2005, pp. 197–227. 12. Eichert, U., ‘Residual Tensile and Tear Strength of Coated Industrial Fabrics Determined in Long-Time Tests in Natural Weather Conditions’, Journal of Coated Fabrics, Vol. 23, April 1994. 13. Topping, A. D., ‘The Critical Slit Length of Pressurized Coated Fabric Cylinders’, Journal of Coated Fabrics, Vol. 3, Oct. 1973, pp. 96–109. 14. Szostkiewicz, C. and Hamelin, P., ‘Stiffness Identification and Tearing Analysis for Coated Membranes under Biaxial Loads’, Journal of Industrial Textiles, Vol. 30, No. 2, Oct. 2000, pp. 128–139. 15. Farboodmanesh, S., Chen, J., Mead, J. L. and White, K., Paper no. 98, Rubber Division, ACS., Technical Conference Fall Meeting, Pittsburgh, PA, 2002. 16. Testa, R. B. and Yu, L. M., ‘Stress-Strain Relationship for Coated Fabrics’, Journal of Engineering Mechanics, 13(11), 1987, 1631–1645. 17. Spivak, S. M. and Treloar, L. R. G. (1968). ‘The Behavior of Fabrics in Shear, Part III: The Relation Between Bias Extension and Simple Shear’, Textile Research Journal, 38:1056–1062. 18. Lebrun, G. and Denault, J., ‘Influence of Temperature and Loading Rate on the Interply Shear Properties of Propylene Fabric’, Proceedings of the American Society of Composites, 15th Technical Conference, College Station, TX, 2000. 19. Prodromou, A. G. and Chen, J., ‘On the Relationship of Shear Angle and Wrinkling on Textile Composite Preforms’, Composites, Part A – Applied Science and Manufacturing, 28A, 1997, pp. 491–503. 20. Godfrey, T. A., Rossettos, J. N. and Bosselman, S. E., ‘The Onset of Tearing at Slits in Stressed Coated Plain Weave Fabrics’, Journal of Applied Mechanics, Vol. 71, Nov. 2004, pp. 879–886. 21. Economic Commission for Europe, Engineering Plastics, United Nations, New York, 1991, pp. 9. 22. Leidner, J., Plastics Waste, Marcel Dekker, Inc., New York, 1981, pp 64–65. 23. Saffert, R., ‘Recycling of PVC Coated Fabrics’, J. Coated Fabrics, V. 23, April 1994, pp. 274. 24. Levin, B. C., A Summary of the Literature Review on the Chemical Nature and Toxicity of the Pyrolysis and Combustion Products from Seven Plastics: Acrylonitrile-Butadiene-Styrenes (ABS), Nylons, Polyester, Polyethylenes, Polystyrenes, Poly(Vinyl Chlorides) and Polyurethane Foams. U.S. Department of Commerce, June 1986.

Structure and mechanics of coated textile fabrics

241

25. Adanur, S., Hou, Z. and Broughton, R., ‘Recovery and Reuse of Waste PVC Coated Fabrics. Part 1: Experimental Procedures and Separation of Fabric Components’, Journal of Coated Fabrics, Vol. 28, July 1998, pp. 37–55. 26. Adanur, S., Hou, Z. and Broughton, R., ‘Recovery and Reuse of Waste PVC Coated Fabrics. Part 2: Analysis of the Components Separated from PVC Coated PET Fabrics’, Journal of Coated Fabrics, Vol. 28, Oct. 1998, pp. 145–168. 27. Craver, C. D., Coblentz Society Evaluated Infrared Reference Spectra, The Coblentz Society, Inc., Norwalk, CT., 1979.