Woven Textile Structure: Theory and Applications (Woodhead Publishing Series in Textiles)

i

Woven textile structure

ii

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 website 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 towards the end of the contents pages.

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Woodhead Publishing Series in Textiles: Number 115

Woven textile structure Theory and applications

B. K. Behera and P. K. Hari

CRC Press Boca Raton Boston New York Washington, DC

Woodhead

publishing limited

Oxford    Cambridge    New Delhi

iv Published by Woodhead Publishing Limited in association with The Textile Institute Woodhead Publishing Limited, Abington Hall, Granta Park, Great Abington Cambridge CB21 6AH, UK www.woodheadpublishing.com Woodhead Publishing India Private Limited, G-2, Vardaan House, 7/28 Ansari Road, Daryaganj, New Delhi – 110002, India www.woodheadpublishingindia.com Published in North America by CRC Press LLC, 6000 Broken Sound Parkway, NW, Suite 300, Boca Raton, FL 33487, USA First published 2010, Woodhead Publishing Limited and CRC Press LLC © Woodhead Publishing Limited, 2010 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 978-1-84569-514-9 (book) Woodhead Publishing ISBN 978-1-84569-781-5 (e-book) CRC Press ISBN 978-1-4398-3116-8 CRC Press order number N10191 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 elemental chlorine-free practices. Furthermore, the publishers ensure that the text paper and cover board used have met acceptable environmental accreditation standards. Typeset by Replika Press Pvt Ltd, India Printed by TJ International Limited, Padstow, Cornwall, UK

v

Contents

The authors

xi

Woodhead Publishing Series in Textiles

xiii

Preface

xix

Part I Fundamentals of woven fabric structure 1 1.1 1.2 1.3 1.4 1.5

The basics of woven fabric structure Introduction: woven fabric formation Elements of woven fabric structure Regular and irregular weaves Modeling different weaves References

3 3 5 5 6 8

2 2.1 2.2 2.3

Geometrical modeling of woven fabric structure Introduction: woven fabric structure A simple geometric model of woven fabric structure Using the model to predict the fabric thickness, cover, mass and specific volume Modeling maximum fabric cover Calculating fabric properties: numerical examples References

9 9 9 17 19 21 29

Using a geometric model to predict woven fabric properties Introduction Predicting woven fabric parameters Predicting the weavability limit Predicting cover in different woven structures Calculating fabric properties: numerical examples Application: calculating tightness values References

30 30 31 41 53 57 70 72

2.4 2.5 2.6 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7

vi

Contents

4 4.1 4.2 4.3 4.4 4.5 4.6 4.7

Woven fabric properties after structural modifications 73 Introduction 73 Crimp interchange phenomena 73 Maximum fabric extension 75 Other structural changes 76 Structural design of woven fabrics using soft computing 76 Calculating fabric properties: numerical examples 82 Reference 105

Part II Mechanics of woven fabric structure 5 5.1 5.2 5.3 5.4 5.5 5.6

Shrinkage in woven fabrics Introduction Mechanisms of fabric shrinkage The relationship between cloth and yarn shrinkage Predicting fabric shrinkage Application of fabric shrinkage model References

109 109 110 112 113 115 117

6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9

Yarn behavior in woven fabrics Introduction The yarn path in woven fabrics and inter-yarn forces The crimp balance equation Predicting the yarn path in woven fabrics The effect of settings on yarn behavior Crimp interchange and crimp balance equations Calculating fabric properties: numerical examples Practical applications References

118 118 118 121 122 127 128 131 136 136

7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8

Tensile behavior of woven fabrics Introduction Fundamentals of axial deformation Tensile properties of woven fabrics Castigliano’s theorem The sawtooth model Fabric extension in the bias direction Factors affecting the tensile properties of woven fabrics References

137 137 138 142 149 152 157 162 163

8 8.1

Buckling behavior of woven fabrics Introduction

164 164

Contents

vii

8.2 8.3 8.4 8.5 8.6

Buckling deformation of woven fabric Buckling behavior of cloth under large deformation Hysteresis in fabric deformation Practical applications References

165 166 172 172 172

9 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12

Bending behavior of woven fabrics Introduction Fundamentals of bending deformation Modeling bending behavior The bending behavior of woven fabrics Bending hysteresis The effect of setting on bending behavior Bending recovery Bending at higher curvatures The time effect in bending deformation Bending in the bias direction Practical applications References

173 173 174 176 178 187 190 191 191 191 192 196 196

10 10.1 10.2 10.3 10.4 10.5 10.6

Creasing in woven fabrics Introduction Mechanisms of creasing Deformation and crease recovery behavior The effect of time on deformation and crease recovery Factors affecting crease recovery of fabrics References

197 197 197 199 202 203 204

11 11.1 11.2 11.3 11.4 11.5 11.6

Shear behavior of woven fabrics Introduction Fundamentals of shear deformation Shear deformation in woven fabrics Shear properties in various directions Predicting shear properties: practical applications References

205 205 206 207 215 216 216

12 12.1 12.2 12.3 12.4 12.5 12.6

Compression behavior of woven fabrics Introduction Fundamentals of compression The compression behavior of textile structures The exponential behavior of compressible fabrics The low stress pressure–thickness curve Predicting compression in woven fabrics

217 217 218 218 222 223 223

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Contents

12.7 12.8

Practical applications References

13

Friction and other aspects of the surface behavior of woven fabrics Introduction Fundamentals of friction and abrasion Measuring roughness and other surface properties of woven fabrics Factors affecting abrasion resistance References

13.1 13.2 13.3 13.4 13.5

229 229 230 230 231 232 236 241

Part III Design and engineering of woven fabrics 14 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9

Textile product design methods Introduction The design process for textiles Traditional design methods Key issues in the design of textile products Computer-assisted design (CAD) of woven fabrics Design engineering using modeling Reverse engineering Expert systems in textile product design References

245 245 246 247 248 250 251 252 252 257

15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8

Modeling for textile product design Introduction Principles of mathematical modeling Modeling methodologies Deterministic models Nondeterministic models Validation and testing of models Summary References

260 260 260 262 262 264 272 273 273

16 16.1 16.2

Building predictive models for textile product design Introduction Building empirical, mathematical and artificial neural network (ANN) models Evaluating mathematical, empirical and artificial neural network (ANN) models Summary References

275 275

16.3 16.4 16.5

276 281 288 290

Contents

17 17.1 17.2 17.3 17.4 17.5 17.6 17.7

Modeling for woven fabric design Introduction Types of computer modeling in fabric design and manufacture The application of modeling to woven fabric design Modeling structure–property relationships: elongation and bending Modeling of woven fabric texture Limitations of modeling References

ix

292 292 292 294 300 302 303 304

Part IV Practical applications 18 18.1 18.2 18.3 18.4 18.5 18.6 18.7

Assessing the comfort of woven fabrics: fabric handle 309 Introduction 309 The objective measurement of comfort 310 Measuring fabric handle 311 Primary and total fabric handle 317 Factors affecting fabric handle 321 Summary 326 References 326

19

Assessing the comfort of woven fabrics: thermal properties Introduction Thermal comfort in humans The function of textiles in enhancing thermal comfort Heat transfer through woven fabrics Moisture vapor transfer through woven fabrics Measuring thermal comfort References

19.1 19.2 19.3 19.4 19.5 19.6 19.7 20 20.1 20.2 20.3 20.4 20.5 20.6 20.7

Modeling woven fabric drape Introduction Two-dimensional and three-dimensional drape Subjective and objective measurement of drape Drape measurement by digital image processing The relationship between drape and the mechanical properties of woven fabrics Low stress mechanical properties of woven fabrics and drapeability Modeling of woven fabric drape

330 330 331 332 333 335 340 341 343 343 343 347 348 352 353 354

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Contents

20.8

Predicting drape using artificial neural network (ANN) modeling 20.9 Modeling dynamic drape 20.10 References Modeling woven fabric behavior during the making-up of garments 21.1 Introduction 21.2 Fabric properties and apparel performance 21.3 The garment making-up process and fabric properties 21.4 Low stress fabric mechanical properties and the garment making-up process 21.5 Measuring fabric suitability for the garment making-up process 21.6 Fabric buckling and tailoring of garments 21.7 Measuring sewability: seam strength 21.8 Measuring sewability: seam puckering 21.9 Measuring sewability: seam slippage 21.10 References

365 367 369

21

22

372 372 373 374 376 379 381 382 383 390 392

22.1 22.2 22.3 22.4 22.5 22.6 22.7

Modeling three-dimensional (3-D) woven fabric structures Introduction: 3-D fabrics 2-D and 3-D fabric weaving Classifying 3-D woven fabrics Modeling equations for weaving 2-D and 3-D fabrics The use of 2-D and 3-D textiles in composites The tensile properties of 3-D textile composites References

23 23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8

Application of woven fabrics 413 Introduction 413 Fundamental aspects of woven textile structure and function 414 Medical textiles 416 Automotive textiles 417 Filter fabrics 421 Textiles for electronics 423 Sports textiles 430 References 435



Index

393 393 394 394 402 405 409 412

436

xi

The authors

Dr B. K. Behera is a Professor in the Department of Textile Technology, Indian Institute of Technology Delhi. His research interests include modeling and simulation, mechanics of textile structure, soft computing applications in the structure – property relationship of fabric, 3D weaving for composite applications and fabric handle and comfort. He has supervised more than 60 Masters and PhD students, published 110 research papers and presented more than 40 papers in various international conferences held in about 13 different countries. Professor Behera has completed 16 sponsored research projects and more than 50 industrial consulting projects as principal investigator. He has contributed a monogram on image processing applications in textiles published in Textile Progress. He has four patents to his credit. He has also contributed chapters in three other books being published by Woodhead Publishing Limited. Professor Behera is a regular contributor to the Textile Research Symposium held under the aegis of the Textile Machinery Society of Japan and has also contributed to the AUTEX world conference. Professor Behera has also worked as a specially-appointed Professor in the Global Centre of Excellence Programme at Shinshu University Japan (bijoy.behera@ yahoo.com). Dr P. K. Hari was Professor and Head of the Textile Department of the Indian Institute of Technology Delhi for over 30 years until his retirement. During his tenure at IIT Delhi, he supervised 10 PhD students in weaving, preparation and structure–property relationships of woven fabrics. Recently he has contributed to fabric structure and textile designing through web-based teaching. He has organised the International Textile Academia, a global forum for Textile Institutes with the sponsorship of Rieter Textile Machinery. He has contributed to Vision 2020 for the Indian Textile Industry sponsored by the Indian Government’s Department of Scientific and Industrial Research. He has been a regular contributor to the international conferences, AUTEX and the Institute for Textile Technik. He has published over 60 papers in international textile journals. He is presently Professor Emeritus at TIT&S, Bhiwani and a textile consultant and can be reached at pk_hari@hotmail. com.

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Woodhead Publishing Series 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 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

xiv

Woodhead Publishing Series in Textiles

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 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 H. M. Behery

Woodhead Publishing Series in Textiles 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 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 65 Shape memory polymers and textiles J. Hu 66 Environmental aspects of textile dyeing Edited by R. Christie

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Woodhead Publishing Series in Textiles

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 technology Edited by N. A. G. Johnson and I. Russell 73 Military textiles Edited by E. Wilusz 74 3D 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 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 81 Engineering textiles: Integrating the design and manufacture of textile products Edited by Y. E. El-Mogahzy 82 Polyolefin fibres: Industrial and medical applications Edited by S. C. O. Ugbolue 83 Smart clothes and wearable technology Edited by J. McCann and D. Bryson 84 Identification of textile fibres Edited by M. Houck 85 Advanced textiles for wound care Edited by S. Rajendran 86 Fatigue failure of textile fibres Edited by M. Miraftab 87 Advances in carpet technology Edited by K. Goswami 88 Handbook of textile fibre structure Volume 1 and Volume 2 Edited by S. J. Eichhorn, J. W. S Hearle, M. Jaffe and T. Kikutani 89 Advances in knitting technology Edited by K.-F. Au

Woodhead Publishing Series in Textiles 90 Smart textile coatings and laminates Edited by W. C. Smith 91 Handbook of tensile properties of textile fibres Edited by A. Bunsell 92 Interior textiles: Design and developments Edited by T. Rowe 93 Textiles for cold weather apparel Edited by J. T. Williams 94 Modelling and predicting textile behaviour Edited by X. Chen 95 Textiles for construction Edited by G. Pohl 96 Engineering apparel fabrics and garments J. Fan and L. Hunter 97 Surface modification of textiles Edited by Q. Wei 98 Sustainable textiles Edited by R. S. Blackburn 99 Advanced fibre spinning Edited by C. Lawrence 100 Fire toxicity Edited by A. Stec and R. Hull 101 Technical textile yarns Edited by R. Alagirusamy and A. Das 102 Nonwovens in technical textiles Edited by R. Chapman 103 Colour measurement in textiles Edited by M. L. Gulrajani 104 Textiles for civil engineering Edited by R. Fangueiro 105 New product development in textiles Edited by B. Mills 106 Improving comfort in clothing Edited by G. Song 107 Textile biotechnology Edited by V. Nierstrasz 108 Textiles for hygiene Edited by B. McCarthy 109 Nanofunctional textiles Edited by Y. Li 110 Joining textiles Edited by I. Jones and G. Stylios 111 Soft computing in textiles Edited by A. Majumdar 112 Textile design Edited by A. Briggs-Goode and K. Townsend

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Woodhead Publishing Series in Textiles

113 Biotextiles as medical implants Edited by M. King and B. Gupta 114 Textile thermal bioengineering Edited by Y. Li 115 Woven textile structure B. K. Behera and P. K. Hari

xix

Preface

Engineering fabrics deals with the application of science to reveal the relationships between the raw material, process and the finished product to achieve desired functional or aesthetic effects in the fabric. The success of fabric engineering depends on reliable objective measurements, prediction and control of fabric quality and performance attributes. The prediction of fabric quality and performance attributes requires an efficient methodology to model the inherent non-linear relationships between fibre, yarn and fabric properties. The science of mechanics has provided the ability to predict quantitatively the mechanical performance of structures, but has rarely been applied to textile materials. Various mathematical models, such as geometrical and mechanistic models, based on forces in the fabric, energy minimization principles and empirical relationships between variables, can be used for the analysis of textile structures and processes to explain the underlying principles and predict fabric properties and behavior. Understanding the theoretical relationships between fabric parameters enables the fabric designer to play with different fibers, yarn tex, threads per centimeter and weave to vary texture and other fabric properties. These relationships provide simplified formulae to facilitate calculations which are of value for cloth engineering, problems of structure and mechanical properties. The authors bring together expertise in fabric structure, mechanical properties of fabric, structure-property relationships and basic principles of design engineering as a tool to support product development, within the framework of fabric structural mechanics. This book is the culmination of teaching, research and methodology in presenting principles and applications related to structure of woven fabrics developed over several years at the Indian Institute of Technology (IIT) Delhi, India. It aims to give readers a good foundation in this area through an in-depth understanding of the principles of physical and mechanical properties of woven textile structures. It is designed as a textbook for graduates and postgraduates in textile technology and also as a reference book for research. The concepts and applications have been demonstrated by liberal use of examples. The book gives a flavor of the basics and builds up to predictive modeling of some fabric properties. The

xx

Preface

book is broad-ranging in covering the physical and mechanical properties of the fabric, the fabric making-up process and applications in newer and emerging areas like sports, e-textiles, etc. SI units have been used throughout the book. Each chapter gives an abstract of the contents and is concluded, wherever possible, with how the contents can be used and applied in practical situations. The book is broadly divided into four sections: Part I Fundamentals of woven fabric structure, Part II Mechanics of woven fabric structure, Part III Design engineering of woven fabrics and Part IV Practical applications. The first four chapters in Part I present the fundamentals of woven fabric structure and some derivatives including some special structures. They discuss the concept of a maximum weavability limit, crimp interchange phenomena, the mechanisms of fabric shrinkage and soft computing applications to predict fabric parameters using the relationship between fabric parameters based on geometrical models. Part II deals with mechanical properties of woven structure in which behavior of fabric under various kinds of deformations is discussed. In Part III, the concept of design engineering, fundamentals of modeling and simulation, modeling methodologies and soft computing application for prediction of fabric properties are described to enable textile researchers to understand the application of various methods for product engineering. Chapters in Part IV demonstrate how fundamental knowledge of theory of fabric structure can be helpful for practical applications in developing fabrics of special construction and achieving various performance characteristics in processing and use. We wish to thank many students in the Textile Department, IIT Delhi for their unstinting support in making this endeavor a reality. We also owe our indebtness to many others who are not mentioned for their indirect contribution in enhancing our knowledge and giving support. We would like to acknowledge Ms Kathryn Picking, Mr Francis Dodds and Woodhead Publishing Limited for their encouragement and assistance. Professor Hari would like to thank his wife Usha for the support and encouragement to take up this benevolent task for contribution of experience to textile technology. It is hoped that this book will fill the vacuum in the literature on woven structures since the last book on structural mechanics of fibres, yarn and fabrics was published in 1969. We welcome suggestions for any errors that may have crept into the book inadvertently. B. K. Behera P. K. Hari

1

The basics of woven fabric structure

Abstract: Different types of fabric formation and typical weaves are described. The mathematical representation of weave is explained for some weaves. Mathematical modeling is used to compare warp and weft properties in fabrics. The two useful parameters, average float and weave value, are explained and calculated for some weaves. Key words: woven fabrics, modeling, warp properties, weft properties, average float, weave value.

1.1

Introduction: woven fabric formation

There are many ways of making fabrics from textile fibers [1]. The most common and most complex category comprises fabrics made from interlaced yarns. These are the traditional methods of manufacturing textiles. The great scope lies in choosing fibers with particular properties, arranging them in the yarn in several ways and organizing in multiple ways interlaced yarn within the fabric. This gives the textile designer great freedom and variation for controlling and modifying the fabric. The most common form of interlacing is weaving, where two sets of threads cross and interweave with one another. The yarns are held in place by the inter-yarn friction. Another form of interlacing where the thread in one set interlocks with the loops of neighboring thread by looping is called knitting. The interloping of yarns results in positive binding. Knitted fabrics are widely used in apparel, home furnishing and technical textiles. Lace, crochet and different types of net are other forms of interlaced yarn structures. Braiding is another way of thread interlacing for fabric formation. Braided fabric is formed by diagonal interlacing of yarns. Braided structures are mainly used for industrial composite materials. Other forms of fabric manufacture use fibers or filaments laid down, without interlacing, in a web and bonded together mechanically or by using adhesive. The former are needle punched nonwovens and the latter spun bonded. The resulting fabric after bonding normally produces a flexible and porous structure. These find use mostly in industrial and disposable applications. Figure 1.1 shows the schematics of fabrics produced by the methods discussed above. All these fabrics are broadly used in three major applications such as apparel, home furnishing and industrial. The traditional methods of weaving and hand weaving will remain supreme for expensive fabrics with a rich design content. The woven structures provide 3

4

Woven textile structure

Woven structure

Knitted structure

Nonwoven (bonded)

Netting

Braided structure

Lace

1.1 Fabric structures produced by different methods of fabric formation.

a combination of strength with flexibility. Flexibility under low strains is achieved by yarn crimp due to freedom of yarn movement, whereas at high strains the threads take the load together, giving high strength.

The basics of woven fabric structure

1.2

5

Elements of woven fabric structure

A woven fabric is produced by interlacing two sets of yarns, the warp and the weft, which are at right angles to each other in the plane of the cloth. The warp is along the length and the weft along the width of the fabric. Individual warp and weft yarns are called ends and picks and their interlacement produces a coherent and stable structure. The repeating unit of interlacement is called the weave [2]. Plain weave has the simplest repeating unit of interlacement and the maximum possible frequency of interlacements. Plain weave fabrics are firm and resist yarn slippage. Figure 1.2 shows plain weave in plan view and in cross-section along warp and weft. The weave representation is shown by a grid in which vertical lines represent warp and horizontal lines represent weft. Each square represents the crossing of an end and a pick. A mark in a square indicates that the end is over the pick at the corresponding place in the fabric, i.e. warp up. A blank square indicates that the pick is over the end, i.e. weft up. One repeat of the weave is indicated by filled squares and the rest by crosses. The plain weave repeats on two ends and two picks.

1.3

Regular and irregular weaves

1.3.1 Regular weave Regular weaves [3] give a uniform and specific appearance to the fabric. The properties of the fabric for such weaves can be easily predicted. Examples of some of the common regular weaves are given in Fig. 1.3. 1

6

2

5

3

4

4

3

5

2

6 1

2

3

4

5

1

6

1

(a)

2

3

4 (b)

5

6

1 (d)

1 (c)

1.2 Plain weave: plan (a), weave representation (b), cross-sectional view along weft (c), cross-sectional view along warp (d).

6

Woven textile structure

1/1 plain

2/2 matt

2/2 warp rib 2/2 weft rib

1/3 twill

1/3 on sateen base (crepe weave)

1/4 sateen

3/1 on sateen base (crepe weave)

1.3 Regular weaves.

1.3.2 Irregular weave Irregular weaves are commonly employed when the effect of interlacement is masked by the colored yarn in the fabric. Such weaves are common in furnishing fabric. In such structures the prediction of mechanical properties is difficult. Examples of some of the common irregular weaves are given in Fig. 1.4.

1.4

Modeling different weaves

The firmness of a woven fabric depends on the density of threads and frequency of interlacements in a repeat. Fabrics made from different weaves cannot be compared easily with regard to their physical and mechanical properties unless the weave effect is normalized. The concept of average float has long been in use, particularly for calculating maximum threads per cm. It is defined as the average ends per intersection in a unit repeat. Recently this ratio, known as weave factor [4,5], has been used to estimate the tightness factor in fabric.

1.4.1 Weave factor The weave factor is a number that accounts for the number of interlacements of warp and weft in a given repeat. It is also equal to average float and is expressed as:

The basics of woven fabric structure

4-end irregular sateen

7

6-end irregular sateen

1.4 Irregular weaves.



M =E I

1.1

where E is number of threads per repeat and I is number of intersections per repeat of the cross-thread. The weave interlacing patterns of warp and weft yarns may be different. In such cases, weave factors are calculated separately with suffixes 1 and 2 for warp and weft respectively. Therefore, M1 = E1/I2; E1 and I2 can be found by observing individual pick in a repeat and M2 = E2/I1; E2 and I1 can be found by observing individual warp end in a repeat.

1.4.2 Calculation of weave factor Regular weave Plain weave is represented as 1 ; for this weave, E1 the number of ends per 1 repeat is equal to 1 + 1 = 2 and I2 the number of intersections per repeat of weft yarn = 1 + the number of changes from up to down (vice versa) = 1 + 1 = 2. Table 1.1 gives the value of warp and weft weave factors for some typical weaves. Irregular weave In some weaves the number of intersections of each thread in the weave repeat is not equal. In such cases the weave factor is obtained as under:

M =SE SI

1.2

Using equation 1.2 the weave factors of a ten-end irregular huckaback weave shown in Fig. 1.5 is calculated below:

8

Woven textile structure

Table 1.1 Weave factors for standard weaves Weave 1/1 Plain 2/1 Twill 2/2 Warp Rib 2/2 Weft Rib

E1

I2

E2

I1

M1

M2

2

2

2

2

1

1

3

2

3

2

1.5

1.5

2

2

4

2

1

2

4

2

2

2

2

1

E1 and E2 are the threads in warp and weft directions. I2 and I1 are intersections for weft and warp threads.

1.5 10-end huckaback weave.



weave factor,



1.5

M = 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 10 + 6 + 10 + 6 + 10 + 6 + 10 + 6 + 10 + 6 = 100 = 1.19 84

References

1. Newton A (1993), Fabric Manufacture: A Hand Book, Intermediate Technology Publications. 2. Robinson A T C and Marks R (1973), Woven Cloth Construction, The Textile Institute. 3. Grosicki Z (1988), Watson’s Textile Design and Colour, Newnes Butterworths. 4. Weiner L (1971), Textile Fabric Design Tables, Technomic. 5. Seyam A M (2002), Textile Progress, The Textile Institute, Vol. 31, No. 3.

9

2

Geometrical modeling of woven fabric structure

Abstract: A geometric model of plain woven fabric is used to describe fabric parameters. The fabric parameters for special structures, such as jammed and crossed threads, are discussed. The model is used to predict fabric properties such as thickness, mass and specific volume, as well as the maximum cover in a woven fabric. Practical applications are given using numerical examples. Key words: geometric model, woven fabric, fabric thickness, maximum cover.

2.1

Introduction: woven fabric structure

The properties of the fabric depend on the fabric structure. The formal structure of a woven fabric is defined by weave, thread density, crimp and yarn count. The interrelation between fabric parameters can be obtained by considering a geometrical model of the fabric. The model is not merely an exercise in mathematics. It is not only useful in determining the entire structure of a fabric from a few values given in technological terms but it also establishes a base for calculating various changes in fabric geometry when the fabric is subjected to known extensions in a given direction or known compressions or complete swelling in aqueous medium. It has been found useful for weaving of maximum sett structures and also in the analysis and interpretation of structure–property relationship of woven fabrics. Mathematical deductions obtained from simple geometrical form and physical characteristics of yarn combined together help in understanding various phenomena in fabrics.

2.2

A simple geometric model of woven fabric structure

The geometric model is mainly concerned with the shape taken up by the yarn in the warp or weft cross-section of the fabric. It helps to quantitatively describe the geometrical parameters. The basic model of Peirce’s [1] analysis is shown in Fig. 2.1. It represents a unit cell interlacement in which the yarns are considered inextensible and flexible. The yarns have circular crosssection and consist of straight and curved segments. The main advantages in considering this simple geometry are as follows: 9

10

Woven textile structure Weft l1/2 d2

D

h1/2 q1

X

d1

X¢ h2/2

Warp p2

2.1 Peirce’s model of plain weave.

∑ ∑ ∑ ∑

It helps to establish the relationships between various geometrical parameters. It is possible to calculate the resistance of the cloth to mechanical deformation such as initial extension, bending and shear in terms of the resistance to deformation of individual fibers. Information is obtained on the relative resistance of the cloth to the passage of air, water or light. It provides a guide to the maximum density of yarn packing possible in the cloth.

From the two-dimensional unit cell of a plain woven fabric, geometrical parameters such as thread spacing, weave angle, crimp and fabric thickness are related by deriving a set of equations. The symbols used to denote these parameters are listed below: d – diameter of thread p – thread spacing h – maximum displacement of thread axis normal to the plane of cloth (crimp height) q – angle of thread axis to the plane of cloth (weave angle in radians) l – length of thread axis between the planes through the axes of consecutive cross-threads (modular length) c – crimp (fractional)

D = d1 + d2

Suffixes 1 and 2 to the above parameters represent warp and weft threads respectively. In Fig. 2.1 projection of yarn axis parallel and normal to the cloth plane gives the following equations:

Geometrical modeling of woven fabric structure



c1 =

l1 –1 p2

11

2.1



p2 = (l1 – D q1) cos q1 + D sin q1

2.2



h1 = (l1 – D q1) sin q1 + D (1 – cos q1)

2.3

Three similar equations are obtained for the weft direction by interchanging suffix from 1 to 2 or vice versa as under:

c2 =

l2 –1 p1

2.4



p1 = (l2 – D q2) cos q2 + D sin q2

2.5



h2 = (l2 – D q2) sin q2 + D (1 – cos q2)

2.6

d1 + d2 = h1 + h2 = D

2.7

Also

In all there are seven equations connecting 11 variables. If any four variables are known then the equations can be solved and the remaining variables can be determined. Unfortunately, these equations are difficult to solve. Researchers have tried to solve these equations using various mathematical means to find new relationships and also some simplified useful equations.

2.2.1 Relation between p, h, q and D From equations 2.2 and 2.3 we get:

(l1 – D q1) =

p2 – D sin q1 h1 – D (1 – cos q1 ) = cos q1 sin q1

or

D(sec q1 – 1) – p2 tan q1 + h1 = 0

substituting

x1 =

tan q1 2

we get

hˆ h Ê x12 Á D – 1˜ – p2 x1 + 1 = 0 ¯ Ë 2 2

12

Woven textile structure

For real fabrics



x1 =

tan q1 = p2 – 2

hˆ Ê p22 – 2 h1 Á D – 1˜ Ë 2 ¯ p2 – p22 – h22 – D 2 = D + h2 2 D – h1

Using the value of x 1, one can calculate q, l and c and also other parameters. Similarly, using equations 2.5 and 2.6, and by eliminating l and substituting x1 as above, we will arrive at a more complex equation:

cˆ c1 Ê + x1 D – x12 Á1 + 1 ˜ = D (1 – x12 ) tan –1 x1 Ë p2 2 2 ¯ p2

It is difficult to solve this equation algebraically for x1. However, one can substitute the value of x1 obtained earlier to solve this equation just for academic interest. These seven equations have been solved by soft computing in order to establish several useful relationships in Chapter 3. However, at this stage, one can generalize the relationship as:

h1 = f (p2, c1)

The function f can be obtained by plotting p and h for different values of c.

2.2.2 Functional relationship between p, h and c Trigonometric expansion of equations 2.2 and 2.3 gives:

p2 = l1 –

l1 q12 D q13 l1 q14 + + +… 2 3 24

h1 = l1q1 –

D q12 l1 q13 D q14 – + +… 2 6 8

When q is small, a higher power of q can be neglected, which gives:

h1 = l1q1 , p2 = l1 , c2 =

q12 , h1 = p2 2c1 2

and these equations reduce to:

1

q1 = (2c1 )2

2.8

Geometrical modeling of woven fabric structure 1

13

2.9



q2 = (2c2 )2



h1 = 4 p2 c1 3

2.10



h2 = 4 p1 c2 3

2.11

These four equations are not new equations in this exercise. They are derived from the previous seven original equations. However they give simple and direct relationships between four fabric parameters h, p, c and q

2.2.3 Jammed structures A woven fabric in which warp and weft yarns do not have mobility within the structure as they are in intimate contact with each other are called jammed structures. In such a structure the warp and weft yarns will have minimum thread spacing. These are closely woven fabrics and find applications in windproof, waterproof and bullet-proof requirements. During jamming the straight portion of the intersecting yarn in Fig. 2.1 will vanish so that in equations 2.2 and 2.3:

l1 – Dq1 = 0



l1 = q1 D

Equations 2.2 and 2.3 will reduce to

h1 = D(1 – cos q1)



p2 = D sin q1

Similarly, for jamming in the weft direction l2 – Dq2 = 0, equations 2.7 and 2.8 will reduce to the above equations with suffix interchanged from 1 to 2 and vice versa. For a fabric being jammed in both directions we have:

D = h1 + h2 = D(1 – cos q1) + D(1 – cos q2)

or

cos q1 + cos q2 = 1 2



2.12 2

Êp ˆ Êp ˆ 1 – Á 1˜ + 1 – Á 2 ˜ = 1 Ë D¯ Ë D¯



2.13

This is an equation relating warp and weft spacing of a most closely woven fabric.

14

Woven textile structure

2.2.4 Cross-threads pulled straight If the weft yarn is pulled straight h2 = 0 and h1 = D. Equation 2.3 will give

D = (l1 – D q1) sin q1 + D (1 – cos q1)



ˆ Êl cos q1 = Á 1 – q1˜ sin q1 ¯ ËD

or

q1 + cot q1 =

l1 D

2.14

This equation gives maximum value of q1 for a given value of l1/D. The above equation will be valid for warp yarn being straight by interchange of suffix from 1 to 2. However, the weft thread can be restricted in being pulled straight by the jamming of warp threads. In such a case,

l1 – D q1 = 0

or

q1 =

l1 D

Equation 2.3 will become:

h2 = D – h1 = D – D (1 – cos q1 ) = D cos

l1 D

2.15

If the weft thread is pulled straight and warp is just jammed, then

l1 = q1 = p 2 D

2.16

These are useful conditions for special fabric structure.

2.2.5 Non-circular cross-section So far, it has been assumed that that yarn cross-section is circular and the yarn is incompressible. However, the actual cross-section of yarn in a fabric is far from circular due to the system of forces acting between the warp and weft yarns after weaving and the yarn can never be incompressible. This inter-yarn pressure results in considerable yarn flattening normal to the plane of the cloth even in a highly twisted yarn. Therefore many researchers have tried to correct Peirce’s original relationship by assuming various shapes

Geometrical modeling of woven fabric structure

15

for the cross-section of yarn. Two important cross-sectional shapes such as elliptical and racetrack are discussed below.

2.2.6 Elliptical cross-section Peirce’s elliptical yarn cross-section is shown in Fig. 2.2. The flattening factor is defined as

e= b a

where b = minor axis of ellipse and a = major axis of ellipse. The area of ellipse is (p/4)ab. If d is assumed as the diameter of the equivalent circular cross-section yarn, then

d = ab



h1 + h2 = d1 + d2 = b1 + b2



b1 + b1 = h1 + h2 = 4 (p1 c2 + p2 c1 ) 3

2.17

Yarn diameter is given by its specific volume, v and yarn count:

dmils = 34.14

v N

where N is the English count, and dcm =

Tex = Tex 280 280.2 f rf

assuming f = 0.65, rf = 1.52 for cotton fiber where f = yarn packing density and rf = fiber density.

b2

b1

Weft

Warp

2.2 Elliptical cross-section.

a2

16

Woven textile structure

This can be used to relate yarn diameter and crimp height by simply substituting in equation 2.17 to obtain:





Ê v h1 + h2 = d1 + d2 = D = 34.14 Á 1 + Ë N1 h1 + h2 = d1 + d2 =



v2 ˆ N 2 ˜¯

T2 ˆ 1 Ê T1 + Á 280.2 Ë f 1 r f1 f 2 r f2 ˜¯

= 1 ( T1 + T2 ) 280

2.18



2.19



2.20



assuming f = 0.65, rf = 1.52 for cotton fiber and where T1 = tex of warp yarn and T2 = tex of weft yarn. These are useful equations to be used subsequently in the crimp interchange derivation.

2.2.7 Racetrack cross-section In the racetrack model [2,3] given in Fig. 2.3, a and b are maximum and minimum diameters of the cross-section. The fabric parameters with superscript refer to the zone AB, which is analogous to the circular thread geometry; the parameters without superscript refer to the racetrack geometry, a repeat of this is between C and D. Then the basic equations will be modified as under:

p2¢ = p2 – (a2 – b2)

2.21



l1¢ = l1 – (a2 – b2)

2.22

a2

b2

h1 2 h2 2

b1

l1

p 2¢ A

p2

C

2.3 Racetrack cross-section.

B D

Geometrical modeling of woven fabric structure



c1 ¢ =

17

l1 ¢ – p2 ¢ c1 p2 = p2 ¢ p2 – (a2 – b2 )

2.23

c2 p1 p1 – (a1 – b1)

2.24

Similarly,

c2 ¢ =



h1 = 4 p2 ¢ = c1 ¢ 3

2.25



h2 = 4 p1 ¢ = c2 ¢ 3

2.26



h1 + h2 = B = b1 + b2

Also if both warp and weft threads are jammed, the relationship becomes

2.3

B 2 – (p1 ¢ )2 +

B 2 – (p2 ¢ )2 = B



2.27

Using the model to predict the fabric thickness, cover, mass and specific volume

Using the fabric parameters discussed in the previous section it is possible to calculate the fabric thickness, fabric cover, fabric mass and fabric specific volume.

2.3.1 Fabric thickness Fabric thickness for a circular yarn cross-section is given by h1 + d1 or h2 + d2 whichever is greater. When the two threads project equally, then

h1 + d1 = h2 + d2

In this case the fabric gives: Minimum thickness = 1/2(h1 + d1 + h2 + d2) = D; h1 = D – d1 Such a fabric produces a smooth surface and ensures uniform abrasive wear. In a fabric with coarse and fine threads in the two directions and by stretching the fine thread straight, maximum crimp is obtained for the coarse thread. In this case the fabric gives:

maximum thickness = D + dcoarse

since hcoarse = D.

18

Woven textile structure

When yarn cross-section is flattened, the fabric thickness can be expressed as h1 + b1 or h2 + b2, whichever is greater.

2.3.2 Fabric cover In fabric, cover is considered as fraction of the total fabric area covered by the component yarns. For a circular cross-section cover factor K is given as: E T d= K = p 280.2 f r f 28.02 f r f



K = E T ¥ 10 –1 where K is cover factor, T is yarn tex and E is threads per cm = 1/p. The suffixes 1 and 2 will give warp and weft cover factors. For d/p = 1 cover factor is maximum and given by: K max = 28.02 f rf Fractional fabric cover is given by: d1 d2 d1d2 + – = 1 p1 p2 p1 p2 28.02

K1K 2 ˆ Ê ˜ ÁË K1 + K 2 – 28..02¯

Multiplying by 28.02 and taking 28.02 ≈ 28 we get fabric cover factor as: KK fabric cover factor = K1 + K 2 – 1 2 2.28 28 For racetrack cross-section the equation will be a= d p 1 ˆ Ê e p 1 + 4 Á – 1˜ ¥ 28.02 f rf p Ëe ¯ K = Ê1 ˆ e 1 + 4 Á – 1˜ ¥ 28.02 f rf p Ëe ¯ (here e = b/a). For elliptical cross-section the equation will be: E T a= d = K = p e p 280.2 e f rf 28.02 e f rf

Here



e = b and d = ab a

2.29

2.30

Geometrical modeling of woven fabric structure

19

2.3.3 Fabric mass per unit area (areal density)

gsm = [T1E1(1 + c1) + T2E2 (1 + c2)] × 10–1

2.31



gsm = √T1 [(1 + c1) K1 + (1 + c2) K2 b]

2.32

where E1, E2 are ends and picks per cm, T1, T2 are warp and weft yarn tex, K1 and K2 are the warp and weft cover factors, c is the fractional crimp and d2/d1= b. In practice the comparison between different fabrics is usually made in terms of grams per square meter (gsm). The fabric engineer tries to optimize the fabric parameters for a given gsm. The relationship between the important fabric parameters such as cloth cover and gsm is warranted. This is shown in Fig. 3.8 in Chapter 3 for jammed fabric.

2.3.4 Fabric specific volume The apparent specific volume of fabric, vF is calculated by using the following formula:

vF =

fabric thickness (cm) fabric mass (g/cm 2 )

fabric mass (g/cm2) = 10–4 ¥ gsm fabric packing factor, f =

vf vF

here vf, vF are respectively fibre and fabric specific volume. A knowledge of fibre specific volume helps in calculating the packing of fibres in the fabric. Such studies are useful in evaluating the fabric properties such as warmth, permeability to air or liquid.

2.4

Modeling maximum fabric cover

Maximum cover in a jammed fabric is only possible by keeping the two consecutive yarns (say warp) in two planes so that their projections are touching each other and the cross-thread (weft) interlaces between them. In this case the weft will be almost straight and maximum bending will be done by the warp: d1/p1 = 1 will give K1 = Kmax, and the spacing between the weft yarn:

p2 = D sin q1 = D (for q = 90°)



p2 = d1 + d2

20

Woven textile structure



d2 d2 = = 2 for d2 = 2d1 p2 d1 + d2 3

This will give K2 = 2/3 Kmax. If d1 = d2 then d1 = d2/p2 = 0.5 and K2 = 0.5 Kmax. This is the logic for getting maximum cover in any fabric. The principles are: ∑ ∑

use fine yarn in the direction where maximum cover is desired and keep them in two planes so that their projections touch each other and use coarse yarn in the cross-direction; as above but instead of coarse yarn insert two fine yarns in the same shed.

Both options will give maximum cover in warp and weft but the first option will give more thickness than the second. The ooziness of yarn, flattening in finishing and regularity further improve the cover of cloth. The cover factor indicates the area covered by the projection of the thread. It also gives a basis of comparison of hardness, crimp, permeability and transparency. A higher cover factor can be obtained by the lateral compression of the threads. It is possible to get very high values only in one direction where threads have higher crimp. Fabrics differing in yarn counts and average yarn spacing can be compared based on the fabric cover. The degree of flattening for racetrack and elliptical cross-section can be estimated from fabric thickness measurements to evaluate b and a from microscopic measurement of the fabric surface. The classic example in this case is that of a poplin cloth in which for warp threads:

p1 = d1



d1 = d2 = D/2

and for jamming in both directions

p1 = D sin q2



d = D/2 = D sin q2



q2 = 30° = 0.5236



q1 = 82°18¢1.4364 (using cos q1 + cos q2 = 1)



p2 = D sin q1 = 0.991D ≈ 2p1



l1 = D q1 = 1.14364



l2 = D q2 = 0.5236



c1¢ = 0.45, c2¢ = 0.0472

Geometrical modeling of woven fabric structure

21

This is a specification of good quality poplin which has maximum cover and ends per cm is twice that of picks per cm.

2.5

Calculating fabric properties: numerical examples

Q1. A plain weave square cotton fabric is woven from 16 tex yarn. Find the maximum threads per cm and crimp. Find the change in count and threads per cm if the weave is changed to 2/2 twill and an increase of 10% in fabric weight is desired. Assume the crimp in 2/2 twill to be 8% assuming q = 0.65, rf = 1.52 for cotton fiber. Solution:

16 = 0.014 36 cm d1 = d2 = 1 226 1.52



D = d1 + d2 = 0.028 71 cm

In square fabric, d1 = d2, p1 = p2 2



Ê pˆ 2 1–Á ˜ =1 Ë D¯



\ p = 0.024 86 cm



threads per cm = 40.23 ≈ 40

Also

c= 3D=2p c 4 \

c=

3D 3 ¥ 0.028 712 = = 0.43311 8 p 8 ¥ 0.024 86



crimp = 0.1876 ª 18.76%



weave 2/2 twill, E = 4, I = 2



M =E=4=2 I 2



weave value for twill =

Plain 1/1

E = 2, I = 2

M = 2 =2 M +1 2+1 3

22

Woven textile structure



M = 2/2 =1



weave value for plain = 1 = 1 1+1 2 (threads per cm)twill = (threads per cm)plain Ê M ˆ Ë M + 1¯ twill ¥ Ê M ˆ Ë M + 1¯ plain



= 53.33 ª 53 È16 (1.08)˘ = 184.32 gsm fabric gsm for 2/2 twill = 1 ¥ 2 Í 10 Î 0.01875 ˙˚

For 10% increase in gsm, both yarn count and thread per cm will change; a coarser count and fewer threads per cm will be required.



[fabric gsm]Old Ê TOld ˆ = [fabric gsm]New ÁË TNew ˜¯



184.31 = 16 = T 202.74 16 = 4.4 New = 202.74 184.31 TNew



required yarn tex = 19.36



(threads per cm)New = (threads per cm)Old (fabric gsm)Old 184.31 = ¥ 53 (fabric gsm)New 202.74 = 48.18 ª 48

¥

Q2. A cotton fabric is made for 24 ends and 18 picks per cm, percentage crimp in warp and weft = 10/5, warp and weft tex are 50/60. Calculate fabric gsm, fabric specific volume and fabric cover factor. What is the implication of fabric specific volume assuming f = 0.65, rf = 1.52 for cotton fiber? Solution:

p1 = 1 = 0.041667 cm 24



p2 = 1 = 0.055 56 cm 18



d1 = 50/1.52 ¥ 0.65 = 0.025 39 cm 280.2

Geometrical modeling of woven fabric structure

23



d1 = 60/1.52 ¥ 0.65 = 0.0278 cm 280.2



fabric gsm = 1 [50 ¥ 24 (1.10) + 60 ¥ 18 ¥ 1.05] = 245.4 10



fabric mass g/cm2 = gsm/(100)2 = 245.4/(100 ¥ 100) = 0.024 54



fabric thickness = h1 + d1 or h2 + d2, whichever is greater



h2 = 4 p1 c1 = 4 ¥ 0.041667 1.05 = 0.056 927 cm 3 3



h1 + d1 = 0.077 78 + 0.025 39 = 0.103 09 cm



h2 + d2 = 0.056 927 + 0.027 81 = 0.084 74 cm



fabric thickness = 0.013 09 cm



0.103 09 = 4.2 fabric specific volume cm 3/g = fabric thickness 2 = fabric mass g/cm 0.024 54



cotton fiber specific volume cm 3 /g = 1 = 0.6579 1.52



packing factor =

fabric specific volume 0.6579 = = 0.1566 4.2 fiber speecific volume

Percentage air space = 84.3, the fabric is less dense and is bulky. It will have a great influence on the warmth, permeability of air and moisture; on absorption of liquid and also strength and extensibility.

warp cover, K1 = 24√50 ¥ 10–1 = 16.97



weft cover, K2 = 18√60 ¥ 10–1 = 13.94



\

cloth cover factor, K1 + K 2 –

K1K 2 = 16.97 + 13.94 – 16.97 ¥ 13.94 28 28

= 30.91 – 8.45 = 22.46 Q3. Calculate the fabric mass, fabric specific volume and fabric cover factor for a cotton square fabric made from 30 tex and 25 thread per cm, assuming f = 0.65, rf = 1.52 for cotton fiber. Solution:

p1 = p2 = 1 = 0.04 cm 25



d1 = d2 = 30/1.52 = 0.019 66 cm 226

24

Woven textile structure



d = 0.019 66 = 0.4915 = 4 c p 0.04 3



\



crimp percent = 13.6



h1 = h2 = (4/3)p√c

c = 9 = ¥ (0.4915)2 = 0.1359 16

= (4/3) ¥ 0.04√0.1359 = 0.019 66 cm

fabric thickness = h + d = 0.019 66 + 0.019 66 = 0.039 32 cm

Also

K1 = K2 = √c ¥ 37.2 = 13.76



fabric cover factor = 13.76 ¥ 2 – 13.76 ¥ 13.76 28



= 27.52 – 6.76 = 20.76

È ˘ fabric gsm = 2 ÍT ¥ n Ê1 + c%ˆ ˙ = 2 [30 ¥ 25 ¥ 1.136] = 170.4 Ë 10 Î 100¯ ˚ 10 fabric mass g/cm 2 =

170.4 = 0.01704 100 ¥ 100

fabric specific volume = 0.03932/0.01704 = 2.3

Q4. A plain weave cotton handkerchief is woven from 10 tex yarn is warp and weft. It has 36 ends and picks per cm. Assume packing coefficient of 0.65 and cotton fiber density of 1.52 g/cm2. Calculate crimp, fabric mass, fabric thickness, fabric specific volume, percentage air in fabric and fabric cover factor. Solution: d=

1 Tex = 1 280.2 f rf 280.2



p = 1 = 0.0278 cm 36



2d = 4 ¥ 2 p c 3



\

c=

3d 4p

10 = 0.011 35 cm 0.65 ¥ 1.52

Geometrical modeling of woven fabric structure 2



2

Êdˆ Ê 0.01135ˆ c= 9Á ˜ = 9Á ˜ = 0.0938 16 Ë 0.0278 ¯ 16 Ë p¯



crimp in warp and weft = 9.38%.



fabric mass, gsm = 2 ¥ 1 (36 ¥ 10 ¥ 1.0938) = 78.75 ª 78.8 16



fabric mass, g/cm2 = 78.8 ¥ 10–4 = 0.007 88



h = 4 p c = 4 ¥ 0.0278 0.0938 = 0.01135 cm 3 3



fabric thickness = h + d = 0.0227 cm



fabric specific volume cm3/g = vF = 0.0227/0.007 88 = 2.88



25

fabric packing factor =

vf 0.6579 = = 0.2284 vF 2.88



% air = 77.16.



warp cover factor = E T ¥ 10 –1 = 36 10 ¥ 10 –1 = 11.38

fabric cover factor = 11.38 + 11.38 – 11.38 ¥ 13.38 = 18.2 28 Q5. A square fabric is woven with the following particulars: threads per cm = 24, yarn count = 50 tex, fiber density = 1.14 g/cm3. Calculate the crimp and cover factor. f = 0.5. Solution:

p1 = p2 = 1/24 = 0.041 67 cm Tex 50 = 0..029 30 cm d1 = d2 = 1 = 1 226 fibre density 226 1.14



D = d1 + d2 = 0.0586 cm



4p c ¥ 2=D 3





c=

3D 8p

c = 0.2782 = 27.82% –1 10 –1 E Tex d = 10 E Tex = p 226 fibre density 24.13

26

Woven textile structure

For d/p = 1, Kmax = 24.13

fabric cover factor =

d1 d2 Ê d1 ¥ d2 ˆ + – p1 p2 ÁË p1 ¥ p2 ˜¯



d1 d2 = = 10 –1 ¥ 24 50 = 16.97 p1 p2



Cover factor = 16.97 ¥ 2 – 16.97 ¥ (16.97/24.13)



= 33.94 – 11.94 = 22

Q6. A shirting cotton cloth is made from the following particulars: c1 = 10%, d1 = 0.016 27 cm, (T2/T1)1/2 = 0.80, K1/K2 = 11.3/9.1, T is the yarn tex and K is the cover factor. Calculate the weft crimp, fabric thickness, fabric mass, specific volume and air space. Solution:

T1 d1 = 1 226 1.52



T1 0.016 27 = 1 226 1.52



\ T1 = 20.55



(T2/T1)1/2 = 0.80

So,

T2 = 0.64T1 = 0.64 ¥ 20.55 = 13.15



T2 d2 = 1 = 1 13.15 = 0.013cm 226 1.52 226 1.52



D = d1 + d2 = 0.029 28 cm



K1 = 10 –1 ends per cm T1



ends per cm =

10 K1 10 ¥ 11.3 = = 24.93 T1 20.55



p1 = 0.0401 cm



K 2 = 10 –1 picks per cm T2



picks per cm =

10 K 2 10 ¥ 9.1 = = 25.1 ª 25 T2 13.15

Geometrical modeling of woven fabric structure



p2 = 0.039 85 cm



h1 = 4 p2 c1 = 4 ¥ 0.039 85 0.1 = 0.0168 cm 3 3



h2 = D – h1 = 0.012 48 cm



h2 = 4 p1 c2 = 4 ¥ 0.0401 c2 = 0.012 48 cm 3 3



27

c2 = 0.233



c2 = 0.0545 = 5.4%



fabric thickness h1 + d1 = 0.0168 + 0.016 27 = 0.033 cm

h1 + d1 is taken as it is greater than h2 + d2.

fabric mass per unit area, gsm



= √T1 [(1 + c1) K1 + (1 + c2) b K2]



2 = 20.55 (1.1 ¥ 11.3 + 1.0545 ¥ 0.8 ¥ 9.1) = 91.15 g/cm



= 0.9115



fabric specific volume = fabric thickness2 = 0.033 = 0.0362 cm 3 /g fabric maass (g/cm ) 0.9115

Q7. A plain weave cotton fabric is made from 20 ends and 30 picks per cm. The percentage crimp in warp and weft is 15 and 10; assume f = 0.65, rf = 1.52 g/cm3. Find the yarn tex if it is to be the same in warp and weft. What will be yarn tex if a flattening race track cross-section is assumed and a/b = 1.3. Solution:

h1 + h2 = d1 + d2



4 [p c + p c ] = 2d 2 1 1 2 3



4 È 0.15 + 0.10˘ = 2d 3 ÍÎ 30 20 ˙˚



4 [0.0129 + 0.01581] = d 6



d = 0.019 15 cm



Tex = 280 ¥ d = 5.36

28

Woven textile structure



Tex = 28.74 ≈ 29



For racetrack cross-section:



È Ê1 ˆ ˘ d 2 = b 2 Íp + Á – 1˜ ˙ Î4 Ë e ¯ ˚



1 = a = 1.3 e b



e = b = 0.769 a b=



b=

d Ê p ˆ Ê1 ˆ ÁË ˜¯ + ÁË – 1˜¯ 4 e d = 0.9599 d 1.0854



b = 0.9599 ¥ 0.019 15 = 0.018 38 cm



a = 1.3 b = 0.0239 cm



p2¢ = 0.033 33 – (a – b) = 0.033 33 – 0.0055 = 0.027 83 cm



c1 ¢ =

0.15 ¥ 0.033 33 c1 p2 = = 0.179 612 4 = 17.96% p2 – (a – b ) 0.027 83

p1¢ = p1 – (a1 – b1) = 0.05 – 0.0055 = 0.0445 cm c2 ¢ =

c2 p1 = 0.1066 = 0.10 ¥ 0.05 = 0.1124 = 11.24% 0.0445 p1 – (a1 – b1 )



4 (p ¢ c ¢ + p ¢ c ¢ ) = b + b 2 1 1 2 1 2 3



fi 4 (0.027 83 0.1796 + 0.0445 0.1124) = b1 + b2 = 2b 3



= 2 ¥ 0.9599 d



fi 4 (0.011794 + 0.014 92) = 2 ¥ 0.9599d 3



d = 0.018 55 cm

Geometrical modeling of woven fabric structure



2.6

Tex = 280 d = 280 ¥ 0.018 55 = 5.195 Tex = 26.98 ª 27 English count

References

1. Peirce F T (1937), J. Text. Inst., 28, T45–112. 2. Kemp A (1958), J. Text. Inst., 49, T 44. 3. Love L (1954), Text. Res. J., 24, 1073.

29

3

Using a geometric model to predict woven fabric properties

Abstract: The fabric designer can vary texture in a fabric through properties such as mass, thickness, specific volume, porosity and extensibility. A model is used to establish relationships between properties such as thread spacing, crimp and cover for all possible fabric structures. Another practical relationship is shown between cloth cover and fabric mass. The maximum weavability limit for plain and non-plain weave fabric is determined by considering fiber density, yarn packing and yarn diameter for circular and racetrack cross-sections. Numerical examples are given to assist in understanding the applications covered in this chapter. Key words: fabric model, weavability, plain weave, crimp, cover.

3.1

Introduction

The actual behavior of fabric structure is not precisely calculable by geometry but many features of the cloth are essentially dependent on the geometrical relationships. These fabric parameters are a tool for an innovative fabric designer in creating fabrics for diverse applications. The theoretical relationships between fabric parameters enable the fabric designer to play with different fibers, yarn tex, threads per centimeter and weave to vary texture and fabric properties. The parameters from the geometrical model enable the following: ∑ ∑

∑ ∑ 30

Obtain a relationship between different fabric parameters and estimate fabric mass per unit area, gsm. Calculate maximum picks per centimeter of a cloth of low reed and when ends are cramped. As a guide it helps in knowing the maximum weavability limit; maximum ends and picks which can be inserted for a given yarn and weave. The weaver avoids attempts to weave impossible constructions and also estimates the difficulty of weaving, yarn breakage rate and measures for appropriate yarn and weaving preparation. Calculate the limits to the stretch along warp or weft direction in the cloth and predict fabric dimensions, crimp and the changes in the fabric parameters. Predict crimp in the fabric; this has a marked influence on the fabric properties.

Using a geometric model to predict woven fabric properties

∑ ∑ ∑

31

Estimate cloth porosity to the passage of air, light, fluid and guide to the maximum density of packing that can be achieved. Predict fabric thickness and estimate apparent fabric specific volume and porosity. This knowledge is useful for estimating fabric warmth, moisture absorption and flow and absorption of liquid. Predict fabric shrinkage.

The geometry provides simplified formulae to facilitate calculations and specific constants which are of value for cloth engineering, problems of structure and mechanical properties.

3.2

Predicting woven fabric parameters

The basic equations derived from the geometrical model are not easy to handle. Research [1,2] has provided solutions in the form of graphs and tables. These are quite difficult to use in practice. It is possible to predict fabric parameters and their effect on the fabric properties by soft computing [3]. This information is helpful in taking a decision regarding specific needs. A simplified algorithm is used to solve these equations and obtain relationships between useful fabric parameters such as thread spacing and crimp, fabric cover and crimp, warp and weft cover. Such relationships help in guiding the directions for moderating fabric parameters. Peirce’s geometrical relationships obtained in Chapter 2 can be written as

p2 = (K1 – q1) cosq1 + sinq1 D

3.1



h1 = (K1 – q1) sinq1 + (1 – cosq1) D

3.2

where K1 = l1/D and two similar equations for the weft direction will be obtained by interchanging the suffix 1 with 2 and vice versa. The solution of p2/D and h1/D is obtained for different values of q1 (weave angle) ranging from 0.1 to p/2 radians. Such a relationship is shown in Fig. 3.1. The flowchart for this algorithm is shown in Fig. 3.2 along with associated module connectors at Figs 3.3, 3.4 and 3.5. Figure 3.1 is similar to that given by Peirce [4]. It is a very useful relationship between fabric parameters for engineering desired fabric constructions. One can see its utility for the following three cases: ∑ ∑ ∑

jammed structures; non-jammed fabrics; special case in which cross-threads are straight.

C = 0.038

C = 0.058

= = = = = = = = C C C C C C C C

C = 0.082

Woven textile structure 0.99 0.49 0.41 0.34 0.23 0.18 0.14 0.11

32

1 C = 0.023 0.8

C = 0.11

h1/D

0.6

0.4 C = 0.003 0.2

0

0

0.5

1.0

1.5 p2/D

2.0

2.5

3.0

3.1 Relation between thread spacing and crimp height.

3.2.1 Jammed structures Figure 3.1 shows a nonlinear relationship between the two fabric parameters p and h on the extreme left. In fact, this curve is for jamming in the warp direction. It can be seen that the jamming curve shows different values of p2/D for increasing h1/D, that is warp crimp. The theoretical range for p2/D and h1/D varies from 0 to 1. Interestingly this curve is a part of circle and its equation is: 2



2

Ê p2 ˆ Ê h1 ˆ ÁË D ˜¯ + ÁË D – 1˜¯ = 1



3.3

with center at (0, 1) and radius equal to 1. For jamming in the warp direction of the fabric the parameters p2/D and corresponding h1/D can be obtained either from this figure or from the above equation. The relationship between the fabric parameters over the whole domain of structure being jammed in both directions can be obtained by

Using a geometric model to predict woven fabric properties

33

Start

q1 = 0.1 l1/D = 0.1

p2 = (K – q1) cos q1 + sin q1 D

h1 l /D = (K – q1) sin q1 + (1 – cos q1), c1 = 1 – 1 D p2 /D

Print h1 p2 , , c D D 1

A

l1 l = 1 + 0.1 D D

q1 = q1 + 0.1 No

B

No

Is q1 = 1.57 ?

Yes

D Yes End

Is l1 = 3? D

No

Is

p2 l £ 1? D D

Yes

E

p2 p = 2 + 0.1 D D

C

3.2 Flowchart for solving Peirce’s seven equations.

using an algorithm involving equations from Chapter 2. The flowchart for this algorithm is given in Fig. 3.6. From these computations the relationships between different useful fabric parameters are obtained and are shown in Figs 3.7–3.11. Figure 3.7 gives the relationship between weft and warp thread spacing in a dimensionless form; that is between p2/D and p1/D. This figure shows that the relationship between these parameters is less sensitive at the two extreme ends. The

34

Woven textile structure C

Êp ˆ l1 1 = Á 2 – sin q1˜ + q1 D ËD ¯ cos q1

Êl ˆ h1 = Á 1 – q1˜ sin q1 + (1 – cos q1) D ËD ¯

Print

E

No

h1 p2 , ,c D D 1

Is p2 = 3? D

Yes D

3.3 Module connector C for Fig. 3.2.

relationship is sensitive in a p/D domain close to 1. In fact this sensitive range corresponds to maximum crimp in one direction only. Another useful relationship between the crimps in the two directions is shown in Fig. 3.8. It indicates inverse nonlinear relationship between c1 and c2. The intercepts on the x and y-axes give maximum crimp values, with zero crimp in the cross-direction. This is a fabric configuration in which the cross-threads are straight and all the bending is being done by the intersecting threads. Figure 3.9 shows the relation between h1/p2 and h2/p1. The figure shows inverse linearity between them except at the two extremes. This behavior is in fact a relationship between the square root of crimp in the two directions of the fabric. Other practical relations are obtained between the warp and weft cover factor and between cloth cover factor and fabric mass per unit area (gsm). Figure 3.10 gives the relation between warp and weft cover factor for different ratios of weft to warp yarn diameters (b). The relation between the cover factors in the two directions is sensitive only in a narrow range for

Using a geometric model to predict woven fabric properties

35

A

h2 h = 1 – 1 D D

q2 = 0.1

x =

q2 = q2 + 0.1

h2 – [(l2 – q2 ) sin q2 + (1 – cos q2 )] D

No

Is x £ 0.00001

Yes ˆ l2 Êh2 = – 1 + cos q2 ˜ 1 + q2 D ÁË D ¯ sin q2

ˆ p1 Ê l2 = – q2 ˜ cos q2 + sin q2 D ÁËD ¯

c2 =

l2 /D – 1 p2 /D

Print h2 p1 , , c D D 2

F

3.4 Module connector at A for Fig. 3.2.

all values of b. The relation between the cover factors in the two directions are inter-dependent for jammed structures. Maximum threads in the warp or weft direction depend on yarn count and weave. Maximum threads in one direction of the fabric will give unique maximum threads in the crossdirection. The change in the value of b causes a distinct shift in the curve. A

36

Woven textile structure F

Is p1 l £ 2? D D

No

B

Yes

p1 p = 1 + 0.1 D D

Êp ˆ l2 1 +q = Á 1 – sin q2 ˜ 2 D ËD ¯ cos q2

Êl ˆ h2 = Á 2 – q2 ˜ sin q2 + (1 – cos q2 ) D ËD ¯

Print

No

h2 p1 , , c D D 2

Is p1 = 3? D

Yes

B

3.5 Module connector at F for Fig. 3.4.

comparatively coarse yarn in one direction with respect to the other direction helps in increasing the cover factor. For b = 0.5, the warp yarn is coarser than the weft; this increases the warp cover factor and decrease the weft cover factor. This is due to the coarse yarn bending less than the fine yarn. A similar effect can be noticed for b = 2, in which the weft yarn is coarser than the warp yarn. These results are similar to earlier work reported by Newton [5,6] and Seyam [7]. The relation between fabric mass per unit area (gsm) with the cloth cover (K1 + K2) is positively linear as shown in Fig. 3.11 [8]. The trend may appear

Using a geometric model to predict woven fabric properties

37

Start

q1 = l1/D = 0.1

p2 h l /D = sin q1, 1 = (1 – cos q1), c1 = 1 –1 D D p2 /D

h2 h = 1 – 1 D D

Ê hˆ q2 = cos –1 Á1 – 2 ˜ Ë D¯

p1 = sin q2 D

l1/D = q1 = q1 + 0.1

Êp ˆ l2 1 = q2 + Á 1 – sin q2 ˜ D ËD ¯ cos q2

c2 =

Print

No

l2 /D – 1 p1 /D

h1 p2 h p , , c , 2 , 1, c D D 1 D D 2

Is q1 = 1.57 ?

Yes End

3.6 Flowchart for fabric parameters in jammed structures.

to be self-explanatory. In practice an increase in fabric mass and cloth cover factor for jammed fabrics can be achieved in several ways, such as with zero crimp in the warp direction and maximum crimp in the weft direction; zero

38

Woven textile structure 1.2

1.0

p1/D

0.8

0.6

0.4

0.2

0 0

0.2

0.4

0.6 p2/D

0.8

1.0

1.2

3.7 Relation between weft and warp thread spacing for jammed fabric. 0.6

0.5

Weft crimp (c2)

0.4

0.3

0.2

0.1

0 0

0.1

0.2

0.3 0.4 Warp crimp (c1)

0.5

0.6

3.8 Relation between warp and weft crimp for jammed fabric.

crimp in the weft direction and maximum crimp in the warp direction; equal or dissimilar crimp in both directions. This explanation can be understood by referring to the non-linear part of the curve in Fig. 3.1.

Using a geometric model to predict woven fabric properties

39

1.2

1.0

h2/p1 (ª ÷c2)

0.8

0.6

0.4

0.2

0

0

0.2

0.4

0.6 h1/p2 (ª ÷c1)

0.8

1

1.2

3.9 Relation between ÷c1 and ÷c2 for jammed fabric.

35

Weft cover factor

30 25 20

b=2 b=1

15

b = 0.5

10 5 0

0

5

10

15 20 25 Warp cover factor

30

35

3.10 Relation between warp and weft cover factor for different b for jammed fabric.

3.2.2 Non-jammed structure It can be seen that the relation between p2/D and corresponding h1/D is linear for different values of crimp. This relationship is useful for engineering non-

40

Woven textile structure 90

Cloth cover factor (K1 + K2)

80 70 60 50 40 30 20 10 0

0

100

200 300 400 500 Fabric areal density (gsm)

600

700

3.11 Relation between fabric cover factor and fabric mass for jammed structure.

jammed structures for a range of values of crimp. The fabric parameters can be calculated from the above non-jammed linear relation between p2/D and h1/D for any desired value of warp crimp. Then h2/D can be obtained from (1 – h1/D) and for this value of h2/D one can obtain the corresponding value of p1/D for the desired values of weft crimp. Thus all fabric parameters can be obtained for desired value of p2/D, picks per cm, warp and weft yarn tex, warp and weft crimp. One can choose any other four parameters to get all fabric parameters. The algorithm mentioned in Fig. 3.2 can be used to get several solutions for the non-jammed fabric.

3.2.3 Straight cross-threads In Fig. 3.1 the intersection of the X-axis corresponding to h1/D = 1 gives all possible structures ranging from relatively open to jammed configurations. In this case h2 = 0, h1 = D. This gives interesting structures which have stretch in one direction only, enabling maximum fabric thickness and also being able to use brittle yarns. The fabric designer can choose from several possible fabric constructions. These options include jamming and other non-jammed constructions. Using the above logic it is also possible to get fabric parameters for: ∑ ∑

fabric jammed in both directions; fabric with maximum crimp in one direction and cross-threads being straight;

Using a geometric model to predict woven fabric properties

∑

41

fabric which is neither jammed nor has zero crimp in the crossthreads.

3.3

Predicting the weavability limit

The maximum number of ends and picks per unit length that can be woven with a given yarn and weave defines the weavability limit [7,9]. This information is helpful to weavers in avoiding attempts to weave impossible constructions, thus saving time and money. It also helps to anticipate any difficulty in weaving and take necessary preparations. Dickson [10] demonstrated the usefulness of theoretical weavability limit and found agreement with the loom performance. Most of the work in this area was done using empirical relationships. The geometrical model is very useful in predicting this limit for a given warp, weft diameter (tex) and any weave. The maximum weavability limit is calculated in the model by using jamming conditions for plain and non-plain weaves for circular and racetrack cross-sections.

3.3.1 Yarn diameter Two important geometrical parameters are needed for calculating weavability for a general case. These are yarn diameter and weave factor. Yarn diameter in terms of linear density in tex for a general case is given as:



d=

T 280.2 frf



3.4

where d = yarn diameter (cm), T = yarn linear density (tex, i.e. g/km), rf = fiber density(g/cm3), ry = yarn density (g/cm3) and f = yarn packing factor. This equation for the yarn diameter is applicable for any yarn type and fiber type. The packing factor depends on fiber variables such as fiber crimp, length, tex and cross-section shape. Tables 3.1 and 3.2 give the fiber density and yarn packing factor for different fiber and yarn type respectively. For blended yarns, average fiber density is given by the following:



n 1 = ∑ pi r 1 pft



3.5

where r = average fiber density, pi = weight fraction of the ith component, pft = fiber density of the ith component and n = number of components of the blend.

42

Woven textile structure Table 3.1 Fibre density (g/cm3) Acetate Cotton Lycra Nylon 6 Nylon 6, 6 Polyester Polypropylene Rayon Wool

1.32 1.52 1.20 1.14 1.13–1.14 1.38 0.91 1.52 1.32

Table 3.2 Yarn packing factor Ring spun Open-end spun Worsted Woolen Continuous filament

0.60 0.55 0.60 0.55 0.65

3.3.2 Effect of variation in fiber density on the relation between warp and weft cover factor for jammed fabrics The change in the fiber density affects the relation between the warp and weft cover factors for jammed structures. It can be seen from Figs 3.12–3.14; with an increase in fiber density from 0.91 to 1.52 g/cm3 the sensitivity in the relation between K1 and K2 increases. The base level and range of cover factor K2 increase, the range of cover factor K1 decreases but shifts to a higher level. Lower values of b (d2/d1) show greater sensitivity in the relation between cover factors. It is a useful ploy to increase the range of cover factors in jammed structures and enables flexibility in designing jammed woven structures.

3.3.3 Effect of variation in yarn packing factor on the relation between warp and weft cover factor for jammed fabrics Rayon and cotton fiber have same density. A packing factor of 0.60 is taken for rayon and 0.65 for cotton. The effect of change in yarn packing factor from 0.60 to 0.65 on the relation between warp and weft cover factors can be seen in Figs 3.15–3.17 for b ranging from 0.5 to 2. The higher yarn packing factor results in increasing the levels of warp and weft cover factors. The increase in b helps in attaining higher weft cover factors and gives a wider range of sensitivity between the warp and weft cover factors.

Using a geometric model to predict woven fabric properties

43

30

25

Different r values and b = 0.5

K2

20

r = 1.52

15 r = 1.44 r = 1.14 10

5

r = 0.91

5

10

15

20 K1

25

30

35

3.12 Effect of fiber density on the relation between warp and weft cover factor (b = 0.5).

30 Different r values and b = 1 25 r = 1.52 r = 1.44

K2

20

r = 1.14

15

r = 0.91 10

5

5

10

15

20 K1

25

30

35

3.13 Effect of fiber density on the relation between warp and weft cover factor (b = 1).

Woven textile structure 30 Different r values and b = 2 25 r = 1.52

r = 1.44 r = 1.14

K2

20

15

r = 0.91

10

5

5

10

15

20 K1

25

30

35

3.14 Effect of fiber density on the relation between warp and weft cover factor (b = 2).

25 Cotton and rayon for b = 0.5

20

Rayon K2

44

15

Cotton 10

5

5

10

15

K1

20

25

30

3.15 Effect of yarn packing factor on the relation between warp and weft cover factor (b = 0.5).

Using a geometric model to predict woven fabric properties

45

30 Cotton and rayon for b = 1 Cotton

K2

25

20 Rayon

15

10 10

15

20

K1

25

30

35

3.16 Effect of yarn packing factor on the relation between warp and weft cover factor (b = 1).

30 Cotton and rayon for b = 2

25

Rayon

Cotton

K2

20

15

10

5

5

10

15

20 K1

25

30

35

3.17 Effect of yarn packing factor on the relation between warp and weft cover factor (b = 2).

46

Woven textile structure

3.3.4 Effect of variation in beta (d2/d1) on the relation between warp and weft cover factor for jammed fabrics An increase in the value of b from 0.5 to 2 increases the range of warp cover factors but raises the level for the weft cover factor. This means with an increase in b higher weft cover factors are achievable and vice versa. However, it may be noted that for cotton fibers having higher fiber density the sensitivity range between the warp and weft cover factor is relatively large compared with polypropylene fiber as shown in Figs 3.18 and 3.19. This shows a very important role played by fiber density in deciding warp and weft cover factors for the jammed fabrics.

3.3.5 Equation for jammed structure for circular crosssection in terms of weave factor Weave factor is useful in translating the effect of weave on the fabric properties. This was discussed in Section 1.4.2. For circular cross-section the general equation for jammed cloth is desired. Thread spacing Pt1 for a non-plain weave per repeat is shown in Fig. 3.20 and is given as: Pt1 = I2p1 + (E1 – I2)d1

3.6

30

25

20 b=2 K2



b = 1.5 15

b=1

10

5

b = 0.5

5

10

15

20 K1

25

30

35

3.18 Effect of b on the relation between warp and weft cover factor: cotton.

Using a geometric model to predict woven fabric properties

47

30

25

K2

20

15

b=2 b = 1.5 b=1

10

b = 0.5 5

5

10

15

20 K1

25

30

35

3.19 Effect of b on the relation between warp and weft cover factor: polypropylene.



p 1

(E1 – l2) d2

p1

Pt1

3.20 Jammed structure for 1/3 weave (circular cross-section along warp).

The average thread spacing is:

P1 =

I 2 p2 + (E1 – I 2 )d1 E1

E1P1 ˆ ÊE = p1 + Á 1 – 1˜ d1 ¯ Ë I2 I2

48

Woven textile structure



M 1P1 = p1 + (M 1 – 1) d1



p1 P d = M 1 1 – (M 1 – 1) 1 D D D



p1 P (M – 1) = M1 1 – 1 D D 1+b

3.7

where b = d2/d1. Similarly, interchanging suffixes 1 and 2 we get

p2 P d = M 2 2 – (M 2 – 1) 2 D D D



p2 b P = M 2 2 – (M 2 – 1) D 1+b D

3.8

For a jammed fabric the following equations are valid: 2



2

Êp ˆ Êp ˆ 1 – Á 1˜ + 1 – Á 2 ˜ = 1 Ë D¯ Ë D¯ 2



2

Ê Ê P (M – 1)ˆ P (M 2 – 1)bˆ 1 – Á M1 1 – 1 =1 + 1 – ÁM2 2 – 1 + b ˜¯ D 1 + b ˜¯ D Ë Ë

These equations can easily be transformed in terms of warp and weft cover factor (K1 and K2): ÈÊ 28.02 frf M 1 ˘ ˆ 1 – ÍÁ – (M 1 – 1)˜ 1 ˙ K1 ¯ 1 + b ˚˙ ÍÎË

2

2



ÈÊ 28.02 frf M 2 ˆ b ˘ + 1 – ÍÁ – (M 2 – 1)˜ ˙ =1 K2 ¯ 1 + b ˙˚ ÍÎË

3.9

The effect of weave in the jammed structures is examined using the above equations for plain, twill, basket and satin weave. M, the weave factor value (average float length) for these weaves is 1, 1.5, 2 and 2.5 respectively for all the discussion which follows. Figure 3.21 shows the relation between p1avg/D and p2avg/D. It can be seen that with the increase in float length, the sensitivity of the curve decreases in general. Also the range of p1/D and p2/D values reduces. This means a weave with longer float length decreases the flexibility for making structures. Figure 3.22 shows the relationship between the warp and weft cover factors for circular cross-section. It is interesting to note that the behavior is

Using a geometric model to predict woven fabric properties

Plain

1.0

1/2 Twill

0.8

P2 avg/D

49

2/2 Basket 1/4 Satin

0.6

0.4

0.2

0

0

0.2

0.4

0.6 p1 avg/D

0.8

1

3.21 Relation between average thread spacing in warp and weft for jammed fabric (circular cross-section).

30

Weft cover factor (K2)

25 20

Satin Basket Twill

15

Plain

10 5 0

0

5

10

15 20 25 Warp cover factor (K1)

30

35

40

3.22 Relation between warp and weft cover factor for jammed fabric (circular cross-section).

similar for different weaves. However, with the increase in float, the curve shifts towards higher values of weft cover factor. It should be borne in mind that the behavior shown in this figure is for virtual fabrics. In real fabrics a jammed structure is unlikely to retain a circular cross-section.

50

Woven textile structure

3.3.6 Equation for jammed structure for racetrack crosssection in terms of weave factor In jammed fabrics, the yarn cross-section cannot remain circular; it must change. It is easy to modify the geometry for circular cross-section by considering the racetrack cross-section. Figure 3.23 shows the configuration of jammed structure for 1/3 weave for racetrack cross-section along weft direction of the fabric. Here:

Ê a – b1ˆ A=Á 1 Ë 2 ˜¯

Thread spacing Pt1 for a non-plain weave per repeat is given as:

Ê a – b1ˆ Pt1 = I 2 p1 + (E1 – I 2 ) a1 + 4 Á 1 Ë 2 ˜¯

3.10



Similarly

Ê a – b2 ˆ Pt 2 = I1 p2 + (E2 – I1) a2 + 4 Á 2 Ë 2 ˜¯

3.11



where p1 and p2 are horizontal spacing between the semicircular threads in the intersection zone. Here, a and b are the major and minor diameters of racetrack cross-section. Average thread spacing P1 = Similarly,

P2 =

p1 Ê ˆ + 1 – 4 ˜ a1 + 4 M 1 ÁË M 1¯ M1I 2

Ê a1– b1ˆ ÁË 2 ˜¯

p2 Ê Êa – b ˆ ˆ + 1 – 1 ˜ a2 + 4 Á 2 2 ˜ M 2 ÁË M 2¯ M 2 I1 Ë 2 ¯

3.12

3.13

Such analysis of circular thread geometry can be applied for the intersection zone of the racetrack cross-section.

A

p 1

A

(E1 – l2) a1

A

p 1

A

Pt1

3.23 Jammed structure for 1/3 weave (racetrack cross-section along warp).

Using a geometric model to predict woven fabric properties



Êa – b ˆ L1 = 4 Á 2 2 ˜ + (E2 – I1)a2 + I1 ¥ l1 Ë 2 ¯

51

3.14

Total warp crimp in the fabric is given by:

C1 =

L1 –1 Pt 2

p1 and p2 can be calculated from the jamming considerations of the circular thread geometry using: 2



2

Êp ˆ Êp ˆ 1 – Á 1˜ + 1 – Á 2 ˜ = 1 Ë B¯ Ë B¯

It should be remembered that p/B corresponds to the semicircular region of the racetrack cross-section and is similar to p/D for the circular cross-section. As such the values of p/D ratio from Fig. 3.1 can be used for p/B: Ê P 1 – Á M1 1 – 4 B BI 2 Ë

a1ˆ Ê a1 – b1ˆ ÁË 2 ˜¯ – (M 1 – 1) B ˜ ¯

2

2



Ê a ˆ P Ê a – b2 ˆ + 1 – ÁM2 2 – 4 Á 2 – (M 2 – 1) 2 ˜ = 1 B¯ B BI1 Ë 2 ˜¯ Ë

This equation can be simplified to the following usable forms: Ê P 2(1 – e) (M – 1)ˆ 1 – Á M1 1 – – 1 B e(1 + b )I 2 e(1 + b )˜¯ Ë

2

2



2(1 – e)b (M 2 – 1)ˆ Ê P – + 1 – ÁM2 2 – =1 (1 + b )I1 e(1 + b ) ˜¯ B e Ë

It is assumed that e1 = e2 = e where e=b/a. The above equation can easily be transformed in terms of warp and weft cover factors: Ê 28.02 frf M 1 1–Á 1+ 4 b K p (1 + ) 1 Ë

Ê 1 ˆ 2(1 – e) (M 1 – 1)ˆ ÁË e – 1˜¯ – e(1 + b )I – e(1 + b )˜ ¯

Ê 28.02 frf M 2 b 1+ 4 + 1–Á p Ë (1 + b )K 2

2

2

3.15 Ê 1 ˆ 2(1 – e)b (M 2 – 1)bˆ ÁË e – 1˜¯ – e(1 + b )I – e(1 + b ) ˜ = 1 ¯

52

Woven textile structure

3.3.7 Relationship between fabric parameters in racetrack cross-section The relationship between fabric parameters such as p2 and p1, p1 and c2 for the racetrack cross-section in jammed condition is discussed below. Figure 3.24 shows the behavior between these pair of parameters is similar to that for the circular cross-section but it shifts towards higher values of thread spacing. This figure shows the behavior of real fabrics. Figure 3.25 shows the relationship between warp and weft cover factors for different weaves. As discussed above in real fabrics the weaves show distinct differences between them unlike in circular cross-section. An increase in float length decreases the scope of cover factors. From these equations crimp and fabric cover can be evaluated using the above two equations along with: 3.16

1.5 Plain

Twill 1.0

Basket Satin

P2 avg/B



È b Ê1 ˆ ˘ d 2 = b 2 Íp + Á – 1˜ ˙ and 2 = b 4 e b1 ¯˚ Ë Î

0.5

0

0

0.5

1

1.5

P1 avg/B

3.24 Relation between average thread spacing in warp and weft for jammed fabric (racetrack cross-section, b =1).

Using a geometric model to predict woven fabric properties

53

45 40

Weft cover factor (K2)

35 30 25 20 Satin Basket Twill Plain

15 10 5 0

0

5

10 15 20 Warp cover factor (K1)

25

3.25 Relation between warp and weft cover factor for jammed fabric (racetrack cross-section).

3.4

Predicting cover in different woven structures

3.4.1 Square cloth A truly square fabric has equal diameter, spacing and crimp: p1 = p2, c1 = c2, d1 = d2, h1 = h2 = D/2, q1 = q2. From the basic equations of the geometrical model from the previous chapter we have:



2 Èp ˘ Ê pˆ tanq /2 = 2 Í – Á ˜ – 0.75˙ 3 ÍD Ë D¯ ˙ Î ˚

3.17

This is valid for all values of (p/D)2 ≥ 0.75 or p/D ≥ 0.866: p/d ≥ 1.732; d/p ≤ 0.5773. Also

D = 2d = h1 + h2 = 2×(4/3)p√c



Tex c = 3 d = 0.75 ¥ 4 p p 280.2 frf 2



Ê 0.026 77K ˆ c=Á ˜ frf ¯ Ë

3.18

54

Woven textile structure

The crimp in percentage can be calculated from %c = (K/3.57)2. For jammed square cloth

cos q1 + cos q2 = 1

will give cosq = 1/2 and q = 60°, p = 2d sinq, l = Dq = 2d(f/3).

f \l =2 d 3



p = d



crimp = 1/d – 1 = 0.2092 = 20.9% p /d

3 = 1.732

Therefore complete cover is not possible with square cloth.

3.4.2 Similar cloth Cloths can be made from same fibers which may differ in respect of yarn count, ratio of yarn count in warp and weft, ratio of yarn spacing, average yarn spacing and weave. Such cloths can be compared in terms of fabric cover. It is possible to consider cloth which differ in many ways as being similar if they possess the same fractional covering power. When comparing cloths for cover such comparisons are only perfectly justifiable for cloths differing in yarn count and average yarn spacing. It will not be correct to say cloths which have equal cover are equally acceptable, equally difficult to make and equally tight. Cloths which differ in the ratio of spacing or weave cannot be made similar by fabric cover concept. Some examples for change of weave, yarn count, threads per cm and fabric mass for square constructions are shown below for similar fabrics that have the same firmness. The mathematical logic for these variables and some examples are given below: Effect of change in weave on thread density Ê threadsˆ ÁË cm ˜¯ New

Ê M ˆ ÁË M + 1˜¯ Ê threadsˆ New ¥ =Á ˜ Ë cm ¯ Old Ê M ˆ ÁË M + 1˜¯ Old

Using a geometric model to predict woven fabric properties

55

Effect of change in weave on yarn count



d µ 1 fid= k N N

where k is a constant for proportionality





Ê N Old ˆ Ê M ˆ fi (threads per cm)Old = Á ˜ Á Ë M + 1¯ Old Ë k ˜¯ Ê N New ˆ Ê M ˆ fi (threads per cm)Old = Á Ë M + 1˜¯ New ËÁ k ˜¯ N New N Old



Ê M ˆ ÁË M + 1˜¯ Old = Ê M ˆ ÁË M + 1˜¯ New

Effect of change in thread density on yarn count



Ê N Old ˆ fi Threads/cm = W ¥ Á ˜ Ë k ¯ \

N New TNew = N Old TOld

Effect of change in fabric mass on thread density and yarn count Changing the fabric mass per unit area (gsm) while maintaining the same firmness can be achieved by using fewer and coarser threads if the fabric is to be heavier, and increasing the number of fine threads if the fabric is to be lighter. fi



[fabric mass]Old Ê N New ˆ = [fabric mass]New ËÁ N Old ˜¯

[threads/cm]New [fabric mass]Old = [threads/cm]Old [fabric mass]New

56

Woven textile structure

Some examples 1. 3/3 twill with 48 ends per cm is to be changed to 3-end twill. How many threads per cm are required in the new weave to give the same firmness as old weave?

MOld = 6/2 = 3



MNew = 3/2 = 1.5



(threads per cm)New = 48

(1.5/2.5) (3/4)

= 38.4

2. A 4-end twill cloth is required with the same number of threads per cm as a plain cloth woven with 36 yarns. Find the count of the yarn to be used to give a twill cloth with the same firmness as the plain cloth.

N New 1/3 = N Old 2/3



N New = 1 ¥ 3 2¥2



N Old = 3 4

36 = 4.5

NNew = (4.5)2 = 20.25.

3. If a given cloth is woven with 28 threads of 64S yarn per cm. It is desired to keep the same weave but to have only 25 threads per cm. What counts must be used?

N New = 25 28

64 = 7.143

NNew = 51S

4. We wish to make a cloth from 64S yarn to be of the same firmness as one with 28 threads per cm of 36S yarn. How many threads per cm will be required? N \ 64 = New 36 28

TNew = 28 64 = 37.3 36

5. A fabric contains 32 threads per cm of 52S yarn in both warp and weft. If gsm = 100, what count and threads per cm will be required to increase the gsm to 125?

N New 100 = 52 125

Using a geometric model to predict woven fabric properties



\ N New = 100 125



NNew = 33.28

52 = 5.7688

(threads per cm)New = (threads per cm)Old ¥ = 100 ¥ 32 = 25.6 125



3.5

57

(fabric mass)Old (fabric mass)New

Calculating fabric properties: numerical examples

Q1. A fabric has the following particulars: ends per cm = 20, warp and weft count = 20 tex, percent warp and weft crimp = 10/5. (i) What is the maximum number of picks which can be inserted in this fabric? (ii) Calculate the fabric cover. (iii) Compare its value if flattening is assumed (racetrack cross-section) and a/b = 1.3. Assumef = 0.65, rf = 1.52g/cm3. Solution: (i)



p1 = 1 = 0.05 cm 20 d1 = d2 =

20 = 0.016 05 cm 226 1.52

D = 0.0321 cm

For calculation of maximum picks per cm the options are: (a) warp should be jammed, that is

p2 = D sin

l1 D

cannot solve it as l1 is unknown. (b) fabric jamming condition gives 2



2

Êp ˆ Êp ˆ 1 – Á 1˜ + 1 – Á 2 ˜ = 1 Ë D¯ Ë D¯

This cannot solve it as

p1 0.066 67 = = 2.08 > 1 D 0.0321

58

Woven textile structure

(c) obtain h1 from h1+ h2 = D and then calculate p2

h2 = 4 p1 c2 = 0.014 91cm 3



h1 = D – h2 = 0.0321 – 0.01491 = 0.0172 cm



p2 =

3h1 = 3 ¥ 0.0172 = 0.040 78 cm 4 c1 4 0.1

picks per cm = 24.5 ª 25

(ii) Fabric cover factor:

warp cover factor, K1 = 10 –1 ends cm weft cover factor, K 2 = 10 –1

picks cm

Tex = 20 ¥ 20 = 8.94 10 Tex = 25 ¥ 200 = 11.18 10

K1K 2 28 = 8.94 + 11.18 – 8.94 ¥ 11.18 = 16.55 28

fabric cover factor, K1 + K 2 –

(iii) For racetrack cross-section:

p ¥ d 2 = p b 2 + b(a – b ) = p b 2 + b 2 ¥ 0.3 4 4 4



p d2 p (0.016 05)2 4 b = =4 = 0.3 p + 0.3 p + 0.3 4 4



\ b = 0.5477



\ a = 1.36 = 0.7121

2

Fabric cover factor:



0.7121 ¥ 0.7121 aa 0.040 78 a + a – p1 p1 = 0.7121 + 0.7121 – 0.05 = 22.8 p1 p2 28 0.05 0.040 78 28

Q2. A woven fabric is made from 45 tex cotton yarn (fiber density 1.54 g/ cm3) in warp and weft. The ends and picks per cm are 20 and 24 and the crimp is 7 and 12% respectively. Calculate fabric thickness. Assume yarn flattening takes place and cross-section is racetrack; for a/b =

Using a geometric model to predict woven fabric properties

59

1.3, calculate major and minor diameter of the yarn in the fabric and maximum picks possible. Assumef = 0.65, rf = 1.52 g/cm3. Solution:

d1 =

Tex = 45/1.54 = 0.020 76 cm 226 226 fiber density



D = 0.04815 cm



p1 = 0.05 cm, p2 = 0.04167 cm



h1 = 4 p2 c1 = 0.0147 cm 3 h2 = 4 p1 c2 = 0.0231cm 3



h1 + d1 = 0.0386 cm, h2 + d2 = 0.0470 cm



fabric thickness = 0.023 09 + 0.020 76 = 0.043 85 cm



p ¥ d 2 = p b 2 + b(a – b ) = p d 2 + b 2 ¥ 0.3b 2 4 4 4 p ¥ d2 0.785 ¥ (0.020 76)2 fi b2 = 4 = p + 0.3 1.085 4



fi b = 0.017 66 cm



fi a =1.3 b = 0.022 96 cm

For maximum possible picks B 2 – h12 + (a – b )



p2 =



B = 2b ¥ 0.017 66 = 0.035 32



p2 = (0.035 32)2 – (0.0147)2 + (0.022 96 – 0.017 66))



= 0.037 41 cm



fi picks per cm = 26.7 ≈ 27

Q3. Calculate the crimp in a square fabric if thread spacing is equal to the yarn diameter. (no jamming). What will be the crimp if d1 = 2d1 and thread spacing is same in both warp and weft and the fabric is jammed Solution:

d1 = d2 = p1 = p2

60



Woven textile structure

4 p c ¥ 2 = D = 2d 3 c = 3d = 0.75 fi c = 0.5625 ª 56.25% 4p

If d1 = 2d2, p1 = p2 and the fabric is jammed.

D = d1 + d2 = 2d2 + d2 = 3d2 = d1 +



d1 3d1 = 2 2

4 p c ¥ 2 = D = 3d 2 3 2



Ê pˆ 2 1–Á ˜ =1 Ë D¯ 2



Ê pˆ ÁË D˜¯ = 0.75



p = sinq = sin l D D



\ l = 1.04715 ª 1.05 D



Crimp = l – 1 = 1/D – 1 = 1.05 – 1 = 21.3% p p /D 0.866

Q4. Calculate the maximum cover factor for the square fabric. (i) How many ends per cm should be employed to produce 40% warp cover using 25 tex yarn? (ii) Calculate the threads per cm in a fabric if the yarn count is 16 tex (cotton). Assume f = 0.65, rf = 1.52 g/cm3 and if weave is plain, 2/4 twill and 1/4 satin. Compare this value with that of a square jammed structure using Peirce geometry. Solution: Maximum cover for square fabric is obtained when the fabric is jammed: 2

gives

Ê pˆ 2 1–Á ˜ =1 Ë D¯

Using a geometric model to predict woven fabric properties



p = 2(0.866) = 1.732 D



\ d = 0.5774 p



0.5774 =

E Tex ¥ 10 –1 22.6 fiber density



For cotton K = 16.088 = 16.1.



maximum fabric cover factor for square construction



= 16.1 + 16.1 – 16.1 ¥ 16.1 28



= 22.99 ª 23

(i) d = 0.017 94 cm for 40% warp cover, i.e.:

d = 0.4 = E Tex ¥ 10 –1 = 5E p 226 fiber density 226 1.52



fi ends per cm = 22.29 ª 22



fi p1 = 0.044 85 cm

(ii) d = 0.014 35 cm For square jammed fabric: 2



Ê pˆ 2¥ 1–Á ˜ =1 Ë D¯ \ p = 0.75 ¥ D = 0.75 ¥ 0.02871 = 0.0249 cm

threads per cm = 40.2 ª 40 Weave value for:

1/1 plain weave = 1/2



2/4 twill weave = 3/4



1/4 satin weave = 2.5/3.5 Ê 40.2(3/4)ˆ = 60.3 ª 60 threads per cm for 2/4 twill = Á Ë 1/2 ˜¯



Ê 400.2(2.5/3.5)ˆ threads per cm for 1/4 satin = Á ˜¯ = 57.4 ª 57 Ë 1/2

61

62

Woven textile structure

Q5. A fabric is made from 38 tex yarn (fiber density 1.54 g/cm3) and ends and picks per cm are 30 and 25. Assume f = 0.65, rf = 1.52 g/cm3. Calculate the crimp in warp and weft, if the warp is jammed and the fabric thickness. Solution:

d=

Tex = 38 = 0.02198 cm 226 rf 226 1.54



D = 0.043 96 cm



p2 l = sin 1 D D



0.04 = sin l1 0.043 96 D



\

l1 = 1.1431 D

\ c1 =

l1 /D –1 p2 /D

Ê 1.1431ˆ =Á – 1 = 0.2563 = 25.63% Ë 0.9099˜¯



h1 = 4 p2 c1 = 4 ¥ 0.04 0.2563 = 0.027 cm 3 3



h2 = D – h1 = 0.043 96 – 0.027 = 0.017 cm



0.017 = 4 p1 c2 3



\ c2 = 3 ¥ 0.017 = 0.3829 4 0.0333



c2 = 0.1466 = 14.66%



fabric thickness = h1 + d = 0.027 + 0.021 98 = 0.049 cm

Q6. A cotton cloth is made from 20 tex warp and 40 tex weft yarn. On the weaving machine there are 28 ends per cm. Calculate the maximum picks per cm for racetrack cross-section. Assume fibre density = 1.5 g/ cm3, a/b = 1.3, f = 0.65. Solution:

p1 = 1 = 0.035 71cm 28

Using a geometric model to predict woven fabric properties

63

For racetrack cross-section:

ab – 0.215b 2 =

Ty 10 5frf

For warp: and

1.3b12 – 0.215b12 =

20 10 5 ¥ 0.65 ¥ 1.5

b1 = 0.013 75 cm a1 = 1.3 b1 = 0.017 87 cm

For weft:

1.3b22 – 0.215b22 =

40 10 5 ¥ 0.65 ¥ 1.5

b1 = 0.019 45, a2 = 1.3, b2 = 0.025 29 cm p1 = 1 = 0.035 71cm 28



p1¢ = p1 – (a1 – b1) = 0.035 71 – (0.017 87 – 0.013 75) = 0.031 59



B = b1 + b2 = 0.013 75 + 0.019 45 = 0.0332 cm 2

2

Ê p ¢ˆ Ê p ¢ˆ 1–Á 1˜ + 1–Á 2˜ =1 Ë B¯ Ë B¯



2

2

Ê p ¢ˆ Ê 0.031 59ˆ 1–Á + 1–Á 2˜ =1 Ë B¯ Ë 0.0332 ˜¯



fi p2¢ = 0.023 95



p2 = p2¢ + (a2 – b2) = 0.029 79



maximum picks per cm = 33.6 ≈ 34

Q7. A cloth is made with warp and weft cover factor = 11/9, c2 = 13%, d1 = 0.015 24 cm, (T2/T1)1/2 = 0.82. Fabric cover = (threads per inch)/ N1/2. Calculate fabric thickness, fabric maximum gsm and fabric specific volume cm3/g. Is this fabric jammed in warp and weft direction? Assumef = 0.65, rf = 1.52 g/cm3. Solution:

d1 = 0.015 24 cm



d1 a √warp tex

64

Woven textile structure

T2 d2 = = 0.82 T1 d1



fi d2 = 0.82 ¥ 0.015 24 = 0.0124 97 cm



D = d1 + d2 = 0.027 74 cm

Using the definition of yarn tex, we get

T1 = p ¥ (0.015 25)2 ¥ 10 5 ¥ 0.65 ¥ 1.52 = 18.05 4



T2 = 0.6724 ¥ T1 = 12.14



warp cover, K1 = 10 –1 ends cm



K ¥ 10 11 ¥ 10 fi ends = 1 = = 25.89 ª 26 cm Tex 18.05



p1 = 0.0386 cm



picks K 2 ¥ 10 9 ¥ 10 = = = 25.8 ª 26 cm Tex 12.14



p2 = 0.0387 cm



h2 = 4 p1 c2 = 4 ¥ 0.0386 ¥ 3 3



D = 0.027 74 cm



h1 = D – h2 = 0.0092 cm



hˆ Ê c1 = Á 3 ¥ 1 ˜ = 0.031 65 = 3.2% Ë 4 p2 ¯



fabric thickness = h2 + d2 = 0.018 56 + 0.0125 = 0.031 06 cm



fabric gsm = (18.05 ¥ 26 ¥ 1.032 ¥ 12.14 ¥ 26 ¥ 1.13) ¥ 10–1



= 84 g/cm2 = 0.0084



fabric specific volume = thickness/mass

Tex

0.13 = 0.018 56 cm

2



= 0.03106/0.0084 = 3.7 cm3/g

l1 p2 = (1 + c1) = 0.0387 (1.032) = 1.444 < p 0.027 74 2 D D

Using a geometric model to predict woven fabric properties

65

This condition shows whether the fabric has a tendency to jam, but not whether it is jammed now, so the following logic is applied:

p2 ¢ Êl ˆ > sin Á 1 ˜ Ë D¯ D

for jamming p2/D = sin(l1/D) so the warp is not jammed.

l2 p1 = (1 + c2 ) = 1.572 > p /2 D D p1 Êl ˆ > sin Á 2 ˜ Ë D¯ D

so the weft is not jammed. Q8. A plain weave cotton duck cloth is woven from 125 tex yarn in warp and weft. The ends and picks per cm are 10.6 and 11.8. Assume f 0.65, rf = 1.52 g/cm3. Is the fabric jammed? Find warp, weft and fabric cover factor. Solution:

p1 = 0.0943 cm



p2 = 0.084 75 cm d=

1 T = 1 280.2 frf 280.2

125 = 0.0405 cm 0.65 ¥ 1.52



D = d1 + d2 = 2d = 0.0803 cm



p1 p = 1.175 and 2 = 1.0554 D D 2

2

Ê p1ˆ Ê p2 ˆ ÁË D ˜¯ = 1.38 and ÁË D ˜¯ = 1.114

The fabric is not jammed since for jammed fabric: 2

2

Êp ˆ Êp ˆ 1 – Á 1˜ + 1 – Á 2 ˜ = 1 Ë D¯ Ë D¯

and both (p1/D)2 and (p2/D)2 are greater than 1; also for jamming p/D = sinq and sinq ≤ 1: warp cover factor = end/cm Tex ¥ 10 –1

= 10.6 125 ¥ 10 –1 = 11.85

66

Woven textile structure

weft cover factor = picks/cm Tex ¥ 10 –1 = 11.8 125 ¥ 10 –1 = 13.19



cloth cover factor = 11.85 + 13.19 – 11.85 ¥ 13.19 = 19.46 28

Q9. A plain weave cotton shirting fabric is made from polyester cotton yarn (67 : 33). The warp cover factor and tex are 14 and 12 respectively. Find the weft cover factor and maximum picks per cm if 12 tex yarn is used in the weft. Polyester and cotton fiber densities are 1.38 and 1.52 g/ cm2. Assume a yarn packing factor of 0 : 60. Find also the cloth cover factor and ends per cm. Solution:

rf blended fiber density =

1 = 1.4233 g/cm 2 0.67 + 0.33 1.38 1.52

density of warp yarn = frf = 0.6 ¥ 1.4233 = 0.854 g/cm 3 1 12/0.854 280.2 = 0.013378g/cm 3

diameter of warp yarn = d1 =

warp cover factor K1 = E1 T1 ¥ 10 –1 = = 25.89

For



d1 ¥ 28.02 frf p1

d1 p1

d = 1, K1max = K2max = 25.89: p

b=

d2 =1 d1

For maximum picks per cm, use the fabric jammed condition:





2

2

2

2

Êp ˆ Êp ˆ 1 – Á 1˜ + 1 – Á 2 ˜ = 1 Ë D¯ Ë D¯ Êp ˆ Êp ˆ 1 – Á 1˜ + 1 – Á 2˜ = 1 d 2 Ë ¯ Ë 2d¯

Using a geometric model to predict woven fabric properties 2

2

2

2

2

2

67

ˆ Ê ˆ Ê 1 – Á 25.89˜ + 1 – Á 25.89˜ = 1 Ë 2K 2 ¯ Ë 2K1 ¯



ˆ Ê ˆ Ê 1 – Á12.95˜ + 1 – Á12.95˜ = 1 Ë 2K 2 ¯ Ë K1 ¯



Ê12.95ˆ ˆ Ê 1–Á + 1 – Á12.95˜ = 1 ˜ Ë K 14 ¯ Ë 2 ¯



2

ˆ Ê 1 – Á12.95˜ = 0.620 03 Ë K2 ¯



K2 = 16.506



K2 16.506 \ picks per cm = 1 = = = 47.66 p2 25.89 d2 25.89 ¥ 0.013 378



p2 = 0.021 cm



cloth cover factor = K1 + K1 = 14 + 16.506 – 14 ¥ 16.506 = 21.58 25.89

Q10. A plain weave cotton shirting fabric is made from 12 tex polyester– cotton yarn (50 : 50). If ends and picks per cm are 30, calculate the crimp, gsm, fabric thickness, fabric specific volume and fabric cover factor. Assume polyester and cotton fiber densities = 1.38 and 1.52 g/cm3 and yarn packing coefficient = 0.60. Solution:

rf blended fibre density =

1 = 1.4466 g/cm 3 0.5 + 0.5 1.38 1.52

density of blended yarn = frf = 0.6 ¥ 1.4466 = 0.868 g/cm3 diameter of polyester cotton yarn =



D = d1 + d2 = 0.026 54,



p1 = p2 = 1 = 0.03333 cm 30



D = h1 + h2



4 [2p c ] = D 3

1 280.2

12 = 0.012 327 cm 0.8868

68

Woven textile structure

3 ¥ 0.026 54 c = 3D = = 0.2986 8p 8 ¥ 0.033 33



c = 0.0892



% crimp = 8.92



fabric mass, gsm = 2 [12 ¥ 30(1.0892)] = 78.4 10



fabric thickness = h + d = 4 p c + d = 0.046 38 + 0.013 27 3 = 0.059 65 cm



fabric specific volume cm 3 /g = fabric thickness 2 fabric mass g/cm 0.059 65 = = 7.61 78.4 ¥ 10 –4 fabric packing factor =



fiber specific volume 0.69127 = = 0.091 fibber specific volume 7.61

fiber = 9.1% and air = 90.9% warp cover factor = 10 –1E1 T1 = d 280.2 frf p



= 28.02 0.868 = 26.11 = 10.39 ª 10.4 fabric cover factor = 10.4 + 10.4 – 10.4 ¥ 10.4 = 16.66 ª 16.7 26.11

Q11. A fabric has the following particulars: ends per cm = 15, picks per cm = 20, warp and weft count = 20 tex, percentage warp and weft crimp = 5/10, f = 0.5 and rf = 1.52 g/cm3. (i) What is the maximum number of picks which can be inserted in this fabric. (ii) Calculate the fabric cover and compare its value if (racetrack) flattening is assumed and a/b = 1.3. solution: (i)

p1 = 1 = 0.066 67 cm 15



p2 = 1 = 0.05 cm 20

Using a geometric model to predict woven fabric properties



d1 = d2 = d = 1 20 = 0.016 05 cm 226 1.52



l1 = p2(1 + c1) = 0.05 ¥ 1.05 = 0.0525 cm



l2 = p1(1 + c2) = 0.0667 ¥ 1.1 = 0.0734 cm

69

When warp is jammed

q1¢ =

l1 0.0525 = = 1.636 D 0.0321



p2¢ = D sin q1¢ = D sin 1.636 = 0.032 03 cm



maximum picks per cm = 31.2 ª 31

(ii)

Fabric cover = d = threads/cm p 280.2 K1 = 28.02 0.65 ¥ 1.52 ¥ K 2 = 28.02 ¥ 0.994 ¥

K Tex = frf 28.02 frf

0.016 05 d1 = 28.02 ¥ 0.994 ¥ = 6.71 0.066 67 p1

0.016 05 d2 = 28.02 ¥ 0.994 ¥ = 13.96 0.032 03 p2



Kc = cloth cover factor = K1 + K2 – K1K2/28



= 6.71 + 13.96 – 13.96 ¥ 8.94 = 17.32 28

For racetrack cross-section:

p d 2 = p b 2 + b(a – b ) 4 4



È Ê1 ˆ ˘ d 2 = b 2 Íp + Á – 1˜ ˙ 4 Ëe ¯˚ Î



d 2 = b 2 Èp + (e – 1)˘ ˙˚ ÍÎ 4



d 2 = b 2 Èp + 0.3˘ ˚˙ ÎÍ 4 b=



d

p + 0.3 4

=

0.016 05 = 0.015 41cm 1.0654

70

Woven textile structure



a = 1.3 ¥ b = 0.02 cm

Fabric cover factor after flattening:

K1 = 28.02 ¥ 0.994 ¥

0.02 = 8.36 0.066 67

K 2 = 28.02 ¥ 0.994 ¥

0.02 = 17.39 0.032 03



Kc = K1 + K2 – K1K2/28



= 8.36 + 17.39 – 8.36 ¥ 17.39 20.56 28

3.6

Application: calculating tightness values

It is easy to consider cloths which differ in many ways as being similar if they possess the same fractional covering power. In comparing cloth for cover only, such comparisons are justifiable, but it will not be correct to say cloths which have same cover are equally acceptable, equally difficult to make and equally tight. The total fabric cover factor when jamming occurs varies with the ratio of thread spacing and weave. The ratio of actual fabric cover to maximum fabric cover factor is a measure of tightness, relative acceptability. This concept has been used by several researchers using weave value. Recent research efforts have been directed towards establishing a standard or a reference fabric which can be objectively compared. The reference fabric is normally of maximum construction. The comparison is expressed in terms of a ratio of a construction parameter of a given fabric to that of the standard fabric. This ratio is called firmness or tightness. The physical, mechanical, aesthetic part of the fabric can be related to its degree of tightness. This is a rational basis for constructing fabrics with predetermined end-use performance. Russell [11] suggested the tightness factor to be the ratio of threads per cm to the maximum threads per cm in a fabric. This ratio can be obtained for the warp and weft directions of the fabric. For a fabric it is given as:

Cf =

t1 + t 2 t1max + t 2max

C1 =

t1 t1max

C2 =

t2

t 2max

Using a geometric model to predict woven fabric properties

71

This concept can be used to compare tightness values of fabric for different weave with a standard fabric. The modified equation considering weave will be as given below. For circular cross-section the total thread spacing is given as:

Pt = I ¥ p + (E – I)d

The maximum threads will be given by: t max =



E I ¥ p + (E – I )d

=

M p + (M – 1)d

=

M (M – 1)d + D sinq



3.19

This is a general equation for tmax for any crimp (q). However, the maximum threads in a fabric are possible when cross-threads are straight. In such a situation the intersecting yarn will have maximum crimp and weave angle is 90º. In this case:

t max =

M (M – 1)d + D

3.20

For a standard fabric one can assume maximum cover in the fabric and corresponding maximum possible ends and picks per cm. In this case, as mentioned before, cross-threads must be straight and maximum bending will be done by the interlacing yarn. The maximum possible threads in the two directions will be different. If weft yarn remains straight, q1 = 90°. The maximum picks per cm from equation 3.20 will be:

t 2max =

M2 (M 2 – 1)d2 + D

3.21

and the maximum ends per cm will be for q2 = 0°:

t1max =

M1 (M 1 – 1)d1

3.22

However, these equations are valid for M > 1. It will be fair to use these equations rather than equation 3.20 for both warp and weft directions. For the racetrack cross-section:

Pt = I ¥ p + 2(a – b) + (E – I)a

The maximum threads will be given by:

72

Woven textile structure

t max =

E = I ¥ p + 2(a – b ) + (E – I )a

=

M 2(a – b ) + (M – 1)a B sinq + I



M 2(a – b ) + (M – 1)a p+ I 3.23

As discussed above, for maximum threads the weave angle is 90º, so: t max =

M 2(a – b ) B+ + (M – 1)a I

3.24

Similarly for a standard fabric the relevant equations will be: t 2max = t1max =

M2 2(a2 – b2 ) B+ + (M 2 – 1)a2 I2

3.25

M1 2(a1 – b1) + (M 1 – 1)a1 I1

3.26

These are equations which a designer can use to construct fabrics with different textures and tightness by varying the yarn and fabric parameters.

3.7

References

1. Love L (1954), Graphical relationships in cloth geometry for plain, twill, and sateen weaves, Text. Res. J., 24(12), 1073–1083. 2. Weiner L I (1971), Textile Fabric Design Tables, Technomic, Stamford, CTA. 3. Nirwan S and Sachdev S (2001), B. Tech. Thesis, I.I.T. Delhi 4. Peirce F T (1937), The geometry of cloth structure, Text. Inst., 28(3). 5. Newton A (1995), The comparison of woven fabrics by reference to their tightness, J. Text. Inst., 86, 232–240. 6. Newton A (1991), Tightness comparison of woven fabrics, Indian Text. Journal, 101, 38–40. 7. Seyam A M (2003), The structural design of woven fabrics: theory and practice, Textile Progress, 31(3). 8. Singhal G and Choudhury K (2008), B. Tech. Thesis, I.I.T. Delhi. 9. Hearle J W S, Grosberg P and Backer S (1969) Structural Mechanics of Fibers, Yarns and Fabrics, Wiley Interscience, New York. 10. Dickson J B (1954), Practical loom experience on weavability limits, Text. Res. J., 24(12), 1083–1093. 11. Russell H W (1965), Help for designers construction factor – an aid to fabric evaluation and design. Text. Industr., 129(6), 51–53.

4

Woven fabric properties after structural modifications

Abstract: There can be significant structural changes to a fabric after mechanical processes such as calendaring. Changes in fabric parameters and physical properties due to extension in the warp or weft direction are useful in achieving desired crimp and also in making fabrics which are difficult to produce on weaving machines. The chapter demonstrates the relationship between crimps in the two directions by manipulating length, which can be used to control crimp and other fabric properties. Numerical examples are given to show practical applications. Key words: fabric model, calendaring, crimp.

4.1

Introduction

A fabric’s structure can be specified by any four of eleven parameters, for example ends per cm, picks per cm, warp crimp, weft crimp; from these one can calculate other fabric parameters. The question is what changes occur in the structure when dimensions are changed? Corrections to the fabric can be made by pulling it in either the warp or weft direction. The effect of stretch along warp or weft on fabric parameters can be predicted. However, it should be remembered that such changes in the fabric parameters do not involve yarn stretch or compression. A very important practical application of Peirce’s geometrical model [1] is to determine fabric parameters after modification.

4.2

Crimp interchange phenomena

A stretch in the fabric, for example in the warp direction, will generally reduce the warp crimp and increase the weft crimp. This phenomenon is known as crimp interchange. It is equivalent to stretching in one direction accompanied by contraction in the cross-direction and vice versa. This is a geometrical change between the fabric parameters in one direction visà-vis the cross-direction. The practical implementation of this concept can be carried out by weft stretch in the stenter machine and by warp stretch in the calendar. This implies that the mechanical act can cause a direct change only in thread spacing, p1 or p2 and the changes in other fabric parameters will be indirect owing to the effect of changes in p1 or p2. 73

74

Woven textile structure

The following equation gives a useful relationship between the two directions of the fabric.

D = h 1 + h 2 = h 1¢ + h 2¢

Primes represents changes in the fabric parameter after modification.



D = h1¢ + h2 ¢ = 4 (p2 ¢ c1¢ + p1¢ c2 ¢ ) 3 Ê l1 c1¢ l2 c2 ¢ˆ D=4Á + 3 Ë1 + c1¢ 1 + c2 ¢˜¯ l1 c1¢ l2 c2 ¢ + = 3D (1 + c1¢ ) (1 + c2 ¢ ) 4

4.1

Equation 4.1 is the crimp interchange equation. It gives the relationship between the warp and weft crimp for the new configuration after the application of stretch in the warp/weft direction. The parameters l1, l2 and D are invariant, i.e. they have the same value in the original fabric and in the new configuration. This means that there is a geometrical change in the deformed fabric with respect to the undeformed fabric. In the crimp interchange equation one of the parameters c1¢ or c2¢ is determined based on the requirement for modification and the other parameter is calculated from the equation. One of the following options can be used to find the parameters of the new fabric. Fabric dimensions changed Either the length or the width can be pulled by a certain amount to change the fabric parameters. ∑ Extension or contraction of fabric length is made by al%; new weft spacing,

a %ˆ Ê p2 ¢ = p2 Á1 ± l ˜ Ë 100 ¯

valid for no jamming in the weft direction. ∑ Extension or contraction of fabric width is made by aw%; new warp spacing,

Ê a %ˆ p1¢ = p1Á1 ± w ˜ Ë 100 ¯

valid for no jamming in the warp direction.

Woven fabric properties after structural modifications

75

Fabric crimps changed Fabric crimp in either the warp or weft direction can be changed by extension to change the fabric parameters: ∑ New crimp, c1¢ = c1[1 ± (ac/100)], where ac is percent change in the warp crimp. ∑ New crimp, c2¢= 2 (1 ± (bc/100)), bc is percent change in the weft crimp. ∑ c1¢ = 0, or c2¢ = 0, or c1¢ = c2¢. Fabric crimp amplitude changed ∑ New h1¢ = h1[1 ± (g1%/100)], where g1 is percent change. ∑ New h2¢ = h2[1 ± (g2%/100)], where g2 is percent change. ∑ h1¢ = 0, or h2¢ = 0, or h1¢ = h2¢

4.3

Maximum fabric extension

The maximum fabric extension will be limited to the following two options: ∑ When the crimp in the direction being pulled becomes zero, the threads will be pulled straight and the changes in the cross-thread will not cause interference. For example, the maximum warp stretch will be equal to the warp crimp.

new crimp, c1¢ = 0



new weft spacing, p2¢ = l1



maximum percent warp stretch =

p2 ¢ – p2 ¥ 100% p2

Similar logic can be applied for extensions in the weft direction. ∑ The maximum warp stretch will be limited to jamming in the crossthreads. For example, maximum stretch in warp will be limited by the weft yarn getting jammed. It can be calculated as: new warp spacing, p1¢ = D sin

new weft crimp, c2 ¢ =

l2 –1 p1¢

l2 D

c1¢ can be calculated from equation 4.1 and the corresponding p2¢ can be obtained.



Maximum percent warp stretch =

p2 ¢ – p2 ¥ 100% p2

76

Woven textile structure

Similar logic can be applied for the other direction. The flowcharts shown in Figs 4.1–4.2 give the logic of the algorithm for computing the parameters of the new fabric configuration on the application of options mentioned in Section 4.1.

4.4

Other structural changes

Once the new fabric parameters are calculated the following can be obtained. New fabric thickness The new h1¢ and h2¢ can be calculated by using equations 2.10 and 2.11. The new thickness will be h1¢ + d1 or h2¢ + d2, whichever is greater. New fabric mass This can be calculated using equations 2.30 and 2.31. New fabric cover factor This can be calculated using equation 2.27. New fabric specific volume The importance of this concept lies in altering the fabric properties. A reduction in the values of parameters in one direction will be accompanied by an increase in the values of parameters in the cross-direction. An extension along warp will cause a contraction in the fabric width and vice versa. This will primarily change thread spacing in warp and weft such as the ends and picks per cm. It will result in a change in the warp and weft cover factor and the cloth cover factor. The extension of warp will also result in reducing warp crimp and crimp amplitude. It is likely to affect fabric thickness and fabric mass.

4.5

Structural design of woven fabrics using soft computing

The crimp in fabric is the most important parameter which influences several fabric properties such as extensibility, thickness, compressibility and handle. Normally the crimp interchange equation is used to predict the change in crimp in the fabric when it is extended in any direction by keeping the ratio of modular length to the sum of thread diameter (l1/D and l2/D) constant. Soft computing can exploit the crimp interchange equation in a different way. Instead of keeping the usual three invariants l1, l2 and D, the relationship between warp crimp, c1, and weft crimp, c2, is determined by varying l1/D

Woven fabric properties after structural modifications Start Enter ends per cm (EPC) picks per cm (PPC) C1, C2 p1 = 1/EPC p2 = 1/PPC l1 = p2 (1 + C1) l2 = p1 (1 + C2) h1 = (P2 ÷ C1) 4/3 h2 = (P1 ÷ C2) 4/3 DC = h1 + h2

Enter t1, t2

Yes

Is yarn count given?

Yes

Is l1/D £ p/2?

No

D = DC

d1 = (1/280.2)÷(t1/0.912) d2 = (1/280.2)÷(t2/0.912)

D = Dd = d1 + d2

Print warp jammed

Print weft jammed

Yes

Is l2/D £ p/2?

No

No

Print warp not jammed

Print weft not jammed

A

4.1 Flowchart for solving crimp interchange equation.

77

78

Woven textile structure A

Enter a or b

No

p2¢ = p2(1 + a)

B

p2¢ = p2(1 – a)

B

p1¢ = p1(1 + b)

C

Is there jamming in any direction?

Yes Is warp jammed?

No

Yes p1¢ = p1(1 – b)

C

C1¢ = C1(1 + a)

B

C1¢ = C1(1 – a)

B

C2¢ = C2(1 + b)

C

C2¢ = C2(1 – b)

C

p2¢ = D sin (l2/D)

p1¢ = D sin (l2/D)

C1¢ = l1/p2¢ – 1

C2¢ = l2/p1¢ – 1

D

D

p1¢ = l2/(1 + C2¢)

p2¢ = l1/(1 + C1¢)

EPC¢ = 1/p1¢ PPC¢ = 1/p2¢

Print C1, C2, p1¢, p2¢, EPC, PPC¢ …

End

4.2 Module connector A for Fig. 4.1.

and l2/D. The algorithm for this approach is shown in Fig. 4.4. Such a strategy enables bias of crimp in a preferred direction. This is a new concept and entirely a different use of the crimp interchange equation.

Woven fabric properties after structural modifications B

C

C1¢ = l1/p2¢ – 1

C2¢ = l2/p1¢ – 1

D

D

C2¢ = l2/p1¢ – 1

C1¢ = l1/p2¢ – 1

79

EPC¢ = 1/p1¢ PPC¢ = 1/p2¢

Print C1, C2, p1¢, p2¢, EPC, PPC¢

End

D

C1¢ C2 ¢ l1 l + 2 = 3 4 Dc 1 + C1¢ Dc 1 + C2 ¢

4.3 Module connector at B, C for Fig. 4.2

4.5.1 Effect of varying l1/D and l2/D on the relation between c1 and c2 It was thought appropriate to exploit this equation as a designer tool by varying l1/D and l2/D to alter the domain of c1 and c2. This attempt is shown in Figs 4.5, 4.6 and 4.7. Figure 4.5 shows that the relation between (√c1)/ (1 + c1) and (√c2)/(1 + c2) is linear for given values of l1/D and l2/D. The relation between warp and weft crimp will be dictated by the unique straight line for crimp interchange. An attempt was made to investigate the effect by progressively decreasing the value of l1/D and increasing the value of l2/D by the same amount. It can be seen that all these lines pass through a point. The domain of relationship between warp and weft crimp is altered,

80

Woven textile structure Start

c1 = 0.001

Enter l1/D, l2/D

A =

B=

c1 = c1 + 0.01

c1 1 + c1

(0.75 – A ¥ l1 /D) l2 /D

Plot A vs B

No

Does c1 = 0.47 ?

Yes End

4.4 Flowchart for solving crimp interchange equations in terms of l1/D and l2/D as variables.

shifting to higher values of warp crimp by increasing l2/D in relation to l1/D and vice versa. Figure 4.6 shows the effect of decreasing l1/D and l2/D by the same amount. This increases the domain of the two axes without altering any ratio of (√c1)/(1 + c1) and (√c2)/(1 + c2). The greater increment in l2/D compared with l1/D gives non-parallel lines in Fig. 4.7 unlike Fig. 4.4. In this case, the ratio of (√c1)/(1 + c1) and (√c2)/(1 + c2) will be altered and the straight line will be biased towards the x-axis. Any line shows the relation between c1 and c2 for constant value of l1/D and l2/D, thus depicting the operating range of c1 and c2 for any desired change in one of them. Thus l1/D and l2/D can be chosen to dictate a desired imbalance between c1 and c2.

Woven fabric properties after structural modifications

81

0.45 3.6, 1.75

0.40 0.35

3.1, 2.25

0.30

c2 1 + c2

2.6, 2.75

0.25 0.20 0.15 0.10 0.05 0

2.1, 3.25 0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

1.6, 3.75 0.40

0.45

c1 1 + c1

4.5 Relation between c1 and c2 with varying l1/D and l2/D.

0.45

1.6, 1.6

0.40 0.35

2.1, 2.1

0.30

c2 1 + c2

2.6, 2.6

0.25 0.20

3.1, 3.1

0.15

3.6, 3.6

0.10 0.05 0

0

0.05

0.10 0.15 0.20 0.25

0.30

0.35 0.40

0.45

c1 1 + c1

4.6 Relation between c1 and c2 with equal decrease in l1/D and l2/D.

82

Woven textile structure

0.30 0.25 0.20

c2 1 + c2 0.15 0.10

3.6, 2.6 3.1, 2.6 2.6, 2.6

0.05 0

0

0.05 0.10

0.15 0.20

2.1, 2.6

0.25 0.30

0.35

1.6, 2.6 0.40

0.45

c1 1 + c1

4.7 Relation between c1 and c2 with decrease in l1/D for constant l2/D.

4.6

Calculating fabric properties: numerical examples

Q1. A fabric with the following properties is required to be pulled straight in the warp direction. How far can the warp be pulled? Find the corresponding contraction in the weft direction. Warp and weft = 50/60 tex, percent crimp = 27/10.2, ends and picks per cm = 20/16, assume f = 0.6, rf = 1.52 g/cm3. Solution:

d1 =

Tex = 50 = 0.0264 cm 280.2 frf 280.2 0.6 ¥ 1.52

d2 =

60 = 0.02895 cm 280.2 0.6 ¥ 1.52

Dd = d1 + d2 = 0.055 38 cm p1 = 1 = 0.05 cm 20



l2 = p1(1 + c2) = 0.05(1.102) = 0.0551 cm



l2 = 0.995 < p 2 D

Woven fabric properties after structural modifications



p2 = 1 = 0.0625 cm 16



l1 = p2(1 + c1) = 0.0625(1.27) = 0.0794 cm



l1 = 0.434 < p 2 D

83

Both warp and weft threads can get jammed, so the warp cannot be pulled straight as the weft will jam before it can be pulled straight. Now weft jamming means

p1¢ = D sin q 2¢ = D sin c2¢ =

l2 = 0.0464 cm D

l2 – 1 = 0.1863 = 18.63% p1¢

contraction in width (weft) =

p1 – p1¢ = 7.1% p1

For c1¢, use the crimp interchange equation:

l1 c1¢ l2 c2¢ + = 0.75 D (1 + c1¢ ) D (1 + c2¢ ) c1¢ = 0.2939



c1¢ = 0.0864 = 8.64% p2¢ =

l1 = 0.0794 = 0.0731cm 1 + c1¢ 1.0864

extension in warp =

p2¢ – p2 ¥ 100 = 16.94% p2

Q2. A fabric is made with the following properties: ends and picks per cm = 18/24, % crimp in warp and weft = 10/15. (i) What is the extent to which it can be pulled in the weft direction? (ii) If the fabric is pulled by 5% in the weft direction, calculate the fabric thickness, crimp, Poisson ratio, and ends and picks per cm. Solution: (i)



p1 = 1 = 0.055 56 cm 18 p2 = 1 = 0.041 67cm 24

84



Woven textile structure

c1 = 0.10 =

l1 –1 p1

\ l1 = p2(1 + c1) = 0.045 84 cm c2 = 0.15 =

l2 –1 p1



\ l2 = p1(1 + c2) = 0.063 89 cm



h1 = 4 p2 c1 = 0.017 57 cm 3



h2 = 4 p1 c2 = 0.028 69 cm 3



Dc = h1 + h2 = 0.046 26 cm



l1 = 0.99 < p 2 D



l2 = 1.38 < p 2 D

Both warp and weft direction of the fabric can get jammed on stretching in the cross-direction. The fabric can be pulled in the weft direction until the warp gets jammed:



l1 = 0.046 26 ¥ 0.836 52 = 0.038 69 cm D p ¢ – p2 contraction in the warp direction = 2 ¥ 100 = 7.14% p2 l c1¢ = 1 – 1 = (0.045 84/0.038 69) – 1 = 0.1848 = 18.48% p2¢

p2¢ = D sin q1¢ = D sin

For c2¢ use crimp interchange equation:



l1 c1¢ l2 c2¢ + = 0.75 D(1 + c1¢ ) D(1 + c2¢ )



c2¢ 0.99 0.1848 + 1.38 = 0.75 1.1848 1 + c2¢



c2¢ = 0.31 c2¢ = 0.096 = 9.6%

Woven fabric properties after structural modifications



p1¢ =

85

0.063 83 l2 = = 0.0583 cm 1 + c2¢ 1.096

Extension in weft = (p1¢ – p1)/p1 = 0.0485 = 4.85% (ii) A 5% extension in the weft gives:

p1¢ = 1.05 ¥ p1 = 1.05 ¥ 0.055 56 = 0.058 34 cm



ends per cm = 17.14 = 17



c 1¢ =

l2 – 1 = (0.063 89/0.058 34) – 1 = 0.095 13 = 9.51% p1¢

For c1¢, use the crimp interchange equation:

l2 c2¢ l1 c1¢ + = 0.75 D(1 + c2¢ ) D(1 + c1¢ )



c1¢ 1.38 0.0951 + 0.99 = 0.75 1.0951 1 + c1¢ c1¢ = 0.4342



c1¢ = 0.1885 = 18.85% p2¢ =

l1 = 0.03859 cm 1 + c1¢

picks per cm = 25.52 = 26 cm contraction in the warp = Poisson ratio =

p2¢ – p2 ¥ 100 = – 7.39% p2

lateral contraction = 0.0739 = 1.478 longitudinal extension 0.05

Q3. A fabric has 18 ends per cm, 24 picks per cm, 12% warp crimp, 15% weft crimp. Can it be pulled in the weft or warp direction? Solution:

p1 = 1 = 0.055 56 cm 18



p2 = 1 = 0.04167 cm 24



c1 = 0.12



c2 = 0.15

86

Woven textile structure



Dc = 4 [p2 c1 + p1 c2 ] = 0.04794 cm 3



l1 = p2 (1 + c1) = 1 (1.12) = 0.0467cm 24



l2 = p1 (1 + c2 ) = 1 (1.15) = 0.06389 cm 18



l1 = 0.9735 < p /2 D



l2 = 1.332 < p /2 D

The fabric can be pulled in the weft direction until the warp gets jammed or in the warp direction until the weft gets jammed, since both directions of the fabric have jamming tendencies. Q4. A fabric has 18 ends per cm, 24 picks per cm, 7% warp crimp, 12% weft crimp. What is maximum extent it can be pulled in the warp and weft directions? Find the changed fabric particulars by stretching the fabric to the maximum extent in the weft and warp directions respectively. Solution:

p1 = 1 = 0.055 56 cm 18



p2 = 1 = 0.04167 cm 24



c1 = 0.07, c2 = 0.12



l1 = p2(1 + c1) = 0.041 67 ¥ 1.07 = 0.044 59 cm



l2 = p1(1 + c2) = 0.055 56 ¥ 1.12 = 0.0622 cm



h2 = 4 p1 c2 = 0.0257 cm 3



h1 = 4 p2 c1 = 0.0147 cm 3 Dc = h1 + h2 = 0.0404 cm

Since the yarn count is not given, we can use Dc to estimate jamming in warp and weft directions.

Woven fabric properties after structural modifications



87

l1 = 1.105 < 1.57 D l2 = 1.541 < 1.57 D

Both the warp and weft can get jammed on stretching the fabric in either weft or warp direction respectively. The weft can be stretched until the warp gets jammed. For maximum stretching in the weft direction until the warp gets jammed, we have:

p2¢ = D sin (l1/D) = 0.0404 ¥ 0.8930 = 0.036 07 cm



picks per cm = 27.7 ª 27



contraction in the warp = c1¢ =

p2¢ – p2 ¥ 100 = 13.44% p2

l1 – 1 = (0.044 59/0.3607) – 1 = 0.2362 = 23.62% p2¢

For c2¢, use the crimp interchange equation:

l2 c2¢ l1 c1¢ + = 0.75 D(1 + c2¢ ) D(1 + c1¢ ) 1.105 0.2362 + 1.541 c2¢ = 0.75 1.2362 1 + c2¢ c2¢ = 0.0452 = 4.52% p1¢ =

l2 = (0.0622/1.0452) = 0.0595cm 1 + c2¢

ends per cm = 16.8 ª 17 extension in weft =

p1¢ – p1 = 0.0709 = 7.1% p1

Similarly the warp direction can be pulled until weft gets jammed. We have:

p1¢ = D sinq 2¢ = D sin

l2 = 0.040 353 ¥ 0.999 56 = 0.040 35 cm D

contraction in the weft = c2¢ =

p1¢ – p1 ¥ 100 = 27.38% p1

l2 – 1 = (0.0622/0.04035) – 1 = 0.542 = 54.2% p1¢

88

Woven textile structure

For c1¢, use the crimp interchange equation:



l2 c2¢ l2 c1¢ + = 0.75 D (1 + c2¢ ) D (1 + c1¢ )



1.105 c1¢ 1.541 0.542 + = 0.75 1 + c1¢ 1.542



c1¢ = 0.0129 = 1.29%



p2¢ =

0.044 59 l1 = = 0.044 cm 1 + c1¢ 1.0129

extension in warp =

(0.044 – 0.041 67) = 0.0559 = 5.6% 0.041 67

Q5. For a fabric the following is given: c1 = 38%, c2 = 5%, p2/D = 0.98, p1/D = 1.60. (i) Can the weft be pulled straight? (ii) Find the new crimp, Poisson ratio, percent change in ends and picks per cm. Solution:

p1 = 1.6 D



p2 = 0.98 D



c1 = 0.38, c2 = 0.05



l2 p1 = (1 + c2 ) = 1.68 > 1.57 D D



l1 p2 = (1 + c1) = 1.3524 < 1.57 D D

The weft cannot be pulled straight as warp direction will get jammed. So:

p2¢ l = D sin 1 = 0.9763 cm D D c1¢ =

l1 /D – 1 = 0.3853 = 38.53% p2¢ /D

Woven fabric properties after structural modifications

89

For c2¢, use the crimp interchange equation:



l1 c1¢ l2 c2¢ + =3 D(1 + c1¢ ) D(1 + c2¢ ) 4



c2¢ = 0.0077 = 0.77%



p1¢ l2 = (1 + c2¢ ) = 1.6672 cm D D



p2¢ p2 – D D p2 0.97 – 0.98 lateral contraction D 0.98 Poisson ratio = = = = 0.09 p1¢ p1 1.6672 – 1.60 longitudinal – extension 1.60 D D p1 D



D – D p1¢ p1 0.5998 – 0.625 = 0.04 = 4% % change in picks/cm = = 0.0625 D p1



D – D p2¢ p2 1.0243 – 1.020 41 % change in ends/cm = = = 0.38% 1.020 41 D p2

Q6. A fabric has the following properties: Ends per cm = 15, picks per cm = 20, warp and weft count = 20 tex, percent warp and weft crimp = 5/10. The fabric is required to be shrunk by 2% in the warp direction. Can it be done? Find the change in crimp, new thread spacing, fabric thickness and weave angle. Fiber density=1.52 g/cm3, f = 0.65. Solution:

p1 = 1 = 0.066 67 cm 15



p2 = 1 = 0.05 cm 20



d=

T 280.2 frf

90

Woven textile structure



d1 = d2 = 0.016 05 cm



Dd = d1 + d2 = 0.0321 cm



c1 = 0.05



c2 = 0.10



l1 = p2(1 + c1) = 0.0525 cm



l2 = p1(1 + c2) = 0.073 33 cm



l1 = 1.636 > p 2 D



l2 = 2.285 > p 2 D

Neither direction of the fabric has jamming tendency. Warp shrinkage of 2%, gives:

weft spacing = p2¢ = 0.98 p2 = 0.049 cm c1¢ =

l1 – 1 = (0.0525/0.049) – 1 = 0.0714 p2¢

c1¢ = 7.14%

For c2¢ use the crimp interchange equation:

l1 c1¢ l2 c2¢ + =3 D(1 + c1¢ ) D(1 + c2¢ ) 4



1.636 0.0714 + 2.285 c2¢ = 0.75 1.0714 1.c2¢



fi c2¢ = 0.0235 = 2.35%

This means weft crimp will be reduced from 10% to 2.35%, which is feasible. Therefore the warp direction of the fabric can be reduced by 2%. The changed fabric particulars will be:

p1¢ =

l2 = (0.07333/1.0235) = 0.07166 cm 1 + c2¢

h1¢ = 4 p2¢ c1¢ = 0.017 46 cm 3

Thickness = h1¢ + d1 = 0.017 46 + 0.016 05 = 0.0335 cm

q1¢ = 2c1 = 2 ¥ 0.0714 = 21.65°

Woven fabric properties after structural modifications



91

q 2¢ = 2c2 = 2 ¥ 0.023 = 12.29°

Q7. Given l1D = 1.5, (l1 – p2)D = 0.30, h1/D = 0.81, (l2 – p1)/D = 0.020. Assume q (degree) = 106√c. (i) In which direction is the fabric jammed? Find the warp and weft crimp. (ii) To what extent it can be pulled in the warp direction? Calculate the new warp and weft crimp and the Poisson ratio for the fabric. Solution:

p2 l1 = = 0.30 = 1.5 – 0.3 = 1.2 D D



h1 4 p2 = D 3D



0.81 = 4 ¥ 12 c1 3



c1

c1 = 0.5063



c1 = 0.2563 = 25.63%



l1 = 1.5 < 1.57 D



h2 h = 1 – 1 = 1 – 0.81 = 0.19 D D



h2 4 p1 = D 3 D



p l /D 0.19 = 4 1 1 –1 3 D p1 /D



c1

p l – p1 =4 1 1 3 D p1 p =4 1 3 D =4 3

D ¥ 0.020 p1

p1 ¥ 0.020 D

92

Woven textile structure



p1 ¥ 0.020 = 0.1425 D



p1 0.020 31 = = 1.015 31 D 0.020



l2 p1 = + 0.020 = 1.0353 < 1.57 D D



c2 =

l2 – 1 = 0.019 70 = 1.9% p1

since l1/D and l2/D are both less than p/2. Both the warp and weft directions of the fabric can get jammed. (ii) The warp can be pulled until the weft gets jammed.

p1¢ = D sin q 2¢ = D sin

l2 D

p1¢ = sin 1.0333 = 0.86cm D c2¢ =

l2 /D – 1 = 1.0353 – 1 = 0.2038 = 20.38% p1¢ /D 0.86

contraction in weft =

p1¢ /D – p1 /D = 0.1529 = 15.29% p1 /D

For c1¢ use the crimp interchange equation:

l1 c1¢ l2 c2¢ + =3 D(1 + c1¢ ) D(1 + c2¢ ) 4



1.5 c1¢ 1.0353 0.2038 + = 0.75 1 + c1¢ 1.2038



fi

c1¢ = 0.2571

c1¢ = 6.61% warp extension = Poisson ratio =

p2¢ /D – p2 /D = 0.1725 = 17.25% p2 /D

lateral contraction = 0.1529 = 0.8864 longitudinal extension 0.1725

Woven fabric properties after structural modifications

93

Q8. A fabric has the following properties: ends per cm = 20, picks per cm = 24, warp and weft count = 20 tex, percent warp and weft crimp = 8/12. (i) Can it be pulled by 8% in the warp direction? (ii) Find the Maximum extension in warp and corresponding contraction in weft and the Poisson ratio. Solution:

p1 = 1 = 0.05 cm 20



p2 = 1 = 0.04167cm 24



l1 = p2(1 + c1) = 0.041 67 ¥ 1.08 = 0.045 cm



l2 = p1(1 + c2) = 0.05 ¥ 1.12 = 0.056 cm



20 = 0.016 05 cm d1 = d2 = d = 1 226 1.52



D = 2d = 0.0321 cm



l1 = 1.402 < 1.57, warp can get jammed if weft is pulled D

l2 = 1.745 > 1.57, warp can be pulled without jamming the weft D (i) Yes, the fabric can be pulled by 8% in the warp direction. (ii) Maximum extension in warp is equal to 8% as crimp will be equal to zero.



c1¢ = 0.

For c2¢ use the crimp interchange equation:

l1 c1¢ l2 c2¢ + = 0.75 D(1 + c1¢ ) D(1 + c2¢ ) 1.745 ¥

c2¢ = 0.75 1 + c2¢

c2¢ = 0.324 = 32.4% p1¢ =

l1 = 0.056 = 0.0423 cm 1 + c2¢ 1.324

contraction in weft = 0.0423 – 0.05 ¥ 100 = 15.41% 0.05

94



Woven textile structure

Poisson ratio =

lateral contraction = 0.1541 = 1.926 longitudinal extension 0.08

Q9. A cotton fabric has 25 ends and 28 picks per cm. The tex of warp and the weft yarn are 30/15 respectively. Assume f = 0.65, rf = 1.52 g/ cm3. If the warp crimp is 12% then calculate fabric thickness and weft crimp. Is the fabric jammed in any direction? Solution:



d1 =

Tex = 30/1.52 = 0.019 66 cm 226 226 fiber density

d2 =

15 = 0.01390 cm 226 1.52



Dd = d1 + d2 = 0.033 56 cm



p1 = 1 = 0.04 cm 25



p2 = 1 = 0.0357 cm 28



c1 =

l1 –1=1 p1



l1 = p2(1 + c1) = 1.12 ¥ 0.0357 = 0.04 cm



l1 = 1.192 < 1.57 D



h1 = 4 p2 c1 = 0.0165 cm 3



fi h2 can be estimated by using D obtained from d1 + d2



h2 = D – h1 = 0.03356 – 0.0165 = 0.0171 cm



h1 + d1 = 0.0165 + 0.1966 = 0.036 16 cm



h2+ d2 = 0.0171 + 0.0139 = 0.031 cm

(i)

Fabric thickness = 0.036 16 cm



h c2 = 3 2 = 3 ¥ 0.0171 = 0.427 4 p1 4 0.04

Woven fabric properties after structural modifications

(ii)

c2 = 0.1827 = 18.27%



l2 = (1+ c2) p1

95

  = (1.1827)0.04 = 0.0473 cm

l2 = 1.41 < 1.57 D

To find out whether the fabric is jammed, we need to compare the thread spacings in the fabric with the one assuming it is jammed. Warp jamming gives minimum weft spacing:

Êl ˆ p2¢ = D sin Á 1 ˜ = 0.033 56 sin (1.092) = 0.0312 cm Ë D¯

Since actual weft spacing in the fabric p2 = 0.0357 cm is greater than that under the jamming condition, the warp direction of the fabric is not jammed. Similarly weft jamming gives minimum warp spacing:

Êl ˆ p1 = D sin Á 2 ˜ = 0.03356 sin (1.41) = 0.03113 cm Ë D¯

Actual warp spacing in the fabric p1 = 0.04 cm is greater than that under jamming conditions, so weft direction of the fabric is not jammed. The fabric is not jammed either in the warp or weft direction. However since both (l1/D) and (l2/D) < 1.57, so the fabric cannot be pulled straight either in the warp or weft direction as the cross-direction of the fabric will get jammed. Q10. A fabric with the following properties needs to be pulled straight in the warp direction. To what extent can the warp be pulled? Find the corresponding contraction in the weft direction. Warp and weft = 50/60 tex, warp and weft crimp % = 27/10.2, ends/picks per cm = 20/16, assume f = 0.65, rf = 1.52 g/cm3. Solution:

d1 =

Tex = 50 = 0.02539 cm 280.2 frf 280.2 0.65 ¥ 1.52

d2 =

60 = 0.02781cm 280.2 0.65 ¥ 1.52



Dd = d1 + d2 = 0.0532 cm



p1 = 1 = 0.05 cm 20

96

Woven textile structure



l2 = p1(1 + c2) = 0.05(1.102) = 0.0551 cm



l2 = 1.036 < 1.57 D

Jamming in the weft direction will take place before straightening of the warp thread so warp cannot be pulled straight.

1 = 0.0625 cm 16 l1 = p2(1 + c1) = 0.0625 ¥ 1.27 = 0.0794 cm p2 =

l1 = 1.492 < 1.57 D

Jamming in the warp direction will take place before straightening the weft thread. Now, weft jamming gives the extent to which warp can be pulled: l2 = 0.045 77 cm D



p1¢ = D sin q2¢ = D sin



ends per cm = 21.8



c 2¢ =



contraction in the width (weft) =

l2 = (0.0551/0.045 77) – 1 = 0.2038 = 20.38% p1 p 2¢ – p 1 = 7.1% p1

For c1¢, use the crimp interchange equation:

l1 c1¢ l2 c2¢ + = 0.75 D(1 + c1¢ ) D(1 + c2¢ ) 1.4924

c1¢ + 1.036 0.2038 = 0.75 (1 + c1¢ ) 1.2038

c1¢ = 0.2585



c1¢ = 0.0668 = 6.68%



p 2¢ =



picks per cm = 13.4



extension in the warp direction,

l 1¢ = (0.0794/1.0668) = 0.0744 cm 1 + c 1¢ p 2¢ – p 2 ¥ 100 = 19.1% p2

The warp can be pulled only by 19.1%. The new ends/picks per cm = 21.8/13.4; new % warp/weft crimp = 6.68/20.38.

Woven fabric properties after structural modifications

97

Q11. A fabric is made with the following properties: ends and picks per cm = 18/24, percent crimp in warp and weft = 10/15. What is the extent to which it can be pulled in the weft direction? If the fabric is pulled by 5% in the weft, calculate the crimp, ends and the picks per cm and Poisson ratio. Solution:

p1 =

1 = 0.055 56 cm 18



p2 =

1 = 0.041 67 cm 24



l1 = p2(1 + c1) = 0.041 67 ¥ 1.1 = 0.045 84 cm



l2 = p1(1 + c2) = 0.055 56 ¥ 1.15 = 0.063 89 cm



h1 = 4 p2 c1 = 0.017 57 cm 3



h2 = 4 p1 c2 = 0.028 69 cm 3



Dc = h1+ h2 = 0.046 26 cm

Since the yarn count is not given, D is calculated as shown above for the following jamming conditions:

l1 = 0.9909 < 1.57 D2



l2 = 1.3811 < 1.57 D

Both warp and weft directions can get jammed on stretching the fabric in the corresponding cross-directions. The fabric can be pulled in the weft direction until the warp gets jammed. For the warp jamming: l1 = 0.046 26 ¥ 0.836 52 = 0.038 69 cm D



p2¢ = D sin q1¢ = D sin



contraction in the warp direction 0.0387 – 0.04167 p ¢ – p2 ¥ 100 = ¥ 100 = 7.13% = 2 0.04167 p2



c 1¢ =

l1 – 1 = (0.045 89/0.387) – 1 = 18.45% p 2¢

98

Woven textile structure

For c2¢, use the crimp interchange equation:



l1 c1¢ l2 c2¢ + = 0.75 D(1 + c1¢ ) D(1 + c2¢ ) 1.3811

c2¢ + 0.9909 0.1845 = 0.75 1 + c2¢ 1.1845

c2¢ = 0.31



c2¢ = 9.62%



l2 p1¢ = 1 + c ¢ = (0.063 89/1.0962) = 0.0582 cm 2



extension in weft =



maximum extension in weft = 4.75%

p 1¢ – p 1 = 4.75% p1

Remember jamming conditions have been worked out using D = h1+ h2. This value is higher than D calculated from the sum of yarn diameters. A 5% extension in the weft direction gives:

p1¢ = 1.05 × p1 = 1.05 ¥ 0.055 56 = 0.058 34 cm



c 2¢ =



ends per cm = 10.23 ≈ 10

l2 – 1 = (0.063 89/0.0582) – 1 = 0.0978 = 9.78% p 1¢

For c1¢, use the crimp interchange equation:



l1 c1¢ l2 c2¢ + = 0.75 D(1 + c1¢ ) D(1 + c2¢ )



c1¢ 0.3891 0.0978 + 0.9909 = 0.75 1.0978 1 + c1¢



c1¢ = 0.421 c1¢ = 0.177 = 17.7% c1¢ =

l1 –1 p2¢

Woven fabric properties after structural modifications



p2¢ =

99

l1 = 0.038 95 cm 1 + c1¢

picks per cm = 25.7 ≈ 26 contraction in the warp direction = Poisson ratio =

p2¢ – p2 ¥ 100 = 6.35% p2

lateral contraction = 0.0653 = 1.31 longitudinal extension 0.05

It is interesting that 5% extension in weft, which is beyond the warp jamming limit restricting weft extension, 4.75% can be achieved. The anomaly is due to the calculated value of D. Q12. A fabric has 18 ends per cm, 24 picks per cm, 7% warp crimp, 12% weft crimp. What is maximum extent it can be pulled in the warp/ weft direction? Find the changed properties of the fabric if it is pulled by 5% in the warp direction. Solution:

p1 =

1 = 0.055 56 cm 18



p2 =

1 = 0.041 67 cm 24



c1 = 0.07, c2 = 0.12



l1 = p2(1 + c1) = 0.041 67 ¥ 1.07 = 0.044 57 cm



l2 = p1(1 + c2) = 0.055 56 ¥ 1.12 = 0.062 22 cm



h2 = 4 p1 c2 = 0.025 66 cm 3



h1 = 4 p2 c1 = 0.0147 cm 3



D = h1 + h2 = 0.040 36 cm

Since yarn diameters are not given, D needs to be estimated using h1 and h 2: l1 = 1.1048 < 1.57 D

l2 = 1.542 < 1.57 D

100

Woven textile structure

Both warp and weft directions can get jammed by stretching the fabric in the cross-direction. For maximum weft stretch the warp will be jammed, so:



l p2¢ = D sin  1 = 0.040 36 ¥ 0.8934 = 0.036 06 cm D maximum picks per cm = 27.73



c 1¢ =



contraction in the warp =



l1 – 1 = 0.2366 = 23.66% p 2¢ p 2¢ – p 2 ¥ 100 = 13.47% p2

For c2¢, use the crimp interchange equation:



l1 c1¢ l2 c2¢ + = 0.75 D(1 + c1¢ ) D(1 + c2¢ )



c2¢ 1.1048 0.2366 + 1.542 = 0.75 1.2366 1 + c2¢



c2¢ = 0.2139 c2¢ = 0.0458 = 4.58% p1¢ =

0.062 22 l2 = = 0.0595 cm 1 + c2¢ 1.0458

% extension =

0.0595 – 0.055 56 p1¢ – p1 ¥ 100 = ¥ 100 = 7.1 p1 0.055 56

Therefore maximum weft extension will be 7.1%. For maximum warp stretch, the weft will be jammed;

l p1¢ = D sin  2 = 0.040 36 ¥ 0.999 58 = 0.040 34 cm D



c 2¢ =



contraction in the weft direction =

l2 – 1 = (0.062 22/0.040 34) –1 = 0.5424 = 54.24% p 1¢ p 1¢ – p 1 = 27.39% p1

Woven fabric properties after structural modifications

For c1¢, use the crimp interchange equation:

l1 c1¢ l2 c2¢ + = 0.75 D(1 + c1¢ ) D(1 + c2¢ ) 1.1048

c1¢ + 1.542 0.5424 = 0.75 1 + c1¢ 1.5424

c1¢ = 0.012 65 c1¢ = 0.00016 = 0.02% p2¢ =

0.044 59 l1 = = 0.044 58 cm 1 + c1¢ 1.0002 0.044 58 – 0.04167 p2¢ – p2 ¥ 100 = ¥ 100 p2 0.04167 = 6.98%

% extension =

Therefore maximum warp extension will be 6.98%. For 5% extension in warp, p2¢ =1.05 p2 = 0.043 75 cm

c 1¢ =

l1 – 1 = (0.044 59/0.043 75) – 1 = 0.019 12 = 1.9% p 2¢

For c2¢, use the crimp interchange equation:

l1 c1¢ l2 c2¢ + = 0.75 D(1 + c1¢ ) D(1 + c2¢ )



c2¢ 1.1048 0.019 + 1.542 = 0.75 1.019 1 + c2¢



c2¢ = 0.4789 c2¢ = 0.2293 = 22.93% p1¢ =

0.062 22 l2 = = 0.0506 cm 1 + c2¢ 1.2293

ends per cm = 19.76 ≈ 20 p1¢ – p1 ¥ 100 p1 0.0506 – 0.055 56 = ¥ 100 = 8.93% 0.055 56

% contraction in weft =

101

102



Woven textile structure

Poisson ratio =

lateral contraction = 0.0893 = 1.79 longitudinal extension 0.05



h1¢ = 4 p2¢ c1¢ = 0.01746cm 3



h2¢ = 4 p1¢ c2¢ = 0.0323cm 3

Q13. For a fabric the following properties are given: c1 = 38%, c2 = 5%, p2/D = 0.98, p1/D = 1.60. Which direction of the fabric (warp and weft) can be pulled straight? Find the new crimp, percentage change in ends and picks per cm and the Poisson ratio by pulling the fabric in the direction which can be straightened. Solution:

l1 = 1.6 D p2 = 0.98 D c1 = 0.38, c2 = 0.05

l1 p2 = = (1 + c1) = 0.98 ¥ 1.38 = 1.3524 < 1.57 D D The weft cannot be pulled straight as the warp direction of fabric will get jammed.

l2 p2 = = (1 + c2) = 1.6 ¥ 1.05 = 1.68 > 1.57 D D The warp can be pulled straight as the weft direction of fabric will not get jammed, so:



c 1¢ = 0



p 2¢ l 1 = = 1.3524 D D

For c2¢, use the crimp interchange equation:



l1 c1¢ l2 c2¢ + = 0.75 D(1 + c1¢ ) D(1 + c2¢ ) 1.68

c2¢ = 0.75 1 + c2¢

Woven fabric properties after structural modifications



103

c2¢ = 0.6112



c2¢ = 0.3736 = 37.36%



l2 p1¢ = D = 1.68 = 1.2231 D 1 – c2¢ 1.3736 p1¢ /D – p2 /D ¥ 100 p2 /D = 1.3524 – 0.98 ¥ 100 = 38% 0.98

extension in the warp direction =

p1¢ /D – p1 /D ¥ 100 p1 /D = 1.2231– 1.6 = 23.56% 1.6

contraction in the weft =

D /p1¢ – D /p1 ¥ 100 D /p1 = 0.8176 – 0.625 ¥ 100 = 30.8% 0.625

change in ends per cm =

D /p2¢ – D /p2 ¥ 100 D /p2 = 0.7394 – 1.0204 ¥ 100 = 27.5% 1.0204

change in picks per cm =

Poisson ratio = 0.2356/0.38 = 0.62

Q14. A shirting cotton cloth is made from the following particulars: c1 = 10%, d1 = 0.01627 cm, (T2/T1)1/2 = 0.80, K1/K2 = 11.3/9.1. Calculate (i) fabric thickness, (ii) fabric gsm, (iii) fabric specific volume and air space and (iv) find the extent to which the fabric can be pulled in the weft direction. Find the new properties of the fabric and the Poisson ratio. Solution: d1 = 0.01627 cm

(T2/T1)1/2 = d2/d1 = 0.8



\ d2 = 0.8 ¥ 0.016 27 = 0.013 02 cm



D = d1 + d2 = 0.029 29 cm



T2 =

p = ¥ (0.013 02)2 ¥ 105 ¥ 0.65 ¥ 1.52 13.15 4

104

Woven textile structure



T1 = 14.70



warp cover, K1 = 10 –1 ¥ ends ¥ cm



Tex

10 K1 10 ¥ 11.3 \ ends = = = 29.5 ª 30 cm Tex 14.7 p1 = 0.0339 cm Weft cover, K 2 = 10 –1 ¥ \

picks ¥ cm

Tex

picks 10 K 2 10 ¥ 9.1 = = = 25.1 ª 25 cm Tex 13.15



p2 = 0.0339 cm



h1 = 4 p2 c1 = 4 ¥ 0.039 84 ¥ 3 3



h2 = D – h1 = 0.0125 cm



hˆ Ê c2 = Á 3 ¥ 2 ˜ = 0.2764 = 27.6% Ë 4 p1¯



l2 = p1(1 + c2) = 0.039 ¥ 1.2764 = 0.043 27 cm



l2 = 1.4773 D



fabric thickness = h1 + d1 = 0.0168 + 0.016 27 = 0.0331 cm



fabric gsm = 10–1[T1E1(1 + c1) + T2E2(1 + c2)]

0.10 = 0.0168 cm

2



= 10–1[14.7 ¥ 29.5 ¥ 1.1 + 13.15 ¥ 25.1 ¥ 1.2764]



= 89.83



g/cm 2 =

89.83 = 0.00898 100 ¥ 100



fabric specific volume, cm3/g = 0.0331/0.008 98 = 3.68



packing coefficient = 1/(1.52 ¥ 3.68) = 0.1785 = 17.85%



air = 82.15%

Weft direction stretch is limited by jamming in the warp direction:

l1 p2 (1 + c1) 0.039 84 ¥ 1.1 = = = 1.496 < p 0.029 29 2 D D

Woven fabric properties after structural modifications

105

so the warp will get jammed and stretch in the weft will be limited by warp jamming. l1 = 0.029 29 sin (1.496) = 0.029 21 cm D



p2¢ = sin q1¢ = D sin



picks per cm = 34.2 = 34



c 1¢ =

l1 – 1 = (0.0438/0.029 21) –1 = 0.4962 = 49.6% p 1¢

For c2¢ use the crimp interchange equation:

l1 c1¢ l2 c2¢ + = 0.75 D(1 + c1¢ ) D(1 + c2¢ )



1.496 0.4962 + 1.4773 c2¢ = 0.75 (1 + c2¢ ) 1.4962



4.7

c2¢ = 0.0312 c2¢ = 0.000 97 = 0.1% p1¢ =

l2 = (0.04327/1.1) = 0.0393cm 1 + c2¢

ends per cm = 25.4 = 25 contraction in warp = extension in weft =

p2 – p2¢ = 0.2668 = 26.7% p2

p1 – p1¢ = 0.1604 = 16.04% p1

Poisson ratio = 0.2668/0.1604 = 1.66

Reference

1. Peirce F T (1937), The Geometry of Cloth Structure. J. Text. Inst., Vol. 28, No. 3.

5

Shrinkage in woven fabrics

Abstract: The mechanism of fabric shrinkage from hydrophilic fibers is explained using a geometrical model. The relationship between yarn and fabric shrinkage is discussed. The prediction of fabric shrinkage is made by considering changes in yarn diameter and length due to swelling, fabric geometry and crimp balance. Practical applications of modeling fabric shrinkage are given. Key words: modeling, fabric geometry, crimp balance, fabric shrinkage.

5.1

Introduction

The shrinkage of natural fiber fabrics on washing has been one of the major problems requiring attention by textile technologists. A part of fabric shrinkage is due to stretching by applied tensions during manufacturing and finishing operations [1, 2]. Fabric shrinkage is a term associated with a reduction in the dimensions of fabric. A fabric on the weaving machine is under warp and weft tensions. As soon as the fabric leaves the templates that hold it in place, its width decreases. Similarly when the fabric is taken off the loom, one can observe a reduction in length and width; which can be checked by an increase in the ends and picks per cm. This is due to the release of tensions in the warp and weft so that the yarns recover to their relaxed state. This equilibrium is achieved by balancing of internal energy with the inter-yarn frictional force. It may be termed a pseudo-equilibrium and is designated as dry relaxation. The dimensional change accompanying the release of fiber strains imparted during manufacturing which have been set by the combined effects of time, finishing treatments and physical restraints within the structure is called relaxation shrinkage [3]. Collins [4] explained that fabric shrinkage is not only due to the release of strains imposed during the manufacturing process but also caused by fiber and yarn swelling produced on wetting, which brings about an internal rearrangement of the material resulting in external shortening. Cotton fiber absorbs water and shows a contraction of 1% and an increase in diameter of about 20%. The swelling is reversible. He postulated that when the yarn diameter is increased by the swelling action of water, the fiber must move around or along the yarn to a lesser degree. In order to pass around the yarn, the swollen fiber undulates, shrinking the yarn. Yarn shrinkage on wetting rarely exceeds 2% for normal twist. Twistless yarn shows no tendency to 109

110

Woven textile structure

stretch the fibre on yarn swelling. He observed that the stretched fibers show a true contraction of about 2%, which does not account for actual fabric shrinkage of the order of 10%. Shrinkage that results from the swelling and deswelling of the fibers due to absorption and desorption of water is called swelling shrinkage. Its magnitude depends upon the way in which the fiber interacts within the complex structure of the yarn and fabric. Shrinkage is the retraction of yarn when the external forces are removed. It is a manifestation of the release of strain in material and will continue until a minimum energy level is achieved. Any material when deformed by external forces will tend to recover to a state balanced by internal frictional force. In a fabric made from hydrophilic material the release of internal residual strain can be catalyzed by either washing and drying or by setting, for example resin finishing. Fabrics made from hydrophobic yarn can be relaxed by thermal setting. In both cases, the fabrics become relaxed and are dimensionally stable at the level of zero energy.

5.2

Mechanisms of fabric shrinkage

The mechanism of shrinkage of fabrics made from hydrophilic yarn is described by Collins [4]. On wetting a fabric, water is absorbed by the fibers in the yarn and causes swelling of fiber and yarn. Typically an increase of 10% in yarn diameter can be expected. Nevertheless, transverse swelling of fibers results in longitudinal shrinkages of only 1%. Yarn shrinkage, which is related to the degrees of twist imparted on the yarn during spinning, can give rise to more shrinkage but accounts for shrinkages of only 2% in typical fabrics. The explanation of cloth shrinkage lies in the fabric structure. Figure 5.1 shows one repeat along the warp. When the cloth is wetted the yarn increases in diameter. If the crossing weft threads are to remain the same distance apart as they are in the dry state, than warp would have to extend. As the cloth is under no constraint, the weft threads move closer together in order that the warp yarn can remain the same length. Therefore the cloth shrinks in the warp direction. A similar explanation is valid for shrinkage in the weft direction. The major cause of fabric shrinkage due to the swelling of threads on wetting is that the thick warp yarn requires more space to enable fibers to pass over and under the swollen weft yarn. The warp adopts an undulating path and shrinks the cloth. Shrinkage may be regarded as a change in yarn spacing, p. From the relation p1 = l2/(1 + c2), the observed shrinkage may be considered as the result of the change in yarn length and the change in crimp. The crimp change is a combination of change in crimp distribution and in the general level of crimps and is dependent on the value of l/D. As a change in the values of l alone also involves a change in crimp, these effects are not independent, but they may be separated for the purposes of the practical analysis.

Shrinkage in woven fabrics

111

Peirce suggested the shrinkage may be imagined to occur in two stages; initially the change in l and D due to the wetting and drying, during which the crimp balance or ratio remain constant, followed by a crimp redistribution to the final shrunk state. In the first stage, the crimps are affected by the changes in yarn lengths but only to a small extent, any large effect being due to the swelling of yarns, resulting in a change in D. It was found that as water is absorbed into the fabric the transverse swelling of the fibers and yarns induced shrinkage in three ways: longitudinal fiber shrinkage, yarn shrinkage and crimp accentuation. The mechanism of crimp accentuation is illustrated in Fig. 5.1, which represents the position of warp and weft yarns before wetting. It also shows the swelling of both yarns when the fabric is wetted. For the fabric to maintain the same external dimensions it had before wetting, i.e. not shrink at all, the warp yarns would have to extend by a given length. An extension would be necessary for the warp yarns to travel around the swollen weft yarns. There is an energetically simpler mechanism that accommodates the increased path of the warp yarns. In this mechanism, the weft yarns move closer together and warp path length remains the same. Likewise, an increase in the diameter of the weft yarns results in the movement of warp yarns closer together. For this reason, shrinkage of the fabric in both directions is observed. From this description it is clear that the fabric structure has a significant effect on a fabric’s response to wetting. The degrees of yarn twist, yarn diameter and sizing have some influence, but the spacing of yarns (degree

Cloth length

Coarse weft

(a)

Fine warp

(b)

5.1 Shrinkage of woven fabric (a) before wetting (b) after wetting.

112

Woven textile structure

of crimp) is the most critical factor. Thus, closer yarn spacing and relatively compacted yarns give greater shrinkage effects. The mechanization of the textile industry gave rise to an abundance of tightly woven fabrics produced with power spinning and power weaving processes. This type of fabric shrinks more than a handmade fabric at high moisture levels.

5.3

The relationship between cloth and yarn shrinkage

Suppose a cloth shrinks s % and that the percentage crimps of thread before and after shrinkage are c0 % and c % respectively. Then the following relations are valid:

l0 = p0 l =p

(100 + c0 %) 100

(100 + c0 %) 100

yarn shrinkage is given by:

sy = 100 (l – l0 )/l0 = (100 – s%)

100 + c % – 100 100 + c0 %

Thus the physical change, the contraction of the yarn, is separated from the more purely geometrical factor in the shrinkage, the change of crimp. It has been found that the yarn shrinkage is almost entirely confined to the first of a series of washing treatments. In later shrinkages, l must therefore be assumed constant and the crimp estimated from the measurements of shrinkage by the relation:

100 + c % 100 + c0 % = 100 100 – s %

In the swollen state D is increased and l decreased; both changes diminish p or the fabric dimensions. On drying, D diminishes and l increases but, in the absence of external tension, the extra length is more easily accommodated by slack inter-weaving than by an increase in external dimensions. Strictly, percentage shrinkages in successive stages are not additive, the total shrinkage s is given by (1 – s) = (1 – s1) (1 – s2) (1 – s3), where s1, s2, s3 are the successive shrinkages. In a fabric free from tension the crimps adjust so that the elastic forces are in equilibrium. The curvature of the crimped threads is not, however, all elastic; if released from all external restraint, they would retain most of the curvature as ‘set’. The setting of crimp has in general more influence on the crimp balance than the active elastic forces.

Shrinkage in woven fabrics

113

Almost any balance of crimps geometrically possible may be imposed on any cloth. That balance of crimps which corresponds to the equilibrium of elastic thread should, however, be favored by cloth subjected to changes of swelling while free from restraint, so that shrunk fabrics should show a tendency to approximate to this balance. According to this analysis, the balance should be given by a crimp balance equation, which may be expressed in the form:

log

5.4

c1 t m = 4 log 1 + 2 log 2 c2 t2 m1

Predicting fabric shrinkage

Peirce [1] separated fabric shrinkage due to yarn shrinkage and yarn swelling from the fabric on the loom and the fabric after a standard washing treatment. He analyzed the contribution of causes of shrinkage in terms of yarn shrinkage, swelling and crimp redistribution from the total fabric shrinkage. The shrinkage was imagined to occur in two stages: first the change in l and D due to wetting and drying, during which crimp balance (ratio) remains constant, followed by crimp redistribution to the final shrunk state. The crimps are affected by the changes in yarn length to a small extent, the significant effect being due to swelling of yarns causing a change in D. The fabric shrinkage was predicted [5] considering the mechanism of fabric shrinkage as explained above and using the changed parameters l¢ and D¢ along with crimp balance using the following four equations and the eligible domain for q1¢ and q2¢ considering the constraints to the value of q1¢ and q2¢. This process is explained in the algorithm as shown in Fig. 5.2.



Ê p2 ˆ ¢ Ê p1 ¢ ˆ Ê p ˆ¢ – q1 ¢˜ cos q1 ¢ + sin q1 ¢ + K , Á 2 ˜ = f (q1 ¢ ) ÁË ˜¯ = ÁË ¯ Ë D¯ D D¢

5.1



Ê p1ˆ ¢ Ê p2 ¢ ˆ Ê p ˆ¢ – q2 ¢˜ cos q2 ¢ + sin q2 ¢ + K , Á 1˜ = f (q2 ¢ ) ÁË ˜¯ = ÁË ¯ Ë D¯ D D¢

5.2



1 = h1/D + h2/D



ˆ ˆ Êl ¢ Êl ¢ 1 = Á 1 – q1 ¢˜ sin q1 ¢ + (1 – cos q1 ¢ ) + Á 2 – q2 ¢˜ ¯ ¯ Ë D¢ Ë D¢



sin q2 ¢ + (1 – cos q2 ¢ ), q1 ¢ = f (q2 ¢ )

sin q1 ¢ q1 ¢ Ê p2 ¢ˆ Ê b2 ˆ ¢ ª = sin q2 ¢ q2 ¢ ÁË p1 ¢˜¯ ÁË b1 ˜¯



5.3

2





5.4

114

Woven textile structure Start

Read l1/D, l2/D, q1¢, q2¢, b1 and b2 No

Is q1 ≥ 1.57?

q1 = q1 + 0.1 Yes

Is q2 ≥ 1.57?

No

Yes

a = (l1/D – q1) sin q1 + 1 – cos q1 b = (l2/D – q2) sin q2 + 1 – cos q2

Is | a + b – 1 | £ 0.001?

q2 = q2 + 0.1

No

Yes Is | R1 – R2 | £ 0.001?

No

End

5.2 Flowchart for prediction of fabric shrinkage.

Constraints:

q 1¢ > q 1



q2¢ > q2, provided q1¢ and q2¢ > p/2

For any q1¢, q2¢ < p/2, the shrinkage will be restricted to this limiting value Logic for shrinkage prediction: for given values of (l1/D) and (l2/D)

p2 Ê l1 p ˆ = Á – q1 ¢˜ cos q1 ¢ + sin q1 ¢ fi 2 = f (q1 ¢ ) ¯ Ë D D D

5.5

Shrinkage in woven fabrics

115



p1 Ê l2 p ˆ = Á – q2 ¢˜ cos q2 ¢ + sin q2 ¢ fi 1 = f (q2 ¢ ) ¯ Ë D D D



ˆ Êl ˆ Êl 1 = Á 1 – q1 ¢˜ sin q1 ¢ + (1– cos q1 ¢ ) + Á 2 – q2 ¢˜ sin q2 ¢ + (1– cos q2 ¢ ) ¯ ËD ¯ ËD

5.6

Therefore

q2 ¢ = f (q1 ¢ )



q1 ¢ Ê P2 /dˆ Ê b2 ˆ = q2 ¢ ÁË P1 /d ˜¯ ÁË b1 ˜¯

5.7 2

5.8

Constraints:

q 1¢ > q 1



q2¢ > q2 , provided (l1/D) and (l2/D) > p/2



A Æ if

p l l1 p l £ then q1 ¢ = 1 and 2 = sin q1 ¢ = sin 1 D D D 2 D

B Æ if

p l l2 p l £ then q2 ¢ = 2 and 1 = sin q2 ¢ = sin 2 5.10 D D D 2 D

5.9

(p1/D) and (p2/D) will be obtained from equations 5.5 and 5.6. Initial start checks (l1/D) and (l2/D) for A and B follow equations 5.5 and 5.6 or else equations 5.1 and 5.2. Initially take q1¢ = q1 + Dq1 (assume small increment) and find q2¢, from equation 5.3. Then find (p1/D) and (p2/D) for corresponding value of q1¢ and q2¢. Finally check if equation 5.4 is satisfied for the calculated values of q1¢, q2¢, (p1/D) and (p2/D). If not give increment to q1¢, get the corresponding q2¢, then again (p1/D) and (p2/D) and recheck validity of equation 5.4. Iterate until equation 5.4 is satisfied for the small value.

5.5

Application of fabric shrinkage model

Q1. A poplin fabric has p1 = 0.023 cm, p2 = 0.042 697 cm, D = 0.020 07 cm and q1 = 21.8525, q2 = 26.6058. After washing, shrinkage percentages of 2.98 in warp and 1.61 in the weft direction of fabric are observed. The percentage crimps are 4.25 in the warp and 6.3 in the weft before shrinkage and 7.03/7.6 in the warp/weft after the shrinkage. The percentage shrinkage in the warp/weft yarn is 0.399/0.415 respectively and the change in D is 17.5%. Predict the thread spacing in the fabric using the above logic given in the algorithm and calculate the percentage

116

Woven textile structure

error in the prediction. Solution:

l1 = p2 (1 + c1) = 0.042 697 ¥ 1.0425 = 0.044 526 cm



l2 = p1 (1 + c2) = 0.023 × 1.063 = 0.024 485 6 cm



D = h1 + h2 = 0.020 066 cm



D¢ = D ¥ 1.175 = 0.020 066 ¥ 1.175 = 0.023 571 2 cm



l1¢ = l1 ¥ 0.9702 = 0.044 526 ¥ 0.9702 = 0.044 348 4 cm



l2¢ = l2 ¥ 0.9839 = 0.024 486 ¥ 0.9839 = 0.024 384 cm



l1 0.044 526 = = 2.218 98 > p D 0.020 066 2



l2 0.024 485 6 = = 1.220 25 < p D 0.020 066 2



l1 ¢ 0.044 348 4 = = 1.88147 > p D 0.0235712 2



l2 ¢ 0.024 384 = = 1.0345 < p D 0.0235712 2



q1 = 106 0.0425 = 21.8525°



q2 = 106 0.063 = 26.6058°

Since (l2/D) ≤ p/2, the fabric before washing has tendency for jamming in the weft if deformed, but the warp direction has no constraints. One can infer that the warp direction can shrink more than the weft direction; the weft direction can shrink only until the weft is jammed. This inference is supported by the actual shrinkage percentage in warp being 2.98 and 1.61 in the weft direction. Again since (l1¢/D’) and (l2¢/D¢) are less than their counterparts in the fabric; therefore crimps in both warp and weft will be greater after washing. In this case the solution is obtained by taking q1¢ > 21.8525°, that is equal to 21.8525 + Dq1 and corresponding q2¢ is calculated from equation 5.3. Then (p1¢/D¢) and (p2¢/D¢) are calculated from equations 5.1 and 5.2 respectively for these values of q1¢ and q2¢. Finally the authenticity of the value is checked using equation 5.4. In this example the ratio of bending rigidity was taken as unity. The iteration for q1¢ and corresponding q2¢ was repeated until equation 5.4 was satisfied.

Shrinkage in woven fabrics

117

In this case the solutions are obtained for q1¢ = 30.21° and q2¢ = 11.68°. Calculated p1¢ and p2¢ are:

p1¢ = 0.023 98 cm



p2¢ = 0.039 44 cm

The actual values are:

p1¢ = 0.022 657 cm



p2¢ = 0.041 427 cm

The percentage error for p1¢ is 5.84 and for p2¢ is 4.8. This is reasonable as the bending rigidity is ignored.

5.6

References

1. Peirce F T (1937), J. Text. Inst., 28, T80 2. Marsh J T (1953), An Introduction to Textile Finishing, Chapman and Hall, London, p 241 3. Abbott N J, Khoury F and Barish L (1964), J. Text. Inst., 55, p T111-T127 4. Collins G E (1939), J. Text. Inst., 30, p 46 5. Hari P K (1970), M. Tech Thesis, IIT Delhi

6

Yarn behavior in woven fabrics

Abstract: An elastic model of woven fabric is considered for calculating fabric parameters. The model helps in predicting inter-yarn forces at the cross-over point. An offshoot of this analysis is a very useful crimp balance equation which can be used to predict desired crimp in the warp and weft directions. The role of inter-yarn forces and setting on deformation and recovery is discussed. Numerical examples are given to understand practical applications. Key words: elastic model, inter-yarn forces, crimp balance equation.

6.1

Introduction

In real fabrics the cross-section of yarn varies considerably for different fabrics. The cross-section can be circular, elliptical, racetrack or any other shape. It all depends on the yarn density and packing of yarn in the fabric. The question arises as to why the cross-section should vary in different fabrics. There has to be some sort of force acting between the yarns in the intersection region. Peirce [1] suggested that textile yarns may be assumed to be perfectly elastic and isotropic materials as they possess rigidity. Their resistance to bending affects the form of the yarn in a fabric and has a marked effect on the balance of crimps. The actual elastic behavior of the yarn deviates from this simple elastic theory. In fact, stress on the yarn will relax as function of time due to the visco-elastic character of textile materials. However elastic theory can be very useful in deciding the equilibrium of crimp balance in a cloth. Olofsson [2] assumed that the yarn will take shape produced by such forces and that the cross-yarn will ‘flow’ into the available space. The yarn takes up the shape of an elastica [3] being bent by point loads acting at the intersections. This approach gives valuable information on the inter-yarn force, balance of crimp between warp, and weft and the degree of setting.

6.2

The yarn path in woven fabrics and inter-yarn forces

The yarn path produced by the inter-yarn forces which spread across the contact region is shown in Fig. 6.1. AB shows half the repeat and O is the point of inflexion as the two curvatures OA and OB are similar. In a relaxed 118

Yarn behavior in woven fabrics

119

B O

q

h1/2 h2/2

A Warp

p2

Weft

6.1 Yarn path produced by inter-yarn force.

fabric these will have a resultant 2V1 acting at A and B on the warp in the vertical direction. The warp yarn path is shown in Fig. 6.2: The intersecting thread only touches the cross-thread at the point of intersection where the curvature is maximum and is equal to 2/D. However, the intersecting thread can be forced into contact for a finite distance over which its curvature will be 2/D. The former shows the condition for point contact and the latter for second order or distributed contact. O is a point of inflexion so that 1/r = 0 and therefore M = 0. The forces here may be expressed as a tension, –T, and a shearing force, –S. These can be resolved as a horizontal force (–U = –T cos q + S sin q) and a vertical force (–V = –T cos q – S sin q). The bending moment at any point P(x, y) on the yarn axis is given by:

B dy/ds = –V x + U y

When the external force U is considerable, the form approaches that of a flexible thread and the rigidity may be ignored. But when the external tension on the cloth is zero, the horizontal component U = 0 and T = S tan q Consider section OP as shown in Fig. 6.3 with force V1 and bending moment M. The bending moment at P is produced by forces V1 and the moment about O gives

M – V1 x = 0



fi M = V1 x

hence

V1 x = – B1 dy/ds

6.1

(the negative sign is due to the inverse relation of s and y, i.e. as s increases y decreases) where B1 = flexural rigidity of warp yarn. Since

dx/ds = cos y



fi V1 x = – B1 cos y dy/ds



fi V1 x dx = –B1 cos y dy

120

Woven textile structure 2V1 B P O T

S

A

2V1

6.2 Yarn shape in fabrics. y V1

p

M

s q1

y M=0

O

x

V1

6.3 Forces acting on elastica.



fi ∫ V1 x dx = ∫ –B1 cos y dy fi

1 V x 2 = – B sin y + const. 1 1 2

At O, x = 0, y = q1

fi const = B1 sin q1

1 V x 2 = – B (sin q – sin y ) 1 1 1 2 At point B, y = 0, x = 1/2 p2. Equation 6.2 then gives fi



1 V p 2 = B sin q 1 2 1 1 8

V1 = 8 B1 sin q1 /p22 Similarly by interchanging the suffix 1 with 2 and vice versa, we get

6.2

V2 = 8 B2 sin q2 /p12

6.3 6.4

Yarn behavior in woven fabrics

121

However, 2V1 and 2V2 are the inter-yarn forces for warp and weft yarn in the repeat as shown in Fig. 6.2. Their magnitudes have an important bearing on the cross-sectional shape and the deformation–recovery behavior of the fabric. It is interesting to understand that bending rigidity of the yarn is a precursor for the growth of inter-yarn force at the cross-over point and this is in equilibrium with an identical inter-yarn force from the cross-thread. There are major implications of these forces in the cross-over region: ∑

∑

The change in the yarn cross-section: the deformed shape depends on the force distribution. This has an indirect effect on the fabric cover, fabric thickness and deformation-recovery of the fabric due to resistance offered by the frictional force in this region. The yarn in the fabric will have two distinct regions whose properties will be very different. The yarn in the fabric will exhibit anisotropy for any deformation and recovery.

The magnitude of the inter-yarn force as determined above is valuable in understanding the level of strains in the fabric.

6.3

The crimp balance equation

In general 2V1= 2V2 for the relaxed fabric, therefore

B1 sin q1 /p22 = B2 sin q2 /p12 2



sin q1 Ê p2 ˆ Ê B2 ˆ = sin q2 ÁË p1 ˜¯ ÁË B1 ˜¯



6.5

2



c1 Ê p2 ˆ Ê B2 ˆ = c2 ÁË p1 ˜¯ ÁË B1 ˜¯ 4



c1 Ê p2 ˆ Ê d2 ˆ = c2 ÁË p1 ˜¯ ÁË d1 ˜¯ 4



c1 Ê p2 ˆ Ê T2 ˆ = c2 ÁË p1 ˜¯ ÁË T1 ˜¯



6.6

8



6.7

4



6.8

This is called the crimp balance equation and is applicable for a relaxed fabric. In a relaxed fabric the inter-yarn forces are negligible and the crimps in the two directions are decided by the thread spacing and yarn diameter according to the above equation. Crimp balance is another important offshoot of the bending rigidity of yarn in the fabric. The ratio of crimps, the balance

122

Woven textile structure

between warp and weft crimps, in the two directions of the fabric will be governed by the given thread spacing and yarn tex. The thread spacing and diameter of the yarn decide the yarn crimp. It should be remembered that crimp interchange is an entirely different concept as it gives the relationship between warp and weft crimp and helps in evaluating the interchange from one direction to the other. Crimp balance gives the balance between the warp and weft crimps, whereas crimp interchange gives the effect of change in one direction to the other direction.

6.4

Predicting the yarn path in woven fabrics

Fabric parameters are obtained by the following equation. Differentiating equation 6.1 with respect to s, gives: B1

d2y = – V1 dx = – V1 cos y ds 2 ds



Ú

2 B1



Ê dy ˆ B1 Á ˜ = – 2V1 sin y + const Ë ds ¯



dy d 2 y = ds ds 2

Ú

– 2V1 cos y

dy ds

2

At O, dy/ds = 0, y = q1

fi constant = 2V1 sin q1 fi B1 (dy/ds)2 = 2V1 (sin q1 – sin y) dy 2V1 =– sin q1 – sin y ds B1



(negative sign since as s increases y decreases)



Ê 2V ˆ = Á 1˜ Ë B1 ¯





=

1/2

È q1ˆ yˆ ˘ 2 Êp 2 Êp Í2 sin ÁË 4 + 2 ˜¯ – 2 sin ÁË 4 + 2 ˜¯ ˙ Î ˚

2V1 B1

= –2

1/2

È Êp ˆ˘ ˆ Êp Ícos ÁË 2 + y ˜¯ – cos ÁË 2 + q1˜¯ ˙ Î ˚

V1 B1

È 2 Ísin Î

Ê p q1ˆ 2 ÁË + ˜¯ – sin 4 2

Ê p yˆ ˘ ÁË + ˜¯ ˙ 4 2 ˚

6.9

Introduce k = sin (p/4 + q1/2) <1. Note that at O, y = q1 fi j0 = p/2 and define k sin j = sin (p/4 + y/2), as at B,

Yarn behavior in woven fabrics



123

y = 0 fi jB = sin–1 (k/√2) (A)

then

Ê p yˆ k cos j d j = 1 cos Á + ˜ dy (B) Ë 4 2¯ 2 2 k cosj d j cosj d j = p yˆ Ê 1 – k 2 sin 2 j cos Á + ˜ Ë 4 2¯

dy = 2k

Substitute this value in equation 6.9:



dy 2 k cosj dj = 2 2 ds 1 – k sin j ds 2 k cosj

dj V = –2 1 (k 2 – k 2 sin 2 j ) ds B1 1 – k sin j 2



2

=2











V1 k cos j B1

ÊB ˆ ds = – Á 1 ˜ (1 – k 2 sin 2 j )–1/2 dj Ë V1 ¯ ÊB ˆ s = – Á 1˜ Ë V1 ¯ ÊB ˆ = Á 1˜ Ë V1 ¯ =

B1 È Í V1 Î

=

B1 V1

Ú

Ú

p /2

p /2

jB

Ú

jB

p /2

0

(1 – k 2 sin 2 j )–1/2 dj

(1 – k 2 sin 2 j )–1/2 dj

(1 – k 2 sin 2 j )–1/2 dj –

È Ê pˆ ˘ ÍÎF Ë k, 2¯ – F (k, j )˙˚

where

F (k, j ) =

Ú

jB

0

6.10



(1 – k 2 sin 2 j )–1/2 dj

Ú

jB

0

˘ (1 – k 2 sin 2 j )–1/2 dj ˙ ˚

124

Woven textile structure

is elliptical integral of first kind, and

E (k, j ) =

Ú

p /2

0

(1 – k 2 sin 2 j )1/2 dj

is elliptical integral of second kind. At B:

ˆ Ê s = l1 /2, j = j B = sin –1 Á 1 ˜ Ë k 2¯ l1 = 2

B1 V1

È Ê pˆ ˘ ÍÎF Ë k, 2¯ – F (k, j B )˙˚

6.11

l1 is the length of warp yarn between two consecutive weft threads. This is also known as the warp modular length. Next dy/ds = sin y:

dy = siny ds dj dj



= – cos Ê p + y ˆ ds Ë2 ¯ dj



Ï È y ˆ ˘¸ Ê = – Ì1 – 2 Ísin 2 Á p + ˜ ˙˝ ds Ë 4 2 ¯ ˚˛ dj Î Ó

using B and equation 6.9 we get:



È B1 ˘ – (1 – 2 k 2 sin 2 j ) Í– (1 – k 2 sin 2 j )–1/2 ˙ Î V1 ˚



Ê B ˆ Ï2[(1 – k 2 sin 2 j ) – 1]¸ = Á 1˜ Ì ˝ Ë V1 ¯ Ó (1 – k 2 sin 2 j )1/2 ˛







ÊB ˆ dy = Á 1˜ [2(1 – k 2 sin 2 j )1/2 – (1 – k 2 sin 2 )–1/2 ] dj Ë V1 ¯ ÊB ˆ y = Á 1˜ 2 Ë V1 ¯ ÊB ˆ = Á 1˜ Ë V1 ¯

Ú

j

p /2

È 2 2 1/2 Í(1 – k sin j ) – Î

Ú

j

p /2

˘ (1 – k 2 sin 2 j )–1/2 ˙ dj ˚

Ï È Ê pˆ ˘ È Ê pˆ ˘¸ Ì2 ÍE (k, j ) – E Ë k, ¯ ˙ – ÍF (k, j ) – F Ë k, ¯ ˙˝ 2 2 ˚˛ ˚ Î Ó Î

Yarn behavior in woven fabrics



y=

B1 V1

Ï Ê pˆ ¸ ÌF Ë k, ¯ – F (k, j ) – 2 [E (k, p /2) – E (k, j )]˝ 2 Ó ˛

125

6.12

At point B, y = h1/2 and j = jB:

B1 {F (k, p /2) – F (k, j B) – 2[E (k, p /2) – E (k, j B)]} 6.13 V1

h1 = 2

h1 is the displacement of warp thread between consecutive weft threads. This is also called crimp amplitude or height. Figure 6.4 shows yarn paths for a limiting weave angle of 49.07° at different thread spacings. It can be seen that with the decrease in thread spacing the yarn path curve flattens out relatively. The yarn path curve is different for different thread spacing for a constant limiting weave angle. Figure 6.5 shows the yarn path for different values of weave angle up to a limiting value of 49.07° for thread spacing p equal to 0.032 cm. It is clear that the yarn path is different for different weave angles for constant thread spacing. It should be noted that the above analysis is for point contact. When a second order contact is made for a finite distance, it is called a distributed contact and the following modifications are required. The above equations hold to x = X = (2B)/(D2V), where, if Y is the value of y at this point. sin Y = sin q – X/D

0.020

Crimp height (cm)



0.015

p = 0.0425 p = 0.0325

0.010 p = 0.0225 0.005

0

p = 0.0125

0

0.005

0.010 0.015 Thread spacing (cm)

6.4 Yarn path for a limiting weave angle of 49.07°.

0.020

126

Woven textile structure 7

¥ 10–3

6

Crimp height (cm)

5 q = 49.07° 4 q = 40° 3 q = 30° 2

q = 20°

1 0

q = 10°

0

1

2 3 4 5 Distance from the point of inflexion (cm)

6

7 ¥ 10–3

6.5 Yarn path for different values of weave angle.

while from geometry, sin y =

p – 2X D

sin q =

p–X D

and therefore:

If Y is the value of y, X that of j when x = X:

h/2D = Y/D + 1 – cos Y



l/D = Y + (2/D) √(B/V)[F–F(X)]

and

Ï ¸ c = D /p Ì 2X [F – F (j ) + Y ]˝ – 1 Ó D ˛

A comparison between the flexible thread geometrical model and these two cases of the rigid thread model can be made. When second order contact is made for a finite distance, the configuration approaches the geometrical model. The analysis of point contact configuration is interesting, though it does not happen in actual fabrics. For p/D = 2 sin q, h/D = 1 gives 23.8%

Yarn behavior in woven fabrics

127

crimp in a flexible thread; whereas for point contact at the cross-over point for q = 49.07°, p/D = 1.511 gives 23.73% crimp. This is the maximum crimp possible in point contact for rigid thread. Crimp in this case is more than that for the flexible thread geometrical model (22.8%) and less than that from the approximate formula (h1 = 4/3 p2√c1) (24.6%). The possible structures are limited by either jamming of the threads, which are identical with those for the flexible thread model or by the straightening of the crossthreads. The point contact holds for smaller crimps until p/D = 2 sin q, and h/D = 1, implying cross-threads are straight (here p/D = 1/(h/p)). For any crimp more than 23.73%, distributed contact applies, as the thread spacing is increased till cross-threads become straight and h = D in equation of crimp. The only important effect of yarn rigidity is the mutual resistance of the threads to bending and its influence on the balance of crimps when external tensions are low. √c = 0.55 q radians or sin q = 1.75√c1.

6.5

The effect of settings on yarn behavior

Being visco-elastic, textile yarns exhibit time-dependent effects such as stress relaxation. This causes decay in the inter-yarn force at the cross-over point and results in some sort of setting. This can be understood by taking out the crimped yarn from the fabric. It will be observed that the yarn does retain some of its crimped configuration. The magnitude of setting can be evaluated by using Olofsson’s approach [2]. Using equation 6.1 we get;

V1 x = B1 (dy/ds – dy0/ds0)

dy/ds represents the curvature of yarn in the fabric and the 0 suffix represents the yarn taken out from the fabric. The yarn curvature in the released state is related to the curvature of the yarn in the fabric as shown below:

dy0/ds0 = (1 + Ø) dy/ds

6.14

where (1 + Ø) is a proportionality constant and is a measure of degree of setting. If the yarn is straight, dy0/ds0 = 0, so (1 + Ø) dy/ds = 0. We get Ø = –1, for no setting. Similarly, dy0/ds0 = dy/ds means the relaxed yarn retains the curvature of the yarn in the fabric and is completely set. We get (1 + Ø) = 1, therefore Ø = 0, for complete setting. We can use Ø as a parameter for the degree of setting in the range 1 ≤ Ø ≤ 0. The modified equation for the warp inter-yarn force will be:

V1 = – 8 Ø B1 sin q1/p22

128

6.6

Woven textile structure

Crimp interchange and crimp balance equations

The crimp balance equation 6.6 gives: 4



c1 Ê p2 ˆ Ê B2 ˆ = c2 ÁË p1 ˜¯ ÁË B1 ˜¯ 4



2

2

4

c1 Ê1 + c2 ˆ Ê B2 ˆ Ê l1 /D ˆ = c2 ÁË 1 + c1 ˜¯ ÁË B1 ˜¯ ÁË l2 /D˜¯

6.15

The important variables of crimp balance equations are B2/B1, l1/D and l2/D. This equation can be solved for c1 and c2 for given values of l1/D, l2/D and for different values of B2/B1 using the algorithm as shown in Fig. 6.6. The crimp interchange equation 4.1 is:



l1 c1 ¢ l c ¢ + 2 2 = 3D (1 + c1 ¢ ) (1 + c2 ¢ ) 4



l1 c1 ¢ c2 ¢ l + 2 =3 D (1 + c1 ¢ ) D (1 + c2 ¢ ) 4

For given values of l1/D and l2/D, these equations can be solved for c1 and c2. Figures 6.7, 6.8 and 6.9 show the interaction of crimp interchange and crimp balance equations corresponding to l1/D = l2/D, l1/D > l2/D and l1/D < l2/D respectively. The scales are also calibrated in terms of crimp. All balanced fabrics must lie on these curved lines. In addition any fabric which maintains a constant value of l during changes in dimension must lie on a straight line. It is interesting to note that in all these curves with the increase in B2/ B1, warp crimp increases and weft crimp decreases. Another interesting result can be seen from these figures when l1/D is not equal to l2/D; l1/D > l2/D or l1/D < l2/D causes a reduction in the range and shift towards lower values for both c1 and c2. These three curves show very interesting ways in which the values of crimp in warp and weft can be varied in a wide range. Therefore the three parameters B2/B1, l1/D and l2/D can influence the crimp in warp and weft in a wide range and this is what gives maneuverability to the fabric designer. Moreover these figures can be exploited for predicting shrinkage in a fabric as demonstrated in Chapter 5.

Yarn behavior in woven fabrics

129

Start

Enter l1/D, l2/D A B = B2/B1 = 0.2

c1 = 0.001, r =

A=

l1 /D l2 /D

B = B + 0.4

No

c1 1 + c1

Yes End

B = (0.75–A ¥ l1/D)/l2/D

Plot A vs B

a=1

c2 = 0.0001

Is a > 0.0001?

No

Plot c1 vs c2

c2 = c2 + 0.001 Yes a = c1/c2 –[(1 + c2)/(1 + c1)]4B2r4 c1 = c1 + 0.001

No

Is B = 2.4?

Is c1 > 0.5?

Yes A

6.6 Flowchart for solution of crimp balance equations.

130

Woven textile structure c2

c2 1 + c2

0.46

0.45

0.45

0.40

0.44

0.35

0.42

0.30

0.40

0.25

0.37

0.20

0.34

0.15

0.29

0.10

0.21

0.05

0

0

B = 0.2 B = 0.6 B=1 B = 1.4

B = 1.8

0

0.05 0.10 0.15

0.20 0.25

0.30

0.35 0.40

0

0.21 0.29 0.34

0.37 0.40

0.42

0.44

0.45 c1

0.45 0.46

c1 1 + c1

6.7 Interaction of crimp interchange and crimp balance equations (l1/D = l2/D). c2 0.46 0.45

0.45 0.40

0.44

0.35

0.42

0.30

c2 0.40 1 + c2 0.37

0.25

0.34

0.15

0.29

0.10

0.21

0.05

0

0

B = 0.2

B = 0.6

0.20

B=1 B = 1.4 B = 1.8 0

0.05

0.1

0.15

0

0.21 0.29 0.34

0.20 0.25 0.37 0.40

0.30 0.35

0.40

0.45 c1

0.42 0.44 0.45 0.46

c1 1 + c1

6.8 Interaction of crimp interchange and crimp balance equations (l1/D > l2/D).

Yarn behavior in woven fabrics c2 0.46

0.45

0.45

0.40

0.44

0.35

0.42

0.30

0.40 c2 1 + c2 0.37

0.25

0.34

0.15

0.29

0.10

0.21

0.05

0

0

B = 0.2 B = 0.6

B=1

131

B = 1.4 B = 1.8

0.20

0

0.05 0.10 0.15

0.20 0.25

0.30

0.35 0.40

0

0.21 0.29 0.34

0.37 0.40

0.42

0.44

0.45 c1

0.45 0.46

c1 1 + c1

6.9 Interaction of crimp interchange and crimp balance equations (l1/D < l2/D).

6.7

Calculating fabric properties: numerical examples

Q1. Calculate the weave angle, radii of curvature and crimp height for a plain cloth from the following particulars: cotton yarn of 54 tex. p1 and p2 are 0.0529 cm and 0.0429 cm respectively, c1 and c2 are 7.01% and 12% respectively. Also calculate a and b (assuming racetrack cross-section and a1 = a2, b1 = b2, a/b = 1.3). Assume f = 0.65, rf = 1.52 g/cm3. Solution:

q1 = 106 c1 = 106 0.07 = 18.04°



q2 = 106 c2 = 106 0.12 = 36.72°



1 = 4 ¥ sin q1 = 4 ¥ sin 28.04 = 47.01cm –1 1/25 r1 p2



1 = 4 ¥ sin q2 = 4 ¥ sin 36.72 = 47.83cm –1 1/20 r2 p1

132



Woven textile structure

d1 = d2 = d =

54 = 0.026 38 cm 280.2 0.65 ¥ 1.52



D = 0.052 76 cm



h1 = 4/3 p2 √c1 = 0.014 11 cm



h2 = 4/3 p1 √c2 = 0.023 09 cm

For racetrack cross-section

p ¥ d 2 = p ¥ b 2 + b (a – b ) 4 4



p ¥ d 2 = p ¥ b 2 + b 2 ¥ 0.3 4 4 fi

p ¥ d 2 p ¥ (0.026 38)2 b =4 =4 p + 0.3 p + 0.3 4 4 2



fi b = 0.0224 cm



fi a = 0.029 cm

Q2. A woven fabric is made from 45 tex cotton yarn in warp and weft. The ends and picks per cm are 20 and 24 and the percent crimps are 7 and 12 respectively. Find the ratio of bending rigidity of warp to weft and fabric thickness. Assume f = 0.65, rf = 1.54 g/cm3. Solution: T d1 = 1 = 45/1.54 = 0.02392 cm m 226 fiber density 226



D = 0.047 84 cm



p1 = 0.05 cm



p2 = 0.041 666 cm



h1 = 4 p2 c1 = 0.0147 cm 3



h2 = 4 p1 c2 = 0.0231cm 3



h1 + d1 = 0.0386 cm



h2 + d2 = 0.0470 cm



fabric thickness = 0.047 cm

Yarn behavior in woven fabrics

133

The crimp balance equation is: 2

c1 Ê p2 ˆ B2 = c2 ÁË p1 ˜¯ B1



2

\ \

0.07 = Ê 20 ˆ B2 Á ˜ 0.12 Ë 24¯ B1



B1 = 0.6944 ¥ 1.3093 = 0.9092 B2

Q3. The ends and picks per cm are 18 and 24. The warp and weft percent crimps required are 5 and 10. What should be the ratio of the warp and weft yarn diameter? Solution: The crimp balance equation is: 2

c1 Ê p2 ˆ B2 = c2 ÁË p1 ˜¯ B1

\



B2 = 0.7071 ¥ 1.778 = 0.2572 B1

Since bending rigidity µ d4 4

\

B2 Ê d2 ˆ = = 1.2572 B1 ÁË d1 ˜¯ d1 = 0.9444 d2

Q4. What should be the ratio of ends to picks per cm if the percent crimp in warp and weft is to be 15 and 5 and the warp and weft tex 15 and 20 respectively? Assume f = 0.65, rf = 1.52 g/cm3. Solution:

15 = 0.0139 cm d1 = 1 226 1.52



20 = 0.016 05 cm d2 = 1 226 1.52



c1 = 0.15



c2 = 0.05

134

Woven textile structure



ends per cm p2 = = picks per cm p1



Ê ˆ B1 Ê d1 ˆ = Á ˜ = Á 0.0139 ˜ = 0.5626 B2 Ë d2 ¯ Ë 0.016 05¯

1

B1 Ê c1 ˆ 4 B2 ÁË c2 ˜¯ 4

4

1

4 p1 = 0.5626 Ê 0.15ˆ = 0.750 ¥ 1.3161 = 0.987 075 Ë 0.05¯ p2



Q5. In a fabric woven from 40 tex, p1 = 0.0508 cm, p2 = 0.0381 cm, c1 = 5%, c2 = 10%. Calculate the minimum radii of curvature. Assume f = 0.65, rf = 1.52 g/cm3. Solution:

40 = 0.022 70 cm d= 1 226 1.52



D = 0.0454 cm 2



2 Ê p2 ˆ Ê 0.0381ˆ = 0.5625 = ÁË p ˜¯ Ë 0.0508¯ 1

c1 = 0.05 = 0.7071 c2 0.10



Using equation 6.1 along with the value of V for x = p2/2 we get: minimum radius of curvature of warp yarn =

q1 = 106 c1 = 106 0.05 = 23.70°



q2 = 106 c2 = 106 0.10 = 33.52°



p2 = 0.0381 4 sin q1 4 ¥ 0.401 95

= 0.0237 cm–1

minimum radius of curvature for weft yarn =



p1 = 0.0508 4 sin q2 4 ¥ 0.5522

= 0.0230 cm–1

Yarn behavior in woven fabrics

135

Q6. Calculate the picks per cm in a plain woven fabric if c1/c2 = 2, warp/ weft = 40/20 tex, ends per cm = 22. Solution: c1 = 2 = 1.4142 c2



T1 40 = =2 T2 20



d1 T = 1 = 2 = 1.4142 d2 T2



ˆ p2 Ê 22 = p1 ÁË picks per cm˜¯ 2

2

2

4

Ê p ˆ Êd ˆ Ê p ˆ ÊT ˆ c1 Ê p2 ˆ B = Á ˜ ¥ 2 = Á 2˜ Á 2˜ = Á 2˜ Á 2˜ c2 Ë p1 ¯ B1 Ë p1 ¯ Ë d1 ¯ Ë p1 ¯ Ë T1 ¯



2

ˆ Ê 1ˆ Ê 22 2=Á Á ˜ Ë picks per cm˜¯ Ë 2¯

\

2

2

1

\

ÈÊ 22 ˆ 2 Ê 1 ˆ ˘ 2 È ˘ picks per cm = ÍÁ ˜ Á ˜ ˙ = Í111 ˙ = 11 = 9.25 ª 9 ÍÎË 2 ¯ Ë 2¯ ˙˚ Î2 4 ˚ 1.189 21

Q7. Calculate the ratio of crimp in a woven fabric if warp/weft = 45/15 tex, ends per cm = 11, picks per cm = 10. Solution: 2



2 Ê p2 ˆ Ê 11ˆ = 1.21 = ÁË p ˜¯ Ë10¯ 1

d1 T = 1 = 45 = 1.7321 d2 T2 15 2



2

4

2

Ê p ˆ ÊT ˆ c1 Ê p2 ˆ B2 Ê p2 ˆ Ê d2 ˆ = = = Á 2˜ Á 2˜ c2 ÁË p1 ˜¯ B1 ÁË p1 ˜¯ ÁË d1 ˜¯ Ë p1 ¯ Ë T1 ¯

2

136

Woven textile structure 2

\

6.8

c1 Ê1ˆ = 1.21 ¥ Á ˜ = 1.21 = 0.1345 Ë 3¯ c2 9 c1 = 0.0181 c2

Practical applications

Consideration of yarn rigidity helps in the analysis of fabric parameters. The analysis is helpful in evaluating the following important parameters which have a bearing on the deformation–recovery behavior and other characteristics such as handle and drape. Evaluation of inter-yarn force and setting gives a direction to the effectiveness of the relaxation treatment given to the fabric. The degree of relaxation can be evaluated using the setting parameter defined in the analysis. The setting parameter is a useful tool to evaluate the effectiveness of setting in processing. Another important gain of the analysis is the crimp balance equation which shows the effect of thread spacing and yarn diameter or tex or bending rigidity on the relative crimp between the two directions of the fabric. All these are useful practical applications of the technique. Finally the interaction between crimp interchange and crimp balance equation in a relaxed fabric is a useful way to predict the crimp in the warp and weft for known values of the ratio of bending rigidity in warp and weft for certain l1/D and l2/D values.

6.9

References

1. Peirce F T (1937), J. Text. Inst., 28, (3). 2. Olofsson B (1964), J. Text. Inst., 55, T541. 3. Hearle J W S, Grosberg P and Backer S (1969), Structural Mechanics of Fiber, Yarn and Fabrics, Vol. 1, Wiley.

7

Tensile behavior of woven fabrics

Abstract: Geometrical changes, the Poisson ratio and tensile modulus during extension at low loads are important tensile parameters. The fabric tensile modulus is calculated by using strain energy and considering a sawtooth model of the fabric. The nature of deformation and the mechanisms involved in the bias extension of fabric are considered. Analysis of bias extension is given to calculate the fabric modulus in the bias direction. The factors affecting tensile strength of a fabric are discussed. Key words: fabric tensile modulus, tensile strength, sawtooth model.

7.1

Introduction

The tensile properties of woven fabrics, together with other mechanical properties such as bending, shear and compression, are of considerable importance in determining how the fabric will perform in use. Traditionally, tensile strength of fibrous materials is regarded as the main criterion of quality. In apparel fabrics, the tensile strains encountered are likely to be small, whereas for certain industrial applications the strain level can be very large. Although tensile strength is of great importance, it must be remembered that properties such as flexural rigidity, compressibility, resilience and, moisture transmission must be considered when designing high quality fabrics. The relative importance of any particular property will depend on the end-use application of the fabric. Achieving desired fabric properties is particularly important in industrial applications where failure can have serious consequences. In cases where the fabric is not called upon to withstand large tensile forces, breaking strength is used to provide some measure of fabric quality. As such, the tensile strength of a fabric should be much higher than the maximum stress likely to be encountered in actual use because the fabric is subjected to repeated stresses which degrade the material during its lifetime and result in deterioration of strength. Besides determination of maximum tensile strength-extension, analysis of tensile behavior of the woven fabric is also necessary to understand the relation between fabric parameters during deformation. The consideration of tensile properties of a woven fabric involves a number of problems mainly because the fabric is anisotropic and has a modulus which varies considerably with strain. Fabrics in most cases are not symmetrical, and therefore the moduli in the warp and weft direction are 137

138

Woven textile structure

different. In this chapter, the tensile behavior of woven fabric is analyzed with the help of various mathematical models. The basic approach highlights the importance of various structural parameters and input material characteristics that determine fabric mechanical behavior. Before discussing the structural mechanics of woven fabrics, it is worth considering the fundamentals of tensile deformation in order to clarify the terminology and units employed in the theory of tensile deformation of woven fabrics.

7.2

Fundamentals of axial deformation

When a specimen is subjected to an external force in its axial direction, a tension develops in the specimen. As a result, the material is deformed and sets up a resistance to deformation. The resistance to deformation set up in the specimen is called tensile stress and the deformation produced is called strain. Tensile properties indicate how the material will react to forces being applied in tension. Tensile tests are used to determine the modulus of elasticity, elastic limit, elongation, proportional limit, tensile strength, yield point, yield strength, work of rupture and many other useful tensile properties. The most important output of a tensile test is a load–elongation curve which can be converted into a stress–strain curve. The stress–strain curve relates the application of stress to the resulting strain. Each material has its own unique stress–strain curve.

7.2.1 Tensile strength Tensile strength is a measure of the force required to pull something such as rope, wire or a structural beam to the point where it breaks. There are three different versions of tensile strength: ∑ ∑ ∑

Yield strength: the stress beyond which the strain in the material changes from elastic deformation to plastic deformation which is a permanent deformation. Ultimate strength: the maximum stress a material can withstand. Breaking strength: the stress coordinates on the stress–strain curve at the point of rupture is called breaking strength.

7.2.2 Stress Stress is the internal resistance or the counter-force of a material to the distorting effects of an external force. The total resistance developed is equal to the external load. It is difficult to measure the intensity of stress generated in the material. However, the external load and the area to which it is applied can be measured. Stress (s) can be equated to the force (F) applied per unit

Tensile behavior of woven fabrics

139

cross-sectional area (A) perpendicular to the force as given below:

Stress = s = F A

Stress is expressed in three basic types of internal load (tensile, compressive and shear) as shown in Fig. 7.1. The plane of a tensile or compressive stress lies perpendicular to the axis of operation of the force from which it originates. The plane of a shear stress lies in the plane of the force system from which it originates. Tensile stress is the stress in which the two sections of material on either side of a stress plane tend to pull apart or elongate as shown in Fig. 7.1(a). Compressive stress is subject to an axial push acting normally across the section; the resistance set-up is called compressive stress. Compressive stress is the reverse of tensile stress as shown in Fig. 7.1(b). Shear stress on a material is the result of by two equal and opposite forces acting tangentially across the resisting section as shown in Fig. 7.1(c) the resistance set up is called shear stress.

7.2.3 Strain When a material is subjected to a load, it is distorted or deformed. If the load is small, the distortion will disappear when the load is removed. The intensity of distortion is known as strain. Strain is the geometrical expression of deformation caused by the action of stress and is normally measured by the deformation per unit length. Strain is a dimensionless quantity. Strain, whether tensile, compressive or shear, is always a number. In case of shear strain (see below), the angular measure ϕ in radian is also a number. There are different types of strain as described below. Force

Force

Force Stress plane

Stress plane

(a) Tensile

(b) Compressive

7.1 Types of applied stress.

Stress plane

(c) Shear

140

Woven textile structure

Normal strain is a ratio of change in dimension to the original dimension. It is denoted by e:

e=

change in dimension original dimension

Normal strain is also called linear strain; the tensile strain is considered positive and compressive strain is considered negative. Shear strain is the angular deformation due to shear stress. Consider a rectangular block held at the bottom subjected to tangential force P as shown in Fig. 7.2. If the face ABCD is distorted to A¢B¢CD through an angle ϕ, the angular deformation produced is called shear strain:

shear strain = AA¢ or BB¢ AD

Volumetric strain is the ratio of change in volume to original volume. Thus volumetric strain can be shown as:

ev =

dV V

where dV = change in volume and V = original volume. Volumetric strain is the sum of strains in the three mutually perpendicular directions:

ev = ex + ey + ez

where ex, ey and ez are strains in three mutually perpendicular directions x, y, z respectively.

7.2.4 Hooke’s law and modulus For deformation within elastic limit, normal stress is directly proportional to normal strain. Mathematically: A

A¢

B

j

D

7.2 Shear strain.

B¢

j

C

P

Tensile behavior of woven fabrics



141

s µ e or s = E e

where E is constant of proportionality known as modulus of elasticity or Young’s modulus. Similarly, shear stress (t) within elastic limit is directly proportional to shear strain. Mathematically.

t µ j or t = G j

where G is the constant of proportionality known as shear modulus. The SI unit of modulus of elasticity (E) is the pascal, N/m2. Modulus can be calculated from the slope of the straight-line portion of the stress–strain curve.

7.2.5 Poisson ratio Tensile or compressive axial strain is accompanied by lateral strain. The lateral strain is a fraction of the linear strain and within the elastic limit bears a constant ratio to the linear strain and is called the poisson ratio. sn represents the Poisson ratio for the lateral direction as it gives the contraction due to longitudinal extension. The suffixn is used for the direction in which contraction takes place due to extension in a longitudinal direction.

7.2.6 Stress–strain diagram The stress and corresponding strain when plotted on a graph constitute a stress–strain diagram. The diagram differs for different materials. A brittle material is one which gives very small deformation before fracture as shown in Fig. 7.3. The yield point is defined as the stress beyond which a material deforms by a relatively large amount for a small increase in the stretching force. Beyond this stress, the material no longer obeys Hooke’s law.

B Fracture

Stress s

A

Proportional limit

Strain e

7.3 Stress–strain diagram for a brittle material.

142

7.3

Woven textile structure

Tensile properties of woven fabrics

The tensile properties of woven fabrics produce several problems and complexities, mainly because the fabric is anisotropic and has a modulus which varies considerably with strain. The variation in the initial modulus is very large and the modulus in the warp and weft directions differs because the cloth is not symmetrical. In fact, the extension which takes place at an angle to the warp or weft is usually much higher and also involves a different mechanism of deformation [1]. For example, the modulus at an angle of 45° is mainly determined by the shear behavior. But if the extension is in the warp or weft direction, shear does not play any role. A woven fabric structure consists of fibers and yarns and its deformation results in a series of complex movement of fibers and yarns. The deformation behavior becomes more complex as both fiber and yarn behave in a non-Hookean manner. However, many researchers [2–4] have tried to obtain the deduction of fabric behavior in a simple way by considering the geometrical changes during extension. It has been possible to deduce the tensile properties of woven fabrics from the properties of the constituent yarn and fiber structure.

7.3.1 Load–elongation behavior of woven fabric Generalized load–elongation behavior of woven fabric is shown in Fig. 7.4. The curve consists of three distinct regions; initial (OA) dominated by frictional restraint, followed by AB (decrimping region) and, finally, BC leading to yarn extension. The initial high modulus of fabric is mainly due to the frictional resistance to bending of the thread which includes inter-fiber friction. Once the frictional restraint is overcome, the modulus decreases gradually because the force needed to unbend the thread in the direction of force decreases. After decrimping, the force rises sharply as the fibers are extended. In the final region the load–extension property of fabric is entirely governed by the load–elongation properties of the yarn. However, in a jammed fabric, decrimping and yarn extension are likely to merge.

7.3.2 Geometrical changes during extension To understand the behavior of cloth during extension, it is necessary to know the geometrical changes during extension. These changes should allow extension of yarn and compression at the intersection region. When such geometrical changes are greatest, the forces are relatively low and therefore extension and compression of yarn is considered negligible. The Poisson ratio of cloth can be calculated using cloth geometry and the basic equations are:

Tensile behavior of woven fabrics

C

Load

Yarn extension

143

Decrimping region Inter-fiber friction effect

B

A

Extension

7.4 Load–elongation behavior of woven fabric.



l = p (1 + c)



h = 4/3p√c

Assuming the yarn is inextensible and incompressible, these equations enable the modulus of several possible variations in loading of cloth to be estimated [5].

7.3.3 Biaxial loading under large forces In the fabric shown in Fig. 7.5, n1, n2 are the numbers of warp and weft threads, p1, p2 are the warp and weft spacings, and F1, F2 are the forces per thread in the warp and weft direction. The fabric width is n1 p1 and the fabric length is n2 p2. Now, the forces acting in the warp and weft direction are n1 F1 and n2 F2. During deformation, suppose:

p1 Æ p1 + dp1



p2 Æ p2 + dp2

In this system, total internal energy will be the work done by the two forces, so, the internal energy = work done by F1 and F2. However, when F1 and F2 are sufficiently large, the internal energy can be ignored. For small deformations, the extension in the warp direction is n2dp2 and in the weft direction it is n1dp1. Thus:

144

Woven textile structure F1 per thread

n 2p 2

F2 per thread

n 1p 1

7.5 Fabric with n1 ends and n2 picks.



(n1 F1) (n2 dp2) + (n2 F2) (n1 dp1) = 0



F1dp2 + F2dp1 = 0



fi dp1F2 = –F1dp2



fi dp1/dp2 = – F1/F2

7.1

Assuming the yarn is inextensible and incompressible, we have, since, l1 = p2 (1 + c1):

0 = dp2 (1 + c1) + p2 dc1



dc1 = – (1 + c1) (dp2/p2) (A)

Similarly for the weft yarn we get by interchanging suffix 1 with 2 and vice versa:

dc2 = –(1 + c2) (dp1/p1)

(B)

Also we know:

p2√c1 + p1√c2 = D3/4



fi dp2√c1 + 1/(2√c1) dc1p2 + dp1√c2 + 1/(2√c2) dc2 p1 = 0

Substituting for dc1 and dc2 from A and B above, we get:





Ê Ê 1 + c1ˆ 1 + c2 ˆ d p2 Á c1 – ˜ + dp1 Á c2 – ˜ =0 2 c1 ¯ 2 c2 ¯ Ë Ë Ê 2c – 1 – c1ˆ Ê 2c2 – 1 – c2 ˆ dp2 Á 1 ˜ + dp1 Á ˜ =0 Ë 2 c1 ¯ Ë 2 c2 ¯

Tensile behavior of woven fabrics



dp2

145

c1 – 1 c –1 + dp1 2 =0 c1 c2

dp1 1 – c1 = dp2 1 – c2

c2 c1

7.2

This equation shows an increase in the thread spacing in one direction of the fabric and gives decrease in thread spacing in the cross-direction due to change in crimp. This equation is analogous to the crimp interchange equation discussed in Chapter 4. The ratio lateral contraction to longitudinal extension, dp1/dp2 is called the Poisson ratio for extension in the warp direction of fabric. From equations 7.1 and 7.2 we get:



1 – c1 F1 =– F2 1 – c2

c2 c1

7.3

The values of c1, c2 in relation to 1 being small, (1 – c1)/(1 – c2) can be taken as 1.



F1 ª F2

c2 c1



dp1 1 – c1 = dp2 1 – c2

7.4 c2 ª c1

c2 c1

7.5

In this analysis, yarn extension, yarn compression and the change in the internal energy are neglected. The applied forces will cause change in the thread spacing due to change in crimp. The change in crimp height with change in pick spacing, (dh/dp) can be obtained using the relation:

h1 = 4 p2 c1 3



È ˘ p dh1 = 4 Ídp2 c1 + 2 dc1 ˙ 3 ÍÎ 2 c1 ˙˚

Substituting the value of dc1, we get



È p dp (1 + c1)˘ dh1 = 4 Ídp2 c1 – 2 2 ˙ 3 ÍÎ p2 2 c1 ˙˚

146

Woven textile structure



(1 + c1)˘ dh1 4 È = Í c1 – ˙ dp2 3 ÍÎ 2 c1 ˙˚



dh1 2 È(c1 – 1˘ = Í ˙ dp2 3 ÍÎ c1 ˙˚

7.3.4 Tensile modulus The modulus of a cloth can be defined as the change in the force per unit width per fractional increase in length:

warp modulus =

dF1 dp2 p2 dF1 = · p1 p2 p1 dp2

Case 1 When stresses are sufficiently large, the internal energy changes in the cloth can be neglected. We have seen, in equation 7.3:

F1 1 – c1 c2 tan q2 = ª F2 1 – c2 c1 tan q1



fi F2 tan q2 = F1 tan q1



F1 c ª 2 F2 c1



fi F1√c1 = F2√c2

7.6

From this relationship, the fabric modulus for increase in F1 when F2 is constant can be obtained for a small change in the extension. Hence, differentiating the above equation, we get:

dF1 c1 +

1 dc F = F 1 dc 1 1 2 2 2 c1 2 c2 F2





(dF1 ) F2constant =

1 dc – F 1 dc 2 1 1 2 c2 2 c1 c1

Ê ˆ 1 1 F2 c2 dc (using equation 7.6) = F2 Á 1 ˜ dc2 – 2c c1 Ë 2 c2 c1¯ 1

Tensile behavior of woven fabrics



147

Ê ˆ 1 = F2 Á dc2 – 13/2 c2 dc1˜ 2c1 Ë 2 c2 c1 ¯

The modulus of fabric, as per definition, is given by,

dF1 dp2 dF1 p2 = · p1 p2 dp2 p1

Substituting the value of dF1 from above, we have:

fabric modulus for warp =



p2 p1

È Ê ˆ˘ 1 dc2 – 13/2 c2 dc1˜ ˙ dp2 ÍF2 Á 2c1 ¯ ˙˚ ÍÎ Ë 2 c2 c1

Substituting for dc1 and dc2, we get:



fabric modulus =

F2 È c2 c ˘ + (1 + c2 ) 2 ˙ = A Í(1 + c1) c1 p1 ˚ 2p1c1 Î

It has been found [3] that at comparatively low loads there is a rough agreement between experimental and calculated modulus. The actual modulus (experimental) is greater than the calculated modulus. This is due to the neglect of internal bending energy changes. Case 2 In this case the modulus is calculated by assuming that the bending energy is negligible, but the elongation of yarns take place. If the yarns are extended during the extension of the cloth, by assuming that its behavior is linear, we get:

dl1 = K dF1 (i)

where K is constant and is the elastic modulus of yarn. It will now be assumed that no crimp interchange can take place due to the assumption that bending energy is negligible, since:

l1 = p2 (1 + c1)



fi dl1 = dp2 (1 + c1) + p2dc1

Since, dc1 = 0

\ dl1 = dp2 (1 + c1) (ii)

148

Woven textile structure

From equations (i) and (ii) we get:

K dF1 = (1 + c1) dp2

so

dF1 =

(1 + c1) d p2 K

the modulus of cloth:



p2 Ê dF1 ˆ p2 Ê1 + c1ˆ = Á ˜ =B p1 ÁË dp2 ˜¯ p1 Ë K ¯

If the cloth is also extended by crimp interchange, the cloth behaves as if there were two springs in series with spring constant 1/A and 1/B. Hence the modulus of the cloth as a whole is given by AB/(A + B). Davidson [4] found agreement between the above predicted and experimental modulus. It is necessary to make an allowance for yarn compression to improve the agreement. The correction is very small and it makes the mathematics more complex. Case 3 This is a case of uniaxial loading of cloth, where the loads are low and the bending energy changes are considered. This analysis is helpful in understanding the initial extension or decrimping of uniaxially loaded cloth. It is justifiable to neglect the yarn extension for such low loads. A fabric from the point of view of bending energy changes can be in different states of relaxation. When fabric is woven, the yarn is straight and force has to be applied to the yarn to keep it in its crimped form. If the yarn remained in this stressed state, the extension of the cloth would result in a decrease in the bending energy of the yarns being extended and vice versa. A corresponding increase in bending energy would take place in the other set of yarns since crimp is increased. However, the yarns do not remain in this condition. The internal forces gradually relax and ultimately a state is reached in which there are no internal forces. Such a cloth on extension requires an increase in bending energy in both sets of threads since the curvatures are being changed from the naturally curved configuration. The modulus of cloth in the different states (set and unset) is different. The completely set condition has the most practical application since it applies fairly accurately to most finished cloths.

Tensile behavior of woven fabrics

7.4

149

Castigliano’s theorem

This theorem [6] is applicable to materials that obey Hooke’s law and are perfectly elastic. These assumptions are not valid for yarns but for small deformations the error is not large. Consider an elastic body (Fig. 7.6), deformed by forces Pi (i = 1, 2, 3, …, n) Suppose the strain energy s of the body can be found. The deformation di in direction of force Pi can be obtained by using the above theorem:

di = ∂s ∂pi

7.4.1 Bending strain energy Consider a rod of length l deformed by couples M at its ends as shown in Fig. 7.7; a small element ds, then rotates one end relative to the other through an angle dq. Hence work done by M on ds = 1/2 Mdq, so total work done by M = 1 2

Ú

q

0 where q = s/r and dq = ds/r. Hence:



M dq

strain energy in the bent rod = 1 2

Ú

l



= 1 M 2r



= M [s ]l0 = Ml 2r 2r

0

Ú

l

0

M ds r

ds

p6

p5

pn

p4

p1

p2

p3

7.6 Deformation of an elastic body.

150

Woven textile structure ds

M

M

dq r

q

7.7 Bending strain energy.

But

M =Bfi1=M r r B

So

2 strain energy in the rod = M l 2B 2 strain energy per unit length = M 2B

7.4.2 Applications Example 1 Consider a cantilever of length l loaded by W at its end as shown in Fig. 7.8. If the deflection is small, bending moment M at point P is W (l–x), hence



2 strain energy = M l 2B

= 1 2B

Ú

l

0

W 2 (l – x )2 ds

Tensile behavior of woven fabrics

151

l x d y

p(x,y)

W

7.8 Cantilever.



ª 1 2B

Ú

l

W 2 (l – x )2 ds

0

l

2 È– (l – x )3 ˘ 2 3 =W Í =W l =s ˙ 2B Î 3 6B ˚0

Using Castigliano’s theorm, deflection d at the free end is: 3



Wl d = ∂s = ∂W 3B

Example 2 Suppose we want to find the inclination of the end of cantilever. Introduce couple C at end. Then the displacement corresponding to C is rotation by q of the end of rod as shown in Fig. 7.9:

M = W (l – x) + C

and,

s= 1 2B

Ú

l

0

[W (l – x ) + C ]2 dx l



Ï– [W (l – x ) + C ]3 ¸ = 1 Ì ˝ 2B Ó 3W ˛0 =

1 [(Wl + C )3 – C 3 ] 6BW

hence:

q = ∂s = 3 [(Wl + C )2 – C 2 ] ∂c 6 BW

152

Woven textile structure

q p(x,y) C

W

7.9 Inclination of a cantilever.

but C = 0, when only load W operates:

7.5

2 2 2 q = 1 = 3W l = Wl W 6B 2B

The sawtooth model

Peirce’s rigid thread model involves the use of elliptic integrals in its description. The resulting equations are highly non-linear and the use of a computer is essential for solving the equations. The sawtooth model used by Leaf and Kandil [7] is an attiring to simplify the procedure. It considers the threads modeled as straight lines rigidly joined at cross-over points by point contacts H1 and H2. Yarns are set in the shape as shown in Fig. 7.10. This model is not physically real but it has reasonably good agreement with experimental data. The yarns are assumed to obey Hooke’s law; where tension is proportional to extension. 2 strain energy per unit length of yarn = M 2B

When the fabric deforms, the forces generated between the yarn will compress the yarn cross-section. In a real fabric the compressive forces will be distributed over the region of yarn contact but in this model they are assumed and represented as point force. It is assumed that the yarn is incompressible and inextensible. The only deformation taking place in the yarn is due to bending. If F1 and F2 are forces acting on individual warp and weft thread and F1¢ and F2¢ are the corresponding forces per unit width, then

F1 = F1¢p1 and F2 = F2¢p2

During deformation the forces 2V1 and 2V2 will be generated along the point of contact between the thread line H1. The tension and shear in the

Tensile behavior of woven fabrics

F2

H1

V2

B1

153

F1

2V1 V1

h1/2

B2

p2/2

A1 F1

2V2

V2 A2

F2

H2

V1

7.10 Sawtooth model for plain weave.

yarn at points, say, A1 and A2 can be resolved into components F1, V1 and F 2, V 2. By symmetry, A1 is the point of inflexion; so the bending moment at this point is zero. For analysis consider half section of A1 B1 of warp thread with point A1 as the origin of axis and the cross-over point as A. Therefore OA will represent half the repeat unit as shown in Fig. 7.11. The bending moment is at P = F1 y – V1 x, where

y = x tan q1 =

xh1 p2

Strain energy S1 in OA is.



S1 = 1 2 B1

Ú

l1 2

0

(F1 y – V1 x )2 ds

where

x = cos q = p2 1 5 l1 s=

xl1 l fi ds = 1 dx p2 p2

so,





S1 = 1 2 B1

Ú

p2 2

0

2

ˆ l1 Ê F1 xh1 ÁË p – V1 x˜¯ p dx 2 2

l (F h – V p )2 l S1 = 1 1 1 1 3 1 2 1 2 B1 p2 p2

Ú

p2 2

0

x 2 dx

154

Woven textile structure A

p y F1

h1/2

s q1

O

x

p2/2

V1

7.11 Force analysis on half repeat of plain weave. p2

l (F h – V1 p2 )2 Ê x 3 ˆ 2 = 1 1 1 ÁË 3 ˜¯ 2 B1 p23 0



=

l1 (F1 h1 – V1 p2 )2 p23 2 B1 p23 24

=

l1 (F1 h1 – V1 p2 )2 48 B1

Similarly S2 =

l2 (F2 h2 – V2 p1 )2 48 B2

so the total strain energy in the whole system of one half repeat unit is:

S = S1 + S2 =

l1 (F1 h1 – V1 p2 )2 l2 (F2 h2 – V2 p1 )2 + 48 B1 48 B2

Now consider deformation in the direction of V1. It is change of O relative to A in the direction of V1. Deformation = dh1/2. Using Castigliano’s theorem we get:

dh1 ∂S1 = 2 ∂V1 =

2l1 (F1 h1 – V1 p2 )(–p2 ) 48 B1

=

– l1 p2 (F1 h1 – V1 p2 ) 24 B1

Tensile behavior of woven fabrics

155

Similarly

dh2 ∂S2 = 2 ∂V2 =

– l2 p1 (F2 h2 – V2 p1 ) 24 B2

=

– l1 p2 (F1 h1 – V1 p2 ) – l2 p1 (F2 h2 – V2 p1 ) + =0 24 B1 24 B2

but since h1+ h2 = D therefore, dh1 + dh2 = 0 and therefore: We know that from static consideration V1 = V2 and can assume that V1 = V2 = V so we get from the above equation:

l1 p2 (F1 h1 – V1 p2 ) l2 p1 (F2 h2 – V2 p1 ) + =0 24 B1 24 B2



Ê l p2 l p2 ˆ F1 l1 h1 p2 F2 l2 h2 p1 + = VÁ 1 2 + 2 1˜ Ë B1 B1 B2 B2 ¯ ÊF l h p F l h p ˆ Ê l p2 l p2 ˆ V = Á 1 1 1 2 + 2 2 2 1˜ ∏ Á 1 2 + 2 1 ˜ Ë B1 B2 ¯ B2 ¯ Ë B1

7.7 Now extension of fabric in the warp direction is dp2 and this is a change in the F1 direction. Using Castigliano’s theorem: since:

∂p2 ∂S1 = 2 ∂F1 S1 =

l1 (F1 h1 – V1 p2 )2 24 B1

dp2 2 l1 (F1 h1 – V1 p2 )h1 = 2 48 B1 dp2 =

l1 h1 (F1 h1 – V1 p2 ) l1 h1 (F1 h1 – Vp2 ) = 12 B1 122 B1

Substituting the value for V from equation 7.7, we get:



È Ê F1 l1 h1 p2 F2 l2 h2 p1ˆ ˘ p2 ˙ + Í ÁË B B2 ˜¯ ˙ lh 1 dp2 = 1 1 ÍF1 h1 – ˙ l1 p22 l2 p12 12 B1 Í + ˙ Í B1 B2 ˚ Î

156

Woven textile structure



ÈÊ F1 l1 h1 p22 F1 l2 h1 p12 F1 l1 h1 p22 F2 l2 h2 p1 p2 ˆ ˘ – + – Í ˜¯ ˙ B1 B2 B2 l h ÁË B1 ˙ = 1 1 Í ˙ l1 p22 l2 p12 12 B1 Í + ˙ Í B1 B2 ˙˚ ÍÎ



ÈÊ F1 l2 h1 p12 F2 l2 h2 p1 p2 ˆ ˘ – Í ˜¯ ˙ B2 l1 h1 ÍÁË B2 ˙ = ˙ l1 p22 l2 p12 12 B1 Í + ˙ Í B B 1 2 ˙˚ ÍÎ

and strain:

e1 =

dp2 p2

A special case in which F2 = 0, gives:



È Ê F1 l2 h1 p12 ˆ ˘ ˙ ÍÁ Ë B2 ˜¯ ˙ lh e1 = 1 1 Í 2 12 B1 p2 Íl1 p2 l2 p12 ˙ ÍB + B ˙ 2 ˙ ÍÎ 1 ˚



Èl1 p22 l2 p12 ˘ + ˙ Í 12 B1 p2 Í B1 B2 ˙ F1 = e1 l1 h1 Í Ê l2 h1 p12 ˆ ˙ Í Á ˜ ˙ ÍÎ Ë B2 ¯ ˙˚







F1 =

F1 =

12 B1 p2 È l1 p22 B2 ˘ 1+ e1 l1 h12 ÍÎ l2 p12 B1 ˙˚ 12 B1 È (1 + c1 ) p23 B2 ˘ Í1 + ˙ e1 + c1 ) Î (1 + c2 ) p13 B1 ˚

h12 (1

3 12 B1 È Ê p2 ˆ Ê (1 + c1 ) ˆ B2 ˘ dF1 Í1 + ˙ fabric modulus = = de1 h12 (1 + c1 ) Í ÁË p1 ˜¯ ÁË (1 + c2 )˜¯ B1 ˙ Î ˚

The above result is quite close to the following obtained by the rigorous analysis [8]:

Tensile behavior of woven fabrics



157

3 ˘ dF1 8 B1 È Ê p2 ˆ B2 = 2 Í1 + Á ˜ f (q2 )˙ de1 h1 Í Ë p1 ¯ B1 ˙˚ Î

where f (q2) is a value near to zero. This result was obtained after some approximations to the computer results. The two results are remarkably similar.

7.6

Fabric extension in the bias direction

So far the load elongation behavior of a fabric is considered in the warp and weft directions. It has been shown that the load elongation behavior and modulus can be deduced from the properties of yarn and cloth structure. In practice, a fabric may be extended in the bias direction at an angle y to warp. If there is an extension at an angle, we have to consider the shear behavior of the fabric. The following example using Fig. 7.12 makes this clear. A fabric can be considered as consisting of trellies. If the fabric is extended at an angle y, it will extend by rotating the members of the trellies relative to each other. If there is no resistance to this rotation of yarns relative to each other, then there will be no resistance to elongation. The cloth will simply swivel in to a new position as shown in Fig. 7.12(b). However, in general there is some resistance to this rotation i.e. a shear force is involved. It can be seen that the force applied will produce at the edges of the fabric an extension stress along warp and a shear stress as shown in Fig. 7.13. Then, considering the bottom edge, F1 and S will have a resultant in the direction of F and F1 = S cot y and F2 = S tan y. Now consider a triangular element in the middle of fabric. (Fig. 7.14) and suppose the length of the hypotenuse is 1. Forces acting on the sides of the element. For equilibrium, resolving horizontally, we have:

y

(a)

7.12 Application of force in bias direction.

(b)

158

Woven textile structure Fy per unit width y

S per unit width

F2 per unit width

S per unit width F1 per unit width

F2

S y

F1 = S cot y

y

F1

F2 = S cot y

7.13 Resolution of forces along fabric edges.



F sin y = F2 sin y + S cos y



= S tan y sin y + S cos y =S

sin 2 y + cos 2 y = S cos y cos y

fi S = F sin y cos y

Now,

F1 = S cot y



= F sin y cos y cot y



= Fcos2 y

S

Tensile behavior of woven fabrics A

Fcosy

159

F

y Fsiny siny

F2siny

1 Ssiny y

C

B

cosy Scosy

F1cosy

7.14 Equilibrium of forces.

and

F2 = S tan y

= Fsin y cos y tan y = F sin2 y If F is known at any angle y, than we know S, F1, F2. Now consider the strain. The applied force and its components are shown before and after deformation in the Figs 7.15 and 7.16 respectively. The components of OC are shown by considering it of unit length:

F = EY ey

where EY and ey are the modulus and strain in the y direction Also

F1 = E1 e1



F2 = E2 e2



S=Ga

where S = shear stress, a = shear strain and G = shear modulus. After deformation.

a = a1 + a2

F1 and F2 are stress per unit width in warp and weft direction. After deformation, OC Æ OC¢, OA Æ OA¢, and OB Æ OB¢. Also, OC¢ = 1 + ey.

160

Woven textile structure F C

cosy

B

O

siny

A

7.15 Strain before deformation.

C¢ B¢

(p/2 + a) a1 O

(p/2 – a)

A¢

a2

7.16 Strain after deformation.

Now if deformation is small:

strain in OA¢ direction = strain in OA direction



= e2 – s2 e1

where s2 is the Poisson ratio for weft direction. Suffix 2 signifies the contraction in weft due to extension in the warp direction.

OA¢ = OA (1 + e2 – s2 e1)



= sin y (1 + e2 – s2 e1)

Similarly

OB¢ = cos y (1 + e1 – s1 e2)

Here, s1 is the Poisson ratio for the warp direction as this gives contraction in warp due to extension in the weft direction.

Tensile behavior of woven fabrics



161

Shear strain a = a1 + a2

using cosine rule:

OC¢ 2 = OA¢ 2 + OB¢ 2 – 2 OA¢ 2 OB¢ 2 cos Ê p + aˆ Ë2 ¯ = OA¢2 + OB¢2 – 2 OA¢ OB¢ sina



(1 + eY)2 = sin2 y (1 + e2 – s2e1)2 + cos2 y (1 + e1 – s1e2)2 + 2 sin y (1 + e2 – s2e1) cos y (1 + e1 – s1e2) sina If strain is small, then squares and product of the strain can be neglected and taking sin a ≈ a we get: 1 + 2 eY = (1 + 2 e2 – 2 s2e1) sin2 y + (1 + 2e1 – 2s1e2) cos2 y + 2a sin y cos y

fi



eY = (e2 – s2e1) sin2 y + (e1 – s1e2) cos2y + a sin y cos y = e1(cos2 y – s2 sin2 y) + e2 (sin2 y – s1cos2 y) + a sin y cos y

therefore,





E = F1 (cos 2 y – s sin 2 y ) + F2 (sin 2 y – s cos 2 y ) 2 1 Ey E1 E3 + S (sin y cos y ) G 2 2 F = F cos y (cos 2 y – s sin 2 y ) + F sin y (sin 2 y – s cos 2 y ) 1 1 Ey E1 E2

+

F sin y cos y · sin y cos y G

4 4 1 = cos y + Ê 1 – s 2 – s1 ˆ (sin 2 y cos 2 y ) + sin y Á ˜ Ë G E1 E2 ¯ Ey E1 E2

Figure 7.17 shows a polar plot of the experimental values of modulus at various angles. These values are scattered around the theoretical curve. It also shows that modulus in the bias direction tends to be greater than the modulus in the warp or weft direction.

162

Woven textile structure

Weft

Ey

y –90

+90 Warp

7.17 Modulus at various angles.

7.7

Factors affecting the tensile properties of woven fabrics

The tensile properties of woven fabrics depend on the fabric structure, i.e. yarn twist, yarn strength, weave, crimp and cover. The degree of yarn twist affects the fabric elongation; highly twisted yarn woven in a close texture give loss of extensibility. A reduction in twist improves cover and reduces air permeability. An increase in pick and twist densities within normal limits significantly improves both tensile strength and surface durability, but a reduction in pick density improves the tear strength in the filling direction. The breaking strength of a textile fabric is enhanced by an increase in the strength of its component yarn and the number of yarns gripped between the jaws of the testing machine. Ring fabrics give higher breaking load than open-end fabrics and the effect of scouring and bleaching in increasing the breaking load is more pronounced with ring fabrics. Cloth strength is affected by the degree of binding of cross-threads, which aids inter-fiber frictional forces and contribute to tensile strength. The degree of binding is dependent on the density of weave and cloth setting. The elongation at break increases with the increase of these variables. The tensile strength of the fabric decreases with an increase in fabric cover. The crimp decreases the strength of the yarn and of the fabric. The initial modulus of the fabric decreases with the increase in the crimp. The straightening of longitudinal threads during the test applies compressive forces at the points of contact with the cross-yarns. If the cross-yarns jam before crimp exchange is complete, then there will be reduction in fabric strength and extensibility.

Tensile behavior of woven fabrics

7.8

163

References

1. Grosberg P (1966), Textile Res. J., 36, 205. 2. Hearle J W S, Grosberg P and Backer S (1969) Structural Mechanics of Fibers, Yarns and Fabrics, Wiley Interscience. 3. Clulow E E and Taylor A M (1963), J. Text. Inst., 54, T323. 4. Davidson D A (1964), U.S. Government Report ML-TDR-64-239. 5. Lindberg J, Behere B and Dahlberg B (1961), Textile Res. J., 31, 99. 6. Shingley J E, Mischke C R and Budynas R G (2003), Mechanical Engineering Design, McGraw-Hill. 7. Leaf G A V and Kandil K H (1980), J Text. Inst., 71, 1. 8. Grosberg P and Kedia S (1966), Textile Res. J., 36, 71–79.

8

Buckling behavior of woven fabrics

Abstract: The contribution of different factors affecting critical buckling load in fabrics is examined to help predict the deformation and recovery behavior of fabrics. The role of buckling deformation during garment making-up and in use is explained. Analysis of deformation, recovery and hysteresis of woven fabrics is made using a buckling model which can also be used to calculate bending rigidity and frictional properties. The concept of formability and its effect on seam pucker and setting of woven fabrics are important applications covered. Key words: fabric model, buckling deformation, bending rigidity, seam pucker.

8.1

Introduction

Any material can take compressive loads up to a critical level known as the buckling load, beyond which bending deformation takes place. In engineering science, buckling is a failure mode characterized by high compressive stress at the point of failure when it is more than the ultimate compressive stresses that the material is capable of withstanding. This mode of failure is also described as failure due to elastic instability. Mathematical analysis of buckling makes use of an axial load eccentricity that introduces a moment which does not form part of the primary forces to which the body is subjected. Euler derived a formula which gives the maximum axial load that a long, slender, ideal column can carry without buckling. An ideal column is one that is perfectly straight, homogeneous and free from initial stress. The maximum load, called the critical load, causes the column to be in a state of unstable equilibrium, i.e., any increase in the load, or the introduction of the slightest lateral force, will cause the column to fail by buckling. The Euler formula for columns is given by:



F=

p2E I (K l )2

where F is the maximum or critical force (vertical load on column), E is the modulus of elasticity, I is the area moment of inertia, l is the unsupported length of column and K is the column effective length factor, whose value depends on the conditions of end support of the column. For hinged ends K = 1. 164

Buckling behavior of woven fabrics

165

The equation clearly suggests that the critical load is directly proportional to the second moment of the area of cross-section. The relationship also reveals that it is the elasticity and not compressive strength of the material of column which determines the critical load. The boundary conditions have a considerable effect on the critical load of slender columns. The boundary conditions determine the mode of bending and the distance between inflection points on the deflected column. The higher resulting capacity of the column depends on the closeness of the inflection points. The strength of a column may therefore be increased by distributing the material to increase the moment of inertia. This can be achieved without increasing the weight of the column by distributing the material as far from the principal axes of the cross-section as possible, while keeping the material thick enough to prevent local buckling. The effect of length on critical load apparently plays an important role. For a given size column, doubling the unsupported length quarters the allowable load. Since the moment of inertia of a surface is its area multiplied by the square of a length called the radius of gyration, the above formula may be rearranged as follows. Using the Euler formula for hinged ends, and substituting A r2 for I, the following formula results:

2 s = F = p E2 A (l /r )

where F/A is the allowable stress of the column and l/r is the slenderness ratio.

8.2

Buckling deformation of woven fabric

The buckling, bending and drape characteristics of woven fabric influence its performance during the making-up process and in actual use of the garment. These properties are important, particularly when the fabric is limp, resulting in large-scale deformation even when a small force is applied. The engineering concept of buckling helps to understand the behavior of fabric during garment manufacturing as well as during its use as a garment. The folding of a garment, bending of sleeves or a trouser leg, cutting and sewing operations, etc., all involve buckling phenomena. The buckling behavior of fabrics is useful in understanding the basic practical problem of residual curvature in the fabric when it is bent and unbent. In bending, a woven fabric exhibits initial non-linearity produced by frictional restraint. This frictional restraint produces a couple when it is overcome, resulting in a linear deformation–recovery behavior of the material. When the bending moment applied to the cloth is less than this limiting frictional couple, no bending takes place. The relationships proposed [1] for these deformations are:

1/r = 0 for M < M0

8.1

166

Woven textile structure



B/r = M – M0 for M ≥ M0

8.2

where M is the applied bending moment, M0 is frictional couple, B is bending rigidity and r is radius of curvature. One of the simplest tests for examining the buckling phenomena in fabric is plate buckling. Much useful information can be obtained during compression as well as in bending and recovery of the fabric during this test. The study of buckling behavior of woven fabric was initiated by Lindberg and co-worker [2,3] to understand deformation–recovery phenomena and setting. Olofsson [4] investigated structural compressional stability in terms of formability and also deformation–recovery for the analysis of hysteresis of woven fabric. Subsequently a more useful model of this deformation was evolved by Grosberg and Swani [5,6]. They built a simple buckling model based on Grosberg’s idealized bending rule [1], taking into account the frictional effect and following the principles of elastic buckling theory for struts reported in classical mechanics. Their model assumed an infinitely large bending rigidity of the cloth for the initial nonlinear region of the bending curve where the applied couple is unable to overcome the frictional restraining couple. They noted, however, that, in practice, real fabrics are fairly rigid for the initial bending region, but they are not infinitely rigid as assumed in the idealized bending rule. Nevertheless, they continued to build their buckling model on the basis of the idealized bending rule in order to avoid the complications arising from the additional mathematical treatments required to obtain precise solutions.

8.3

Buckling behavior of cloth under large deformation

Analysis of buckling behavior of a cloth under large deformation requires consideration of the analysis of buckling of an elastic plate. Consider a rod of length l and flexural rigidity B, buckled by two equal and opposite forces P acting towards the center of the rod as shown in Fig. 8.1. The following analysis is for a simply supported beam. Consider the axis as shown in the figure and assume the length of arc OP = s, tangent at P makes angle y with the x-axis:

bending moment at P = Py



curvature at P = – dy/ds



fi – B dy/ds = Py



fi – B d2y/ds2 = P dy/ds = P sin y



fi 2B dy/ds · d2Y/ds2 = –2 P siny · dy/ds

Buckling behavior of woven fabrics Initially

167

l P

P

Finally

A P s y P

a D

O

P

8.1 Buckling model.

integration gives:

fi B (dy/ds)2 = 2P cos y + constant

8.3

at O, dy/ds = 0 (no bending moment), y = a. Substituting these two values in equation 8.2 gives:

constant = – 2P cos a

Therefore equation 8.2 becomes

B(dy/ds)2 = 2P (cos y – cos a)



= 4P (sin2 a/2 – sin2 y/2)



fi dy/ds = 2√(P/B) (sin2 a/2 – sin2 y/2)1/2

8.4

let

k = sin a/2:



sin y/2 = k sin j

at

O, y = a, j = p/2 and at B, y = 0, jB = 0:



dy = 2 k cos j dj/(1–k2 sin2 j)1/2



dy/ds = 2 kcos j (dj/ds) (1–k2 sin2 j)–1/2

Using equation 8.3 we get:

2(P/B)1/2 (k2 – k2sin2 j)1/2 = 2 kcos j (dj/ds) (1 – k2 sin2 j)–1/2



ds = (√(B/P)(1– k2 sin2 j)1/2 dj



s = (B /P )1/2

Ú

jA

p /2

(1 – k 2 sin 2 j )–1/2 dj

8.5

168

Woven textile structure



s = (B/P)1/2 [F(k, p/2) – F(k, j)]

8.6

At B, s = l/2, j = 0:

(l/2) = (B/P)1/2 F(k, p/2)



fi l = 2(B/P)1/2 F(k, p/2)



2

Pl /B = 4 {F(k, p/2)}

8.7

2

For small values of a Æ 0, k = 0, F = p/2 the above equation gives:

Pl 2/B = 4p2/4 = p2

This gives minimum critical load, Pcritical, at which buckling takes place. To assess the compressed length of fabric, we have:

dx/ds = cos y = 1– 2 sin2 y/2 = 1– 2 k2 sin2 j



dx = (1 – 2k2 sin2 j)[–(B/P)1/2 (1 – 2k2 sin2 j)–1/2dj]



= –(B/P)1/2 [2(1– k2 sin2 j)1/2 – (1 – k2 sin2 j)–1/2] dj



x = (B/P)1/2 {2[E(k, p/2) – E(k, j)] – [F(k, p/2) – F(k, j)]}

At B, j = 0, x = x/2:

x = 2 (B/P)1/2 [2 E(k, p/2) – F(k, p/2)]

Fractional compression is:

(l – x)/x = 1– x/l = 1 – (2E – F)/F = 2(1–E/F)

8.8

The theoretical relationship between load and compression is shown in Fig. 8.2. When cloths get buckled, they do so in a very different way. The

Load

10 p2 9

Pl2 B

Compression (1 – x/l )

8.2 Theoretical relation between load and compression.

Buckling behavior of woven fabrics

169

experimental set-up shown in Fig. 8.3 consists of four sections. The fabric is clamped at both ends. The fabric load compression curve shown is very different from the theoretical curve (Fig. 8.4). The curve shows a decrease in load after an initial high load needed to start compression. On removal of the load, the recovery curve is quite different, leaving a residual compression OB. The fabric will follow the law given by equations 8.1 and 8.2. In Fig. 8.5 the bending moment has not exceeded M0 in the region OA and CD so OA and CD will be straight. At point A:

Pl1 sin a = M0



l1 = (M0/P) cosec a

A

B

E

C

D

Experiment

Load

Theory

O

B

Compression

8.3 Experimental set-up and load-compression behavior.

170

Woven textile structure

K = 2.0 K = 1.0 Pl2

K=0

B

K = 1.0 K = 2.0

K = M0l/2B (1–x/l)

8.4 Theoretical buckling curves. Y

l2 A

C

l1 a P

X

O

D

P

8.5 Buckling model for fabric.

In the region AC the cloth will obey the law given by equation 8.2. Section AC will have the curvature of an elastic plate of length l2 and with force P at A. Therefore from equation 8.2 we get:

l2 = 2(B/P)1/2 F(k, p/2)

Total length of cloth specimen l is:

l = l2 + 2l1



l = 2(B/P)1/2 F(k, p/2) + 2M0 cosec a/P



Pl 2/B = 2(Pl2/B)1/2 F(k, p/2) + 2(M0 l/B) cosec a 2

8.9

This is a quadratic equation for Pl /B and can be solved when values of M0l/B are known. When a Æ 0, F(k, p/2) Æ p/2 and cosec a Æ ∞, so Pl 2/B Æ ∞.

Buckling behavior of woven fabrics

171

Thus with this theory an infinite load is needed to buckle the cloth. The reason is that to bend at all, we must have Py = M0 and if y = 0, this can only happen if P Æ ∞. The compressed length of center section l2 from equation 8.8 is:

x2 = 2(B/P)1/2 [2E(k, p/2)]



x1 = l1 cos a = (M0/P) cot a

So the total compressed fabric length, x, is given by:

x = x2 + 2x1 = 2(B/P)1/2 [2 E(k, p/2)] + 2 (M0/P) cota

and fractional compression is given by:

= 1 – x/l = 1 –2 (B/Pl 2)1/2 [2 E(k, p/2)



– F(k, p/2)] + 2(M0/P) cota



= 1 – 2 (B/Pl 2)1/2 [2E(k, p/2) – F(k, p/2)]

+ 2(B/Pl 2)1/2 (M0l/B) cot a

8.10

Equations 8.9 and 8.10 are parametric equations for relation between Pl 2/B and l – x/l, and can be solved for a given value of M0l/B. In the actual test the fabric is clamped. It consists of two sections, each of which reproduces the same conditions as in the above analysis for a simply supported beam. So it is necessary to substitute Pl2/4B for Pl2/B and M0l /2B for M0l /B in equations 8.9 and 8.10. It will be assumed that, except for frictional resistance, recovery is purely elastic. The existing deformed curvatures will be retained until the bending moment has been reduced by 2M0. This results in some part of the curved portion remaining curved after the load has been removed. This is shown in Fig. 8.6. As the load is reduced from P, the center region EF is straightened where the bending moment has been decreased by 2M0. There are three sections in the curve: OA is straight, AE has the initial curvature on recovery and EF has a new curvature. For this section the analysis is repeated by assuming it as a plate of length EF. Grossberg and Swani used numerical integration to get the curves as shown in Fig. 8.5. The parameter M0 l/2B affects the deformation and recovery. E A

F C

a0 O

8.6 Recovery from buckling deformation.

D

172

Woven textile structure

8.4

Hysteresis in fabric deformation

The recovery curve for the fabric is not elastic; there is energy loss as the elements of the fabric offer resistance to both deformation and recovery. This energy loss is explained in terms of hysteresis which is dissipative. Hysteresis is a function of residual stresses in the fabric and becomes negligible in a set fabric. Indirectly the degree of setting can be evaluated in terms of percentage hysteresis loss. It is a good parameter with which to compare the degree of setting within a fabric or with other fabrics. Grosberg and Swani evaluated frictional restraints M0 from this analysis and got very good correlation in fabrics having different setting treatments with parameter M0. The major impact of the hysteresis is on non-recovery from deformation. They were able to correlate non-recovery with parameter M0/B which by definition represents residual frictional curvature.

8.5

Practical applications

Buckling behavior can detect the effectiveness of the setting treatment by evaluating the area under the deformation–recovery curve. The puckering tendency of a cloth during stitching can also be evaluated by this technique. Formability, which is a measure of the ability of a fabric to absorb compression in its own plane without buckling, is estimated based on this principle. Formability value is used as a direct indicator of the likelihood of seam pucker occurring during sewing of garment.

8.6

1 2 3 4 5 6

References

Grosberg P (1966), Textile Res. J., 36, p. 205 Lindberg J, Behere B and Dahlberg B (1961), Textile Res. J., p. 99. Lindberg J (1961), Textile Res. J. 31, p. 664. Olofsson B (1967), J. Text. Inst., 58, p. 221 Grosberg P and Swani N M (1966), Textile Res. J., 36, p. 332. Grosberg P and Swani N M (1966), Textile Res. J., 36, p. 338.

9

Bending behavior of woven fabrics

Abstract: The factors affecting the bending behavior of woven fabrics are discussed. Some useful terms such as bending rigidity, bending recovery and frictional restraint are explained. The prediction of fabric bending rigidity and inter-yarn frictional restraint is demonstrated. Time effects in bending and relaxation are explained. Bending in bias is analyzed using a sawtooth model. Practical applications are given. Key words: fabric model, fabric bending rigidity, inter-yarn frictional restraint.

9.1

Introduction

In most uses fabrics are subjected to bending deformations. The yarn woven into the fabric during bending or creasing will be subjected to stresses additional to those incurred during weaving. A relatively low density yarn will tend to become more compact and flattened at the crease of the fabric. This suggests fiber movement in the yarn structure. A dense yarn will prevent inter-fiber movement but suffer intra-fiber strain. Moreover bending a fabric means bending the yarns along the direction of bend, causing a change in the curvature with respect to the cross-threads. This entails movement of the cross-threads. Therefore one can expect intra-fiber, inter-fiber and inter-yarn displacements. The fibers in the yarn are under transverse pressure due to twist in the yarn and also under additional transverse force at the cross-over point in the fabric. As such the fiber and yarn displacement in the fabric due to bending will be restrained by frictional resistance. The translation of bending rigidity of fiber into yarn and subsequently to fabric will be affected by the frictional resistances as mentioned above. The normal forces between fibers enable fibers to act together and thus increase the yarn bending rigidity manifolds. Similarly the inter-yarn force at the cross-over points increases the bending rigidity of the interacting yarn segment enormously. Bending rigidity is directly related to fabric stiffness which is an important component of the fabric handle. Bending rigidity is a measure of the couple required to bend the fabric to a certain curvature. It is very closely related to fabric mass and thickness. The bending properties of fabric govern many other fabric performances such as drapeability, formability and tailorability. As a result, the study of bending behavior has received considerable attention from researchers in recent years. With the advent 173

174

Woven textile structure

of powerful soft computing tools, some researchers have tried to develop various models to predict the bending behavior of fabric which is considered to be of complex deformation. Computational models have been formulated to solve large deflection elastic problems which are useful for the apparel industry and also for fabric engineering. However, basic bending theory must be understood before the concepts can be applied to various complex deformations of the fabric.

9.2

Fundamentals of bending deformation

9.2.1 Bending stress When bending a piece of metal, the outer surface of the material stretches in tension while the inside surface compresses. It follows that there is a line or region of zero stress between the two surfaces called the neutral axis. In order to determine the stress–strain relationship and modulus in such deformation, some assumptions are made in simple bending theory. The beam is initially straight, unstressed and symmetric; the beam is linearly elastic, homogeneous and isotropic; the proportional limit is not exceeded; Young’s modulus for the material is the same in tension and compression; and deflections are small, so that planar cross-sections remain planar before and after bending. Using classical beam formulas and section properties, the following relationship can be derived:

bending stress, s b = 3Pl2 2wt 3 bending or flexural modulus, Eb = Pl 3 4wt y

where P is normal force, l the beam length, w the beam width, t the beam thickness and y the deflection at load point. The reported flexural modulus is usually the initial modulus from the stress–strain curve in tension. The maximum stress occurs at the surface of the beam farthest from the neutral surface (axis) and is given by:

maximum surface stress, s max = Mc = M I Z

where M = bending momentum, c the distance from neutral axis to outer surface where maximum stress occurs, I the moment of inertia and Z = I/c is section modulus. For a rectangular cantilever beam with a concentrated load at one end, the maximum surface stress is given by:

Bending behavior of woven fabrics



s max =

175

3dEt 2l 2

The methods to reduce the maximum stress are to keep the strain energy in the beam constant while changing the beam profile; other beam profiles are trapezoidal, tapered and torsion.

9.2.2 Bending equations when a beam is supported on both ends with a single load at the center This configuration is shown in Fig. 9.1; the stress distribution and deflection are as under:

stress between load and support point, s = – Wx 2Z



stress at the cengtre of constant cross-section is – Wl 4Z deflection between load and support points, y =



Wx 48El (3l 2 – 4x 2 )

3 maximum deflection at load = Wl 48 EI

where E is the modulus of elasticity (N/m2).

9.2.3 Bending equations when a beam is cantilevered with load applied at end The deflection and bending moment are shown in Fig. 9.2:

stress at specific point, s = W (l – x ) Z



stress at the support (constant cross-section) = WL Z W

W

x

x

2

l/2

l/2 l

W 2

9.1 Bending of a beam supported on both ends and single load at center.

176

Woven textile structure Wl

W

x l W

9.2 Bending of a beam cantilevered with a load at end.



deflection at specific point, y =

Wx 2 6EI (3l – x)) 3



deflection at the unsupported end = Wl 3EI

where E is modulus of elasticity (N/m2).

9.3

Modeling bending behavior

An idealized approach sheds light on understanding particular factors in practical problems and thus aids in their solution. The concepts which arise out of the analysis are useful in providing improved understanding. Consideration of classical bending of a homogeneous beam exhibits compression in the elements of the beam lying between the central axis and the center of curvature, while the other elements are in tension as shown in Fig. 9.3. Maximum strain (e) arises at the extreme surfaces and is given by:

e max = ± d 2r

where d is the beam thickness and r is radius of curvature of the bent beam; the positive sign refers to tensile strain and negative to compressive strain. Abbott et al. [1] estimated the average maximum fiber strain in a bent yarn for simple case of parallel fibers having no interaction with each other. They considered the bending of yarn and fabric as a non-homogeneous structure consisting of many homogeneous elements (fibers), assumed to be parallel to each other and to the yarn axis and assumed no buckling during bending. The fibers are bent through different radii of curvature depending on their position in the yarn. There will be a distribution of maximum fiber strain from the extreme position decreasing in magnitude to the center of curvature. They obtained the average strain by calculating the average fiber curvature as:

Bending behavior of woven fabrics

177

r = 2R

b

q

d

9.3 Bending of a homogeneous beam.



1 = 1 È1 + 1 R 2 + 1 R 4 + …˘ ˙ r r ÍÎ 4 r 2 8 r 4 ˚

where r is the radius of curvature of central axis of the yarn and R is the radius of the yarn. For r = 2R, the average maximum fiber strain can be approximated by the maximum strain of the central fiber (error not exceeding 6%) and for r > 2R, the average maximum fiber strain can be assumed to be that of central fiber with negligible error. In the real case there is restriction of individual fiber movement, the fibers act in groups (cluster) rather than singly. This will increase the average maximum strain in the fibers as under:

(e max ) fiber with clustering = (e max ) fiber with clustering

n P

where n is the average number of fibers per cluster and P is the packing factor within the cluster. The clustering will also increase the flexural rigidity of the yarn by a factor n/P:

EI yarn with no clustering = P

The extent of clustering can be estimated by comparing the actual flexural rigidity with that calculated from the total flexural rigidity of the fibers. When the yarns in the fabrics are bent in a plane it tends to develop a couple directed towards buckling the yarn out of that plane. Platt et al. [2] suggested that three-dimensional buckling will take place if no restraining matrix is present. However, for low twist yarn the motivation towards buckling is

178

Woven textile structure

less and the surrounding matrix resists the three-dimensional movement, thereby restraining the yarn to be bent in a plane.

9.4

The bending behavior of woven fabrics

Bending is a very common phenomenon during the use of fabrics in garments. It is also associated with the selection of fabrics to determine handle. It has some influence on drape property of the fabric in relation to upholstery, furnishing and curtain. Creasing and wrinkling of fabrics and garments are also associated with bending deformation. As such it is a very important deformation affecting functional and aesthetic aspects. In the late 1960s research was focused on studies in bending. An innovative instrument was designed and developed by Livesey and Owen [3] to study the bending behavior of fabrics. The fabric was uniformly bent in both the directions by the application of a couple and the corresponding curvature was observed. A typical bending curve for the fabric is shown in Fig. 9.4. The bending deformation is nonlinear along the curve OABC to curvature K as shown by arrows. The bending recovery is along CEM; the point D on the x-axis represents non-recovery from bending deformation. The point M on the y-axis shows the negative couple required to straighten the fabric. The negative deformation is shown along MFG and recovery along GHL. The intercept DH on the x-axis shows non-recovery during the complete cycle of deformation. The intercept LM on the y-axis reveals frictional restraints during the deformation. The area enclosed within the Couple M (mN mm/mm)

C

B N

L J

D

A

H

K Curvature, (mm–1) 1/r E

M F

G

9.4 Typical bending curve of woven fabric.

Bending behavior of woven fabrics

179

curve is energy loss due to friction and is termed as hysteresis. Some useful terms from Fig. 9.4 are explained below. The intercept OD on the curvature axis is called as the residual curvature. In practice it is calculated as half of the intercept HD, to eliminate asymmetry.



bending recovery percent Rb = KD ¥ 100 OK = KD + JH ¥ 100; for better result of JK HD residual curvature, K y = 2

The coercive couple (mN mm/mm) is the couple required to restore zero curvature, M0 = LM/2. The initial flexural rigidity G1 (mN mm2/mm) is the ratio of couple to curvature at A. The elastic flexural rigidity G0 is the mean slope of EF and HB. The final flexural rigidity Gj is the mean slope of BC and FG. Grossberg [4] and Olofsson [5] suggested that above behavior can be idealized as shown in Fig. 9.5.

1/r = 0, M < M0



B/r = M – M0, M ≥ M0

9.1

C

M

L H E M

C

9.5 Idealized bending curve.

1/r

180

Woven textile structure

9.4.1 Bending rigidity The bending rigidity of fabrics measured by the cantilever stiffness test using the bending length gives high values as the mean curvature lies between 0.02 and 0.1 mm–1; this should be analogous to G1. Several studies [6] of warp and weft bending of woven fabrics have shown that the bending resistance is made up of bending resistance of thread lying in the direction of bending, frictional restraint and some unspecified interaction between the threads. G0, the elastic component comprises of the sum of single fiber flexural rigidities, Gmin, is the sum of fiber flexural rigidities with no interaction between fibers. It gets modified by geometrical restraints and inter-fiber adhesions to a level G0 or greater. An estimate of Gmin is given by Owen [7]:

Gmin = NGFm/mF



GF = E pr4/4, and r2 = mF/pr

where E is the initial tensile modulus of the fiber, r is the fiber radius and r is the fiber density. Thus:

GF = MmF2/4/pr2

and

Gmin = N EmF/4pr2

9.2

The four main factors directly influencing Gmin are: fiber tensile modulus, fiber linear density, yarn linear density and the number of threads per unit cloth width. In real fabrics the twist and crimp in the yarn cause length of fiber per unit length of fabric to be greater than unity. The correction for twist and crimp in the yarn [3] taking into account bending and twisting of fibers in the yarn gives: Gmin = NGF m mF



È ˘ È GF ˆ ˘ 2 2Ê Í ˙ Í a a ÁË1+ G F ˜¯ ˙ 2 ¥ 2.303 Í ˙¥ 1 ˙ log10 Í1+ 2 G Ê ˆ F Ía 2 a 2 1+ ˙ (1+ C ) 9.3 ˙ Í ÁË G ˜¯ ˙ ÍÎ ˙˚ ÍÎ F ˚

where N is the number of yarns per unit width in the direction of bending, GF is the single-fiber flexural rigidity, m/mF is the yarn to single-fiber linear density, n is the number of fibers, a is the twist in radians per unit length, a the yarn radius, GF is torsional rigidity of the single fiber and c is the yarn crimp. The twist correction factor ranges from 0.7 to 0.95; the crimp correction factor lies between 0.8 and 1. The combined correction factor (0.55–0.9) reduces bending rigidity by 25%.

Bending behavior of woven fabrics

181

The geometrical constraints may increase the elastic component of fabric stiffness by a factor of three or more. Geometrical restraints increase with an increase in cover factor and reduced by relaxation and setting. Inter-fiber adhesions can increase elastic fabric stiffness considerably. The theoretical maximum flexural rigidity of a fabric by considering the yarn as a solid rod in which fibers are bound together is given by: Gmax = NGF (m/mF)2/(1 + c)



9.4

Therefore

Gmax/Gmin ≈ m/mF ≈ n

where n is the number of fibers in the yarn cross-section. G0 lies between Gmax and Gmin; a small degree of adhesion is sufficient to increase G0 considerably as n is usually of the order of 100. The frictional component of the stiffness is obviously proportional to the coefficient of friction and to the inter-fiber pressures. The coefficient of friction can be modified by a factor of about two by the presence or absence of lubricant or finishes, and these have been found to alter the coercive couple. The effect of different factors on the bending rigidity of fabrics is summarized in Fig. 9.6.

9.4.2 Prediction of fabric bending rigidity Abbott, et al. [8] investigated M0 and B in terms of yarn and fabric parameters. Peirce’s rigid thread model with finite contact region is assumed in which Fiber tensile Fiber linear density Theoretical minimum (G)

Yarn linear No. of yarns per unit cloth width

Elastic (G0)

Cover factor

Geometrical restraints (GM) Stiffnes

Weave factor Relaxation

Adhesion

Coefficient of friction Frictional (M0) Interfiber pressures

Cover factor Weave factor Relaxation

9.6 Factors contributing to cloth stiffness.

182

Woven textile structure

the yarn bends around weft in the manner shown in Fig. 9.7. This is more realistic than the model previously considered which had point contact. In fact it turns out that the region of contact has important role to play. During bending the region AB tends to increase and the region DE tends to decrease, as shown in Fig. 9.8. To calculate the flexural rigidity for thread one has

C2

A B q0

q0

C

q0 D E

C1

9.7 Yarn configuration in fabric.

A B

M

B¢ b1 C1

b2 C2 D D¢

y

M

g

E

g

9.8 Bent configuration of fabric.

Bending behavior of woven fabrics

183

to calculate the strain energy in the bent cloth and equate the change in energy to the work done by external couple. Thus on AB¢, D¢E no change in curvature takes place, On B¢D¢ a change does take place and most of calculation are concerned with finding these changes. A bent fabric can be visualized as shown in Fig. 9.9, which shows a single thread spacing bent through an angle g. The forces V1, H1 and couple M are in equilibrium (before deformation for unset fabric V1 = V0, for set fabric V1 = 0) but in order that the cross-yarns can be crimped by equal and opposite forces, the resultant along AO must be equal to the resultant along EO, i.e.:

V1 = V1 cosg + H1 sing



H1 = V1 tan (g/2)

The calculation of the shape of B¢D¢ (free section) then proceeds much along the same lines as in Peirce’s rigid thread model. Once the shape of the thread is known, change in the curvature can be found and hence strain energy can be calculated: M

H1

A

x B¢

V1 Central plane of bent fabric D¢ H1

h/2 E V1

y

g

O

9.9 Force equilibrium in the bent fabric.

M

184

Woven textile structure



Strain energy in warp = U1 = (1/2 B1 )

Ú

Ú

l

0

M 2 ds

l

(1/r – 1/r0 )2 ds 0 The weft also changes since V changes from V0 (= 0 in set case) to V1. This involves change in energy in the weft. According to Grosberg and Kedia [9] the change in V with h is given by: dV/dh = 23.6 B2/p13 = Ks hence we get V = V0 + Ks (h20 – h2) where h is new crimp amplitude, and work done on weft is given by: U2 = 1/2 [V0 + (V – V0)/2] (h20 – h2) = 1/4 (V + V0) (h20 – h2) = 1/2 (V + V0) (h0 – h)/2 = mean force × mean change in crimp height So the total strain energy in system is = B1 /2

l

U = U1 + U 2 = B1 /2Ú (1/r – 1/r0 )2 ds + 1/4(V + V0 )(h20 – h2 )

9.5 This strain energy must be equal to the work done by external couple, 1/2 M g. If rf is radius of curvature of new central plane of fabric, then: 0



M = Bf/rf (1/2) Bf g/rf = U fi Bf = 2rfU/g

The ratio Bf/B1 depends essentially on D/2p2 and q10 (crimp) in case of distributed contact. For small values of D/2p2 there is point contact rather than distributed contact and in that case Bf /B1 is independent of D/2p2. This is shown in Fig. 9.10. The calculations for unset fabrics tends to be similar, except Bf/B1 values are rather small, for some fabrics Bf/B1 < 1. This means the flexural rigidity of fabric is less than the yarn from which they are made. This effect is associated with either very slack fabric D/2p2 < 0.5 or with high D/2p2 values, with low crimp. This effect was also observed experimentally by Owen [7].

9.4.3 Abbott model A simple model [1] suggested that the warp can be thought of as consisting of rigid (due to inter-yarn forces) and flexible sections as shown in

Bending behavior of woven fabrics 0.8

185

0.7 0.6

3.0 D/2p2 0.5

Bf/B1

2.0

1.0 0.4

q10 Non-real models

9.10 Point contact.

Fig. 9.11, where r + f = l1. Assume properties of the section of the model for bending as below. For rigid section;

M < Mor; 1/rr = 0



M ≥ Mor; B1r /rr = M – Mor

For flexible section:

M < Mof; 1/rf = 0



M ≥ Mof; B1f/rf = M – Mof

where Mof < Mor and B1f < B1r. Consider the fabric is bent by couple M > Mor, both sections are bent. This is shown in Fig. 9.12. We have:

Yr = r/2rr, Yf = f/rf, Y = p2/r

and

Y = 2Yr + Yf



p2/r = r/rr + f/rf



fi p2(M – M0)/Bf = r (M – Mor)/B1r + f(M – Mof)/B1f

and this equation must hold for all values of M; it is an identity. So:

p2/Bf = r/B1r + f/B1f

and

M0 p2/Bf = Mor r/B1r + Mof f/B1f

9.6

186

Woven textile structure

a

f

r

p2

9.11 Rigid and flexible sections of yarn in a unit repeat. r/2

f

Yr

Pr

r/2

Yf r Yr

y

9.12 Fabric bent by a couple M > M0.



fi r Æ 0 gives point contact and the fabric becomes slack.



fi p2/Bf = f/B1f and since f Æ l1, B1f Æ B1



fi Bf = B1. p2/p2(1 + c1) = B1/(1 + c1)



fi Bf < B1

This is an interesting result: for point contact, the fabric bending rigidity is less than that of the constituent yarns. There is a good correlation between the measured and calculated values though the measured values are usually

Bending behavior of woven fabrics

187

higher. This is attributed to the neglect of yarn compression which would increase strain energy and hence greater theoretical flexural rigidity.

9.5

Bending hysteresis

The area enclosed by the bending moment–curvature curve represents frictional energy dissipation during bending–unbending of the fabric. This has been estimated in terms of coercive couple by Abbott et al. [10] by considering the bending of a set of plates which are pressed together. Consider the fabric to be made of yarns consisting of flat plates, obviously a gross simplification since the effect of twist is not taken into account and assuming along the plate of fibers there is a pressure v per unit length which (arises during bending by interaction of fibers). Each plate is long and thin, and hence one can neglect shear effects during bending. Forces acting on each plate are identical. This is shown in Fig. 9.13. Suppose bending takes place up to s = s1, where s1 is the length from the free end. The friction that is limiting in this section is not limiting elsewhere, and hence there is no bending. The bending moment at a distance s from free end is given by:

M /n –

s

Ú0

Dmv ds = M /n – mvsD

vds µvs1 s1 s M

y

ds µvs1 vds

dj

9.13 Force distribution on an element during bending.

188

Woven textile structure

where D = thickness of each plate. Further curvature at s = s is – dj/ds so if B is the flexural rigidity of yarn,

n (M/n – mvsD) = – B dj/ds

or

M – nmvsD = – B dj/ds



fi M – dmvs = – B dj/ds   (s ≤ s1)

9.7

where d = n D = yarn diameter. Therefore;

–B

0

Új

dj =

0

s1

Ú0

(M – mdvs ) ds

B j0 = Ms1 – mvd s12/2

Now the average radius of curvature of bent plates as shown in Fig. 9.14 is given by:

rj0 = l¢/2

where l¢ is the length of the plates.

B l¢/2r = Ms1 – (1/2) mvds12



B/r = 2 Ms1/l¢ – mvds12/l¢  (0 < s1< l/2)

l1¢/2 j0 (90° – j0)

j0

9.14 Initial inclination of plate during bending.

9.8

Bending behavior of woven fabrics

189

and when s1 = l¢/2 (that is when whole set of plates has bent completely), we get

B/r = M – mvdl¢/4

which is of the form

B/r = M – M0

9.9

where M0 = mvdl¢/4. This is the case before plates are completely bent, i.e. in the very initial region of the bending curve. At s = s1 we have dj/ds = 0. So using equation 9.7:

M = dsmvs1



fi s1 = M/(dmv)

while from equation 9.9:

M0 = mvdl¢/4



fi M/M0 = 4s1/l¢

hence from equation 9.8 we get

B/r = M.M/2 M0 – mvd s1s1/l¢



= M2/2M0 – mvd MM/mvd 4 M0



= M2/2M0 – M2/4 M0 = M2/4 M0

9.10

and this nonlinear equation is valid until M = 2 M0. Therefore we get:

M – M0 = M2/4 M0



fi M2 – 4 M0 M + 4 M 02 = 0 fi (M – 2 M0)2 = 0 fi M = 2 M0

So a law such as the following is predicted for the initial non-linear behavior shown in Fig. 9.15. For the initial curve OA (0 < M < 2M0), the bending law B

1/r

A

O

M0

2 M0

9.15 Frictional restrain during recovery.

M

190

Woven textile structure

will be B/r = M2/4 M0 and for the curve AB (M ≥ 2 M0), the bending law will be B/r = M – M0. There is a good agreement between these equations and experimental results. M0 is estimated more accurately by considering twist and it is given as:

M 0 = 0.128mVd L 2l

where L is length of one turn of twist in the yarn, l the modular length is the length of yarn in a weave repeat, and V is the inter-yarn pressure at each intersection. Now from equation 9.9 we have:

M0 = (1/4) mdv l¢

Comparing the last two results it seems that the friction component can be deduced by considering a set of parallel plate. For parallel plates

M0 = (1/4) mdv l¢

with twist:

M0 = (1/8)md (V/2l)L = (1/4) md (V/4l)L

These results are similar, provided one regards the plates as being of length L (= one turn of twist) and has a distributed force = V/4l, where V is interyarn pressure and l = modular length.

9.6

The effect of setting on bending behavior

Textile yarns being visco-elastic exhibit time-dependent effects such as stress relaxation. This causes decay in the inter-yarn force at the cross-over point and results in some sort of setting. In addition fabrics can be set by finishing treatments to relax internal stresses in the fabric and lower its internal energy level. The area enclosed by the bending moment–curvature curve represents frictional energy loss due to internal stresses in the fabric and those imposed during deformation. Setting causes a reduction in the area and shape of the bending moment–curvature curve [7,11]. The effect of internal stresses in the fabric can be understood by taking out crimped yarn from the fabric and one will observe the yarn does retain the same crimped configuration. The magnitude of setting can be evaluated using Olofsson approach described in Chapter 7.

Bending behavior of woven fabrics

9.7

191

Bending recovery

The bending recovery Rb for a given curvature K is defined by coercive couple M0 and the low curvature elastic flexural rigidity G0:

Rb = K – M0/G0

Good bending recovery is expected in fabrics having low value of M0/G0. A low M0 is found in fully relaxed open fabric. The bending recovery of a fabric is the measure of its ability to recover from gentle crushing. A fabric having poor recovery has a crumpled appearance after being gently crushed. It can be easily smoothed out as no permanent fiber deformation has occurred.

9.8

Bending at higher curvatures

Most of the studies on bending behavior of fabrics are made at low curvatures below 0.05 mm–1. Deformations under these conditions are more relevant to fabric handle and non-recovery from inter-fiber and inter-yarn friction. However, the contribution of fiber strain on non-recovery during wrinkling and creasing necessitates bending at higher curvatures. Elder et al. [12] studied bending behavior at curvatures close to creasing and separated the non- recovery due to fiber visco-elastic deformation as under:

Kr – M0/G0

where Kr is the residual curvature from bending curve. They found that for fabrics M0 increases rapidly up to 1 mm–1 (= 10 cm–1) and then increases linearly with increase of curvature. Similarly G0/Gj decreases rapidly up to 1 mm–1 and then decreases gradually with increase of curvature. This demonstrates inter-fiber and yarn movement even at higher curvatures. M0 increased significantly, three-fold at 4.5 mm–1 compared with 0.4 mm1, low curvature which is a usual limit for bending behavior by most researchers. The contribution of fiber visco-elastic deformation was discovered by bending at curvatures ≥ 3 mm–1 (= 30 cm–1). Interestingly high co-relation between bending recovery from medium curvatures and crease recovery was found.

9.9

The time effect in bending deformation

Textile materials are visco-elastic as such time plays a significant role in deformation and recovery. A commonly used technique indicative of timedependent mechanisms is stress relaxation. It gives valuable information at molecular level of the rearrangements within a fiber. Initial work [13] on relaxation behavior during bending of fabric was done for small to medium

192

Woven textile structure

curvatures upto 70 cm–1. The rate of relaxation during bending is expressed as RCR, a term analogous to stress relaxation during tensile testing. RCR is calculated as under:

RCR =

d (log C ) 1 d C = d (log t ) C d (log t )

The use of a logarithmic couple scale automatically provides a normalization factor for RCR without requiring the use of couple at zero relaxation time. The RCR, relaxation rate, is a useful tool to identify the level of strain in the material. Hari et al. [14] discovered for a range of fabric the relaxation rate RCR to be constant and representative up to 20 cm–1 curvature, beyond this the rate has a different value. They also compared the relaxation behavior in bending with tensile deformation. Interestingly, the strain level for a certain bending curvature was obtained at identical relaxation rate in the two deformations. This gives a useful correspondence between the two modes of deformations. The relaxation rate is also a useful tool to identify fabrics in terms of non-recovery due to flow during bending and creasing.

9.10

Bending in the bias direction

In practice fabric tends to get bent in any direction. Consider bending in the bias direction (Fig. 9.16); that is let the fabric be bent into the form of a cylinder of radius R as shown in Fig. 9.17. Consider the warp threads. Assume initially they are not crimped in the fabric but straight with flexural rigidity B1s and torsional rigidity C1s. Strain energy in the fabric will be the

Wefts

p2

Y

p1 Warps

9.16 Fabric bending in bias.

Direction of axis of bending couple

Bending behavior of woven fabrics

193

y

9.17 Fabric bent into a cylinder.

sum of strain energy due to bending and twisting and will equal work done by twisting. Assume, bending moment = B1s/e = B1s K, twisting moment = C1s t (t = twist). The warp lies along helical path on a cylinder (Fig. 9.18), then

length of one turn of helix = 2pR cosec y



curvature = sin2y/R = constant



bending energy per turn of helix = (B1s /2)

2p Rcos ecy

Ú0

sin 4y /R 2 ds

= pB1s sin3y/R



One end of warp is rotated through 2p relative to other end in one turn of helix. But this twist is along the helix axis, so the component along yarn is equal to 2pcosy and the length of yarn is equal to 2pR cosecy.

twist inserted in the yarn = 2pcosy/2pR cosecy = siny cosy/R



= torsion of helix

twisting energy per turn of helix = (C1s /2)

2p Rcos ecy

Ú0

sin 2y cos 2y ds /R 2

= C1spsiny cos2y/R

thus

strain energy in one warp = (p/R) siny(B1s sin2 y + C1s cos2y)

Consider unit length of cylinder: if warp spacing is p1, warp yarns in unit length of cylinder will be 1/p1 cosecy = siny/p1.

194

Woven textile structure R Y l

h Y

Y 2pR

9.18 Analysis of bent fabric cylinder.



strain energy in warp per unit length of cylinder



= siny p sin y (B1s sin2y + C1s cos2y)/p1R

Similarly the strain energy in the weft is obtained by putting y = p/2 – y and interchanging suffixes in the above, thus

strain energy in the weft = p cos2y (B2s cos2y + C2s sin2y)/p2R



total strain energy in unit width of fabric

= (p/R) [sin2y/p1(B1ssin2y + C1s cos2y) + cos2y/p2(B2s cos2y + C2s sin2y)]

9.11

Now suppose BY = bending rigidity of fabric in the bias direction

external bending couple = BY/R

hence

strain energy in unit width of the fabric = (By /2)



2p R

Ú0

K 2 ds = By /2.1/R 2 .2p R = By p R



9.12

Using equations 9.11 and 9.12 we get;

BY p/R = (p/R)[sin2y/p1(B1ssin2y + C1scos2y)



+ cos2y/p2(B2s cos2y + C2s sin2y)]

fi BY = (sin2y/p1)( B1ssin2y + C1scos2y)



+ (cos2y/p2)(B2s cos2y + C2s sin2y)

9.13

The effect of crimp in the warp and weft for bending and twisting rigidity is incorporated by using the sawtooth model shown in Figs 9.19 and 9.20 respectively as below:

Bending behavior of woven fabrics

195

l1/2

l1/2

M

M p2

9.19 Sawtooth model for analysis of bent yarn.

l1/2

M

p2 q1

M

9.20 Sawtooth model for analysis of twisted yarn.



bending energy = 2(1/2B1 )

l1 /2

Ú0

M 2 ds = M 2 l1 /2 B1

Now if B1s is the equivalent flexural rigidity then

bending energy = 2(1/2B1 )

p2

Ú0

M 2 ds = M 2 p2 /2 B1s

Equating the two gives:

M2 p2/2B1s = M 2l1/2B1



fi B1s = B1p2/l1 = B1/(1 + c1)

Twisting is dealt with in the same way. M tends to both bend and twist the yarn:

component of M tending to twist = M cosq1



component of M tending to twist = M sin q1

196

Woven textile structure

Hence total strain energy = 2[(1/2 B1)M2 sin2q1(l1/2)



+ (1/2 C1) M2 cos q1(l1/2)]



= (M2l1/2)(sin2q1/B1 + cos2q1/C1)



but this is equal to M2p2/2C1s, hence: M2p2/2C1s = (M2l1/2)(sin2q1/B1 + cos2q1/C1)

so that

1/C1s = (l1/p2)(sin2q1/B1 + cos2q1/C1)





= (1 + c1)(sin2q1/B1 + cos2q1/C1)

B1s and C1s can be substituted in equation 9.13 to obtain the expression for BY in terms of warp and weft spacing, crimp, flexural and torsional rigidities.

9.11

Practical applications

Bending in the biased direction is very helpful for certain fabrics in giving a graceful drape to a certain 3-D shape; the biased direction bending brings into interplay different mechanical properties to accommodate the deformation. A classical example [15] to prevent puckering in a jammed fabric is to have the seam line in the biased direction of the fabric.

9.12

1. 2. 3. 4. 5. 6.

7. 8. 9. 10. 11. 12. 13. 14. 15.

References

Abbott J, Coplan M J and Platt M M (1960) J Text. Inst., 51, T1384. Platt M M, Klein W G and Hamburger W G (1959) Text. Res. J., 29, 611. Livesey R G and Owen J D (1964) J. Text. Inst., 55, T516. Grosberg P (1966), Text. Res. J., 36, 205. Eeg-Olofsson, T(1959) J. Text. Inst., 50, T112. Grosberg P (1970), Studies in Modern Fabrics, Textile Institute, Manchester, p. 112. Owen J D (1968) J. Text. Inst., 59, 313. Abbott G M, Grosberg P and Leaf G A V (1973) J Text. Inst., 64, 346. Grosberg P and Kedia S (1966) Text. Res. J., 36, 71. Abbott G M, Grosberg P and Leaf G A V (1971) Text. Res. J, 346(41), 345. Lindberg J, Behre B and Dahlbarg B (1961) Text. Res. J., 31, 99. Elder H M, Hari P K and Steinhauer D B (1974) J. Text. Inst., 65, 519. Hari P K (1973) Ph.D. Thesis, University of Strathclyde. Hari P K, Steinhauer D B and Elder H M (1975) J. Text. Inst., 66, 154. Dorkin C M C and Chamberlain N H (1961) Seam Pucker: Its Cause and Prevention, Clothing Institute Technological Report No. 10.

10

Creasing in woven fabrics

Abstract: The mechanism of creasing via inter-fiber and inter-yarn movement during deformation is explained. The factors affecting crease deformation and recovery of fabrics are discussed. Practical suggestions for maximizing crease recovery of fabrics are given. Key words: fabric model, crease deformation, crease recovery.

10.1

Introduction

In practical use, textile fabrics are subjected to a wide range of complex deformations such as bending, folding, creasing and wrinkling, which may be added deliberately during manufacturing or produced by body movement during use. Among these, wrinkling and creasing affect the aesthetic characteristic of fabrics. Unintentionally developed short irregular wrinkles are seen as unsightly in apparel. The ability of a fabric to resist creasing or wrinkling and to recover from such deformations is determined by many factors, the most important being the mechanical properties of its fibers such as tensile, bending and torsion properties, the geometrical and constructional parameters of the yarns and fabric, and the presence or the absence of finishing agents on or within the fiber. The inclination of fibers in the yarn leads to torsional and bending strains but the contribution of the torsional component to the fabric recovery behavior is insignificant for creases parallel to the thread direction.

10.2

Mechanisms of creasing

Gagliardi and Gruntfest [1] explained the nature of creasing phenomenon of a homogeneous material. A permanent crease or wrinkle may form by subjecting such a material to bending stresses, if the deformations exceed the elastic limit of the material. Figure 10.1 shows a homogeneous rod being bent to a close fold. On the outside of the bend in this rod, elements of the material must be stretched while the bend is being made, and on the inside of the bend other elements must be compressed. Somewhere in the middle of the rod there are elements which are neither stretched nor compressed. These are in the neutral plane of deformation. The amount of deformation suffered by any element in the bend is determined by its distance from this 197

198

Woven textile structure

plane. During the formation of a close fold (180° bend) in a homogeneous material, the tensile deformations which occur are of the order of 100%. Since very few materials can recover from such deformations, the strains produced in the fibers of a fabric in a close fold must be of a much lower order of magnitude. How this reduction in strain may be brought about in creasing a fabric is shown in Fig. 10.1. Figures 10.1(a) and (b) give a schematic view of a multifilament yarn which, unlike the homogeneous rod of Fig. 10.1(a), is composed of fibers that give some freedom of motion relative to each other. During the bending of a fabric, and consequently of the yarns, the strains produced in the individual fibers can be relieved by two mechanisms. As shown in Fig. 10.1(b), the fibers can slip if their freedom of movement is not hindered by high frictional forces caused either by twist, inter-yarn force at the cross-over point or the presence of

Elements stretched Elements compressed Neutral plane

(a) Bending of monofilament rod

(b) Bending of multifilament yarn – strains relieved by fiber slippage

(c) Bending of multifilament yarn – strains relieved by fiber movement toward neutral plane of deformation

10.1 Bending of monofilament and multifilament materials.

Creasing in woven fabrics

199

sizing agents. If the freedom of movement of the fibers in the bend were completely unhindered, the fibers could adjust themselves around the bend and hence suffer minimum deformation. This cannot ordinarily take place except in fabrics made from yarns which have zero twist. The second method by which fiber strains can be minimized is shown in Fig. 10.1(c). Again, if the fibers movement is not completely hindered during the formation of the fold, the fibers will tend to move towards the neutral plane of deformation, where the tensile strains are at a minimum. As to which of these two methods of strain reduction is more likely to occur in the folding of any fabric, the second would appear to be more likely. The ability of a fabric to minimize deformations by allowing its fibers to move about to positions of minimum strains is due to the multifilament character of its yarns. This is in contrast to continuous sheets, rods or fabrics made of monofilament yarns which, during folding, must suffer large deformations because their composing elements are rigidly fixed.

10.3

Deformation and crease recovery behavior

The most common method to test crease and wrinkle recovery is to bend a strip of fabric over itself using a heavy load under certain conditions for a certain time and, after releasing the load, measure the angle of recovery after a certain period of time. Wrinkles are bent and creased in multiple directions and, as such, involve complex deformations. Creasing is a bending deformation limited to the maximum extent in any fabric. However, this maximum varies depending on the yarn and fabric structure and is affected by the compressed fabric thickness. The deformation and recovery depends on the extent of deformation [2]. As such studies on recovery from different curvatures are useful. Hari et al. [3] studied creasing of fabrics at different curvatures by sandwiching the fabric fold with metal spacers of different thickness. The mean fabric curvature Km is expressed as 2/(D + t). A typical relation between bending and crease recovery and fabric curvature is shown in Fig. 10.2 for untreated and resin-treated fabrics. The data at low curvatures, for Km < 5 cm–1 were taken on the Shirley bending hysteresis tester and at high curvatures, for Km > 13 cm–1, were obtained from the crease recovery measurements. It can be seen that the crease recovery increased with decrease of curvature and tended towards a limiting value. The difference between the untreated and resin-treated fabrics disappeared at low curvature. The bending nonrecovery at low curvature is attributed to inter-fiber and inter-yarn frictional restraints and at higher curvatures to the ductile response of the fiber [4,5]. The bending behavior of yarn and fabrics at different curvatures is shown in Fig. 10.3. The yarn bending behavior gives the inter-fiber friction. The inter-yarn friction is the difference between the fabric and yarn bending

200

Woven textile structure 100

Treated fabric

R(W + F)(%)

80

60 Untreated fabric 40

20 0.0

1.0

2.0

Log Km

10.2 Bending recovery at different curvatures. M0

B0

Fabric Yarn

Bending recovery 90

5

4

2

80

Mof

3 Gof

70

Brf

2

1

1

0

1

2

3

4

5

10.3 Bending behavior of yarn and fabrics.

behavior. Inter-fiber friction Mof is dominant and increases with the increase of curvature, whereas the inter-yarn friction Moy is constant and independent of curvature. The bending rigidity B0 and bending recovery behavior for the yarn Bry and fabric Brf converge at higher curvatures. This is interesting and important as it shows that, at higher curvatures, and also during creasing,

Creasing in woven fabrics

201

it is mainly fiber deformation that plays a role in the bending and creasing of yarn or fabric. Such behavior of fibers during high curvature bending or creasing of yarn can be useful in investigating ways of improving crease recovery of fabrics since inter-yarn effects can be superimposed. Moreover, as mentioned in Chapter 9 on bending, owing to the similarity in the behavior of bending couple relaxation and tensile stress relaxation, one can perform appropriate tensile deformation tests to improve crease recovery of fabrics. An elastic strip constrained between two parallel planes takes up an elastica configuration as shown in Fig. 10.4(a). For a thin strip the length of the bent portion is related to the plane of separation D as:

lc = 2.2D

where lc is the length of fabric bent at crease and the mean radius of curvature of the bent portion is

R = 0.7D

Skelton [6] applied these results to a creased fabric by giving due consideration to the geometry of the crease. He suggested a creased fabric configuration by considering lc/lt, where lt is the distance between the threads parallel to the crease line. The ratio was used as a measure of the degree of crossing thread interference at the crease. For lc/lt >2 the degree of interference is high and there are at least two crossing threads at the crease. For lc/lt <1 the degree of interference is small and, on average, there is less than one crossing thread at the crease. This is shown in Fig. 10.4(b). The calculated radius of curvature Rf of the mean fiber in a creased fabric was calculated as:

Rf = 2.8t(1 – lc/4lr)(1 + c)[(1 + a2d2)1/2 – 1]/loge(1 + a2d2)

10.1

where c is the crimp, a is the twist in radians per unit length and d is the yarn radius. Crimp and twist correction factors have been applied in this equation. He estimated the fabric crease recovery from the fiber tensile deformation–recovery data. This clearly establishes the fact that fiber properties play a dominant role in the crease recovery of fabrics. From his results, the following useful and practical generalizations can be made: ∑ The crease recovery of well-relaxed fabrics woven from high recovery fibers is independent of fiber linear density and fabric construction. ∑ The full potential of high recovery fibers can be realized in a wellrelaxed fabric. ∑ The crease recovery of fabric woven from poor recovery fibers can be improved significantly by choosing more open fabric construction.

202

Woven textile structure

lc/lr > 2 (a)

Central plane of yarn

3t/2

lc/lt < 1 (b)

10.4 Yarn configurations in creased fabrics.

10.4

The effect of time on deformation and crease recovery

The crease recovery of fabrics depends on the time of creasing, the time of recovery and the extent of crease curvature. The deformation–recovery behavior of most fibers is time-dependent because the fibers are viscoelastic, one would expect the crease recovery behavior of a fabric to depend in some way upon time. Time effects are often regarded as a small perturbation superimposed upon some time-independent phenomenon. This is of considerable practical significance because, in some cases such as with a packaged garment, the fabric may be subjected to creasing deformations for long periods of time. Creasing and crease recovery as a function of time has been studied by several researchers [7–9]. However, the mechanism elucidating the contribution of different components to non-recovery has been reported [9] by studies for different creasing times, instantaneous and

Creasing in woven fabrics

203

long-term recovery times for medium to maximum fabric curvatures. The limiting crease recovery for a certain curvature is obtained by extrapolating the instantaneous and long-term recovery for different creasing times. The relative contribution of retarded elastic recovery and flow (time-dependent deformation) is segregated as shown by the curves in Fig. 10.5. It is shown that the time-dependent recovery and flow for fabrics can be obtained using the relationship between crease loading time and crease recovery time. The segregation between friction and yield can only be made from the bending behavior of fabrics using the expression Kr – (M0)/G0. The yield, nonrecoverable deformation, depends on curvature and its contribution increases significantly at higher curvatures. The inter-fiber and inter-yarn friction can be separated as shown in Chapter 9 on bending. Such an analysis is useful in taking a decision on the appropriate processing and selection of fiber for fabric development.

10.5

Factors affecting crease recovery of fabrics

The creasing of textile material is a complex phenomenon which involves tensile, bending, compression and torsional stresses. The bending elasticity plays an important role in the creasing phenomenon of fabrics. Among all commonly used textile fibers, linen is very poor in creasing owing to a very high degree of orientation of cellulose present in the fiber. Cellulosic materials are highly susceptible to creasing. The materials which resist creasing also resist deformation and therefore they behave as rigid material. Ideally a fabric should be deformed but at the same time it should recover from deformation rapidly. It is well known that wool has very good elastic recovery power and therefore it has power of resistance to and recovery from creasing. The resistance and recovery power of creasing

100

Friction

DR(t) = 0, Km Æ 1

Yield DR(t) = 0, Km

4

tr = 10  mm

tr = 100 mm

R

0

Flow

Retarded elastics

logtl

10.5 Relative contribution of non-recovery from creasing.

204

Woven textile structure

are largely influenced by the type of woven structure in which wool is employed.

10.6

References

1. Gagliardi D D and Gruntfest I J (1950), Creasing and crease proofing of textiles, Text. Res. J., 20, 180–188. 2. Chapman B M (1973), J. Text. Inst., 64, 250. 3. Hari P K, Steinhauerand D B and Elder H M (1975), J. Text. Inst., 66, 154. 4. Elder H M, Hari P K and Steinhauer D B (1975), J. Text. Inst., 66, 519. 5. Olofsson B (1968), Text. Res. J., 38, 773–779. 6. Skelton J (1968), J. Text. Inst., 59, 261. 7. Wilkinson P R and Stanley H E (1958), Text. Res. J., 28, 669–673. 8. Hilyard N C, Elder H M and Hari P K (1972), J. Text. Inst., 63, 627. 9. Hari P K (1973), Phd Thesis, University of Strathclyde, Glasgow.

11

Shear behavior of woven fabrics

Abstract: The importance of shear deformation in performance and appearance of woven apparels is discussed. The fundamentals of shear and definition of shear stress, strain and modulus are explained. The types of shear are discussed. The mechanism of shear in woven fabrics and typical shear deformation behavior are described. A model to predict shear behavior is described. Key words: fabric model, woven fabrics, shear deformation.

11.1

Introduction

Shear behavior is one of the most important characteristics that contributes to the performance and appearance of woven fabrics. Shear properties influence drapeability, pliability and hand behavior of apparel fabric. The study of shear behavior of fabrics has special significance particularly when the end use is apparel and the fabric is to be processed in an automatic garment manufacturing system. This is mainly because the cloth is deformed in all directions during mechenical handling as well as in actual use. In fact, the ability of a fabric to be deformed by shearing distinguishes it from other flat, flexible materials such as paper and polymer thin films. Shear properties play an important role both in designing a garment and in fabric engineering. Shear angle is one of the main criteria for characterizing the formability of the fabrics. This property enables a 2-D fabric to undergo complex deformations and helps the 3-D garment to conform to the body contour to impart desired mechanical comfort. The shear deformation in fabrics also influences anisotropy of mechanical properties of fabrics in tensile and bending in bias direction. Apart from conventional clothing applications, shear characteristics are considered important in designing space suits, inflatable shelters and parachutes in which the cloth is subjected to biaxial and multiaxial stresses. Shear property is also important when fabric is subjected to very high and complex stress in applications such as textile composites. Therefore, a quantitative knowledge of shear properties and detailed analysis of the mechanism of shear deformation are of great interest in the study of fabric mechanics.

205

206

11.2

Woven textile structure

Fundamentals of shear deformation

Shearing in continuum mechanics refers to the occurrence of shear strain, a deformation of material in which parallel internal surfaces slide past one another. It is induced by shear stress in the material. Shear strain is distinguished from volumetric strain, the change in a material’s volume in response to stress. Often, shearing refers more specifically to a mechanical process that causes a plastic shear strain in the material, rather than merely an elastic one. A plastic shear strain is a continuous (non-fracture) deformation that is irreversible, so that the material does not recover its original shape. It occurs when the material is yielding. The process of shearing a material may induce a volumetric strain along with the shear strain.

11.2.1 Definition of shear stress and shear strain When a section is subjected to two equal and opposite forces P acting tangentially across the resisting section, the resistance set-up is called shear stress (F).

F = R/A

where R is the resistance to P set up at the interface A of the area of crosssection. If P is gradually applied, R = P, then

F = P/A

Shear stress is expressed as force per unit width or force per unit width per unit thickness or force per unit width per unit fabric mass per unit area; N/m, N/m2 and N/tex respectively. The corresponding deformation produced is called shear strain (with the unit of radian), measured in terms of angular deformation accompanying shear stress. A cube of side l is subjected to equal and opposite forces P across the top and bottom faces. If bottom face AB is fixed, the face ABCD will be distorted to ABC¢D¢ through an angle y as shown in Fig. 11.1. By definition, shear strain is the deformation per unit length. Therefore:

shear strain = CC¢ = DD¢ = y l l

11.2.2 Shear modulus The shear modulus is concerned with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences an opposing force:

shear modulus = shear stress = F shear strain y

Shear behavior of woven fabrics

C¢

C

D

C D¢

l

A

B

C¢

P

D

D¢

y

y

A

207

B

11.1 Representation of shear deformation.

11.2.3 Classical definition of shear Pure shear is defined as the deformation of a body by uniform extension in one direction and contraction in the perpendicular direction, so that the area remains constant. For solid objects, thickness also remains constant. Figure 11.2 demonstrates a pure shear in which a body is deformed by tension in one direction and compression in perpendicular direction. Consider a square abcd with diagonals in the direction of principal strain. It deforms as shown so that area abcd = area a¢b¢c¢d¢. Deforming forces can be resolved along the sides of abcd; these are defined as shear stress. After deformation, the sides make an angle a with their previous direction as a result angle between corners change from p/2 Æ p/2 + 2a (2a = shear strain). If strain in direction of extension is e, then length l0 parallel to extension direction increases to l0(1+ e) and in order to keep the area constant, length l0 perpendicular to strain direction will be l0/1+ e. Simple shear can be explained is follows. Imagine a≤b≤c≤d≤ rotates so that a≤b≤ is parallel to ab, that is it becomes parallel to the original direction. In this case, the strains (Fig. 11.3a) are in the directions aa≤, bb≤, cc≤ and dd≤ are also parallel to each other and are called simple strain. It may also be seen that simple shear is equivalent to pure shear and rotation. If we now consider the square whose sides are parallel and perpendicular aa≤, It will be deformed as shown in Fig. 11.3(b). In this case shear strain is defined as ee≤/(1/2)eh = tan 2a = 2a = q (say) and for small q, tanq Æ q. This is shown in Fig. 11.4 and corresponds to normal idea of shear. Shear stress F is force per unit length.

11.3

Shear deformation in woven fabrics

Now consider a fabric deformed by shear stresses as shown in Fig. 11.5. The threads rotate through a certain angle by swiveling and take the shape shown

208

Woven textile structure B

A

B¢

A¢

a d¢

y

a¢

b¢

b

d c¢ c

D¢

C¢ D

C

11.2 Pure shear. a

e a≤ b

2a

e≤

h b≤

d≤ d

2a

h≤

f

c≤

f≤

g≤ (a)

c

g

(b)

11.3 Simple shear (a) and deformed simple shear (b).

q

11.4 Normal shear.

in Fig. 11.5(b), if there is no resistance to shear. The resistance to shear is provided by friction at the cross-over points (Fig. 11.5c), and resistance to the bending of threads. Similar phenomenon occurs when the fabric is laid on a surface with double curvature. Certainly the area would not remain constant as shown in Fig. 11.6, but in shear deformation, the relation between F and q can be taken as representing shear stress–strain curve.

Shear behavior of woven fabrics

(a) Force in a bias direction

209

(b) No resistance to shear

(c) Resistance to shear

11.5 The concept of shear.

q

F

Shear

11.6 Fabric deformed by shear stress.

The actual deformation that takes place is very complex; in particular buckling takes place. The reason can be understood from the deformation of pure shear as discussed above. There is compression in the direction ac, but the fabrics cannot stand much compression, hence buckling takes place; to avoid this it is usual to apply a tensile force along ac. It can be shown that it is possible to eliminate compressive stresses in all directions by this technique; eventually the specimen will buckle but if tension is large enough then a reasonable stress–strain curve can be obtained. This raises one or two problems in practice. It is virtually impossible to apply forces to a sheet in such a way that a shear stress is produced.

210

Woven textile structure

Treloar’s [1] simple apparatus shows a fabric clamped at AB and DE and subjected to a vertical load W and a horizontal force F, giving shear angle q. The resultant of F and W through C is as shown in Fig. 11.7; the non-symmetry is obvious, so stress distribution is not uniform. Further this asymmetry varies as F is increased (constant W). Treloar suggested that the asymmetry can be minimized by using specimen of short length and more width. Consider what happens when a fabric is deformed. A unit repeat of warp and weft intersection is shown in Fig. 11.8. At first, owing to friction at intersections, no rotation will take place; hence the yarn between intersections will bend like a cantilever. In this case the initial shear modulus is high, but after a while some slippage will take place gradually at the intersections from outside the contact region and progressively make way inwards.

11.3.1 Calculation of shear force Suppose the fabric is replaced by threads, there will be no shear. Even in this case a shear force equal to W tanq is required to hold the system in equilibrium at a shear angle q. This amount should be subtracted from the B A q

F

C

F

E

D

W

W

11.7 Shear test.

(a) Shear forces

(b) Yarn bending as cantilever

11.8 Deformation at cross-over points in a fabric.

Shear behavior of woven fabrics

211

measured shear force to compensate the effect of tensile force W. Thus the effective shear stress = F – W tanq = S (say). A plot of S against q gives the correct shear stress–strain curve. This is a purely arbitrary definition but it seems to be the best one can do for woven fabrics.

11.3.2 Theory of shear deformation Woven fabrics are subjected to a variety of complex deformations during use. Among those deformations, shear deformation takes place in many practical applications. When bending occurs in more than one direction, the fabric is subjected to double curvatures and shear deformation is involved. During wearing of a cloth, the fabric needs to fit to the body contour. This becomes possible due to shearing of the angle between the warp and weft threads. Shear plays an important role in determining drape, handle, fit body, creasing, tear and most of the bias properties of the woven structure. Shear measurement systems were developed by several researchers [2,3] in order to understand the mechanism of shear deformation. Later [4,5] mathematical models were developed to describe the shear properties of woven fabrics. In the analysis it is revealed that the hysteresis produced during shear is wholly by the frictional restraints arising from the rotation of yarn at the cross-over points in the fabric.

11.3.3 Stress–strain relationship and modulus during shear deformation A typical shear stress–strain curve is shown in Fig. 11.9. This curve can be considered as three distinct zones. OB refers to the frictional restraint zone. When all frictional resistance is overcome the warp and weft yarns can swivel about each other, as shown by the curve BC. CD shows the jamming of warp and weft threads during rotation when resistance to shear increases sharply. Prediction of initial behavior (OA) Consider first a piece of fabric of dimensions L1, L2 with shear forces S1, S2 as shown in the Fig. 11.10. Taking moments, we have.

S1 L1 ¥ L2 = S2 L2 ¥ L1



fi S1 = S2 = S = shear stress

the following assumptions are made: ∑ shear force is less than frictional restraint at the interactions (fabric behaves as if intersection are welded);

212

Woven textile structure D Shear force

B

C

A O

Shear strain

11.9 Shear behavior of a fabric.

S1

L1

S1/unit width

S2

L2 S2/unit length

11.10 Shear forces on a fabric.

∑ deformation in the yarn is due only to bending; ∑ shear force is distributed along the sides of fabric; ∑ the yarn is inextensible. The forces Sp1, Sp2 are acting along the warp and weft directions of a unit cell consisting of one intersection, along with the deformations are shown in Fig. 11.11. r1, r2 are the length of the intersections along the warp and weft directions. Shear strain Y is the change of angle between the warp and weft and is equal to Y1 + Y2. The yarn behaves like a cantilever of length (1/2)(l1 – r1) and (1/2)(l2 – r2) along the warp and weft respectively.

deflection at free end, d = force (length)3/3B

where B is the bending rigidity, thus

d1 = [Sp1(l1 – r1)3/8]/3B1

and

tanY1 = Y1 = d1/(p2/2) = Sp1(l1 – r1)3/12 p2B1

Shear behavior of woven fabrics S1

213

Sp1 Sp2 y1

p2/2

S2

r1 y2 r2

p1/2

Sp2 Sp1

11.11 Shear deformation on a unit cell.

similarly

Y2 = d2/(p1/2) = Sp2(l2 – r2)3/12 p1B2

so that

Y = (S/12)[p2 (l2 – r2)3/p1B2 + p1 (l1 – r1)3/p2B1]

The initial modulus defined by S = G Y gives

G = 12[(l2 – r2)3/p1B2 + (l1 – r1)3/p2B1]–1

This equation is difficult to solve as r1 and r2 are unknown. A reasonable approximation can be obtained from Peirce’s geometrical model. We know that:

r1/2 = q1D/2



fi r1 = D q1 = D ¥ 1.88√c1

In contact regions, there is a pressure between yarns of magnitude 2V1:

V1 = 8B1sinq1/p22

In fact this is the resultant of distributed force over a contact area. It would be interesting to know what this area is, but v is difficult to establish. In addressing this question Hertz analyzed the case of a rod bent over a straight rod and found the contact area to be elliptical. Based on this, one can conjecture, that the contact area should be composed of two ellipses. Hertz also found that the pressure distribution with, in the elliptical area is parabolic. However, for simplicity one can assume the contact area consisting of two straight lines as shown in Fig. 11.12. Assuming the following:

214

Woven textile structure

v1 r2 v10

r1

v1(x) dx r1/2

x

11.12 Force distribution in the contact region.

∑ distribution of 2V is triangular rather than parabolic as it would lead to fairly complex mathematics that is probably not justified; ∑ force 2V is split between the two lines of contact region in the ratio r1 : r2; ∑ slipping takes place gradually, starting at outer ends of contact region, where the distribution force is smallest; the resultant force in the r1 direction is 2V r1/(r1 + r2):

r1 /2

Ú0

area under triangle = 2

v1 (x ) dx = 1 v1 (0)r1 2

fi v1(0) = 4V1/(r1 + r2)

Hence by similar triangles

v1(x)/v1(0) = ((r1/2) – x)/(r1/2) = 1 – 2x/r1



fi v1(x) = 4V/(r1 + r2) (1– 2x/r1)

Similarly

v2(x) = 4V/(r1 + r2)(1– 2x/r2)

where V = 8B1sin q1/p22 = 8 B2 sin q2/p12. It is assumed that V remains same throughout these small deformations. Consider now the bending moment acting when a length s1/2 has slipped as shown in Fig. 11.13. Bending moment due to friction



=

(1/2)r1

Ú(1/2)(r – s ) mv1(x )[x – (1/2)(r1 – s1)] dx 1

1

= m [2V /(r1 + r2 )]

(1/2)r1

Ú(1/2)(r – s )(1 – 2x /r1)[x – (1/2)(r1 – s1)] dx 1

= [4mV/(r1 + r2)]s13/24r1

1

Shear behavior of woven fabrics

215

l1/2 Due to Sp1 Sp1

µv1(x)dx O A s1 r1/2

B

A

B

C

C Due to friction

11.13 Estimation of frictional resistance in the contact region.

Now at A this must be equal to bending moment due to Sp1 since no bending takes place at A:

Sp1[l1/2 – ½(r1 – s1)] = 4mVs13/24(r1 + r2)r1 = mVs13/6(r1 + r2)r1



fi s1 = [6Sp1r1(r1 + r2)/mV]1/3

so Y can be calculated by replacing l1 – r1 by l1 – r1 + s1, that is

Y1 ≈ Sp1(l 1 – r1 + s1)3/12p2B1

Similarly we have

11.4

s2 = [6Sp2r2(r1 + r2)/mV]1/3

Shear properties in various directions

The shear behavior of woven fabrics in principal directions still attracts wide attention because it affects fabric behavior. Less attention has been paid to fabric shear properties in bias directions because these involve complex mechanisms. It would be useful to obtain quantitative knowledge of shear in various directions where the angles between two sets of yarns change in the intersecting points. We can characterize the shear behavior of a woven fabric by shear rigidity (G) and shear hysteresis at two angles; 2HG is shear hysteresis at shear angle 0.5° and 2HG5 at shear angle 5° with the KESF instrument. Shear rigidity is the resistance of a fabric to shear, while shear hysteresis is the energy loss within a shear deformation cycle. With data obtained from the KESF instrument for a wide range of woven fabrics in different directions, we have established a model for predicting fabric shear rigidity in various directions. The existing literature has demonstrated a strong relationship between shear rigidity and shear hysteresis. The correlation coefficients of shear rigidity and shear hysteresis are very high, although the mechanisms governing shear rigidity and hysteresis of woven fabrics may be different.

216

11.5

Woven textile structure

Predicting shear properties: practical applications

The polar diagram of fabric shear properties is symmetrical in the warp and weft directions and crests at the maximum 45°. In addition, polar diagrams of shear rigidity and shear hysteresis move inward to outward with increasing weave density. Strong linear relationships exist between shear rigidity and shear hysteresis of woven fabrics in various directions. The coefficients of determination R2 of these properties for different woven fabrics are higher than 0.90. This finding proves that a strong relationship between shear rigidity and shear hysteresis exists not only in the warp and weft directions, but also in various directions, further justifying the use of this model for shear rigidity to the prediction of shear hysteresis in various directions. When a fabric is bent in more than one direction, it is subjected to double curvature and therefore a shear deformation occurs. Shear property is found to have a strong bearing with the bending behavior of the fabric. Many researchers have given a qualitative description to the shear property of woven fabric as the hysteresis produced during shearing is mainly due to the frictional restraints arising during rotation of the yarn at the intersecting points of the fabric. The characteristic shear stress–strain curve of woven fabric can be used for structural analysis. However, the conclusions inferred by various researchers while devising models to predict shear property differ widely and therefore the analytical results obtained in various models cannot be readily used for practical purposes. Cover factor is found to have a very good correlation with fabric shear properties. A higher cover factor produces high shear rigidity and shear hysteresis. The ability of a woven fabric to accept shear deformation is an essential prerequisite to acquire a conformable fitting to a 3-D surface such as the contour of the body surface for apparel manufacturing. Shear deformation is very common during wearing of a cloth since the fabric has to be stretched to some extent depending on the nature of body movement. Therefore, shear properties decide the suitability of a woven construction as a clothing material. It is also important for a wide range of industrial applications involving formation and molding operations. Low stress shear rigidity and shear hysteresis values are used to determine fabric handle value.

11.6 1. 2. 3. 4. 5.

References

Treloar L R C (1965), J. Text. Inst., 56, T533. Morner B and Olofsson T E (1957), Text. Res. J., 27, 611. Cusick G E (1964), Text. Res. J., 34, 1102. Grosberg P and Park B J (1966), Text. Res. J., 36, 421. Grosberg P, Leaf G A V and Park B J (1968), Text. Res. J., 38, 1085.

12

Compression behavior of woven fabrics

Abstract: This chapter deals with fundamental aspects of compression. Various theories of compression for fibrous material are summarized. Low stress compression behavior of woven fabric and its application in determination of fabric hand is also highlighted. Finally a theoretical model for the prediction of compression behavior of woven fabric is described. Key words: fabric model, compression behavior, fabric handle.

12.1

Introduction

Compression is defined as a decrease in intrinsic thickness with an increase in pressure. Intrinsic thickness is the thickness of the space occupied by a fabric subjected to barely perceptible pressure. Compression of fabrics is an inevitable phenomenon during fabric handling and processing. Compressive properties are concerned with the surface smoothness, softness and fullness of the fabric. The compressive properties of textile materials have direct relevance to the bulk, yarn structure and handle of fabrics. For example, compressive forces may play a very important part in pile carpets. The lateral compression property of yarn influences mechanical properties of fabrics to a large extent. The softness of the fabric is directly affected by the compressibility of yarn, which in turn is governed by the level of twist in the yarn to a large extent; highly twisted yarn will be less compressible. The effectiveness of compression behavior of woven fabric depends upon the degree of pressure provided, which is itself determined by a number of factors, including the physical and elastomeric properties of the fabric, and the type and structure of the yarns used. There are numerous applications in which textile materials are used as much for their bulk characteristics as for their other physical and mechanical properties. Typical examples can be found in the fields of filtration, health care, geotextiles, and fiberfill, etc. In most of these applications, the textile materials are called upon to perform under constant or repetitively changing transverse compressive loads. Compressible fabrics are commonly used in apparel manufacturing. Compressible fabrics also find application in various areas such as medical and industrial applications. The effectiveness of compression behavior of woven fabrics depends upon the degree of pressure provided and, this in turn is determined by a number of factors, including 217

218

Woven textile structure

the physical and elastomeric properties of the fabric, the type and shape of the yarns used, and most importantly the compressive stress produced in the fabric during the application process.

12.2

Fundamentals of compression

When a specimen of material is loaded with an axial push in such a manner that it shortens, it is said to be in compression. It is opposite to tension, in which a specimen is subjected to an axial pull so that it extends. On compression, the specimen will shorten. The material will tend to spread in the lateral direction and hence increase the cross-sectional area. Compression properties are generally characterized by two parameters; compressive strength and compressive modulus. The compressive strength of a material is that value of uniaxial compressive stress reached when the material fails completely. Compressive strength is the capacity of a material to withstand axially directed pushing forces. When the limit of compressive strength is reached, materials are crushed. On a macroscopic scale, these aspects are also reflected in the fact that the properties of most common materials in tension and compression are quite similar. Of course, the major difference between the two types of loading is the strain which would have opposite signs for tension (positive) and compression (negative). In general, compressive strengths are usually greater than tensile strengths. Concrete and ceramics are examples of materials with a much higher compressive strength than tensile strength. The ratio of the compressive or tensile force applied to a substance per unit surface area to the change in volume of the substance per unit volume is called the compression modulus. It is also known as bulk modulus, modulus of compression or modulus of volume elasticity. The ratio of mechanical stress to strain in an elastic material when that material is being compressed is called modulus of elasticity. Modulus of compression is the compressive force per unit area per change in volume per unit volume. The ability of the fiber mass to recover from compression – its resilience – can be expressed in different ways, for example the amount of energy recovered on the removal of the load expressed as a percentage, or the ratio of the energy expended by the testing machine in compressing the material between the same limits of pressure, the ability to absorb work, area of the hysteresis loop, etc.

12.3

The compression behavior of textile structures

Textile materials are compressible in nature and the thickness of these materials depends to the pressure applied to them. Compressibility of fibrous assembly depends on the structure and composition of the material. In the

Compression behavior of woven fabrics

219

case of loose fiber mass, compressibility is generally defined as the percentage reduction in volume of the fiber mass resulting from a specified increase in the applied pressure. The measurements of the thickness and compression properties of fabrics form an integral part of objective measurements for apparel fabrics. During determination of the handle of fabrics, the fabric is compressed between the fingers. This subjective judgment of fabric softness, that is compressibility, is then compared with the objective measurements of fabric compressibility. Compressibility of woven fabrics is studied as one of the major factors affecting fabric ‘handle’. The compressional properties of fiber assemblies as a relationship between pressure and thickness of the assemblies have been studied by many researchers. However, the oldest investigation was carried out by Peirce [1] who experimentally demonstrated typical compressional curves of two fabrics one hard, (A) and the other soft, (B) in compression, shown in Fig. 12.1. Based on this work, Hoffman and Beste [2] descriped Peirce’s equation as follows:

Tw = T0 exp(–cP)

12.1

where Tw is thickness of fabric under pressure P, T0 is thickness of fabric under no pressure and c is a constant to be determined. The pioneering work of Van Wyk [3] and subsequently its review by Carnaby [4] focused on the mechanics of the compression of fiber assemblies. They discussed a relationship describing the compression behavior of the fibrous mass as: 12.2

25 A

B

20 Pressure (kPa)



È ˘ P = l Í 13 – 13 ˙ v0 ˚ Îv

15

10

5

0

0

0.1

0.2 0.3 Thickness change (mm)

12.1 Typical compression curves.

0.4

0.5

220

Woven textile structure

where v is the volume of the fiber mass and v0 is the value of v when P is equal to zero. In addition to the above relationship for the load–compression of fibrous assemblies, Van Wyk also suggested a correction to equation 12.2 for assemblies which have been compressed to a volume which is small enough for the incompressible volume of the fibers to become significant at zero pressure. The corrected relationship was described as:



È ˘ 1 P=l Í 1 3 – 3˙ ( v – v ¢ ) ( v – v ¢ ) 0 Î ˚

12.3

where v¢ represents its limiting volume at large pressure. For a very loose structure, v¢ may be negligible and the equation takes the form of 12.2. Postle’s [5] study on compression was mainly on wool fibers where the pressure P exerted on the sample is generally inversely proportional to the cube of the volume v of the sample. It is denoted by

P=

l (t – t¢ )3

12.4

where is a constant of proportionality. Another well-known relationship called the ‘1/3’ power law is denoted by

V = aP–1/3

12.5

where V is the assembly volume and P is the pressure proposed by Van Wyk. It was used extensively in studies of compressibility of bulk masses of fibrous material and non-woven fabric structures. This law describes the behavior of a fibrous assembly in situations when fibers are more or less free to change their positions in the assembly. The process of applying Van Wyk’s law to dense textile structures is limited, because the freedom of yarns in fabrics and fibers in yarn is restricted owing to the ‘locked’ compressed state. When further deformation is not possible with compression of the fibers, this point is reached earlier and the process of applying Van Wyk’s law then refers to the modeling of pressure–thickness curves. In this situation the ‘1/3’ law cannot be applied or must be used with discretion. A correction was proposed by Van Wyk by altering equation 12.2; the value of P representing the pressure on a unit area of fabric, v is replaced by the fabric thickness t, Postle applied the relationship:

P=

l (t – t¢ )3

12.6

where, the thickness t or volume per unit area of fabric is large and undefined at zero pressure and t¢ represents the thickness of incompressible core.

Compression behavior of woven fabrics

221

The normal requirements for lightweight woven fabrics for internal change in thickness is effective around 0.5–50 gf/cm2 [6], which is known to be sufficient to cause the change in thickness. The design load may vary in certain fabrics like canvas and for certain industrial fabrics such as nylon tyre cord and medical compression fabrics. Also, the design load may vary due to external load exposure, such as in car seat fabrics and airbags. The most renowned system for objective evaluation of low stress compression properties is the Kawabata Evaluation System (KES). There exists a close relation between fabric hand and compressibility. The KES–FB3 system measures the compression energy required to compress a fabric laterally from thickness T0 to Tm given by:

WC =

Tm

ÚT

0

Pdt

12.7



where P is the maximum pressure which is 50 gf/cm2 in case of apparel fabrics. T0 and Tm stand for mechanical thickness at 0.5 gf/cm2 and 50 gf/ cm2, respectively. The close to linear relationship between pressure and thickness at the latter part of the pressure–thickness curve under a pressure larger than 20 to 50 gf/cm2 indicates the level of pressure to be applied for apparel fabrics. This section of curve is also characterized by a very steep slope, which indicates that fabrics are extremely incompressible. Thus the general shape of the curve is largely governed by pressure in the range from 0 to 50 gf/cm2. Matsushima and Matsuo [7] studied pressure–deformation curves for blankets and carded fiber mass and explained equation 12.8 assuming that the fiber assembly is composed of springs and a spring is sustained by bending resistance of a fiber as Van Wyk:

P = A exp(ax)

12.8

where A and a are constants, and x is compressional deformation. Matsuo [8] derived a compressional model, introducing a loading path which sustains pressure, and will each path composed of n ¥ m pieces of fiber elements having m–1 contacting points:



P – P0 = C V02 · g

˘ ÈÊV0 ˆ g ÍÁË V ˜¯ – 1˙ ÍÎ ˚˙

12.9

where C is introduced on the assumption that overlapping ratio of fibers, fiber orientation, crimping ratio of fiber, and bending restriction of fiber are in proportion to the power of (V0/V), g is a constant and equation 12.9 becomes Van Wyk’s equation when g is 3.

222

Woven textile structure

Most of the study by De Jong et al. [9] and Van Wyk concentrates on compression of fiber assemblies. Their extension to the study of woven wool fabrics with measured values from KES-FB3 and other compression testers does not take into account change in structural configuration of fabrics and cross-section shape. Variation in T0 and Tm along with large deviations obtained from KES-FB3 instruments need to be authenticated using empirical methods such as statistical linear, non-linear and neural networks.

12.4

The exponential behavior of compressible fabrics

In general the behavior of compressible fabrics on a macro-scale should be studeed over time with different performance parameters. Figure 12.2 indicates the general trend in performance with compression. The interesting point to note is that most fabrics change over time in an exponential fashion. They experience a condition during start-up, which may lie outside the traditional range of acceptable performance. This is most often deemed as the ‘start-up phase’, and depends mainly upon the handling capacity of the fabric, its density and compressibility. Further examination of this curve reveals that there is a certain time in compressible fabrics normally called as usable lifetime after which the compressible fabric ceases to function properly. Changes in fabric design can change compression. A design change can significantly flatten this curve, minimizing the rate of change over time. However, a change in the slope of this curve can also imply negative impacts on the start-up phase. In fact, this is quite often the case, as in many cases heavier, higher void volume press fabrics are provided in order to lengthen Performance parameter

Steady state compressing

Acceptable performance

Ideal fabric = no change over time 1 2 Time

12.2 Fabric compression and performance.

Fabric Design

Compression behavior of woven fabrics

223

the product’s usable lifetime, only resulting in a drastic lengthening of the start-up curve. This is true particularly for pressure-controlled fabrics such as filter fabrics.

12.5

The low stress pressure–thickness curve

The nonlinearity of pressure and thickness is quantified separately for each fabric under conditions of low stress. This nonlinearity measure compares an exponential curve with a straight-line fit of the data over the same command range. Since the measure quantifies slope differences, regions of the curve with higher nonlinearity values are minimized using a least square and iterative method of curve fitting. According to the compression graph shown in Fig. 12.3, a woven fabric compressive curve is considered to consist of three parts. The first and third step of the compressional curve is linear and is assumed to follow linear regression. The general equation for the linear regression relationship is given by:

Y = k + mx

12.10



Y = kemx

12.11



Êy ˆ ln Á 2 ˜ Ë y1 ¯ m= x2 – x1



k = Y1e1–mx

12.6

Predicting compression in woven fabrics

Pressure (gf/cm2)

Compressibility of a woven fabric primarily depends upon the load applied, together with the geometrical properties of the fiber, yarn and fabric. Different fiber parameters (density and fineness), yarn parameters (count,

Linear

Exponential Linear

Thickness (mm)

12.3 The pressure–thickness relationship.

224

Woven textile structure

twist, etc.) and the fabric parameters (threads per centimeter, crimp, etc.) influence fabric compressibility. Fabric compressibility will change if any of these parameters is altered. Different researchers have proposed different models of fabric compression as detailed in Section 12.3. Despite their work there is stll no model of fabric compressibility relating fiber, yarn and fabric parameters.

12.6.1 General response of fabric to compression load Fabric compression generally does not take place instantly after the application of a load, but occurs in steps. The protruding fibers on the surface of the fabric first tend to resist the load. The fabric surface is not regular due to the bending of warp and weft yarns. Owing to this irregularity the yarn at the topmost position will be deformed first, resulting in unbending which in turn induces slippage of fibers in the yarn. As a result bending rigidity and frictional coefficient are important parameters. If there is a gap between the warp and weft, bending deformation of the yarn takes place. As the contact areas between the yarn increases, the reaction forces between the yarns also increases. As compressive forces increases, the yarn becomes compact by slippage of fibers in the yarn, and the yarn will become flattened and compact. If the twist value of the yarn is high, it will resist the load in more efficient manner.

12.6.2 Mathematical model of fibrous assembly The following assumptions can be used for developing a model to predict the compressibility of a fabric: ∑ The yarn is circular and uniform along its length. ∑ Frictional coefficient between the fibers is taken into consideration, but that between yarns is not. ∑ Fiber crimp is taken into account, but the yarn crimp in fabric is not considered. ∑ The type of fiber is not considered. ∑ The type of spinning technology is not considered. ∑ The model is aimed at woven fabric. ∑ Yarns are not interlaced but lie over each other The following can be assumed: ∑ ∑ ∑ ∑

tex of a fiber and yarn is t and ty respectively; twist of yarn is T; twist per unit length, c, is fiber crimp; frictional coefficient betweens fibers in the yarn cross-section is µ;

Compression behavior of woven fabrics

225

∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑

packing density of yarn is f; g is bending rigidity of fibers; G is bending rigidity of fabric; N is threads per unit length in the fabric; Young’s modulus of the fiber is y; I is the moment of inertia of fiber; r is the radius of a single fiber; the density of a single fiber is d; m is the fiber wad mass; the applied load is P; volume at zero and at load P is v0 and v is maximum volume filled with fiber wad under pressure is v¢; ∑ d is fiber wad density;

The number of fibers in a yarn = ty /t.

12.12

Yarn bending rigidity depends upon the number of fibers in the yarn, single fiber bending rigidity, fiber crimp, fiber frictional coefficient and yarn twist and packing density. Considering these factors:



ÈK ¥ t y ¥ g ˘ Èm ¥ f ¥ T ˘ yarn bending rigidity = Í ˙¥Í ˙˚ t c Î ˚ Î

12.13

where K is a constant. The fabric bending rigidity G will be G = N ¥ yarn bending rigidity:

G =N ¥

K ¥ ty ¥ g ¥ m ¥ f ¥ T t¥c

12.14

G =K ¥

N ¥ ty ¥ g ¥ m ¥ f ¥ T t¥c

12.15

Again we know that 4 g=Y ¥ I =Y ¥ p ¥ r 4 Now fiber density, f = mass per volume:



f =

12.16

mass per unit length volume per unit length



= t per unit area



= t/p r2



r2 = t/p f

12.17

226

so,

Woven textile structure 2

g = Y ¥ I = Y ¥ p r 2 /4 = Yp ¥ 2t 2 4 p f 2 = Yt2 2 4p f





12.18

by putting the value of r2 from equation (12.17) in equation (12.16). Again putting the value of g from equation (12.15) in equation (12.18), we get

G= = Y =

2 K ¥ N ¥ ty m¥f¥T ¥ Yt2 2 ¥ t c 4p f

K ¥ N ¥ Y ¥ t ¥ ty ¥ m ¥ f ¥ T 4p f 2 ¥ c G ¥ 4p f 2 ¥ c K ¥ N ¥ t ¥ ty ¥ m ¥ f ¥ T

12.19

Now Van Wyk’s formula for compression can be written as: 3



ˆ Ê mˆ Ê 1 P = K1 ¥ Y Á ˜ Á 1 3 – Ë d ¯ Ë (v – v¢ ) (v0 – v¢ )3˜¯

12.20

By putting the value of Y from equation (12.19) to equation (12.20) we get: P = K1 ¥

G ¥ 4p f 2 ¥ c K ¥ N ¥ t ¥ ty ¥ m ¥ f ¥ T 3



ˆ Ê mˆ Ê 1 ¥Á ˜ ¥Á 1 3– Ë d ¯ Ë (v – v¢ ) (v0 – v¢ )3˜¯

12.21

Let K¢ = K1/K. Therefore: P = K¢ ¥

G ¥ 4p f 2 ¥ c N ¥ t ¥ ty ¥ m ¥ f ¥ T 3

ˆ Ê mˆ Ê 1 ¥Á ˜ ¥Á 1 3– Ë d ¯ Ë (v – v¢ ) (v0 – v¢ )3˜¯

12.22

The volume of fabric equals fabric thickness ¥ fabric area. As fabric area is constant, any change in fabric volume can be interpreted as a change in thickness. Let us consider a particular fabric so that v¢ is always constant. If we take always the same initial pressure-free volume v0 and compress it always to the same volume v whatever the pressure required , so, v, v¢, v0

Compression behavior of woven fabrics

227

become constant and also the term (1/(v – v¢)3 – 1/(v0 – v¢)3 also becomes constant for a particular fabric. As a result, we get a particular change in volume from v0 to v. The corresponding change in thickness also become constant for the same fabric. For a particular change in thickness, the required pressure increases with increase in bending rigidity of fiber, fiber density and Crimp in fiber. From equation (12.19) as the term (1/(v – v¢)3 – 1/(v0 – v¢)3 is constant, the required pressure for a particular change in thickness decreases with increase in packing density of yarn, twist in yarn, frictional coefficient, diameter of fiber, diameter of yarn and threads per unit length.

12.6.3 Evaluation of KES compression parameters using modeling Compression energy from KES theory is given by WC:

WC =

T0

ÚT P dT m

where T0 = d + h (at P = 0.5 gf/cm2), d is yarn diameter and h is crimp height, and

Tm = b + h at P = 50 gf/cm2

where b is minor yarn diameter and h is crimp height. From this equation compression energy can be calculated from 0 to P. If v0 is not very high compared with v and v¢ then

È ˘ 1 P=a Í 1 3 – 3˙ Î(v – v¢ ) (v0 – v¢ ) ˚

12.23

with a = K1Y(m/d)3. v a a dv + Ú dv 3 v (v – v¢ )3 (v – v¢ ) 0 p v – v0 = (v – v¢ ) + 1.5a 2 (v0 – v¢ )3

WC = –



v

Úv

0

0

12.24

Now volume = area ¥ thickness. Let A be the fabric area. Therefore:

v = ATm

12.25



v0 = AT0

12.26



v¢ = AT ¢

12.27

Here T is incompressible thickness. Putting the values of v, v0 and v¢ from

228

Woven textile structure

equations 12.25, 12.26 and 12.27 in equation 12.24 we get: ATm – AT0 WC = P (ATm – AT ¢ ) + 1.5 ¥ a ¥ 2 (AT0 – AT ¢ )3

12.28

Now by putting the value of P from equation 12.22 and of a from equation 12.23 in equation 12.28, we get the required compression energy. 3 K¢ ¥ G ¥ 4p d 2 ¥ c ¥ m3 2 ¥ N ¥ t ¥ ty ¥ m ¥ f ¥ T d

WC =

Ê 1 ˆ (AT – AT ¢ ) ¥Á 1 3– m Ë (v – v¢ ) (v0 – v¢ )3˜¯ 3 ATm – AT0 + 1.5 ¥ K1Y ¥ m3 ¥ d (AT0 – AT ¢ )3



The linearity of the compression thickness curve, LC, and compression resilience, RC, can be calculated as:

LC =

T0

ÚT

m

P dT 0.5Pm (T0 – Tm )

Compression resilience is:

RC =

T0

ÚT

m

P dT ¥ 100 WC

In order to list this theoretical prediction, plain woven P/V (70/30) suiting fabric samples of 220 aerial density (gram per square meter) were tested on a KES compression tester to determins compression energy and other related parameters. The compression energy determined theoretically using mathematical model was correlated with the results obtained through the KES-FB3 instrument as shown in Fig. 12.4. The correlation between the

Theoretical value y = 0.8415x + 0.041

0.4 R2 = 0.861 0.3 0.2 0.1 0

0

0.2 KES-FB3 value

0.4

12.4 Correlation graph of compression energy WC (gf cm/cm2).

Compression behavior of woven fabrics

229

compression energy predicted theoretically and measured by KES-FB3 instrument was very good (R = 0.927). This model can be very useful for prediction of fabric compressibility without testing the fabric samples if the fiber, yarn and fabric parameters are known.

12.7

Practical applications

In a woven construction, warp and weft yarns are compressed due to inter-yarn pressure. The softness of the fabric is determined by its compressibility, which in turn depends on the compressibility of yarn and the fabric construction. Compressibility of a fabric has been seen as an integral component of fabric hand. Tailorability of cloth depends significantly on fabric compression behavior. The compressibility of fabrics significantly influences drapeability. When a fabric is draped on the edges of a contour, there is compressional deformation at the point of bending. Fabrics with higher compressional energy have a higher drape coefficient. A highly compressible fabric has high compressional energy and can absorb or withstand compressive forces to a greater extent at the deforming points. This prevents folding at the deforming points and a higher drape coefficient results. In the case of industrial and technical applications such as geotextiles, filter fabrics, floor coverings, paper making felts, and many household applications, fabrics produced by weaving and nonwoven technology are subjected to compressive loads. The compression and recovery behavior of these fabrics is extremely important in these applications.

12.8 1. 2. 3. 4. 5. 6. 7. 8. 9.

References

Peirce F T (1930), J. Text. Inst., 21, T377–T416. Hoffman, M and Beste L F (1951), Text. Res. J. 21(2), 66–77. van Wyk C M (1946), Textile Inst., 37, T285–T292. Carnaby G A (1979), The compression of fibrous assemblies with application to yarn mechanics, Wool Research Organisation of New Zealand, Report No. 66. Postle R (1971), J. Textile Inst., 62, 219–231. de Jong S and Postle R (1977), J. Text. Inst., 68(10), 324. Matsushima M and Matsuo M (1960), Sen-I Gakkaishi, 16, 105–109. Matsuo M (1968), Mechanical Properties of Fiber Assemblies, PhD Thesis of Tokyo Institute of Technology. DeJong S, Snaith J Wand Michie N A (1986), Text. Res. J., 56(12), 759–767.

13

Friction and other aspects of the surface behavior of woven fabrics

Abstract: In this chapter fabric surface properties are discussed to explain friction and abrasion resistance of fabrics as well as their physical appearance. The effect of various fabric parameters such as fiber type, thread linear density, thread density, weave type and yarn twist on fabric handle is discussed in detail. Key words: fabric model, frictional behavior, abrasion resistance, fabric handle.

13.1

Introduction

Fabric surface properties are important because of their psychological and physical effects on a person’s appreciation of a fabric. The sensations perceived from the contact of clothing with the skin can greatly influence the overall feeling of comfort. The subjective feeling of fabric is a complex result of psychological and physiological responses of the human body and physical properties of the fabric. Fabric characteristics such as fiber type, thread linear density, thread density, weave type and yarn twist affect how a fabric feels to the touch. Surface properties also help in perception of the smoothness and crispness of the fabric. Geometrical roughness is another important factor affecting perceived softness of a fabric. In the determination of fabric handle, fabric smoothness/roughness plays an important role. This is evaluated by friction and surface unevenness measurements. The physical parameters taken into account to estimate the fabric handle are coefficient of friction and geometrical roughness of the fabric surface. These two parameters influence fabric abrasion resistance. Abrasion is basically the wearing away of any part of a material by rubbing against another surface. Textile materials become unserviceable due to abrasive wear. Abrasive wear is caused mainly due to friction between the fabric and solid objects in contact with fabric, the wearer’s body and environmental particles such as dust and grit. It is important to consider abrasion and friction characteristics from a mechanical damage point of view which subsequently results in the loss of aesthetic and physical fabric quality. 230

Friction & other aspects of the surface behavior of woven fabrics

13.2

231

Fundamentals of friction and abrasion

Friction is the force resisting the relative lateral or tangential motion of solid surfaces, fluid layers or material elements in contact. Friction results from two surfaces rubbing against each other. It can hinder the motion of an object or prevent an object from moving at all. The strength of frictional force depends on the nature of the surfaces that are in contact and the force pushing them together. This force is usually related to the weight of the object. In cases involving fluid friction, the force depends upon the shape and speed of an object as it moves through air, water or other fluid. Friction occurs to some degree in almost all situations involving physical objects. When friction affects a moving object, it converts the kinetic energy of the object into heat. The force of friction between an object and a surface can be calculated from a free-body diagram of a block resting on a rough inclined plane as shown in Fig. 13.1:

F=m¥N

where F is the force of friction, m the coefficient of friction between the two surfaces and N the normal force.

13.2.1 Coefficient of friction The coefficient of friction is a dimensionless scalar value. It is a ratio of the force of friction between two bodies and the force pressing them together. The coefficient of static friction is the ratio of the maximum static friction force (F) between the surfaces in contact before movement commences to the normal (N) force. The coefficient of kinetic friction is the ratio of the kinetic friction force (F) between the surfaces in contact during movement to the normal force Ff/N. Both static and kinetic coefficients of friction depend on the pair of surfaces in contact. Their values are determined experimentally. For a given pair of surfaces, the coefficient of static friction is larger than the kinetic friction. The coefficient of friction depends on the materials used. As an example, ice on steel has a low coefficient of friction – the two materials slide past each other easily – while rubber on pavement has a high coefficient of friction – the materials do not slide past N F

w

13.1 A free-body diagram of a block resting on a rough-inclined plane.

232

Woven textile structure

each other easily. The coefficients of friction ranges from near 0 to greater than 1. Under good conditions, a tire on concrete may have a coefficient of friction of 1.7.

13.2.2 Types of friction Static friction occurs when two objects are not moving relative to each other, like a rock on a table. The coefficient of static friction is typically denoted as μs. The initial force to get an object moving is often dominated by static friction. The static friction is in most cases higher than the kinetic friction. Rolling friction is the frictional force that occurs when one object rolls on another, like a car’s wheels on the ground. This is classified under static friction because the patch of the tire in contact with the ground, at any point while the tire spins, is stationary relative to the ground. Kinetic friction occurs when two objects are moving relative to each other and rub together, like a sledge on the ground. The coefficient of kinetic friction is typically denoted as μk, and is usually less than the coefficient of static friction. Sliding friction is when two solid surfaces slide against each other. Putting a book flat on a desk and moving it around is an example of sliding friction. Factors affecting sliding friction include weight and the stickiness of the two surfaces. Fluid friction is the friction between a solid object as it moves through a liquid or a gas. The drag of air on an airplane and of water on a swimmer are two examples of fluid friction.

13.2.3 Abrasion Abrasion is a kind of wear in which rubbing away of component fibers and yarns of the fabric takes place. During abrasion, a series of repeated applications of stress takes place. Abrasion may be classified as flat abrasion, edge abrasion or flex abrasion. Abrasion resistance can be seen is the capacity to absorb energy. It is the ability to resist wear from the continuous rubbing of fabric against another surface. Garments made from fabrics that possess both high breaking strength and abrasion resistance can often be worn for a long period of time before signs of wear appear.

13.3

Measuring roughness and other surface properties of woven fabrics

13.3.1 Measurement techniques Investigation of the geometry of fabric surface was carried out by Butler et al. in 1955 by designing an instrument to record the cloth profile [1].

Friction & other aspects of the surface behavior of woven fabrics

233

The main objective of the instrument was to assess fabric faults such as repping and the differences in pick spacing along the warp direction. The objective measurement of fabric surface roughness by the KES system was introduced by Kawabata [2]. A multi-purpose tester has been designed by Amirbayat and co-workers to measure drape and bending stiffness and also the surface properties of fabrics and their variation during wear [3,4]. Since a force is imposed during testing in the KES surface tester which affects the measurement of fabric surface, a non-contact method for fabric surface assessment using a laser triangulation technique has been developed [5]. The KES instrument for surface study uses a sensor and smooth steel piano wire to measure thickness variation together with geometrical roughness and frictional force over a 2 cm fabric length along the warp and weft directions by moving the fabric or sensor forward and backward. A normal load of 10 g on the probe is used for surface roughness studies while a heavier load 50 g is used for frictional force studies. The principle of measurement for surface roughness and surface friction is shown in Figs 13.2 and 13.3 respectively.

13.3.2 Fabric surface geometrical roughness The geometrical roughness is a measure of the surface contour of fabric. A typical output of fabric thickness variation from KES is shown in Fig. 13.4. The troughs represent the lowest places on the fabric surface and P = 10 g 0.5 mm

13.2 Surface roughness. P = 50 g 5 mm

13.3 Surface friction.

234

Woven textile structure

µm 20 0 –20

L1 cm

1

0

2

13.4 Surface roughness chart measured by a KES instrument.

the peaks the crowns of the yarn in the fabric. Although the waves produced on the chart during measurement are not very regular, the number of the waves is normally found to be equal to the sett of the fabric in the crossdirection. The geometrical roughness of the fabric in this measurement is represented by SMD which is the mean deviation of surface contour. Mathematically it is given as:

SMD = 1 X

x

Ú0

Z – Z dx



13.1

where Z is the average thickness and X is the span of measurement. A graphical representation SMD is shown in Fig. 13.5. The roughness measured by SMD is the average height of the area make by the average line and the zigzag curves. The variation in fabric thickness is measured along the warp and weft direction to evaluate the fabric surface topology. The two values SMDI and SMD2, for warp and weft, complete the geometrical roughness of the fabric surface. An increase in SMD reflects an increase in the surface variation of a fabric. The average thickness of the fabric is located at the center of the lowest and the highest places on the fabric surface on the tested side. The geometrical roughness is a measure of the variation of fabric thickness around the central point. Fabric roughness depends on yarn spacing, irregularity, weave design and other fabric geometrical factors.

13.3.3 Fabric surface frictional coefficient The coefficient of friction between the fabric surface and the probe is another fabric surface property measured by KES surface tester. The instrument calculates the frictional coefficient as the ratio of sliding force along the fabric plane sensed as frictional force to predetermined compressional load. A typical output of fabric surface frictional coefficient is shown in Fig. 13.6. The mean friction coefficient (MIU) is given by:

MIU = 1 X

x

Ú0

m dX



13.2

Friction & other aspects of the surface behavior of woven fabrics

235

Thickness Z (cm)

SMD = Area/X

Z

X (cm)

X

13.5 Geometrical roughness (SMD). MIU-1 (warp direction) 20

–20

13.6 Output of friction coefficient from a KES instrument.

Its deviation from mean MMD is given mathematically as:

MMD = 1 X

x

Ú0

m – m dX



13.3

where X is the testing difference and m the average function coefficient. The deviation of coefficient of friction MMD is a measure of slip-stick behavior. As the probe sticks and binds on the irregular fabric surface the frictional force changes and gives a deviation from the mean frictional value. The concept of MMD is shown in Fig. 13.7. Barker et al. [6] separated the coefficient of surface friction into two parts. The first part is associated with the friction between the fabric and the surface of a rigid body. The second component comes from fabric thickness compression studies. It is assumed that the energy loss caused by inter-fiber friction during compressional deformations is related to a fabric subjected to rubbing, denting and crushing. The relative importance of these two terms varies with the type of surface contact and the applied load. For many fabrics friction property charts are closely related to their roughness charts and the correlation coefficient for the deviation of friction coefficient (MMD) and the measured geometrical roughness (SMD) is high [7]. This suggests that the geometrical roughness contributes to the measured fabric frictional coefficient.

Woven textile structure Coefficient of friction µ

236

MMD = area/x

µ

x (cm)

13.7 Principle of MMD.

13.4

Factors affecting abrasion resistance

The abrasion resistance of a fabric is dependent upon many factors including fiber properties, yarn structure and size, fabric mass and geometry, fabric finish including lubricating and sizing agents, and the type of abradant. For hydrophilic fibers, the amount of moisture present also affects abrasion resistance.

13.4.1 Fiber properties Hamburger [8] stated that the inherent abrasion resistance of a fiber should correlate with the energy absorption of a mechanically conditioned fiber and the ability of the fiber to release this energy after stressing without the occurrence of failure. The area under the stress–strain curve is considered to be one of the best measures of the ability of a fiber to absorb energy or fiber toughness. The larger area under the stress–strain diagram refers to higher abrasion resistance. Hamburger reported that the energy coefficient is found to be a function of fiber properties such as low modulus of elasticity, large immediate elastic deflection and high ratio of primary to secondary creep, high magnitude of primary creep and high rate of primary creep for high abrasion resistance. Abrasion is a repeated stress caused by forces of comparatively low magnitude. Strength, elongation and elastic recovery during and after repeated stress applications are important factors in abrasion resistance. McNally and MeCord [9] theorized that elongation and elastic properties are more important than strength, especially when fiber bending and flexing are included as part of the abrasive stress. They emphasized the role of flexural and shear properties of fibers as important factors in abrasion resistance. Fiber length, diameter and cross-sectional shape influence abrasion resistance by affecting the inter-fiber cohesion within the yarn as a result of abrasive forces. When fibers are removed from yarns, the loss of interfiber cohesion can cause rapid deterioration of the yarn structure. Longer

Friction & other aspects of the surface behavior of woven fabrics

237

fibers are usually more difficult to remove from a yarn than shorter ones and also make stronger yarns at equal twist and diameter. Studies have shown that filament yarns are usually more abrasion resistant than staple yarns comprising the same fibers. Although fine fibers produce stronger yarns, the use of moderately coarse fibers may improve abrasion resistance because they require more force than fine fibers to rupture. However, fibers that are too coarse may develop high strains on the outer portion of the bend if fiber flexing or bending is involved. Little work has been reported on the effect of fiber cross-sectional shape on abrasion resistance. However flat, elliptical or hollow fibers might wear better than round ones [9].

13.4.2 Yarn and fabric structure The yarn and fabric parameters that influence a fabric’s abrasion resistance are those that affect the ability of the fabric to absorb energy repeatedly without failure or rupture. Geometric parameters in yarn and fabric construction affect the total energy absorption capability of a fabric, as well as the evenness with which abrasive stresses are distributed throughout all elements of the fabric. They also affect the ability of fibers and yarns to move away from the abradant but then regain or retain their original positions within the fabric. Backer and Tanenhaus [10] postulated that a large area of contact between the fabric and abradant would allow a better distribution of abrasive stresses, thus decreasing the localized load at any one fiber point. This would decrease frictional wear, surface cutting, fiber plucking, slippage and tensile fatigue. Those geometric factors which have been found to be most important in determining the fabric abrasion resistance are yarn twist, diameter, ply, crimp fabric thickness, thread density, and type of weave. Yarn twist Yarn twist is the means used to convert fibers into yarns. Consequently the amount of twist inserted has a major effect on the degree of fiber binding within the yarn. As twist is increased, the inter-fiber frictional forces are increased and the tendency for fibers to be plucked from the yarn is reduced. However, high amounts of twist may also stiffen the yarn so that it does not flatten or rotate under the abradant pressure. This could lead to stress concentration on relatively high points of the yarn rather than allow an even distribution of abrasive stress throughout the yarn. High twists also reduce the tensile energy absorption capability of yarns [11,12]. Several studies have shown that fabric abrasion resistance rises as twist is increased to an optimum point and then decreases as twist is further increased. The

238

Woven textile structure

optimum level of twist necessary for a staple yarn is higher than that for a filament yarn. A more recent series of studies indicated that varying the twist multipliers from 3.10 to 4.10 for 10/1 and 15/1 cotton yarns had no significant effect on either the flex abrasion resistance or edge-wear properties of the durable-press fabrics [13,14]. Yarn diameter Coarse yarn usually improves the resistance of fabrics to flat or plane abrasion. This increased abrasion resistance is the result of the presence of a larger number of fibers so that more fibers must be ruptured before the yarn fails [12,15–17]. There may also be better stress distribution over the larger number of fibers present in the surface layers of a coarse yarn than a fine yarn. In weave patterns such as sateens or warp-faced twills, where one set of yarns predominates on the fabric surface, it is advantageous to use coarse yarns for the float. McNally and McCord [9] theorized that the use of coarse yarn might be less advantageous in fabrics subjected to flex abrasion because of high strains imposed on the fibers lying on the outside curvature of the bent yarn. A study indicated that the flex abrasion resistance of 7.5–9.0 oz per sq yd (279–335 g/m2) durable-press cotton suiting fabric decreased as filling yarn size was increased from 15/1 to 7.5/1 [14]. However, the edge wear on simulated trouser cuffs during laundering was better, especially for twillweave fabrics, when the coarser filling yarns were used in spite of the fact that the degree of fabric bend in an edge-wear test is nearly double that in a flex abrasion test. These results indicate that better yarn mobility within the fabric gained by employing fewer coarser yarns more than offset any additional fiber strains caused by bending the coarser yarns when the degree of fabric bending was severe. Yarn ply In a study, by Schiefer and Cleveland [17] it was found that the abrasion resistance of a fabric can be increased greatly by the use of a two-ply yarn rather than a single yarn of equal count. Another study indicated that when fiber abrasion and cutting was severe at the crown of the yarn crimp wave, the outside layer of fibers in single yarns tended to peel away from the central core of the yarn [18]. When two-ply yarns of equivalent size are used, this peeling effect is restrained by the presence of the second ply. Instead fibers are cut off across the top of the crown and tufts of cut fiber ends are formed at each side of the crown.

Friction & other aspects of the surface behavior of woven fabrics

239

Yarn crimp The amount of crimp present in a yarn determines the elevation of yarn above the fabric plane. Abrasive degradation usually occurs first at the surface, causing damage to those yarns [10]. Thus, the balance between warp and filling yarn crimps often determines which set of yarns will be preferentially damaged and to what extent. In a plain-woven fabric, the highest degree of abrasion resistance would probably be obtained by having the same yarn tex, yarn crimp and thread density in both the warp and filing directions. This type of structure would give even stress distribution across the maximum number of yarn crowns, thus decreasing the localized load at any one point. When the crimp balance shifts so that one set of yarn contains more crimp than the other, the set containing higher crimp rises further out of the fabric plane and sustains a greater amount of damage. The other set of yarns will be protected until the crimp crowns of the first set have been worn down enough for the abradant to come into contact with the protected yarns [10,18]. Any change in the crimp balance between warp and filling yarns during laundering or wear may change both the degree of abrasion and the point of abrasive attack. Fabric thickness Fabric thickness is largely determined by yarn diameter and yarn crimp [10]. Consequently an increased yarn size and an increase in fabric thickness usually raise fabric abrasion resistance. However, if the surface appears damaged to the point of consumer dissatisfaction with the garment appearance before a yarn is ruptured or a hole is formed, then the additional abrasion resistance of the thick fabric no longer contributes to longer garment life. The changes in surface appearance are often more of a problem than fabric rupture in pile fabrics such as corduroy, velvet or velveteen. Thread density An increase in fabric thread density increases yarn interlacing which increases the number of yarn crowns over which the abrasive stress can be distributed. The large number of yarn cross-over points increases fiber and yarn cohesion within the fabric and decreases the probability of fibers being plucked or slipped out of place within the structure. Consequently an increase in the thread density up to an optimum point tends to increase flat abrasion resistance. However, very high thread density causes yarn jamming and restricts yarn mobility during use. Abrasion resistance then decreases as the yarn crowns form high rigid knuckles, especially if the abrasive stress also involve large flexing or bending stresses [9,10,14,19].

240

Woven textile structure

Weave type The influence of weave pattern on fabric abrasion resistance is highly dependent on the type of abradant used, the degree of fabric flexing or bending occurring during abrasion and the direction of stress application. Plain weaves provide the best fiber binding for flat and multidirectional abrasion. balanced yarn size and crimp give equal exposure of warp and filling yarn at the fabric surface. However, modified plain weaves, such as oxford or basket, provide greater yarn mobility to absorb stress by moving away from the abradant. Twill and sateen weave provide adequate yarn mobility while reaping the advantages of weaving with higher thread counts than is possible with plain weaves [10]. The counterbalance to the advantages of greater yarn mobility in twill and sateen weaves is the increasing vulnerability of the longer floats as they cover more and more of the fabric surface. Longer float lengths are more vulnerable to plucking and snagging of fibers and the entire yarn. However, the yarn floats in twill and sateen weaves protect the cross-threads from abrasive damage [14]. This becomes valuable when, for example, the warp yarns are to withstand higher tensile stress during wear and can be protected against abrasive damage by the filling yarn floats in a sateen weave. Twill and sateen weaves give maximum abrasion resistance when the abrasive stress is applied parallel to the direction of the floats. However, one study [14] reported that durable press suiting fabrics woven with both twill and sateen weaves exhibited better flex abrasion resistance when the abrasive action was applied perpendicular to or across the float. These authors reported that plain-weave fabrics gave better flex abrasion resistance than oxford, basket, twill or sateen weaves, although the abrasion resistance order was reversed for simulated trouser cuff edge wear during laundering. High yarn mobility is an important factor in edge wear but it is less important than good fiber and balanced distribution of abrasive stress over both warp and filling yarn systems in the flex abrasion tests.

13.4.3 Fabric finishes Fabric finish improves handle, wrinkle resistance, stain or soil resistance of the fabrics. Lubricants such as the silicones or polyethylene compounds may improve flex abrasion resistance by increasing fiber and yarn mobility within the fabric structure [9,20–22]. They have less effect on the flat abrasion resistance of a fabric since this property is more dependent on good fiber binding than on fiber and yarn mobility. Contradictory results have been reported for the effects of cationic softeners, often used in home laundry, on abrasion resistance. Murry [23] reported that these softeners increase tear strength and elongation of resin-treated viscose fabrics but reduce flat

Friction & other aspects of the surface behavior of woven fabrics

241

abrasion resistance and marginally affect the flex abrasion resistance. The American Association of Textile Chemists and Colorists (AATCC) reported that cationic softeners reduce tumbling abrasion resistance of cotton print cloth, corduroy, acetate and nylon tricot fabrics but improved the abrasion resistance of polyester and cotton shirting, acrylic and polyester doubleknit fabrics [24]. Coating finishes often increase flat abrasion resistance of a fabric by covering the fabric face with polymeric material and by increasing fiber binding. However, they are less successful in improving flex abrasion resistance [9]. However, flexible polymer lattices such as polyacrylates and polyurethanes applied using polymer deposition to fibers, yarn and fabric surfaces increase both flex and edge-wear abrasion resistance of durablepress cotton fabrics [25,26–29]. These films are tough and flexible and have less tendency to stiffen the fabric than vinyl and rubber coatings. They protect the fiber from surface damage by coating rather than absorbtion of the abradant’s energy [25]. A large proportion of apparel, bedlinen and drapery fabrics containing cellulosic fibers are reacted with cross-linking resins to improve fabric wrinkle resistance. These finishes increase elastic recovery but reduce tenacity and elongation of cellulosic fibers, especially cotton, thus drastically reducing the ability of these fibers to absorb energy to resist abrasion [30,31].

13.5

References

1. Butler K J, Cowhig W T and Michie N A (1955), Skinner’s Silk and Rayon Rec. 29, 732. 2. Kawabata S (1980), Examination of effect of basic mechanical properties of fabric hand, Mechanics of Flexible Fiber Assemblies, NATO Advanced Study Institute Sciences, 405. 3. Hearle J W S and Amirbayat J (1988), J. Text. Inst., 79, 588. 4. Amirbayat J and Cooke W D (1989), Text. Res. J., 59, 469. 5. Ramgulam R B, Amirbayat J and Porat I (1993), J Text Inst., 84, 99. 6. Barker R et al. (1985–1987), Report to North Carolina State University, Kawabata Consortium, School of Textiles, NCSU. 7. Hu J (2004), Structural Mechanics of Woven Fabrics, Woodhead Publishing Limited, Cambridge, p. 77. 8. Hamburger W J (1945), Mechanics of abrasion of textile materials, Text. Res. J., 15, (5), 169–177. 9. McNally J P and McCord F A (1960), Text. Res. J., 30, 715–751. 10. Backer S and Tanenhaus S J (1951), Text. Res. J., 21, 635–654. 11. Platt M M (1950), Text. Res. J., 20, 519–538. 12. Walker A C and Olmsted P S (1945), Text. Res. J., 15, 201–222. 13. Kyame G J Lofton J T and Ruppenicker G F (1968), Jr. Text. Bull., 94, 37–39. 14. Ruppenicker G F Jr., Kyame G J and Little H W (1968), Proceeding of Eight Cotton Utilization Research Conference, New Orleans, La, pp. 111–122.

242 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

Woven textile structure Hicks E M and Scroggie S C (1948), Text. Res. J., 18, 416–423. Tait J H (1945), Rayon Text. Monthly, 26, 171. Schiefer H F and Cleveland R S (1934), Text. Mfr., 60, 182–183. Galbraith R, Boyle M, Cormany E, Davidson S, Ginter A, Ericson J, Lapitsky M, Lund L and Cooper M (1969), Text. Res. J., 39, 329–338. Kaswell E R (1946), Text. Res. J., 16, 19–21. Anon (1958), Am. Textile Reptr., 72, (20), 19–21. Nuessle A C (1954), Text. World, 104, 92–94. Simpson B G (1957), Am. Dyestuff Reptr., 46, 991–998. Murry E A (1955), Am. Dyestuff Reptr., 44, 141–149. Midwest Intersectional Paper Committee (1973), AATCC, Textile Chemist and Colorist, 5, 31–37. Rollins M L, DeGruy I V, Hensarling T P and Carra J H (1970), Text. Res. J., 40, 903–916. Blanchard E J, Harper R J, Gautreaux G A and Reid J D (1967), Text. Ind., 131, (1), 116–119, 122, 143. Harper R J, Blanchard E J and Reid J D (1967), Text. Ind., 131, (5), 172, 174, 177, 181, 184, 186, 233–234. Wolfgang W G (1966), Text. World, 116, (1), 104–106, 108, 110. Lofton J T, Harper R J, Little H W and Blanchard E J (1968), Proceeding of Eight Cotton Utilization Research Conference, New Orleans, La, pp. 123–138. Gagliardi D D and Shippee F B (1961), Text. Res. J., 31, 316–327. Tovey H (1961), Text. Res. J., 31, 185–226.

14

Textile product design methods

Abstract: This chapter discusses various fundamental aspects of design engineering including its need and approach. Since most fabric manufacturing processes follow a traditional method of design, a critical review of traditional and modern computer-assisted design (CAD) is provided. The future scope of non-conventional methods of designing and reverse engineering are also discussed. Key words: textile design, traditional design, computer-assisted design (CAD), reverse engineering.

14.1

Introduction

Designing is the process of planning a product to meet functional and aesthetic performance criteria through the efficient use of resources. The design process should satisfy certain criteria such as simplicity, testability, manufacturability and reusability. Engineering is an applied science dealing with relationships between the raw material, the fabric and the finished product. The design engineer has to engineer fabrics with predetermined properties that fit specific applications. The design of textile products has been carried out for thousands of years in a traditional and intuitive way. More recently the textile industry has recognized the importance of design in response to the growing needs of industry and consumers. The everincreasing application of textile products in various fields is making the design task more important and challenging. Textile products have found a wide range of industrial and technical applications apart from apparel and domestic uses. These applications include not only clothing and accessories, bedding and interior decorations but also textile structures that are used to make cables, cords, parachutes, hot-air balloons, tents, etc. New composite and other textile materials are being used in aerospace applications, machine parts, medicine, civil engineering, musical instruments, and so on. These applications require a systematic approach to the manufacturing of textile product in place of traditional more intuitive manufacturing based on trial and error. The design process is subject to certain restrictions such as time, personnel, cost, etc. Traditionally it has been carried out manually, based on experience and trial and error. In recent years, more inexpensive computers have encouraged the use of simulation and other technologies to design and develop quality products. 245

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Woven textile structure

14.2

The design process for textiles

Designing is a complex process which cannot be described as a simple sequence of activities or as a computer algorithm. It may be considered from many points of view such as planning, organizing, innovation and creativity, selection of design tools and task assignments, etc. [1]. When proposing methods and procedures to aid the designer, one must be very distinct about the view one takes and the scope within which the methods are valid. A suitable framework for describing design comprises three levels of resolution such as (i) product analysis for understanding, (ii) product synthesis based on technical requirements and (iii) product development based on organizational expectation. Any design task will require activities related to these three levels. For each level one can divide the design activities into phases and recommend various design methods and models for each phase. Problem solving is related to finding and deciding on a solution to a given problem. A complex problem is an open-type problem which may have many possible solutions, as opposed to a closed-type problem with one or two solutions that can be found by calculation. General problem solving involves five sequences [2] of activities as presented in Fig. 14.1. Product synthesis, shown in Fig. 14.2, means establishing the characteristics of a technical system within four domains of process, function, organ and parts [3]. The goal of product development is not the product itself but also involves market research, sales and promotion. With increasing international competition and pressure to reduce lead-time, activities must be performed in parallel to ensure successful product development [1]. These concepts are embodied in new design strategies such as integrated product development, simultaneous engineering or concurrent engineering. Integrated product development strategy is illustrated in Fig. 14.3. The starting point of the process of integrated product development is need to be fulfilled. The process is then divided into five phases to be fulfilled in sequence by the joint forces of marketing, product design and production.

Formulate problem

Define criteria

Search for solutions

Evaluate/ choose

Implementation

14.1 Five phases of general problem solving.

Task

Process domain

Function domain

14.2 Product synthesis.

Organ domain

Parts domain

Total specifications

Textile product design methods Determining the basic need

The need

User investigation

Determine the type of product

Product principle design

Consideration Determining of process type of type production

0 1 Recognition Investigation of need of need phase phase

2 Product principle phase

Market investigation

Preliminary product design Determine production principles

3 Product design phase

Preparation for sales

Modification for manufacture Preparation for production

4 Preparation for production

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Sales

Product adaptation

Production

5 Execution phase

14.3 Integrated product development.

14.3

Traditional design methods

In traditional design [4], as shown in Fig. 14.4, the market expert formulates the rough concept of fabric requirements. Thereafter the fabric designer, in consultation with experts from various departments such as marketing, production, quality assurance, finance and others, prepares a detailed description of the fabric design. From this design a sample fabric is woven and tested until the customer is satisfied. The fabric is then taken for mass production. This process of fabric design is carried out by experience, heuristic reasoning and intuition. The basic problem in this process is the amount of expert knowledge available and its consistency as well as the fact that no single expert understands the whole process. A typical manual design procedure [5] for industrial fabrics is illustrated in Fig. 14.5. This is a rough procedure for designing a fabric structure through several sub-tasks once a design brief has been agreed. As a first step, the designer chooses the fiber type according to its cost, physical properties, etc., along with the type of yarn and its strength. The yarn linear density based on the individual yarn components is also determined. At this point fabric tensile strength is specified, and fine adjustment of yarn properties is made by the type of yarn twist. The fabric weave is then selected, depending on the tearing strength, thickness, fluid permeability, etc. The stages of the traditional approach based on mathematical and physical principles are depicted in Fig.14.6 [6]. Fiber properties are specified by the parameters of the linear or nonlinear equations. Geometry is defined by algebraic and trigonometric equations. Mechanical properties are analyzed by differential or integral calculus.

248

Woven textile structure Customer

Fabric

Modification

Sample

Testing

Customer satisfaction

Mass

14.4 Traditional fabric design cycle.

Fiber selected

Yarn type

Yarn size

Yarn twist

Fabric density

Fabric weave

14.5 Manual design procedure for industrial fabrics. Specific problem

Material (algebra/trigonometry/ structure differential equations)

Fiber properties

Parametric equations

Test

Define geometry (analytical calculus)

Establish mechanics

Solve directly or by computation

14.6 Mechanics of textile structure: traditional route.

14.4

Key issues in the design of textile products

Overall, the major areas of designing textile products can be broadly classified into aesthetic and material design. Table 14.1 depicts the difference in aesthetic and engineering design approaches. Aesthetic design deals with the visual

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Table 14.1 Aesthetic design versus engineering design in computeraided design (CAD) for woven fabric CAD for aesthetic design

CAD for engineering design

Color Pattern Weave Motif

Thread count Thread density Weave Areal density, etc.

appearance of the product, that includes motif [7–10], color [11–17] and patterns [18–30] that will be aesthetically pleasing to the consumer. Aesthetic design is traditionally accomplished through ‘pencil and paper’ sketching. To begin with, the creative idea is expressed by free-hand sketching. If the design is thought to have commercial potential, it is then processed by the designer from the sketch onto a special design paper. At this stage the design is modified according to the process for which it is intended, that is knitting, weaving or printing, etc. [31–33]. The advent of computers has transformed the work of the designer. Much innovative work has been carried out in the area of colour and pattern design [34] by using computer-assisted design (CAD). Material design can be defined broadly as design that deals with the structural, aesthetic and functional behavior of the material based on product type [35]. The logic of material design involves mapping a specified function onto a realizable structure [36]. A correct material design is one whose basic structure meets the specified function or effect. In this system, material behavior mediates function and structure. Aesthetic and material design have a common region that is the surface or texture appearance caused by the material. Both will overlap in producing a successful product. Although a considerable amount of research has been carried out on color or pattern designing related to fabric appearance and fashion, material design technology for textile products remains at the development stage. There are steel no standard procedures available for carrying out the material design process.

14.4.1 Partial and total material design In general, as far as a textile product is concerned, design involves several phases: conceptualization, research and development, design, testing, manufacturing and marketing. During this process, people from various disciplines interact to produce a product [37]. So far the design of textile products has been mainly performed by partial approaches. The partial design refers to designing a product targeted to satisfy only one or a set of special functions and structures, for example to improve the strength of fabric, to increase dimensional stability [38] or to

250

Woven textile structure

optimize mechanical properties [39,40], etc. The major drawback of this is that interdependence between structures and functions cannot be exploited, resulting is a huge potential waste of time and labour. This type of practice has been in use for thousands of years, and it is still being widely used. Yet it may not be very effective in textiles because of the complex dynamic behavior of structures and functions. Total material design [41] refers to the design of a textile product starting from conceptual design up to the manufacturing method [42,43]. Though it may not be feasible in practice, this process tries to include all necessary factors for a quality product. This type of designing procedure involves a huge amount of information and a good organization. With the aid of computers total material design can now be achieved. The main advantage of this type of design is that the effect of each design parameter on the others can be determined or analyzed. This helps to manipulate the overall design parameters to achieve a target product [44–46].

14.4.2 Creative design versus modificational design Creative [47] design deals with the development of new products based on functional requirements. Here the logic structure is creative rather than routine. The simple example for this can be found in the design on industrial textile products which uses fundamental geometrical principles to create a wide variety of potential textile structures. Modificational design is more popular. This is the type of design procedure often carried out by many apparel fabric manufacturers. The procedure is to modify or adjust only one or a set of structural or functional parameters for a new design in comparison with certain previous products. This repetition of a basic design with modifications can lead to more radical solutions. If the number of possible modifications is small, then an exhaustive exploration of combinations may be feasible.

14.5

Computer-assisted design (CAD) of woven fabrics

Compared with other fields of engineering, textiles took a long time to realize the potential of CAD [48] for innovation and creativity in product design. This is primarily attributed to the constraints imposed by the materials used. Computer technology and the efforts of textile product designers have resulted in remarkable developments in colour and pattern design. The introduction of the jacquard loom in fabric manufacturing is itself an advanced form of a mechanical computer. Subsequently, the advent of electronic jacquard is considered as one of the most significant developments in the history of textile innovations

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which use CAD and computer-assisted manufacture (CAM) in a true sense. Use of CAD, CAM and computer integrated manufacturing (CIM) [49–57] for clothing and fashion have had a tremendous impact on design engineering. CAD for material technology to design textile products needs more integrated knowledge and expertise to handle a very large number of variables since many parameters related to material function, structure and manufacturing method and cost need to be considered simultaneously [58,59]. CAD for product design must meet the expectations of consumers for a high level of product performance, quick responses from the organization to market needs, competitiveness and cost effectiveness etc. [60]. The general requirements for CAD for material design include integrated systems, information for structural mechanics calculations, data on material functions and structures suitable to a computer environment and well-defined targets for product attributes.

14.6

Design engineering using modeling

A theoretical model describes a type of object or system by attributing to it what might be called an internal structure which will explain the various properties of that object or system. A theoretical model, therefore, analyzes a phenomenon that exhibits certain known regularities by reducing it to more basic components, and not simply by expressing those regularities in quantitative terms or by relating the known properties to those of different objects or systems. A theoretical model is considered as an approximation that is useful for certain purposes. It can be used for the purpose of explanation, prediction, calculation, systematization, derivation of principles, and so on. The most important characteristic of a theoretical model is that it consists of a set of assumptions about the concept or system. Models provide explanations but these explanations are based on assumptions that may be simplified, and this condition must be borne in mind when they are used. It is also important that a theoretical model is often formulated and developed and sometimes even named on the basis of an analogy between the object or system that it describes. The model simulates the behavior or activity of systems, processes or phenomena. They include the use of mathematical equations, computers and other electronic equipment. Some of the theoretical models that are used in the formulation of textile structure can be classified as: ∑ ∑ ∑

pure geometrical model; mechanistic models; rigid thread model, energy model, finite element theory model; empirical models.

252

14.7

Woven textile structure

Reverse engineering

Reverse engineering is the process of discovering the technological principles of a device, object or system through analysis of its structure, function and operation. It often involves taking something apart and analyzing its workings in detail [4]. The purpose is to deduce design decisions from end products with little or no additional knowledge about the procedures involved in the original production. Reverse engineering is carried out under several circumstances such as lost documentation (the documentation of a particular device has been lost or was never written and the person who built it is no longer available), product analysis (to examine how a product works, what components it consists of, estimate costs, identify potential), security auditing, removal of copy protection, circumvention of access restrictions, creation of unlicensed and unapproved duplicates and also for academiclearning purposes. Reverse engineering is taking apart an object to see how it works in order to duplicate or enhance the object. Someone doing reverse engineering on software may use several tools to disassemble a program. The term forward engineering is sometimes used in contrast to reverse engineering. Details of various modeling methods and product engineering applications for fabric engineering are described in Chapters 15 and 16 which can be used for reverse engineering purposes by choosing appropriate input and output parameters to the models.

14.8

Expert systems in textile product design

The engineering design of woven textile structures is a complex task and makes extensive use of empirical knowledge accumulated over time. Only a few, highly experienced experts in the industry know rule-of-thumb principles and methods for complex structural synthesis under performance constraints. If the knowledge and expertise of the experts in the field and from the literature are used to develop a scientific database, computer software can be prepared using such acquired knowledge, which in turn will provide expert advice on a given problem. Such a knowledge-based system is called an expert system. It is a system that has been engineered to simulate a human expert. Such systems are well suited to database manipulations, symbolic reasoning and decision making. They have conflict resolution principles so that mutually antagonistic requirements are satisfied to the greatest extent possible and with minimal compromise. Expert systems permit the use of different design knowledge representational modes such as heuristic, procedural and factual knowledge and the reasoning methods working with each of these representational modes. The technology of artificial intelligence (Al) and expert systems (ES) enables computers to be applied to less deterministic design tasks, which

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253

require symbolic manipulation and reasoning instead of routine processing. ES can be used to diagnose, repair, monitor, analyze, interpret, consult, plan, design, instruct, explain, learn and conceptualize problems. ES provide powerful tools for solving problems such as design and are very suitable for database manipulation and decision making. The modularity of ES enables them to accommodate changes or modifications easily by changing or adding facts or rules [61–63]. In order to construct successful ES, the problem domain must be well defined, and there must be at least one human expert acknowledged to perform well within the application. Additional knowledge relevant to the problem domain can be obtained from other sources. Experts must have special knowledge, judgment and experience. There must also be adequate programming tools, ideally a set of ES software building tools. High level programming languages such as LISP and PROLOG are often considered to be languages of ES development.

14.8.1 Basic structure of ES The basic structure of ES is shown in Fig. 14.7. The various components are listed below: ∑ ∑ ∑ ∑

∑

The knowledge base consists of the domain facts and heuristics associated with the problem area, which must be well bounded and narrow. The inference engine is the control structure or strategy for utilizing the knowledge base in the solution of the problem. The dynamic and global database is the working memory for keeping track of the problem status, the input data for the particular problem, and the relevant history of what has been done. A user-friendly interface facilitates interaction of the system with the user and provides a human window to its operations, it is preferably a natural language framework. Additionally, an explanation module should be included to allow the user to query and understand the reasoning process underlying the system’s answers. The knowledge acquisition module facilitates the transfer and transformation of problem-solving expertise from the knowledge source to the knowledge base. Since knowledge is central to intelligence, the performance of ES is primarily a function of the size and quality of

User

Facts Expertise

Knowledge base Inference engine Expert system

14.7 Basic structure of an expert system.

254

Woven textile structure

the knowledge base the system possesses. The facts constitute a body of information that is widely shared, publicly available, and generally agreed upon by experts in the field. The heuristics are mostly private, little discussed rules of good judgment or guessing that characterize expert level decision making in the field. The knowledge must be represented or organized into a suitable form so that the inference engine can readily access it. In order to create a knowledge base for a given problem, the expert’s knowledge must be formulated according to the knowledge representation scheme employed by the ES shell. The latter, with a debugging facility, represents the knowledge acquisition module. The difference between ES and conventional computer programming can be understood from the following representation:

Data + Algorithm Æ Program



Knowledge + Inference Æ ES

14.8.2 Application of ES in the textile field The importance of AI for textile and garments has been emphasized since the late 1980s. In garment manufacturing, the applications of artificial intelligence, such as expert systems, neural networks and neuro-fuzzy algorithms, have been introduced and outlined by Stylios and co-workers [64–67] to predict the sewability of fabrics. Srinivasan et al. [68], developed knowledge-based software systems called the fabric defects analysis systems (FDAS) for inspection of visual fabric defects. Cruycke [69] compared a computer expert system for weaving operations with the performance of human experts. Frei and Walliser [70] and Karamantscheva et al. [71] reported an ES that was both a decision making instrument and a reference for the wool dyer. Gailey [72] reported a color expert system. Curiskis and Grant [73] introduced a rule-based expert system for fiber identification. Chang and Lee [74] presented a knowledge-based garment manufacturing system to optimize the garment manufacturing process. Knowledge can be acquired through meetings with experts, technical reports and case studies. The knowledge engineer then formulates rules from this acquired knowledge. The acquired knowledge is classified into materials, processing, problems and total reviews. In the material properties there are four sub-groups: appearance, sewability and tailorability, formability and auxiliary materials. Similarly in the processing group there are six sub-groups including quality control systems. The database and the knowledge base are designed using an object diagram, in which the organic relationship between the attributes of the materials and processing parameters is defined. The structure of the semantic network and frame is represented through an object diagram in a hierarchical network. Rules in the form of IF… hypothesis… THEN Do…

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ELSE Do… are written using the rule editor in the development tool. Based on the knowledge base, the inference engine is designed by setting the strategies using the strategy editor, depending on the inferences from the rules and connection between object and rules. The user can interact with it using natural language or from the database. Dastoor et al. [75–77] developed a generalized knowledge-based CAD system called ‘FABCAD’ for fabric design and an analytical module for simulation of the uniaxial and biaxial load deformation behavior of plainwoven fabric. The overall operation of the system has been structured as a design phase and an analytical phase working closely with each other. The design phase suggests design alternatives and formulates fabric structures to meet specified functional requirements through revision stage and synthesis stage modules of the heuristic design component. The analysis phase serves to validate the design alternatives by carrying out detailed predictive tests of fabric performance. The work demonstrates the capability of actually creating a CAD environment that preserves and utilizes an expert’s knowledge to aid in preliminary structural design and predictive evaluation of industrial fabrics economically. Fan and Hunter [78, 79] described a worsted fabric expert system (WOFAX) to provide advice during fabric design and predict and evaluate the properties and performance of the designed fabric. The system has eight advisors for determining fabric composition, weave, yarn count and sett, weaving details, yarn type, twist, fiber specifications, and finishing procedures. After the fabric is designed, a neural network model that incorporates a fabric databank predicts its properties. Suresh et al. [80,81] reported a differential total material design (D-TMD) system for textile products. In this system a certain reference sample is used, and the designs are focused on the differences between the product to be designed and the reference sample. This system is more suitable for modificational design than the creative design. The major hierarchical design phases constituting a D-TMD shown in Fig. 14.8 can be classified as under: ∑ ∑ ∑ ∑

conceptual design phase for deducing the concept of the product to be produced; basic structural design for selection of suitable structure to realize the functions of the target product; basic manufacturing design for selection of appropriate process and treatments to achieve basic structural and functional elements including preliminary costing; detailed manufacturing design phase for selection of detailed manufacturing conditions or methods with a detailed cost analysis to produce target product.

256

Woven textile structure Conceptual design a1

Sensory expression conversion module b3

Aesthetic effect/ functional design a2

Functional database of previous products c1

Basic structural design a3 Inference module b1 Designer

Basic manufacturing design a4

Textile science

Relational database of product properties and structure c2 Databases for selecting structure c3 Cost estimation module b5

Detailed manufacturing design a5

Section I

Section II

Textile industry

Database for manufacturing design c5 Section III

14.8 The frame of total material design system for textiles.

Section I provides interaction between the designer and the system. This can be done by using simple hierarchical query-based interaction. Section II carries out the overall design procedures. This consists of five design stages from conceptual design to manufacturing design. a1–a3 provide the satisfactory design format related with fabric characteristics. On the other hand, a4 and a5 give the suitable manufacturing method design format to achieve the target design. The design process flows from a1 to a5 works hierarchically in the system. Section III belongs to different kinds of databases derived from the textile science and industries to support the design task. c2, c3 and c4 can be based on the theories and relationships organized from the scientific research conducted in the textile field. c1, c2, c3 and c5 can also be obtained from industrial information. In short, the design logic flow starts through a1 by retrieving information from c1 based on the facts of the reference sample data. The a2 can be obtained from a1, b3 and c1. Then the procedure takes a step to achieve the task of a3 in consultation with c1, c2, c3 and b5. The next immediate step is to outline the manufacturing method design a4 using c5. At this point the determined design parameters can be modified according to the processing constraints. Finally, a5 can be mapped to complete the total material design format for manufacturing.

Textile product design methods

14.9

257

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32. Nakano K et al. (1993), Technical Report of Fukui Prefecture Technological Center, Japan, No. 3, 108. 33. Nakano K et al. (1991), Technical Report of Fukui Prefecture Technological Center, Japan, No. 7, 28. 34. Aldrich W (1994), Metric Pattern Cutting, Blackwell Scientific Publications (3rd ed.), London. 35. Suresh M N (1995), in ‘Conf. Proc. 24th Text. Res. Symp.’, Mt. Fuji, Japan, 127. 36. Matsuo T (1993), J. Text. Mach. Soc. Japan (English ed), 39, No. 4, 73. 37. Donaldson R A (1987), in ‘Proc. Text. Inst. Annual World Conf.’, Como, Italy, 59. 38. de Araujo M D and Costa (1986), J. Text. Inst., 77, No. 4, 288. 39. Hearle J W S, Konopsek M and Newton A (1972), Text. Res. J., 42, No. 10, 613. 40. Hearle J W S (1992), Text. Horiz., Oct, TH16. 41. Matsuo T (1994), J. Text. Mach. Soc. Japan (Japanese ed), Part I, 47, No. 5, 1. 42. Matsuo T (1994), J. Text. Mach. Soc. Japan (Japanese ed), Part II, 47, No. 6, 9. 43. Matsuo T (1994), J. Text. Mach. Soc. Japan (Japanese ed), Part III, 47, No. 7, 16. 44. Hearle J W S, Newton A and Grigg P J (1984), ‘Proc. Text. Inst. Annual World Conf.’, Hong Kong, 1. 45. Hearle J W S, Grosberg P and Backer S (1969), Structural Mechanics of fiber, yarn and fabrics (Vol. 1 and 2), Wiley-Interscience, New York. 46. Pragg V L (1987), in ‘Proc. Text. Inst. Annual World Conf.’, Como, Italy, 303. 47. Matsuo T and Suresh M N (1996), J. Text. Mach. Soc. Japan (Japanese ed), 42 No. 3, 57–65. 48. Hearle J W S (1993), Text. Horiz, 13, No. 5, TH15. 49. Grigg P J (1983), Computer Aided Design, 15, No. 1, 37. 50. Schnyder H (1991), Int. Text. Bull., Fabric Forming, 37, 4/91, 48. 51. Major C (1993), Textiles, No. 4, 12. 52. Philippe L (1984), in ‘Proc. Text. Inst. Annual World Conf.’, Sydny, Australia, 333. 53. Probst B (1986), Int. Text. Bull., Fabric Forming, 32, 2/86, 5. 54. Fujomoto S and Torimaru S (1985), Technical Report of Fukuoka Prefecture Ind. Lab., Japan, 26. 55. Arai M (1995), Technical Report of Gunma Prefecture Ind. Lab., Japan, 42. 56. Nakano K et al. (1992), Technical Report of Fukui Prefecture Ind. Lab., Japan, No. 8, 126. 57. Baechinger Th and Krause H W (1984), in ‘Proc. Text. Inst. Annual World Conf.’, Hong Kong, 613. 58. Burnip M S and Moscovitch T J (1987), in ‘Proc. Text. Inst. Annual World Conf.’, May, Como, Italy, 19. 59. Jayaraman S (1990), J. Text. Inst., 81, No. 2, 185. 60. Verret R. (1984), in ‘Proc. Text. Inst. Annual World Conf.’, Hong Kong, 695. 61. Waterman D A (1986), A Guide to Expert System, Addison-Wesley, London. 62. Hayes-Roth F, Waterman D A and Lenat D A (1983), Building Expert Systems, Addison-Wesley, London. 63. Forsyth R (1984), Expert Systems, Chapman and Hall, London. 64. Stylios G (1989), Int. J. Clothing Sci. Technol., 1, No. 3, 4–5. 65. Stylios G (1990), Knitting International, 97, No. 1164, 98–99. 66. Stylios G, Fan J, Sotomi J O and Deacon R (1992), Int. J. Clothing Sci. Technol., 4, No. 5, 45–48.

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Stylios G (1993), Int. J. Clothing Sci. Technol., 5, No. 5, 24–27. Srinivasun K Dastoor P (1992), J. Text. Inst., 83, 431–448. Cruycke B (1988), Milliand Textilber, 69, No. 8, 548. Frei G and Walliser R (1991), J. Soc. Dyers Colour, 107, No. 4, 147. Karamantscheva I, Martin D, Rappoport E, Rohner E and van Hout F J (1994), Text Horizon, 8, 33. Gailey I (1992), Int Dyer, Text Printer, Bleacher Finisher, 174, No. 5, 31. Curiskis J I and Grant C W C (1988), Expert System in Textile Technology – The Fiber Experiment, Annual World Conference, Textile Institute, Manchester, 208. Chang K P and Lee D H (1996), Int. J. Clothing Sci. Technol, 8, No. 5, 11–28. Dastoor P H, Hersh H P, Batra S K and Rasdorf W J (1994), J. Text. Inst. 85, No. 2, 85–109. Dastoor P H, Hersh H P, Batra S K and Rasdorf W J (1994), J. Text. Inst. 85, No. 2, 110–134. Dastoor P H, Hersh H P, Batra S K and Rasdorf W J (1994), J. Text. Inst. 85, No. 2, 135–157. Fan J and Hunter L (1998), Textile Res. J., 68, No. 9, 680–686. Fan J and Hunter L (1998), Textile Res. J. 68, No. 10, 763–771. Suresh M N, Matsuo T and Nakajima M (1999), Differential total material design for textile products, in The Textile Industry: Winning Strategies for New Millennium, The 79th World Conference of the Textile Institute, 357–369. Matsuo T and Suresh M N (1997), Text. Progress, The Textile Institute, 27, No. 3.

15

Modeling for textile product design

Abstract: Modeling and simulation are essential tools for textile product engineering. This chapter deals with modeling principles and methodologies for deterministic and nondeterministic models commonly used for fabric engineering applications. Since textile materials are quite different from engineering materials in respect of their mechanical behavior, the limitations of various modeling methods and their scope of application are discussed. Key words: fabric engineering, deterministic models, nondeterministic models.

15.1

Introduction

A model is a description or an analogy used to help visualize something that cannot be directly observed. It can be a system of postulates, data and inferences presented as a mathematical description of an entity or state of affairs. Modeling is an activity in which we think about and make models to describe how the objects of interest behave. There are several ways by which objects and their behavior can be described. We can use words, drawings, physical models, computer programs or mathematical formulae. In designing an engineered product, mathematical equations and/ or logical concepts are normally used in models to simulate and predict real events and processes. In modeling it is important to know how to generate mathematical representations (equations) and how to validate them. It is also important to know how model equations are used and their limitations. Before analyzing these issues, it is worthwhile to understand why we use mathematical modeling.

15.2

Principles of mathematical modeling

Modeling of phenomena is essential to both engineering and science. Modeling methodologies for predicting fabric properties are essential to design fabrics to meet the specifications desired by the customer. If the relationships between different parameters that determine a specific fabric property are known, they can be used to optimize that particular property for different end-use applications. Predictive modeling methodologies can also be used to identify different combinations of process parameters and material variables that may yield the desired fabric property. From this 260

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range a specific combination of process and material variables resulting in maximum savings in cost and time can be selected. The conceptual world is the world of the mind. The conceptual world has three stages: observation, modeling and prediction. In the observation stage of scientific method we measure what is happening in the real world. We gather empirical evidence and facts on the ground. Modeling is concerned with analyzing these observations. The model describes the phenomena observed and allows us to predict future behaviors that are yet unseen or unmeasured. These predictions are followed by observations that serve either to validate the model or to suggest why the model is inadequate. Mathematical modeling is formulated using certain principles [1]. The basic approach to formulating a model is shown in Fig. 15.1.

Object/style Why? What are we looking for? Find? What do we want to know?

Model, variables, parameters

Given? What do we know? Assume? What can we assume? Predict? What will our model predict?

Why? How should we look at this model? Find? How can we improve the model?

Valid? Are the predictions valid? Model predictions

Test

Verified? Are the predictions good?

Valid, accepted predictions

15.1 Key principles of mathematical modeling.

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15.3

Woven textile structure

Modeling methodologies

Over the years, many attempts have been made to develop predictive models for textile properties using different modeling methodologies. These are essentially of two kinds: deterministic and nondeterministic. Empirical models, simulation models using methods such as finite element analysis (FEA), are deterministic models, whereas models based on genetic methods, neural networks, chaos theory and soft logic are nondeterministic [2]. Each has its own merits and limitations. More and more processes and systems are now modeled and optimized using nondeterministic approaches. This is due to the degree of complexity of systems and consequently the inability to study them efficiently with conventional methods only. In a nondeterministic approach there are no precise, strict mathematical rules. No assumptions regarding the form, size and complexity of models are made in advance. Hence this approach offers a flexible means to provide solutions to a wide variety of textile problems with reasonable prediction accuracy [3]. A brief overview of various soft computing tools is given in this chapter. For a detailed explanation of these tools and other soft computing tools, one can refer to the standard texts available [4–6].

15.4

Deterministic models

Mathematical models are derived from first principles and appeal because they have their basis in applied physics. They can be used to explain the reasons that determine structure–property relationships. In textiles they provide tools to enable the industry to design textile structures to meet end-use specifications. Mathematical modeling has certain limitations. The development of theory is cumbersome and requires many years to yield results. The models are normally problem specific and any change in the system requires a new analysis and new programs to solve equations. They often produce large prediction errors and the procedures are not user-friendly.

15.4.1 Empirical modeling The most common approach has been to develop predictive models for fabric properties and performance through experimental investigations. In this case, large numbers of experiments are conducted under controlled conditions and statistical techniques are used to derive empirical models. Data generated from experimental results are used to develop regression models to predict a desired property parameter. Equations are based on the linear multiple regression technique. The coefficient of multiple determination (R2) which defines the fraction of variability in the dependent variable is explained by

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the regression model. If the R2 values of the models are high, it suggests that empirical model fits the data reasonably well. Empirical models can have limited applications for two reasons. In the first case the size of the experiments is generally limited due to cost and time factors, which means that selection of materials and processes can be considered only in a narrow range. Secondly, existing tools and techniques are inadequate for accurately modeling and optimizing complex nonlinear processes such as woven fabric manufacturing. There is a need for attitude models that can accurately predict process and product design for fabric.

15.4.2 Finite element modeling (FEM) The finite element method is a powerful tool for the numerical solution of a wide range of engineering problems. Application of FEM ranges from deformation and stress analysis of automotive, aircraft, building and bridge structures to field analysis of heat flux, fluid flow, magnetic flux and other flow problems. In recent years, FEA has also been applied to modeling flexible materials such as textile fabrics. In this method of analysis, a complex region defining a continuum is discretized into simple geometric shapes called finite elements. The material properties and the governing relationships are considered over these elements and expressed in terms of unknown values at element corners. An assembly process results in a set of equations. The solution of these equations gives the approximate behavior of the continuum. FEM is considered useful for textiles because the complexity of textile structures, the anisotropic properties of yarns and fabrics, and the complex interaction phenomena between fiber, yarn and fabric preclude the use of more basic analytical methods. With FEM-based models, phyical processes can be understood in depth and it is possible to change important parameters quickly to generate new products [7]. From a structural point of view, woven fabrics are discontinuous in microstructure and therefore do not satisfy the continuity required in solid mechanics. However, discontinuity in the fabric is small in comparison to the finite element mesh size, and therefore fabric continuity is a reasonable assumption to make. Lloyd [8] applied the finite element method to study fabric in-plane deformation using membrane elements with no bending resistance. Gan and Ly [9] studied fabric deformation of shell plate elements using nonlinear finite elements. Fabrics were assumed to be linearly elastic and orthotropic. Two-dimensional bending of fabrics was studied and the results were compared with the experimental values obtained by a cantilever bending test. Bending hysteresis was not accounted for by the FEA. Jeong and Kang [10] developed a computer model for analyzing the compressional behavior of a woven fabric using the finite element method. A

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Woven textile structure

3-D unit cell was defined to describe the compressional deformation of fabric in three dimensions. The geometry of the unit cell was determined using the equilibrium requirements of planar-elastica-boundary value problems. The yarns in the fabric were assumed to be elastic and isotropic. The contact conditions at the yarn cross-over point were determined by equilibrium equations. Two kinds of second order isoparametric solid elements were used to describe warp and weft yarns. The total number of elements and nodes for the modeling of the 3-D geometry were 876 and 5426 respectively. The analysis was carried out with the aid of the ABAQUS FEM package. The results showed that the compressional resistance of fabric is influenced by the geometrical structure of the fabric unit cell as well as the yarn properties. Compressional resistance also increased with the Poisson ratio [11].

15.5

Nondeterministic models

Models based on genetic methods, neural networks, chaos theory and soft logic are nondeterministic models and are referred to as soft computing methods of predicting properties and performance. Soft computing is a collection of methodologies, which differs from conventional (hard) computing in that it is tolerant of imprecision, uncertainty, partial truth and approximation. Fuzzy logic has been developed to handle qualitative information. A neural network is a kind of soft computing technology as it provides a relatively easy way for acquiring the information about a system through learning. The inclusion of neural computing and genetic computing in soft computing is a more recent development. There are a number of publications in this field of computing covering wide range of application domains including that of textiles. Notable ones are a book on soft computing in textile sciences by Sztandera and Pastore [12] and a textile institute monograph on artificial neural network (ANN) applications in textiles by Chattopadhyay and Guha [13].

15.5.1 Fuzzy logic Knowledge representation and processing are the keys to any intelligent system. In logic, knowledge is represented by propositions and is processed by the application of various laws of logic, including an appropriate rule of inference. Fuzzy logic uses the fuzzy set theory and approximate reasoning to deal with imprecision and ambiguity in decision making. A crisp set is defined by the characteristic function that can assume only the two values {0,1}, whereas a fuzzy set is defined by a ‘membership function’ that can assume an infinite number of values: any real number in the closed interval [0,1]. The idea of fuzzy logic was introduced by Zadeh in his paper on fuzzy sets [14].

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Consider a universe of discourse X with x representing its generic element. A fuzzy set A ~ in X has the membership function mA~(x) which maps the elements of the universe onto numerical values in the interval [0, 1]:

mA(x): X Æ [0,1] ~

15.1

Every element x in X has a membership function µA(x): X Œ [0,1] A ~ is then ~ defined by the set of ordered pairs: A 15.2 ~ = [(x, µA~(x))| x Œ X, mA~(x) Œ [0,1]] A membership value of zero implies that the corresponding element is definitely not an element of the fuzzy set A ~. A membership value of unity means that the corresponding element is definitely an element of fuzzy set A ~. A grade of membership greater than zero and less than unity corresponds to a noncrisp (or fuzzy) membership of the fuzzy set A ~. Classical sets can be considered as special case of fuzzy sets with all membership grades equal to unity. Membership functions characterize the fuzziness in a fuzzy set [15]. Models designed based on fuzzy logic usually consist of a number of fuzzy if–then rules expressing the relationship between inputs and desired output. For instance, in the case of two-input, single-output systems, it is expressed as:



Ri: IF x is Ai and y is Bi THEN z is Ci

15.3

where Ri is a fuzzy relation representing the ith fuzzy rule; x, y, z are linguistic variables representing two inputs and the output; and A i, Bi, Ci are linguistic values of x, y, z, respectively. In these models, inputs are fuzzified, membership functions are created, association between inputs and outputs are defined in a fuzzy rule base, and fuzzy outputs are restated as crisp values. Fuzzy modeling can be categorized into two categories: subjective modeling and objective modeling. In the subjective modeling approach, it is assumed that a priori knowledge about the system is available and that this knowledge can be directly solicited from experts. By contrast, in objective modeling it is assumed that either there is no a knowledge about the system, or the expert’s knowledge is not soluble enough. Instead of any a priori interpretation of the system, raw input and output data is used to augment human knowledge or even generate new knowledge about the system. This approach was initially proposed by Takagi-Sugeno-Kang [16] and called TSK fuzzy modeling. Fuzzy logic has been used in several areas of textiles which include color grading of cotton into different classes, prediction of tensile strength and yarn count of melt spun fibers, an intelligent diagnosis system for fabric inspection and automatic recognition of fabric weave pattern. Raheel and

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Liu [17] used a fuzzy comprehensive evaluation technique to calculate fabric handle of lightweight dress fabrics. Thickness, weight, flexural rigidity, wrinkle recovery and 45° filling elongation were used to describe the handle of lightweight fabrics. In order to obtain the fuzzy transformation R, five membership functions corresponding to the five properties were selected. A decreasing half Cauchy distribution was used to describe the membership degrees of fabric weight, fabric thickness, fabric flexural rigidity and 45° filling elongation. For wrinkle recovery, a linear membership function was used. From a survey of judges, the importance of each property selected was ascertained and expressed as a weighted vector. By using the weighted vector and the fuzzy transformation matrix, fabric handle was calculated. The same approach was followed by Park and Hwang [18] for predicting total handle value from selected mechanical properties of double weft knitted fabrics and by Chen et al. [19] for grading softness of 100% cotton and cotton/polyester blended fabrics. Huang and Yu [20] investigated the use of a fuzzy logic controller for controlling concentration, pH and temperature in dyeing process.

15.5.2 Neural networks The term neural network is used to describe a number of different models intended to imitate some of the functions of the human brain, using certain of its basic structures. The development and use of neural networks is part of an area of multidisciplinary study that is commonly called neural computing, but is also known as connectionism, parallel distributed processing and computational neuroscience. Neural computing is a powerful data modeling tool that is able to capture and represent each kind of input–output relationship. A neural network is composed of simple elements called neurons or processing elements operating in parallel and inspired by biological neuronal systems. As in nature, the network function is determined largely by weighted connections between the processing elements. The weights of the connections contain the knowledge of the network. There are different types of neural networks. An important distinction can be made between supervised and unsupervised learning. In supervised learning the network is presented with pairs of input and output data. For each set of input values there is a matched set of output data. The key point is that if the desired output of the network is known for each set of input values, then the weights of the network can be modified accordingly. Supervised neural networks are typically used to solve what is known as function approximation, using examples of the function in the form of input–output pairs. In unsupervised learning, the output is not known; the network is simply presented with input data.

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Neural networks that are based on the multilayer perceptron (MLP) account for approximately 80% of all practical applications. In an MLP, the units are arranged in distinct layers and each unit receives weighted input from each unit in the previous layer. A neural network is usually adjusted or trained so that a particular input leads to a specific output. The process of training involves adjusting these weight values and sliding down the error surface. Among the various kinds of algorithms for training neural network, back propagation is most widely used. Artificial neural networks (ANN) produce the fewest errors as well as lower spread in the error than mathematical and regression methods of modeling. ANN has the advantage of approximating any functional relationship between large numbers of input–output (independent variables–dependent variables) parameters. No prior assumptions need to be made on the statistical nature of the variables of the data, since ANN are nonparametric in nature. ANN require a much smaller data set than that required for conventional regression analysis for capturing the nonlinear relationships between the input and output parameters. Even with a small training data set, the network generalizes the functional relationships very well. In an industry where large amount of data are continuously available, ANN can be expected to perform significantly better. The major advantage of ANN is that there is no restriction on the levels of interaction between the variables. It can therefore capture the dynamics of the real world situation very well. The input vectors X for the input layer are expressed in the vector form as X = (x1, x2….xn). Predicted parameters (network outputs) are denoted as Y. As shown in equation 15.4, the ith component of the input signal xi comes out from the unit i and is transferred to the unit j of the model through the synapse weight Wj, where bj is the bias term connected to the jth unit.



Ên ˆ u j = Á ∑ W ji xi + b j ˜ Ë i =1 ¯

15.4

The unit j nonlinearly transforms the total input uj (equation 15.4) by means of a transfer function (hyperbolic tangent transfer function), which is propagated forward to the unit of the next layer as the input signal yi (equation 15.5): 2 15.5 –1 (–2u ) 1 + e The difference in the output yi from the target output tj is used to adjust the synapse weights according to the calculated mean squared error (MSE), as shown in equation 15.6: yj +

j

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Woven textile structure p



MSE =

N

∑ ∑(tij – yij )2

j =0 i =0

NP

15.6



where yij is the network output for data set i at neuron j, tij is the target network output for data set i at neuron j, P indicates the number of output neurons, and N refers to the number of data sets. The ANN is trained by updating the weights with a back-propagation rule. The change in synapse weight wji is based on the gradient descent rule according to equation 15.7:

Dw ji = –h

∂(MSE ) ∂w ji

15.7



where h is the learning rate. Image processing analysis and neural networks have been widely used for fabric defect detection. Lin [21] used feed-forward back-propagation (BP) neural nets to find the relationships between the shrinkage of yarns and the cover factors of yarns and fabrics. A typical multilayer feed-forward network is shown in Fig. 15.2. Beltran et al. [22] also studied the use of MLP-BP neural networks to model the multilinear relationships between fiber, yarn and fabric properties and their effect on the pilling propensity of pure wool knitted fabrics. Behera and Muttagi [23] predicted the low stress mechanical, dimensional, and tensile properties of woven suiting fabrics using a back-propagation network (BPN) and a radial basis function neural network (RBFN). Fiber, yarn and fabric constructional parameters of wool and wool–polyester blended fabrics were given as input variables. Radial basis function neural networks were found to have better predictability and are faster to train and easier to design than back propagation neural Input layer xk x1

Hidden layer hj

x2

Output layer yi Prediction

x3 wij

xk

wjk

15.2 Multilayer feed-forward network.

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networks. A reverse engineering approach is also reported for prediction of constructional particulars from the fabric properties. Hui et al. [24] predicted sensory fabric handle from fabric properties using a resilient back-propagation neural network (RBP). Shyr et al. [25,26] studied the use of neural networks for discriminating generic handle of cotton, linen, wool, and silk woven fabrics. They established translational equations for the total handle value (THV) of fabrics using back-propagation nets. Wong et al. [27] investigated the predictability of clothing sensory comfort from psychological perceptions by using a feed-forward back-propagation network.

15.5.3 Genetic algorithms A relatively new area of study in artificial intelligence is that of genetic algorithms (GAs). GAs are a powerful set of stochastic global search techniques that have been shown to produce very good results for a wide class of problems. GAs can find good solutions to nonlinear problems by simultaneously exploring multiple regions of the solution space and exponentially exploiting promising areas through mutation, cross-over and selection operations [28]. GAs are programs that attempt to find optimal solutions to problems when one can specify the criteria that can be used to evaluate the optimal solution. They are useful when a problem has multiple solutions, some of which are better than others. Unlike deterministic, linear and non-linear optimization models, GAs test a variety of solutions and, through an evolving process, attempt to find the best solution through processes that parallel the metaphors of survival of the fittest, genetic cross-over, mutation and natural selection. Evolutionary algorithms differ substantially from more traditional search and optimization methods. The most significant differences are: ∑ GAs work with a coding of the parameter set, not the parameter themselves; ∑ GAs search from a population of designs, not a single design; ∑ GAs use objective function information, not derivatives or other auxiliary knowledge; ∑ GAs use probabilistic transition from design to design; they do not use deterministic rules; ∑ Evolutionary algorithms can provide a number of potential solutions to a given problem but the final choice is left to the user. In building a genetic algorithm, six fundamental issues that affect the performance of the GA must be addressed: chromosome representation, genetic operators, selection strategy and initialization of the population,

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Woven textile structure

termination criteria and evaluation measures. The initial population is randomly generated, which is the most common method, while the GA is run for a specified number of generations as its termination criteria. For any GA, a chromosome representation is needed to describe each individual in the population of interest. The representation scheme determines how the problem is structured in the GA and also determines the genetic operators that are used. The operators are used to create new solutions based on existing solutions in the population. There are two basic types of operators: cross-over (recombination) and mutation. Mutation operators tend to make small random changes in one parent to form one child in an attempt to explore all regions of the state space. Mutation serves the crucial role of preventing the system from being stuck in the local optimum. Cross-over operators combine information from two parents to form two offspring such that the two children contain a ‘likeness’ (a set of building blocks) from each parent. The application of these two basic types of operators and their derivatives depends on the chromosome representation used. The selection of individuals to produce successive generations plays an extremely important role in a genetic algorithm. A probabilistic selection is performed based upon the individual’s fitness such that the better individuals have an increased chance of being selected. However, all the individuals in the population have a chance of being selected to reproduce into the next generation. Evaluation functions of many forms can be used in a GA, subject to the minimal requirement that the function can map the population into a totally ordered set. The evaluation function is independent of the GA (i.e. stochastic decision rules) [29]. The basic procedure of genetic algorithms can be explained as follows. Let P(g) and C(g) be parents and offspring respectively in the existing generation g: Procedure for g: = 0; initialize population P(g); evaluate P(g); for recombine P(g) to generate C(g); evaluate C(g); select P(g + 1) from P(g) and C(g); g: = g + 1 end end Genetic algorithms are being used to solve wide variety of problems in textiles from production of fibers to apparel design and manufacturing.

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Amin et al. [30] reported the detection of sources of spinning faults from spectrograms using the genetic algorithm technique. Blaga and Draghici [31] reported the application of GA in knitting technology. Lin [32] investigated the use of GA for searching weaving parameters for woven fabrics. A searching mechanism was developed to find the best combinations of warp and weft counts and yarn densities for cost-effective fabric manufacturing. This helps the designer to select appropriate combinations of these parameters to achieve the required weight of fabric at a predetermined cost. Grundler and Rolich [33] developed an evolutionary algorithm based software for creating different weave patterns. Only the weave and yarn color were considered as attributes for fabric appearance with different patterns created by various combination of weave and color of warp and weft threads. Jasper et al. [29] investigated fabric defect detection using a GAs-tuned wavelet filter. Patrick et al. [34] studied the application of GA on the roll planning of fabric spreading in apparel manufacturing. It was demonstrated that use of GAs to optimize roll planning will result in reduced wastage in cutting and hence can reduce cost of apparel production. Keith et al. [35] investigated the problem of assembly line balancing in the clothing industry. Inui [36] presented a computer-aided system using a GA applied to apparel design. In this study, a computer technique that helps consumers to take part in apparel design was presented. An interactive computer-aided system for designing was constructed on the basis GA search method.

15.5.4 Hybrid modeling A trend that is growing in visibility relates to the use of fuzzy logic in combination with neurocomputing and GAs as shown in Fig. 15.3. The

Neural nets

NN + GA

NN+ FL

Fuzzy logic

NN + FL + GA FL+ GA

Genetic algorithms

15.3 Hybrid models using soft computing tools.

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Woven textile structure

marriage of fuzzy logic with computational neural networks has a sound technical basis, because these two approaches generally attack the design of intelligent systems from quite different angles. Neural networks are essentially low level, computational algorithms that offer good performance in dealing with large quantities of data often required in pattern recognition and control. Fuzzy methods often deal with issues such as reasoning on a higher (i.e. on a semantic or linguistic) level than do neural networks. Consequently, the two technologies often complement each other: neural networks supply the brute force necessary to accommodate and interpret large amounts of data, and fuzzy logic provides a structural framework that utilizes and exploits these low level results. Neural networks (NNs) are known for their ability to perform complex, non-linear mapping of input–output data. But it is difficult to decide which input data, network structure and learning parameters to utilize. GAs can be applied as an optimization search to determine the optimal neural network structure design, including input data combination optimization, network structure optimization, learning rate and momentum optimization. In this way computational complexity and the time required to design the NN is reduced [37,38]. Hybrid modeling has been used in the prediction of fiber, yarn and fabric properties. The prediction accuracy of the neuro-fuzzy system has been found superior to that of a conventional multiple regression model and comparable with an ANN model. Wong et al. [39] predicted clothing sensory comfort from fabric physical properties by building eight different hybrid models combining statistical, fuzzy logic and NN methodologies. Results showed that the TS-TS-NN-FL model has the highest ability to predict overall comfort performance followed by TS-TS-NN-NN model (TS, NN, FL refers to statistical, neural network and fuzzy logic method respectively). The data reduction and information summation ability of statistics, self-learning ability of neural nets and fuzzy reasoning ability of fuzzy logic was exploited to develop these hybrid models.

15.6

Validation and testing of models

While building mathematical models, it is inevitable that one has to use numbers derived from experimental or empirical data, or from analytical or computer-based calculations. Errors are produced from limits in data or data manipulation. Error is defined as the difference between a measured or calculated value and its true or exact value. Error is unavoidable but how much error is present depends on how skillfully the data is read or manipulated. Therefore, error analysis is an integral part of the modeling process. There are two types of error: systematic and random. Systematic error occurs when an observed or calculated value deviates from the true value in a consistent way. This error occurs in experiments when instruments

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are improperly calibrated. Random errors do not occur due to chance. They arise mainly in experimental work because unpredictable things happen due to ignorance or accident. There is one absolute error which is defined as the difference between the true or experimental value and the measured value. The true value may be known or it may have an expected value based on a calculation or some other data source.

15.7

Summary

With globalization there is increased need to reduce product lead-times. Activities must be performed in parallel i.e. integrated product development (IPD), to ensure that sufficient attention is paid to market needs and manufacturing technologies during the design process for successful product development. The design of textile products is still often based on traditional techniques, experience and intuition. This leads to dependence on a limited number of experts and their expertise; difficulty in finding a systematic approach for an optimum solution; and more time and money. Compared with modeling from first principles and other techniques, ANN can be a powerful tool to model the nonlinearities and complexities involved in predictions of fabric properties. A system needs to be developed to provide scientific databases, overall structure–function relationships, optimization procedures, suitable computer algorithms and standardization of these algorithms. The successful applications of soft computing in various applications indicate that the impact of soft computing will be felt increasingly in coming years. The employment of soft computing techniques leads to systems which have high MIQ (machine intelligence quotient).

15.8

References

1. Dym C L (2006), Principles of Mathematical Modeling, Reed Elsevier, India. 2. Muttagi S (2002), Artificial Neural Network Embedded Expert System for Design of Woven Fabrics, IIT Delhi. 3. Dubrovski P D and Brezocnik M (2002), Text Res J, 72, 187. 4. Haykin S (1994), Neural Networks: A Comprehensive Foundation, Macmillan Publishing, USA. 5. Jang J S R, Sun C T and Mizutani E (1997), Neuro-fuzzy and Soft Computing Prentice Hall of India, New Delhi. 6. Goldberg D E (1989), Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, USA. 7. Somodi Z, Hursa A, and Rogale D (2003), Int J Clothing Sci Technol, 15(3/4), 276–283. 8. Lloyd D W (1980), ‘The analysis of complex fabric deformations’ in Mechanics of Flexible Fiber Assemblies, Sijthoff and Noordhoff. 9. Gan L and Ly N G (1995), Textile Res J, 65(11), 660–668. 10. Jeong Y J and Kang T J (2001), J Text Inst, 92, 1–14.

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11. Tarfaoui M and Akesbi S (2001), Numerical study of the mechanical behavior of textile structures, Int J Clothing Sci Technol, 13(3/4), 166–175. 12. Sztandera L M and Pastore C (2003), Soft Computing in Textile Sciences, Springer. 13. Chattopadhyay R and Guha A (2004), Textile Progress, 35, 1. 14. Zadeh L A (1965), Fuzzy Sets, Information and Control, 8, 338. 15. Gopal M (2004), Digital Control and State Variable Methods, Tata McGraw-Hill, New Delhi. 16. Takagi T and Sugeko M (1985), Fuzzy identification of systems and its application to modelling and control, IEE Transactions on Systems, Man and Cybernetics SMC15 (1): 116–132. 17. Raheel M and Liu J (1991), Text Res J, 61, 31. 18. Park S W and Hwang Y G (1999), Text Res J, 69, 19. 19. Chen Y, Collier B, Hu P and Quebedeaux D (2000), Text Res J, 70, 443. 20. Huang C C and Yu W H (1999), Text Res J, 69, 914. 21. Lin J J (2007), Text Res J, 77, 336. 22. Betran R, Wang L and Wang X (2006), J Text Inst, 97(1), 11–16. 23. Behera B K and Muttagi S B (2004), J Text Inst, 95, 283. 24. Hui C L, Lau T W, Ng S F and Chan K C C (2004), Text Res J, 74, 375. 25. Shyr T W, Lin J Y and Lai S S (2004), Text Res J, 74, 354. 26. Shyr T W, Lai S S and Lin J Y (2004), Text Res J, 74, 528. 27. Wong A S W, Li Y, Yeung P K W and Lee P W H (2003), Text Res J, 73, 31. 28. Michalewicz Z (1996), Genetic Algorithms + Data Structures = Evolution Programs, 3rd ed. AI Series, Springer-Verlag, New York. 29. Jasper W, Joines J and Brenzovich J (2005), J Text Inst, 96, 43. 30. Amin A E, El-Gehani A S, El-Hawary I A and El-Beali R A (2007), Autex Res J, 7, 80. 31. Blaga M and Draghici M (2005), J Text Inst, 96, 175. 32. Lin J J (2003), Text Res J, 73, 105. 33. Grundler D and Rolich T (2003), Text Res J, 73, 1033. 34. Patrick C L H, Frency S F N and Keith C C C (2000), Int J Clothing Sci Technol, 12, 50. 35. Keith C C C, Patrick C L H, Yeung K W and Frency S F N (1998), Int J Clothing Sci Technol, 10, 21. 36. Inui S (1994), Sen-i-Gakkaishi, 50, 593. 37. Liang Y H (2008), Int J Quality and Reliability Management, 25, 201. 38. Ozturk N (2003), Eng Computation, 20, 979. 39. Wong A S W, Li Y and Yeung P K W (2004), Text Res J, 74, 13.

16

Building predictive models for textile product design

Abstract: Empirical, mathematical and artificial neural network (ANN) modeling methodologies and their applications in fabric engineering are described. A comparative analysis of modeling methods is made to understand the predictability of each model. The chapter also demonstrates how ANN-embedded expert systems can be developed for engineering new woven constructions. Key words: fabric engineering, modeling, artificial neural networks (ANN).

16.1

Introduction

Designing is a process of conceptualizing a product to meet functional and aesthetic performance specifications with efficient use of available resources at minimum cost. Designing of fabrics is a multifaceted activity. Traditionally the fabric designer, in consultation with experts from various departments, prepares detailed specifications for fabric design and proceeds through a development cycle till the fabric is ready for mass production as shown in Fig. 14.4 [1]. This process involves a great deal of expertise and experience and a certain amount of trial and error. The designer is handicapped by the lack of a sound understanding of relationships between design specifications, fiber–yarn–fabric structure–properties, manufacturing parameters and fabric behavior during clothing manufacture and wear. It is the designer’s intuition skill and expertise which largely govern fabric designing. The ultimate goal of fabric design is to engineer fabric construction with predetermined properties that fit the specific applications required by the customer with minimum cost and delay. The success of fabric engineering depends on reliable objective measurements, prediction and control of fabric quality and performance attributes. For the prediction of fabric quality and performance attributes, an efficient methodology to model the inherent nonlinear relationships between fiber, yarn and fabric properties is required. Various mathematical models such as geometrical and mechanistic models, based on properties in the fabrics and empirical relationships between variables, are used for the analysis of textile structures and processes to explain the underlying principles and predict fabric properties and behavior. Some of these models for predicting 275

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Woven textile structure

fabric properties based on the structure of fabrics have been developed but have limited application in fabric design. This is because the simplifying assumptions made in developing these models result in large prediction errors. These models are problem specific and any change requires a new analysis and new programs to solve equations. They may not work well in practice owing to uncertainties associated with real world dynamics.

16.2

Building empirical, mathematical and artifical neural network (ANN) models

Modeling methodologies for predicting fabric properties are required to design fabrics as per the specifications desired by the customer. If the relationships between different parameters that determine the specific fabric property are known, they can be handled to optimize that particular property for certain end-use applications. Predictive modeling methodologies can also be used to identify different levels of combination of process parameters and material variables that yield the desired fabric property. Then a specific combination of process and material variables resulting in maximum savings in cost and time can be selected. The fabric structure and properties are primarily influenced by fiber properties (length, fineness), spinning methods (ring, rotor, air jet, etc.), yarn parameters (count, twist, single and doubled, fiber blends), fabric structural parameters (end and pick density, weave), and finally finishing treatments [2]. The relationship between fabric structure and properties is complex and inherently nonlinear. There are three commonly used modeling methods for predicting fabric properties: empirical models based on statistical techniques; mathematical models derived from first principles; and artificial neural network (ANN) models that are the part of artificial intelligence [3]. It is necessary to understand the basic principles of these models and the situations where they can be used. A realistic modeling system for efficiently handling nonlinear and complex fabric parameters can help in predicting fabric properties accurately.

16.2.1 Empirical model Empirical modeling is an art of making mathematical models of any phenomenon based on the observed data structures, with no necessity of a priori hypotheses. An empirical model is used when the knowledge of the underlying physics is insufficient to characterize the system and the model equations and parameters are constructed to represent observed or expected behavior of the measurement system. The empirical model consists of a function that fits the data. The graph of the function goes through the data points approximately. Although we cannot use an empirical model to explain

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a system, we can use such a model to predict behavior where data does not exist. We use data to suggest the model, estimate its parameters and to test the model. We can derive an empirical model by using polynomial and trigonometric functions that capture the trend of the data. The complexity of mathematics used and the assumptions made to formulate approximate theoretical relationship results in very high error. Besides errors, authentication of theoretical model is time consuming and expensive. Linear regression is a method of estimating the expected value of one variable Y dependent on some other independent variable(s) X. The relationship between Y and X is modeled in a simple way in equation 16.1:

Y = a + b1 ¥ X1 + b2 ¥ X2 +... + bp ¥ Xp

16.1

Regression models which are not a linear function of the parameter are called nonlinear regression models. One such example is given by equation 16.2:

Y = a + b1 ¥ X12 + b2 ¥ X22+ ... + bp ¥ Xp2

16.2

16.2.2 Mathematical model A mathematical model usually describes a system by a set of variables and a set of equations that establish relationships between the variables. The values of the variables can be practically anything; real, integer, boolean or strings. The variables represent some properties of the system, for example measured system outputs often in the form of signals, timing data, counters, event occurrence (yes or no). The actual model is the set of functions that describe the relations between the different variables. There are six basic groups of variables: decision variables, input variables, state variables, exogenous variables, random variables and output variables. Since there can be many variables of each type, the variables are generally represented by vectors. Decision variables are sometimes known as independent variables and exogenous variables are known as parameters or constants. The variables are not independent of each other as the state variables are dependent on the decision, input, random and exogenous variables. Furthermore, the output variables are dependent on the state of the system, represented by the state variables. A common approach is to split the measured data into two parts: training data and verification data. The training data is used to train the model, that is to estimate the model parameters. The verification data is used to evaluate model performance. Assuming that the training data and verification data are not the same and if the model describes the verification data well, then we can assume that the model describes the real system well. Let us consider the buckling behavior of a cloth under large deflection. The differential equation of this type of deflection is given by Euler’s equation as:

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Woven textile structure

B

dj =–P ¥y ds

where s = distance measurement along the curve, P × y = bending moment, dj/ds = radius of curvature and B = flexural rigidity. Euler’s equation helps to determine the critical buckling load given by: 2 Pcr = 4p 2 B L

16.3 where Pcr = critical compressive load, L = gauge length and B = bending rigidity.

16.2.3 ANN model The main feature that makes neural networks the ideal technology for modeling fabric interactions is that they are nonlinear-regression algorithms that can model multi-dimensional systems and have a very simple, uniform user interface. ANN can be thought of as a functional approximation that fits the input–output data with a many dimensional surface. The major difference between conventional statistical methods and ANNs is the basic functions that are used. Standard functional approximation techniques use complicated sets of orthonormal basic functions (sines, cosines, polynomials, etc.). In contrast, an ANN uses very simple functions (sigmoids), combined in a multilayer nested structure. A neural network is a parallel distributed processor that natural propensity stores experimental knowledge and makes it available for use [4]. It resembles the brain in that knowledge is acquired by the network through a learning process. Inter-neuron connections known as synaptic weights are used to store the knowledge. The procedure used to perform the learning process is called the learning algorithm, the function of which is to modify the synaptic weights of the network in orderly fashion so as to attain a desired objective. ANN has following useful properties and capabilities: universal approximation (nonlinear input–output mapping), ability to learn and adapt, evidential response, contextual information and fault tolerance, uniformity of analysis and design, neurobiological analogy. As shown in Fig. 16.1, an ANN is composed of artificial neurons. These are the processing elements. Each of the neurons receives inputs, processes the inputs, and delivers a single output [5–9]. The major elements in an artificial network are: the processing elements, the contacts among the processing elements, the inputs and the outputs, and the weights. Weights express the relative strengths given to input data before it is processed. Each neuron has an activation value that is expressed by summing the input values multiplied by their weights. The activation value is translated to an output

Building predictive models for textile product design

Input layer of neurons

279

Output

Hidden layer of neurons

16.1 Fully connected feed-forward network with one hidden layer and one output layer.

by going through a transformation function. The output can be related in a linear manner, a non-linear manner or as a threshold value. The activation function should be continuous and differentiable. Sigmoid function, Y, is one of the popular activation functions.

Y = 1/(1 + e–Y)

16.4

Figure 16.2 shows the schematic of the development process of ANN. Learning is the process by which the free parameters (weights and threshold value) of neural network are adapted through a continuous process of simulation by environment in which the network is embedded [10]. An ANN learns from historical cases. The learning produces the required values of the weights, which makes the computed output equal and close to desired outputs. The type of learning determines the manner in which the parameter changes take place [2, 6–9,11–21]. A prescribed set of well-defined rules for the solution of the learning problem is called a learning algorithm. Basically, learning algorithms differ from each other due to the adjustment of the synaptic weight. Several learning algorithms are used for various applications. These are: error-correction learning, Hebbian learning, competitive learning, stochastic learning, supervised learning and unsupervised learning. Learning theories primarily deal with the mathematical structure describing the underlying learning process. A learning machine, which is capable of implementing a set of input–output functions is described by:

y = F(x, w)

16.5

where y is the actual output vector produced by the machine in response to the input vector x, and w is a set of free parameters (synaptic weights) selected by the machine from the parameter (weight) space w.

280

Woven textile structure Collect data

Separate into training and test sets

Define network structure

Select a learning algorithm

Set parameter values

Transfer data to network inputs

Start training and determine and revise weights

Stop and test

Implementation

16.2 Development process for an ANN.

The network can be classified as single layer feed-forward, multilayer feed-forward and recurrent neural networks. Single layer feed-forward networks are networks with a single layer of computational neurons that process input signals in the feed-forward direction. Multilayer feed-forward networks are networks with two or more layers of connections with weights that process the inputs in a forward direction. The main feature of this class of networks is the presence of hidden layers, whose computational nodes are correspondingly called hidden neurons or hidden units. The function of the hidden neurons is to intervene between the external input and the network output. By adding one or more hidden layers, the network is enabled to extract higher order statistics, which is particularly valuable when the size of input layer is large. The source nodes in the input layer of the network supply respective elements of the activation pattern, which constitutes the input signals applied to the neurons in the second layer (that is the first hidden layer). The outputs of the second layer are used as inputs to the third layer and so on for the rest of the network. The set of output signals of the neurons in the output layer of the network constitutes the overall response of the network to the activation pattern supplied by the source nodes in the input layer. Recurrent neural networks are networks that have feedback connections which propagate outputs of some neurons back to the inputs

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of other neurons (including self-feedback connections) to perform repeated computations on the signals [22].

16.3

Evaluating mathematical, empirical and artificial neural network (ANN) models

The selection of suitable models for prediction of various properties and their analysis is important in fabric engineering. The predictive power of each methodology can be estimated by comparing the predicted fabric property values with experimentally obtained results. In an attempt to investigate the relative potential of each modeling method, three modeling methodologies are examined to predict fabric properties: mathematical, accurately empivical and ANN. The predictability of the modeling methodologies was examined by using the published data and mathematical models of Leaf et al. for fabric initial tensile modulus and bending rigidity properties [23,24]. This data is given in Table 16.1. The predictability of a statistical model using multilinear regression was examined. An ANN based on radial basis function algorithm was used to model fabric structure–property relationships.

16.3.1 Evaluating mathematical models Mathematical models are appealing because they have their basis in applied physics. They can be used to explain the reasons that determine structure– Table 16.1 Experimental data for tensile moduli of fabrics [28] Fabric p1 no. (mm)

p 2 (mm)

l 1 (mm)

l 2 (mm)

b1 b2 E 1 E2 (mN mm2) (mN mm2) (N/cm) (N/cm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

0.588 0.624 0.713 0.67 0.679 0.849 0.779 0.839 0.691 0.589 0.749 0.532 0.548 0.637 0.756 0.465 0.538 0.662

0.701 0.758 0.835 0.798 0.871 0.983 0.939 1.022 0.847 0.704 0.827 0.606 0.598 0.722 0.832 0.509 0.597 0.73

0.514 0.515 0.508 0.514 0.515 0.513 0.508 0.507 0.509 0.504 0.616 0.615 0.622 0.622 0.624 0.621 0.639 0.608

5.62 5.62 5.62 5.62 5.62 5.62 5.62 5.62 5.62 4.44 4.44 4.44 4.44 4.44 4.44 4.44 4.44 4.44

0.485 0.488 0.485 0.49 0.492 0.495 0.494 0.494 0.491 0.476 0.587 0.549 0.556 0.591 0.594 0.568 0.577 0.571

6.06 6.06 6.06 7.05 7.05 7.05 8.16 8.16 8.16 4.44 4.44 4.44 4.25 4.25 4.25 2.96 2.96 2.96

14.3 9.4 14.2 15.9 15.5 14.6 13.7 10.6 14.9 9.2 9.1 12.7 24 13.3 11.7 23.2 18 12

36.6 29.8 34.1 42.9 33.8 28.6 53.6 45.5 42.4 25.5 14.8 13.4 13.8 19.7 14.5 22 12.8 13

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property relationships. To model the fabric properties, a unit cell of woven fabric based on the sawtooth model was used as a starting point. Leaf and co-worker [25,26] suggested a method based on mathematical modeling for designing woven fabrics using low stress mechanical specifications of fabrics meant for garment end use. The approach to engineering the design of woven fabrics was to minimize the cost function constrained by mechanical and physical fabric properties. The equations for the physical and mechanical properties are [23]: Fabric mass (g/m2):

W =

T1 (1 + c1) T2 (1 + c2 ) + p1 p2

16.6

Fabric cover factor

K=

d1 d2 d1d2 + – p1 p2 p1 p2

16.7

Crimp balance equation (mN):



Bc =

b1sinq1 b 2 sinq 2 + p22 p12

16.8

Tensile moduli (mN/mm):





E1 =

E2 =

12b1 2 p1 p2 (1 + c1)3sin 2q1

p2 p12 (1

È b 2 p23 (1 + c1)3cos 2q1 ˘ 1 + Í b p 3 (1 + c )3cos 2q ˙ 1 1 2 2˚ Î

12b 2 + c2 )3sin 2q 2

È b1 p13 (1 + c2 )3cos 2q 2 ˘ Í1 + b p 3 (1 + c )3cos 2q ˙ 2 2 1 1˚ Î

16.9

16.10

Shear modulus (mN/mm):



È p (p (1 + c1) – 0.8Dq1)3 p2 (p1 (1 + c2 ) – 0.8Dq 2 )3 ˘ G = 12 Í 1 2 + ˙ 16.11 b1 p2 b 2 p1 Î ˚

Bending moduli (mN mm2/mm)

B1 = b1p2 ∏ p1 [p2(1 + c1) – 0.8758Dq1]

16.12



B2 = b2p1 ∏ p2 [p1(1 + c2) – 1.0778Dq2]

16.13

Notations: d = yarn diameter in mm = 4.44 ¥ 10–2(yarn tex and fiber density)1/2 D = sum of the warp and weft diameters, i.e., D = d1 + d2

Building predictive models for textile product design

b q p c

= = = =

283

yarn flexural rigidity weave angle in radians = 1.85÷c thread spacing in mm, between two adjacent yarns in the fabric yarn crimp in fabric

In all these equations, subscripts 1 and 2 refer to parameters in the warp and weft directions respectively. The cost function of grey woven fabric is:

S = (1 + c1)/P1 ¥ (0.528Tw1 + 0.011 075T1)



+ (1 + c2)/P2 ¥ (0.523Tw2 + 0.0109 55T2)



+ 0.209/P2 + 0.25 (£ per square meter)

16.14

where Tw 1 and Tw 2 are the warp yarn and weft yarn twist per cm respectively. The system takes upper and lower boundaries of fabric properties such as bending moduli, tensile moduli, shear rigidity, fabric weight, fabric cover as the input and generates fabric structural parameters such as tex, crimp, thread spacing and twist as its outputs. The computer program is based on an algorithm for nonlinear constrained optimization. The model equations for tensile and bending moduli 16.9, 16.10 and 16.12, 16.13 were based on a saw tooth model of the plain-woven fabric. Theoretical values of initial moduli of the fabrics were calculated and compared with the experimental data from Table 16.1. The predictive power of mathematical model is determined by estimating the%age prediction error as percent error of prediction =



predicted value – experimental value ¥ 100 experimental value 16.15

Predictability of warp tensile modulus ranges from –58.12% to 24.12% with average absolute error percentage of 20.53%. Similarly, the error of predictability ranges from –9.53% to 36.85% for weft-way initial modulus of fabric with average error of 13.65%. The theoretical values of initial bending behavior of plain-woven fabric were calculated by using equations 16.11 and 16.12 and compared with the experimental data from Table 16.1. The predictive error of this model varies from –100.8% to 20.7% with an average prediction error of 18.7% for warp-way bending, and from –46.8% to 56.9% with an average of 16.9% for weft-way fabric bending rigidity. Mathematical models give a high prediction error due to several assumptions used in the models. However, these models help to make clear the relationships between structural and material parameters and fabric properties. Alternative methodologies are required to predict the properties more accurately.

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Woven textile structure

16.3.2 Evaluating empirical models Experimental data of tensile moduli and bending rigidity used in the mathematical model was reused to develop regression models to predict initial tensile moduli and bending moduli of fabrics. The following empirical equations using linear multiple regression technique were used:

E1 = – 21.429 + l1(–64.582) + l2(87.234) + p1(–51.112)



+ p2(50.034) + b1(4.814) + b2(1.217)



(R2 = 0.527)



E2 = 38.161 + l1 (–48.801) + l2(–370.5280) + 1(362.866)



+ p2(–1.122) + b1(3.09) + b2(5.100)



(R2 = 0.904)



B1 = 69.363 + d1 (–385.299) + d2 (–181.981) + l1 (–13.631)

16.16

16.17



+ l2(232.493) + p1(–289.970) + p2(24.084) + tex1(1.529)



+ tex2(0.491) + b1(–0.703) + b2(1.336)



(R2 = 0.842)



B2 = 18.916 + d1 (300.380) + d2 (–438.798) + l1 (132.455)

16.18



+ l2(159.367) + p1(–174.684) + p2(–137.467) + tex1(–0.798)



+ tex2(1.137) + b1(–0.334) + b2(2.425)



16.19

(R2 = 0.903)

The coefficient of multiple determinations (R2) defines the fraction of variability in the dependent variable explained by the regression model. Except for E1, the R2 values of other models are high, and suggest that empirical model fits the data reasonably well. In further analysis of models, these empirical equations 16.15 to 16.18 were used to predict initial tensile moduli and bending rigidities of the fabric. It is observed that prediction error in fabric tensile modulus range from –5.43% to 44.5% and –22.63% to 22.18% with average error of 20.4% and 12.33% in warp and weft directions. Similarly prediction error in bending rigidities ranges from –19.24% to 24.46% and –24.87% to 77.1%, with average error of 10.74% and 25.35% in warp and weft directions. The high error in prediction of fabric properties by empirical modeling may be due to the inability of the multilinear regression techniques to map exactly the nonlinearities in the fabric structure–property relationships.

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16.3.3 ANN modeling A radial basis function (RBF) network has been suggested as one of the most suitable multilayer network algorithms, quick to train and efficient to map any nonlinear input–output relationships. It has been used to model fabric structure–property relationships in this example [27–30]. The strategy used in RBF networks consists of approximating an unknown function with a linear combination of nonlinear functions, called basis functions. The basis functions are radial functions, that is, they have radial symmetry with respect to a center. The schematic of the RBF network with n inputs and a scalar output is shown in Fig. 16.3. Let n denote the dimension of the input space, and then in an overall fashion, the network represents a map from n-dimensional input space to single-dimensional output space. Such a network implements a mapping for: Rn Æ R according to

fr(x) = l0 + ∑i = 1 nrlij ( || x – ci || )

16.20

where x Œ Rn is the input vector, j ( · ), is a given function from R + to R, || · ||, denote the Euclidean norm, li, 0 £ i £ nr are the weights or the parameters, ci Œ Rn, 1 £ i £ nr, are known as the RBF centers, and nr is the number of centers. In RBF networks the functional form j (.) and the centers ci are assumed to be fixed. By providing a set of input x (t) and the corresponding desired output d (t) for t = 1 to N, values of the weights li can be determined using linear least square (LS) method. Theoretical investigation and practical results suggest that the choice of the nonlinearity j(.) is not crucial for performance of the RBF network. The functions may be thin-plate spline function, j(v) = v2log(v), the Gaussian function, j(v) = exp(–v2/b2); multiquadric function, j(v) = (v2 + b2)1/2, or inverse multiquadric function: j(v) = (v2 + b2)–1/2. Any way it is usual to choose j(v) in such a way that j(–v) = j (v) and j(v) Æ ±• = 0. However, the performance of RBF networks critically depends on the chosen centers. In practice the centers are normally chosen from the data points {x(t)}t = 1N. Such a mechanism results in poor performance and numerical ill-conditioning frequently occurs owing to near linear dependency caused by, for example, x1 x2 xn

l1 l2 ln

l0 Â Linear combiner

Nonlinear transformation j (|| x – ci ||)

16.3 Schematic diagram of a RBF network.

fr(x)

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Woven textile structure

some centers being too close. A common choice for distance function || · || i is a bi-quadric form. To study the predictability of initial tensile moduli of fabric, the fabric data given in Table 16.1 was randomly divided into 14 sets of input–output pairs for training of the RBF network and four input–output data sets were used to test the generalization ability of the trained network. The input to the net was made up of fabric constructional parameters p1, p2, l1, l2, and yarn bending rigidities b1, and b2. The output set consisted of fabric initial tensile moduli, E1 and E2. Before feeding to the network, the input–output data set was scaled down to be within (0,1), by dividing each value of the data by the maximum value of the overall data. The outputs of the network were de-scaled by multiplying the network outputs by the maximum value of the overall data. For each training run, the input–output data pairs were fed randomly to the network. Once the maximum neurons of the radial radial basis layer have been fixed, the only design parameters that are to be optimized are the error goal and the spread of the radbas neuron. Therefore, training of network is quite fast. Several combinations of net parameters were experimented with, to ensure relatively small prediction error. The training was stopped when the prediction error with test data-set was minimum. A similar process was followed to train the RBF network to predict fabric bending rigidities. The fabric data shown in Table 16.1 was randomly divided into 26 sets of input–output pairs for training and 7 input–output data pairs for testing the network. The inputs to the net were fabric constructional parameters, namely, warp tex, weft tex, d1, d2, p1, p2, l1, l2, and yarn bending rigidities b1 and b2. The output set consisted of fabric bending rigidities, B1 and B2. The analysis that follows is based on prediction of initial tensile moduli of the fabric. The average percentage error of prediction of initial moduli by RBF network is the average of both warp and weft error percentages. The number of neurons required to reach the error goal depends on the size of the input vector, desired training error goal, and the spread of the neuron in the radbas layer. Therefore, the values of input data size at 14, sum squared error goal at 0.05 and spread constant at 0.8 were kept constant and neurons in the hidden layer were varied from 5 to 15. The percentage of prediction of error in initial moduli for test data set was recorded. It can be seen from Table 16.2 Table 16.2 Effect of hidden layer neurons on prediction performance of an RBF network No. of neurons

5

6

7

8

9

10

11

12

13

14

15

Average error % 19.5 21.5 20.9 11.5 10.4 9.41 9.41 9.41 9.41 9.41 9.41 of prediction

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that the prediction error is high for neurons up to 9 in the hidden layer, and minimum at 10 neurons in the radbas layer. Thereafter, the network learns the input–output relationship and reaches the set error goal to produce a good generalization of the network with minimum error in prediction [31]. To study the effect of error goal on performance of the network, the spread constant of the neuron was fixed at 0.8 and number of neurons in hidden layer was varied to meet the error goal. It is obvious that as error goal for training the network becomes smaller, higher neurons are required in the hidden layer to meet the error goal. But a higher number of neurons in hidden layer in combination of a small error goal do not necessarily yield low prediction error. In fact, as depicted in Table 16.3 this particular network shows an error of 99.3% in the prediction of initial modulus of fabric. This may be due to over-fitting of data, and the function the network forms does not generalize well. The prediction error reaches minimum at error goal of 0.05. Thereafter, the prediction error of the network increases with increase in error goal. The spread constant affects the bias value of the hidden layer neuron:

bias = 0.8326/spread

Therefore spread constant affects the response space of the hidden neuron. To analyze the effect of spread constant on network generalization, neurons in the hidden layer and the error goal were kept constant at 10 and 0.05 respectively. Too high or too low values of spread constant inhibit good function generalization, which can be seen from Table 16.4. The spread constant chosen should be larger than the distance between adjacent input vectors, but smaller than the distance across the whole input space. Considering the above factors the design of the RBF network was optimized and trained to produce minimum error of prediction. Table 16.5 shows the network parameters of the trained and optimized RBF network model. Table 16.6 shows the experimental values, predicted outputs and the percentage error of prediction for initial tensile moduli of the fabric. It can Table 16.3 Effect of error goal on prediction performance of an RBF network Error goal 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.2 Neurons 13 12 11 11 10 9 8 8 7 6 2 Average error 99.3 24.7 16.5 16.5 9.41 10.4 11.5 11.5 20.9 21.5 29.1 % of prediction Table 16.4 Effect of spread constant on prediction performance of an RBF network Spread constant

0.1

0.6

0.7

Average error % 21.2 15.1 13.7 of prediction

0.8

0.9

1

1.5

2

5

10

9.41 12.4 11.8 11.4 11.8 11.7 11.8

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Table 16.5 Design parameters for an optimized RBF network Fabric property

Radbas neurons

Sum squared error goal

Spread constant

Initial modulus Bending rigidity

10 6

0.05 0.07

0.8 0.8

Table 16.6 Predictability of initial tensile moduli of fabric using an RBF network model Fabric sample no. (from Table 16.1)

Experimental values (N/cm)



E1

E2

RBF network values (N/cm) E1

E2

1 14.3 36.6 13.78 32.77 7 13.7 53.6 13.18 46 11 9.1 14.8 10.54 14.88 18 12 13 14.1 14.2 Average absolute error percentage

Percentage error E1

E2

–3.63 –3.77 15.86 17.53 10.2

–10.47 –14.17 –0.0.58 9.27 8.63

be observed that the predictive errors of trained networks for E1 and E2 are very low, 10.2% and 8.63%, and range of errors is from –3.77% to 17.53% and –14.17% to 9.27% respectively. The network predictions for fabric bending rigidities are shown in Table 16.7. The average prediction error percentage for fabric bending rigidity for warp and weft is 8.7% and 9.92% and prediction error ranges from –13.17% to 11.43%, and from –4.91% to 31.74% respectively. From where the values for sample numbers 24, 27 are 31 have been taken when in Table 16.1 there are only 18 samples.

16.4

Summary

Table 16.8 shows the summary of percentage prediction error with range for all the three methodologies. Comparisons of results indicate that RBF network produces least error and lowest range among the three models for the prediction of fabric modulus and bending rigidity. RBF networks can model the input–output relationships more accurately than other modeling methodologies. Apart from least error, it produces lower spread in the error than mathematical and regression methods of modeling. ANN has the property of approximating any functional relationship between large numbers of input–output parameters. No prior assumptions are required to be made on the statistical nature of the variables of the data, since ANN are nonparametric in nature. ANN requires a much smaller data set than the one required for conventional regression analysis for capturing the nonlinear relationships between the input and output parameters. The major advantage of ANN is

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Table 16.7 Predictability of bending moduli of fabric using an RBF network model Fabric sample no. (from Table 16.1)

Experimental values (mN/mm)



B1

B2

RBF network model (mN mm) B1

B2

4 9.88 7.54 9.41 7.38 7 7.02 8.06 7.37 7.74 13 7.11 9.25 6.17 12.18 15 5.92 8.17 6.45 9.38 24 18.48 20.55 20.5 22.1 27 18.25 19.62 20.33 18.65 31 20.5 12 19.01 11.48 Average absolute error percentage

Percentage error B1

B2

–4.7 4.36 –13.17 8.98 10.96 11.43 –7.24 8.7

–2.1 –3.86 31.74 14.92 7.56 –4.91 –4.3 9.92

Table 16.8 Summary of range and prediction errors Fabric Mathematical model Empirical model Artificial neural property network model (RBF) Range Error % Range Error % Range Error % E1 (N/cm) E2 (N/cm) B 1 (mN mm) B 2 (mN mm)

–58.12 20.53 to 24.1 –9.53 13.65 to 36.85 –100.8 18.7 to 20.7 –46.8 16.9 to 56.9

–5.43 20.4 to 44.5 –22.6 12.33 to 22.18 –19.24 10.74 to 24.5 –24.9 25.35 to 77.1

–13.17 to 1.43 –14.17 to 9.27 –13.2 to 11.47 –4.91 to 31.74

10.2 8.63 8.7 9.22

that there is no restriction on the levels of interaction between the variables. It can therefore capture the dynamics of the real world situation very well. Once trained, neural networks are very easy to use and require very little human expertise. Since the network can accurately capture the nonlinear relationships between input–output parameters, they have extremely good predictive power and therefore can be a better and accurate predicting tool to design and engineer woven fabric products. The design of woven fabrics is a very complex process. Traditional methods of fabric design have several limitations. Mathematical modeling helps to construct a fabric with predetermined properties. However, the prediction error is very high owing to the assumptions incorporated in the formulating theory and inherent non linearity between fiber, yarn and fabric structure-property relationships. Anns can be successfully used both for forward engineering as well as backward engineering. Both networks give high coefficient of correlation between actual and predicted values of fabric parameters. Expert systems embedding ANNs can be developed for engineering new woven constructions. Several other training algorithms can be tried for research work to train ANNs to examine their suitability for fabric engineering.

290

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Woven textile structure

References

1. Muttagi S B (2002), Artificial Neural Network Embedded Expert System for Design of Woven Eabrics, PhD Thesis, Department of Textile Technology, Indian Institute of Technology Delhi, July. 2. Shakyawar D B (2000), Studies on Hand Value of Woven Fabrics Produced from Indian Wools and Their Blends, Doctoral thesis, Department of Textile Technology, Indian Institute of Technology Delhi, January. 3. Rajmanickam R, Steven H and Jayaraman S (1997), Analysis of Modeling Methodologies for Predicting the Strength of Air-Jet Spun Yarns, Text Res. J., 67 (1), 39. 4. Aleksander I and Morton H (1990), An Introduction to Neural Computing, Chapman and Hall, London. 5. Haykin S (1994), Neural Networks: a Comprehensive Foundation, Macmillan Publishing Company, New York. 6. Fausett L (1994), Foundations of Neural Networks: Architecture, Algorithms and Applications, Prentice Hall International, Inc., New York. 7. Freeman J A and Skapura D M (1992), Neural Networks: Algorithms, Applications and Programming Techniques, Addison-Wesley, New York. 8. Blum A (1992), Neural Networks in C++, John Wiley and Sons, New York. 9. Masters T (1993), Practical Neural Network Recipes in C++, Academic Press Inc., Harcourt Brace Jovanovich, Publishers, Boston, San Diego, New York. 10. Mendel J M and McLaren R W (1970), Reinforcement Learning Control and Pattern Recognition Systems, in Adaptive Learning and Pattern Recognition System: Theory and Applications, Eds, J. M. Mendel and K. S. Fu, Academic Press, New York. 11. Postle R, Carnaby G A and De Jong S (1988), The Mechanics of Wool Structures, John Wiley & Sons, New York. 12. Matsuo T and Suresh M N (1997), The Design Logic of Textile Products, Text. Progress, The Textile Institute, 27, No. 3. 13. Fan J and Hunter L (1998), A Worsted Fabric Expert System, Part I: System development, Textile Res. J. 68(9), 680–686. 14. Fan J and Hunter L (1998), A Worsted Fabric Expert System, Part II: An Artificial Neural Network Model for Predicting the Properties of Worsted Fabric, Textile Res. J. 68 (10), 763–771. 15. Dastoor P H, Hersh H P, Batra S K and Rasdorf W J (1994), Computer-assisted Structural Design of Industrial Woven Fabrics, Part I: Need, Scope, Background, and System Architecture, J. Text. Inst. 85 (2), 85–109. 16. Dastoor P H, Hersh H P, Batra S K and Rasdorf W J (1994), Computer-assisted Structural Design of Industrial Woven Fabrics, Part II: System Operation, Heuristic Design, J. Text. Inst. 85 (2), 110–134. 17. Dastoor P H, Hersh H P, Batra S K and Rasdorf W J (1994), Computer-assisted Structural Design of Industrial Woven Fabrics, Part III: Modeling Fabric Uniaxial /Biaxial Load Deformation, J. Text. Inst. 85 (2), 135–157. 18. Ramesh M C, Rajamanickam R and Jayaraman S (1995), The Prediction of Yarn Tensile Properties by Using Artificial Neural Network, J. Text. Inst., 86, 459–69. 19. Cheng L and Adams D L (1995), Yarn Strength Using Neural Networks Part I: Fiber Properties and Yarn Strength Relationship, Text. Res. J., 65, 495–500. 20. Vangheluwe L, Sette S and Kiekens P (1996), Modelling Relaxation Behaviour of Yarns part II: Back Propagation Neural Network Model, J. Text. Inst., 87, 305–310.

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21. Stylios G and Parsons-Moore R (1993), Seam Strength Prediction Using Neural Computing, Int. J. Clothing Sci. Technol., 5, 24. 22. Patterson D W (1996) Artificial Neural Network, Theory and Applications, Prentice Hall, Singapore. 23. Leaf G A V and Kandil K H (1980), Initial Load–Extension Behavior of Plain Woven Fabrics, J. Text. Inst. 71, 1–7. 24. Leaf G A V, Chen Y and Chen X (1993), The Initial Bending Behavior of Plainwoven Fabrics, J. Text. Inst., 84, 419–428. 25. Grosberg P and Leaf G A V (1988), Modern Computational Methods in the Design of Wool Textile Structures, in Application of Mathematics and Physics in the Wool Industry, Eds., Carnaby G A, Wood E J and Story L F, WRONZ and The Textile Institute (New Zealand Section), Christchurch, 83–91. 26. Chen X and Leaf G A V (2000), Engineering Design of Woven Fabrics for Specific Properties, Text. Res. J., 70, 437–442. 27. Park S W, Hwang Y G and Kang B C (2000), Applying Fuzzy Logic and Neural Networks to Total Hand Evaluation of Knitted Fabrics, Text. Res. J., 70(8), 675– 681. 28. Ertugrul S and Ucar N (2000), Predicting Bursting Strength of Cotton Plain Knitted Fabrics Using Intelligent Techniques, Text. Res. J., 70(10), 845–851. 29. Debnath S, Madhusoothanan M and Srinivasmoorthy V R (2000), Modeling of Tensile Properties of Needle-Punched Nonwovens Using Artificial Neural Networks, Ind. J. Fiber and Text. Res., 25 (1), 31–36. 30. Kim E H (1999), Objective Evaluation of Wrinkle Recovery, Text. Res. J., 69(11), 860–865. 31. Chen S, Cowan C F N and Grant P M (1991), Orthogonal Least Squares Learning Algorithm for Radial Basis Function Networks, IEEE Transaction on Neural Networks, 2 (2), 302–309.

17

Modeling for woven fabric design

Abstract: The primary objective of a computer simulation system in weaving is to provide a fast, easy, virtual design and realistic simulation of woven structures on the computer screen to enable manufacturers to assess their designs before the actual fabric production starts. In this chapter the simulation of woven structures are discussed. Simulation of structure– property relationships and their effects on fabric deformation, texture, weave pattern and color scheme are discussed. Finally the limitations of computer simulation in textile applications are reviewed. Key words: woven fabric design, modeling, fabric deformation, fabric texture.

17.1

Introduction

A system is defined as a group of objects that are joined together in some regular interaction or interdependence towards the accomplishment of some purpose. A system that does not vary with time is called a static system. If it varies with time, it is known as a dynamic system. Models are used to study system behavior at the design stage, before new systems are built. One of the major applications of a model is to predict the performance of new systems under varying sets of circumstances. Simulation is the process of designing a model of a real system and conducting experiments with it for the purpose of understanding the behavior of the system or of evaluating various strategies (within the limits imposed by a set of criteria) for the operation of the system. A simulator is a computer program which mimics both the internal behavior of a real-world system and the input processes which drive or control the simulated system. The simulator output is a set of measurements concerning the observable reactions and performance of the system.

17.2

Types of computer modeling in fabric design and manufacture

In weaving, the primary aim of a computer simulation system is to provide a fast, easy and realistic simulation of woven structures on the computer screen to enable manufacturers to assess their designs before the real weaving process. An ideal fabric simulation system should have the following features: 292

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∑ 3-D computer simulation of the fabric. In reality, yarn and fabric have a 3-D structure, so simulation must consider it. ∑ Real simulation of yarn surface. There are several parameters that affect the yarn surface appearance including hairiness, amount of twist, unevenness of yarn, etc. All of these parameters have to be included in the simulation system. ∑ Simulation of fabric behavior under real wear conditions. There are several changes to the fabric surface during wear of garment, such as pilling, and abrasion. These have to be considered in the system. ∑ Presentation of mechanical and physical properties of fabric. There are several important structural properties of a fabric such as dimensional change, spirality, bursting strength, bending and shearing behavior. These have to be simulated by the computer. Computer simulation of fabrics is very important for both producer and customer. Some of the advantages of simulation in woven construction are as follows: ∑ The appearance of fabric can be seen before production on the machine. ∑ Actual production of sample on the machine is eliminated. Thus time and money can be saved during preparation of the sample. ∑ Errors in the design can be identified and eliminated. ∑ Design can be transmitted electronically to buyers and customers. Most of the computer simulation systems give only 2-D computer images, which do not truly represent the displayed sample. However, if 3-D models can be created on the computer screen, designers and customers will have realistic and adequate representation of structures. They can manipulate the models (e.g. zooming, rotating and scaling) and consider aesthetic and other aspects of the fabric as well. In fact, there is a general trend towards 3-D modeling in all fields parallel to the advancement in computing in terms of both hardware and software. However, the application of 3-D solid modeling in textiles is more difficult than in other fields owing to the complexity, flexibility and irregularity of the structures [1,2]. A number of computer software programs have been developed and are being used in industry for designing woven fabrics of both simple and complex structures. They enable the designer to create a fabric, guiding him or her in the selection of numerous design parameters and simulating fabric appearance. There are, for example, software programs from Fashion Studio, Nedgraphics, Pointcarré and Wonder Weaves Systems that provide fabric simulations from yarn images. Uster Zellweger, Zweigle and Loepfe, on the other hand, provide fabric simulation software to examine probable fabric faults resulting from defective yarns. Pascal et al. [3] have developed

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an interactive package that allows the hierarchical specification of up to three types of yarn and simple tools for the modification of colors through the use of color maps. Adanur and Vakalapudi [4] have developed an image recognition program of spun yarns. Researchers have also developed a yarn measurement system which, analyzes and compares density profiles obtained from several spun yarns. Using 3-D models, they can also predict fabric appearance and other quality attributes [5,6]. Adabala et al. [7] have developed a technique for visualizing woven textiles in real time. Krˇ emenáková et al. [8] have developed a textile design system that focuses on the prediction of the structure as well as properties of the fibers, yarns and fabrics. The principal aim of the system is to obtain fabric design optimization on the basis of virtual fabrics. Keefe [9] has proposed a model to take into account potential effects of compressibility on a twisted assembly. His approach assumes that an individual yarn in compression could be approximated by a single element with an elliptical cross-section. Keefe [10] has used elliptical cross-sectional yarns in the basic plain-weave pattern to create a simulation package. The yarn images used in these fabric simulations are generally images simulated from given yarn parameters developed by mathematical algorithms [11]. Ozdemir [12] has developed a method to simulate plain-woven fabric appearance based on actual yarn photographs taken by a stationary camera. Other than the simulation methods mentioned above, techniques have been developed to compute some properties of woven fabrics such as deformation of fabric, filtration behavior, etc. Some simulation systems based on CAD have been developed to compute the appearance of warp and weft knitted fabrics. There are also methods to estimate weave pattern and appearance of 3-D multilayered and orthogonal fabrics.

17.3

The application of modeling to woven fabric design

17.3.1 Simulation of woven construction There are a number of computer software programs available for designing woven fabrics of simple and complex structures that enable the designer to create a fabric. The yarn images used in these fabric simulations are generally images simulated from given or measured yarn parameters developed by some mathematical algorithms. Ozdemir [12] has developed a way to simulate plain-woven fabric appearance based on actual yarn photographs taken by a stationary camera. The yarn image is considered to be the projection of a cylindrical surface on a plane perpendicular to the direction of viewing and parallel to the yarn axis. A circular yarn surface is generated from the yarn image. This

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surface is transformed into an elliptical surface which is projected on to the fabric plane [11]. Yarn photographs are resized in order to simulate the yarn flattening perpendicular to the yarn axis. While resizing, the sinus curve is applied between midpoints and the elastica curve is applied between crossover points [11]. As a result of this resizing, the increments of Dx in the yarn image are resized to smaller increments of Dxi¢ or Dxi≤ as shown in Fig. 17.1. A reasonable value of the eccentricity of elliptic yarn cross-section, e = 0.6, is assumed in the application of the theory developed to calculate resizing factors. In the calculation of resizing factors to be applied to the yarn photographs in the direction of yarn axis when a weave angle of 30° was assumed, crimp factor k, which is the ratio between the arc length S and yarn interval p, was found to be approximately 1, instead of the actual value of 1.14 calculated from Peirce’s geometry. This is due to both rounding off the pixel numbers resized for each segment to integers and the need for the arc length S to be a whole multiple of the number of segments. By assuming a weave angle q of 40°, the crimp factor was calculated as 1.27, which is quite close to the value of 1.24 obtained from Peirce’s geometry, and hence was utilized as an assumed parameter. A computer program is used to calculate the resizing values as well as to resize the cropped yarn image in vertical and horizontal directions. The resized yarns images are placed side by side in vertically and horizontally to align intersecting yarn sections [11]. The space for an array of fabric simulation whose numbers of rows and columns are equal to the numbers of columns of resized horizontal image in pixel is allocated in RAM by the computer program. To obtain a vertical yarn image, the horizontal yarn image was rotated clockwise by y

y

DS2

DS3 DS4

DS5 DSe2 DS6

DS1 Dx Dx Dx Dx Dx Dx

(a)

DSe3 DSe4 DS e5 DSe6

DSe1 x

Dx ¢1 Dx ¢2 Dx ¢3 Dx ¢4 Dx ¢5 Dx ¢6

x

(b)

17.1 Yarn behavior: (a) surface development of yarn cylinder from the yarn photographic image; (b) resizing of the yarn image based on elliptical yarn cross-section.

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90°. Procedures are built in the program to simulate weave structures by transferring pixel values of horizontal or vertical image arrays to fabric simulation arrays according to the plain-weave structure. In an intersection area where warp is up the weft, yarn is transferred to this area in the ground portions only by controlling ground color thorough the rows of pixels from left to right. The reverse is done when the weft yarn is up. The method is shown in Fig. 17.2 for both warp up and weft up stages. The program code in Linux is debugged and run by Cygwin, a user interface that simulates Linux in Windows. Arrays for fabric simulation, horizontal image, vertical image and processed images are defined in the C file containing the main function. Functions declared in the header file are called step by step in this file. Examples of fabric simulations obtained by this method are shown in Fig. 17.3.

17.3.2 Deformation of woven fabrics A computer animation method has been developed to estimate the deformation of woven fabric based on the trellis model [13]. According to this method, cloth deformation is classified as macro-deformation which results in folds and creases, and a micro-deformation, which changes visual perception of

Warp up

Weft up

17.2 Simulation steps for two different yarn intersections.

(a)

(b)

(c)

(d)

17.3 Fabric simulations obtained from a fancy yarn: (a) yarn separated from background by filtering; (b) plain weave with circular cross-section; (c) plain weave with elliptic cross-section resized according to the elastica curve; and (d) plain weave with elliptic cross-section resized according to the sinus curve [3].

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the cloth texture. A micro-deformation model of woven fabric deformation is suggested through computer animation. The crimp theory proposed by Peirce in his geometrical model is considered using a surface model. Bkzier surface is chosen as the surface model because it allows for the representation of smooth and complex shapes by a few points called control points. Coordinates of the control points in 3-D space are determined by approximation using the geometric model. Because the control points correspond to the surface shape, the movements of the control points deform the geometric model. Woven fabrics are constructed by warp and weft crossings. A simple trellis model is used to represent the anisotropy of the woven fabrics. The computer animations of the woven fabric deformation by this method are shown in Fig. 17.4. Figure 17.5 illustrates woven fabric deformation for various fabrics which takes into consideration the anisotropy by using the simple trellis model. The boundary condition of this deformation fixes the top and bottom.

17.4 Computer animation of woven fabric elongation.

Plain

1/2 twill

2/2 twill

17.5 Deformation of plain and twill fabrics.

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17.3.3 Visualization of woven textiles Neeharika and others have created a real-time technique that enables rendering of complex weave patterns. The ability to visualize the appearance of the textile realistically is important for the completeness of digital representation of textiles. Such digital virtual textiles have application in fashion industry where computer-aided prototypes of clothing are gaining importance, in e-commerce where an authentic representations of products are needed, etc. The objective of the technique is to provide cloth and graphic designers with the capability of generating textures with various designs of weave patterns without having to use scans or photographs of sample textiles. The problem is divided into the following steps in visualizing the fabric: ∑ ∑ ∑ ∑ ∑

Representing the weave pattern. Modeling the microstructure of the threads of the textile. Modeling the interaction of light with textile. Reflection behavior. Shadowing behavior between the threads in the weave pattern.

Adabala et al. [7] have used a standard in the textile industry known as the weaving information file (WIF) to obtain the complex weaving patterns and represent patterns suitably for generating color texture. The microstructure of the threads is incorporated into a procedural texture and it is used along with the WIF information to generate a color texture. The WIF information is also used to define a suitable bi-directional reflectance distribution function (BRDF) that corresponds to the reflection behavior of the textile. The shadowing that occurs between the threads when they are woven together is captured in the horizon maps that are generated with information from the WIF. They are thus able to start from the grammar representation for weaving a textile and generate a visualization of the woven textiles. One of the important aspects of their work is that one cannot only capture the appearance based on the weave grammar but also include the way light interacts with the material.

17.3.4 Example color scheme of a weave pattern The algorithm [5] uses the information in WIF that describes the weave pattern. It is interpreted by the WIF interpreter and made available to the modules namely, the micro-geometry shader, the BRDF generator and the horizon map generator, (Fig. 17.6). The micro-geometry shader makes use of a procedural thread texture generator to create a color texture based on the WIF. The procedural thread texture generator is responsible for creating the shading that results from the twisting of the fibers that are spun into

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the threads. Figure 17.7 shows an example of a color scheme of a weave pattern. The BRDF generator takes as input the characteristic of the textile obtained from the weave pattern described in the WIF. It generates a BRDF to correspond to these characteristics. However, the pattern of weaving contributes significantly to the way the light interacts with a fabric. This is very well exemplified by the fact that the satin weave results in textiles with glossy appearance.

WIF

WIF interpreter Procedural thread texture generator

Micro-geometry shader

BRDF generator

Color texture

BRDF textures

Mesh of clothes

Multi-texturing cloth renderer

Horizon map generator

Horizon maps

Final visualization of clothes

17.6 Outline of algorithm [5].

17.7 Sample color scheme for a weave pattern [5].

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The WIF contains the weave grammar and therefore from this information it is possible to learn which facets of the threads are longer and hence tend to be higher on the surface of the textile. This in turn dictates how such facets of textile cast shadows on the neighboring threads of the textile. The horizon map generator module uses the WIF information to define these shadows that are essential to convey the feeling of depth in the weave pattern. The real-time constraint prompted the use of multi-texturing approach to realize the solution to the algorithm given in Fig. 17.6. Each of the above modules results in a texture and the final rendering of the textile is done by composing the images suitably. Figure 17.8 shows examples of the thread shading textures that are generated procedurally by this technique. These thread textures can be used along with the weave pattern to generate a color texture of a weave pattern that has the appearance of being woven from twisted fibers. An example of such a texture is shown in Fig. 17.9.

17.4

Modeling structure–property relationships: elongation and bending

Simulation of structure–property relationships of textile materials has been subject of interest to many textile researchers. Selected examples are reviewed in this section.

(a)

(b)

(c)

(d)

17.8 Thread shading textures: (a) very loosely twisted thread without shading; (b) more tightly twisted thread (noise is added to simulate the presence of fibers about the thread); (c) thicker fibers twisted into thread; (d) tightly twisted thread [5].

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17.9 Color texture generated for the sample color scheme [5].

17.4.1 Elongation The studies conducted by Kawabata and co-workers [14–20] on elongations have been particularly successful. The theoretical model is based on the force balance and the movement of yarn in thickness direction at the contact point of crossing yarn. In the case of biaxial stretching, the contact force Fc1 caused by the yarn tension FY1 and the tensile force FBI required for straightening the bent yarn 1 balances with Fc2 of the crossing yarn caused by Fc2 and FB2. By the contact force, compressional deformations of yarns 1 and 2 occur, and they cause the movements of both yarn in the thickness direction. On the other hand, yarns 1 and 2 are elongated by yarn tensions 1 and 2, respectively. Then the fabric stretch ratio gi can be geometrically related with yarn stretch ratio gyi and the location of the yarn i in the thickness direction at the contact point. So by giving the input data of structural parameters such as yarn density, yarn crimp ratio and yarn characteristics such as tensile force versus strain function and bending hysteresis, the tensile force versus strain relation of the fabric can be numerically obtained. In the case of uniaxial stretching, Fcl is induced by the yarn tension. However, Fc2 is caused by the bending stiffness of the crossing yarn. They were also successful to derive theoretical equation for calculating uniaxial stretching characteristics [19]. They also presented a linear method for estimating the load–strain relation in the general biaxial deformation mode [20]. Grosberg and Kedia [21], Leaf [22], Hearle and Shanahan [23] and de Jong and Postle [24] have carried out the theoretical analysis on tensile deformation by using minimum energy method. The main difference between Kawabata’s and these studies is that the later ones missed the compressional effect at the cross-over point and considered the effect of yarn bending deformation. Therefore, the later studies are mainly suitable for the initial extension behavior.

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Woven textile structure

17.4.2 Bending Many papers [25–30] on the bending of woven fabrics have been presented. The curve can be approximated by the following equation:

M = ± H F + H Fk

where M is bending moment and k is curvature of the bent yarn. Furthermore, each term on the right-hand side of the equation can be expressed by [29]:

HF = Hy + HI



KF = Ky + K1

The subscripts F, Y and I mean fabric, yarn and inter-yarn effect, respectively. Furthermore the slope Ky can be approximated by [29]:

Ky = [tw/(l +C)] Ny Ns Ks

where Ny is yarn density, Ns is the number of single fibers within a yarn, Ks is the stiffness of single fiber, C is the crimp ratio of yarn within the fabric and tw is the (fiber length along helical coil of twisted yarn)/(yarn length). HI and KI are decreased by several finishing treatment such as desizing, heat setting, relaxation, lubricating, sericin removing and peeling. HI is increased by the swelling treatment of the fiber [29,30].

17.5

Modeling of woven fabric texture

The last 25 years have shown considerable development leading to a change in the computer graphics design process in textiles [31–36]. Computers and interfaced equipment are being utilized as tools to improve the design and manufacture of textiles with its related products. Also, computers are used to generate multiple alternatives for the image of real fabrics at an incredible rate and store hundreds of images and colour references in an electronic library; thus providing the designer with more substantive information to make more visual design decision. Although CAD is gaining importance, it has not yet become a complete tool for the textile designers because of the vast range of materials to be simulated. The 1984 Annual World Conference of the Textile Institute was entitled as Computers in the World of Textiles [37]. Eight out of 47 papers dealt with the design of textile materials using some form of a computer-generated graphical images of the final product and its economical impact. The World Reviews of Textile Design [38–40] also provide the state-of-the-art of textile design. Research in this area

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is being reviewed by many authors and the latest developments and new systems can be seen at ITMA exhibitions [41]. Part of the design process includes the simulation of fabric texture using the fabric weaves and patterns, colors, or simulating the fancy yarns on the screen related with yarn structure to fabric texture and appearance [42–44]. Also, many commercial systems are now available especially for woven and knitted fabrics that can even simulate starting from yarns up to the fashioned fabrics [45,46]. Denton and Seth [47] worked on the computer simulation of the appearance of fabric woven from blended fiber yarns, especially for worsted suiting. They also presented a brief review of CAD systems available on the market. The content of a simulation program developed by them is as follows: (1) choice of warp and weft yarn diameter, (2) choice of working space, (3) choice of the distribution function describing the length of shade variations along the yarn axis, (4) selection of color ranges for warp and weft yarn, (5) weave structure and (6) total plotting area. The logic of the program is simple in nature. At first, all the necessary parameters have to be fed, and then the program generates the warp yarn and simultaneously starts plotting the first warp thread within the work space. Then it considers the float UP and DOWN conditions for warp and weft. At this stage the colors of the generated threads are random. Finally, the program provides a printout of the simulated fabrics with six input information as mentioned above. Sakagawa et al. [48] worked on the simulation of color and pattern and texture design of the weaves as an alternative to the real sample images. They have used regular and colored yarns. The main logic works as shown in Fig. 17.10 [49]. At first the base patterns for graduation will be done by brushing the images. Then the pattern will be simulated by individual yarn composition. The combination of these will give the simulated image of fabric surface and texture that looks similar to the real fabric image. Further, they applied the same techniques for the yarn composed of different colored fibers and also for slub yarns, fancy yarns, loop yarns, knotted yarns, etc. Kondo et al. [50] presented computer graphics of material texture of knitted fabrics. They tried simulating the knit loop form using spline curve method. Here the original loop will take the form of simulated curve. They also attempted to simulate the equivalent real fabrics providing random variation to the yarn thickness and knitting lo.

17.6

Limitations of modeling

2-D images of the samples do not give realistic representation of structures. Designers and customers want to predict the comfort, drape and handling characteristics of the fabrics as well as the aesthetic aspects of the design.

304

Woven textile structure Set of boundary conditions and required accuracy

Set of mechanical Input characteristics

Set of initial conditions and parameters

Mechanical model of stress–strain behavior

Solution

Boundary value–boundary conditions< required accuracy? No Change of free initial conditions and parameters towards satisfying of boundary condition Yes Information about stress, strain and geometry

Output

17.10 Computation of the boundary value problem.

Therefore most of them still prefer to make their decisions after seeing the physical samples instead of 2-D computer images. 3-D solid models can be created on the screen but the application of 3-D solid modeling concept is a more difficult task than in other fields owing to complexity, flexibility and irregularity of the structure. Approaches using scans and photographs suffer from the problem of presence of features resulting from the illumination under which the images were generated. Swelling that exists on the fabric surface is also not clear in the simulation, so improvement in the simulation by means of 3-D simulation is needed.

17.7

References

1. Ucar N, Goztas O and Ucar M, (2008) ‘Two-dimensional Computer Simulation (CAD) of the appearance of the Weft Knitted Fabrics,’ Technical Report, Istanbul Technical University, Turkey. 2. Goktepe O (2001), Turk J Environ Sci, 25, 369–378. 3. Pascal J, Giralt J and Brunet P (2003), Computers and Graphics, 10(4), 359–368. 4. Adanur S and Vakalpudi J S (2003), Yarn and fabric design and analysis system in 3-D virtual reality, ‘Annual Report,’ National Textile Center, PA, November 2003. 5. Jasper W, Suh M W and Woo J L (2000), Real time characterization and data compression using wavelets, ‘Annual Report’, Textile Center, PA, November 2000.

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6. Suh M W, Jasper W and Cherkasssky A, Journal of the Textile Institute, 100(3), 282–292. 7. Adabala N, Thalmann N and Fei G (1995), ‘Real Time Visualization of Woven Textiles,’. Textile Inst., 86(4), 635–648. 8. Krˇemenáková D (2004), ‘System for textile design, Part 1, fiber–yarn’, Research Center Textile, Textile Faculty Technical University of Liberec. 9. Keefe M (1994), J. Text. Insti., 85(3), 338–349. 10. Keefe M (1994), J. Text. Insti., 85(3), 350–358. 11. Ozdemir H and Baer G (2009), Journal of the Textile Institute, 100(3), 282–292. 12. Ozdemir H (2007), Computational Textile, 55, 75–91. 13. Furukawa T, Okamoto T, Kitagawa S and Shimizu Y (1997), ‘Computer Animation of Woven Fabric Deformation Based on Simple Trellis Model’, IEEE/ASME International Conference on Advanced Intelligent Mechatronics ’97, Tokyo. 14. Kawabata S (1989), in Textile Structure Composite (edited by Chou T W and Ko F K), Elsevier, Amsterdam, 73. 15. Kawabata S, Niwa M and Kawai H (1973), J. Text. Inst., 64(2), 21. 16. Kawabata S, Niwa M and Mastudaira M (1985), J. Text. Mach. Soc. Japan, (English ed.), 31, 7. 17. Kawabata S and Niwa M (1984), in ‘Proc. 13th Text. Res. Symp.’, Mt. Fuji, 1. 18. Kawabata S (1985), in ‘Proc. 14th Text. Res. Symp.’, Mt. Fuji, 1. 19. Kawabata S and Niwa M (1979), J. Text. Inst., 70(10), 417. 20. Kawabata S, M Niwa and Kawai H (1973), J. Text. Inst., 64(2), 47. 21. Grosberg P and Kedia S (1966), Text. Res. J., 36(1), 72. 22. Leaf G A V (1980), in ‘Mechanism of Flexible Fiber assembly’ (edited by Hearle J W S, Thwaits J J and Amirbayat J), Sijthoff & Noordhoff, USA, 143. 23. Hearle J W S and Shanahan W J (1978), J. Text. Inst., 69(4), 81. 24. Jong S de and Postal R (1977), J. Text. Inst., 68(10), 307. 25. Livesey R G and Owen J D (1964), J. Text., 55(10), T 516. 26. Grosberg P (1966), Text. Res. J., 36(3), 205. 27. Abbott G M, Grosberg P and Leaf G A V (1971), Text. Res. J., 41(4), 345. 28. Grosberg P (1980), in ‘Mechanism of Flexible Fiber Assembly’ (edited by Hearle J W S, Thwaits J J and Amirbayat J), Sijthoff and Noordhoff, USA, 197. 29. Matsuo T J (1969), Text. Mac. Soc. Japan (England ed.), 15(1), 19. 30. S de jong R Postle (1977), J. Text. Inst., 68(11), 362. 31. Cao Shouzhen J (1984), CTEA China, 5(3), 29. 32. Hearle J W S (1993). Text Horiz, 13(5), TH15. 33. Holmes J (1992). Text. Mon., May, 45. 34. Donaldson A (1993), Can. Text. Manual, 110(5), 28. 35. Holmes J (1992), Textiles, 1, 12. 36. Moore R and Miller J (1989) Text. Inst., 80(3), 337. 37. (1984) ‘Computer in the world of Textile’. ‘Proc. Text. Inst. Annual World Conf.’, Hong Kong. 38. Higginson S (ed.) (1993), World Review of Textile Design, The Textile Institute, Manchester. 39. Higginson S (ed.) (1994) World Review of Textile Design’, The Textile Institute, Manchester. 40. Higginson S (ed.) (1995) World Review of Textile Design’, The Textile Institute, Manchester. 41. Thomas H (1993), Am. Text. Inst., 22(6), 74.

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42. Renner F (1987), Inst. Text. Bull., Fabric Forming, 33(2/87), 49. 43. Hoskins J A and King M W (1984), in ‘Proc. Text. Inst. Annual World Conf.’, Hong Kong, 32. 44. Szczesny C et al. (1991), Int. Text. Bull., Fabric Forming, 37(3/91), 73. 45. Holme I (1989), Text. Month, June, 54. 46. MIles L (ed.) (1989) Computer in Textiles, The Textile Institute, Manchester, Manchester, UK. 47. Denton M J and Seth A K (1989), J. Text. Inst., 80(3), 451. 48. Sakagawa N, Itoh M and Masui H (1989), A report of Aichi Prefecture Owari Text. Tech. Centre, Japan, No. 10, 128. 49. Hearle J W S, Konopsek M and Newton A (1972), in New Ways to Produce Textiles’ (edited by Harission P W), The Textile Institute, Manchester. 50. Kondo M, Iwasakari K and Koizumi Y (1988), Res. Report of Tokyo Prefecture Text. Ind. Tech. Centre, Japan, No. 36, 70.

18

Assessing the comfort of woven fabrics: fabric handle

Abstract: Objective evaluation of fabric properties has received more attention not only to assess fabric properties but to facilitate development of high quality fabrics for several new applications. This chapter describes the objective evaluation of fabric handle. The factors affecting the low stress mechanical properties of fabric are also discussed. Key words: modeling, objective measurement, fabric handle.

18.1

Introduction

The performance of clothing materials can be classified as [1,2]: ∑ ∑ ∑

utility performance measured in terms of strength, durability, etc.; comfort performance evaluated by considering mechanical fitting to human body and physical comfort; fabric performance during clothing manufacture.

The primary objective of clothing is to protect the human body from the external climate by creating a comfortable environment next to the skin. Fabric handle therefore has become the primary consideration for design and development of apparel fabrics. With the increasing demand for high quality fabrics, it has become essential to understand the physical and physiological interrelationship between clothing and the human body. The mechanical properties of the fabric are closely related to the comfort properties of clothing. These are three fundamentals requirements to model fabric, handle [2,3]: ∑ ∑ ∑

Theories for fabric mechanical properties. Objective evaluation technology for fabric handle and other primary attributes. Use of fiber and yarn properties for the design of fabric in terms of comfort and aesthetics performance.

Traditional fabric quality evaluation comprises measurement of durability characteristics like strength and elasticity as well as comfort and aesthetic characteristics. Textile and clothing industries have traditionally used individuals’ subjective assessments of these fabric qualities as the basis of 309

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Woven textile structure

evaluation. However, in view of ever-increasing diversity of fabrics and clothing, rapidly increasing automation in textile and clothing manufacture, and the retirement and non-replacement of experts with extensive experience in textiles and clothing, it has become imperative to minimize the increasing difficulties in subjective assessment of fabric quality attributes. As a result, objective evaluation of fabric properties has received more attention not only to assess fabric properties but to facilitate development of high quality fabrics for new applications. This chapter describes fundamental requirements for objective evaluation technology for fabric handle measurement.

18.2

The objective measurement of comfort

Aesthetics and comfort are generally understood to be subjective. Leaving apart aesthetic appearance, overall comfort performance can be divided into two more measurable components: mechanical and thermal comfort. While thermal comfort is assessed by the permeability of fabric to air, water and heat, mechanical comfort has traditionally been evaluated by visual and tactile means. When professional experts judge the handle, they express a feeling perceived from touching a fabric by hand using a standard washing. However, researchers in recent years have attempted to express fabric handle in terms of physical parameters such as tensile and shear properties, bending rigidity, hysteresis of deformation, compressibility and surface smoothness. They have expound other comfort characteristics in terms of air permeability, thermal insulation capacity, water repellency and water vapor transmission. The basic concept underlying objective fabric measurement technology is that appropriate instrumental measurements should be made on fabrics to specify and control the quality, tailorability and ultimate performance of the garment [3,4]. This approach has become feasible due to the development of instruments for measuring low stress fabric mechanical and physical properties and also to the development of analytical methods and soft computing tools for interpretation of data. The objective measurement of fabric mechanical properties was initially reported by Peirce [2]. However, the pioneering research work was carried out at the Swedish Institute for Textile Research (TEFO) in the late 1950s and 1960s involving evaluation of low stress mechanical properties of apparel fabrics [5] such as bending, buckling, tensile and shear properties and compression for tailorability and formability to be used for garment manufacturing. Subsequently, Lindberg et al. [6] introduced the theory of buckling to textile fabrics in garment technology. He also emphasized that longitudinal fabric compression is a fabric mechanical property that is important in tailoring, that is the forming and sewing of flat pieces of fabrics into 3-D shaped garments.

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In 1972, the Hand Evaluation and Standardization Committee (HESC) was formed by the efforts of Professor Sueo Kawabata of Kyoto University and his associates, with the support of the Textile Machinery Society of Japan, for the purpose of standardization of handle evaluation [7]. Based on the standardization of primary handle values and development of their numerical expression, the research on the interaction between these handle values and the mechanical properties of fabrics was initiated by Kawabata and Niwa in the mid-1970s. Finally, this work, along with the vision and technical skill of Kawabata, led to the development of KES-F instruments in 1972 [8]. These were subsequently upgraded to KES-FB set of equipment and used for fabric assessment, first in the Japanese industry and then in the rest of the world [9–11].

18.3

Measuring fabric handle

Experimental techniques for the measurement of low stress mechanical properties have evolved over a number of years and a variety of equipment and test methods are now available for objective evaluation of fabric [12]. However, KES-FB and FAST systems have received the maximum attention both in the research laboratory and industry. The KES-system has retained the basic design of Kawabata’s four instruments for the investigation of six characteristic aspects related to fabric handle. The KES-system involves instruments for measuring fabric parameters such as tensile and, shear properties, bending, compression, surface friction and surface roughness [13]. These instruments are designed to make measurements at low stress levels. The instruments allow data on a wide range of parameters, including both deformation and recovery, for each mechanical property to be measured. During the testing of materials, it is important to select the maximum tension/ compression/bending/shear value for the recovery part of the cycle. These are likely to reflect the values experienced in the performance of the garment. Kawabata has chosen 17 different parameters as the objective features influencing fabric handle. All or only some of these parameters can be used to define the behavior of a fabric as it affects the appearance and/ or performance of a garment or the processability of the fabric depending on their field of application.

18.3.1 Tensile properties The tensile property of the fabric is one of the basic low stress mechanical properties, which plays important role in fabric handle and tailorability of the fabric [14]. An important parameter that affects the load–elongation curve of the woven fabric is the ratio of crimp of the two yarns in the structural repeating unit, since this parameter influences the inter-yarn force dramatically.

312

Woven textile structure

Other factors, which influence the tensile behavior of fabric are weave crimp, degree of sett, weave, yarn structure and finishing treatments. A typical deformation–recovery curve for a fabric subjected to extension is shown in Fig. 18.1. The fabric is extended at a constant strain rate until a pre-set load is reached before starting the recovery cycle. The required tensile characteristic values are obtained from the deformation–recovery curve and are given in equations 18.1–18.4:

EM = 2.WOT/Fmax em



LT =

Ú0

 F de

18.2

0.5 Fm e m

WT =

em

Ú0

em



18.1

Ú RT = 0e Ú0

m

 F de

18.3



 F de ¥ 100  F de

18.4

The hysteresis shown in the graph represents energy loss during the complete deformation–recovery cycle as a result of inelastic inter-fiber friction and fiber visco-elasticity. EM represents the extensibility of the fabric at 500 gf/ cm; LT represents the linearity of the load–elongation curve and influences fabric extensibility at initial strain range. A low value of LT gives high fabric extensibility but low fabric dimensional stability. WT represents the tensile energy per unit area (area under the load–elongation curve). The tensile resilience (RT) is the ratio of energy recovered to energy needed to extend the fabric at low stress level.

5 cm

20 cm

500 Force, F (gf/cm)

Tensile force

0

0

Fm

Æ

F

¨

F Strain, e

18.1 Tensile behavior at low deformation.

em

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313

18.3.2 Shear properties The mechanical properties of fabrics under shear stress are important characteristics. Shear properties influence fabric handle and permit the fabric to conform to intended garment shape. The fabric shear rigidity gives a measure of the resistance to relative movement of warp and weft threads within a fabric when subjected to low levels of shear deformation [15]. It is a function of the contact area at cross-over points, initial modulus and inter-yarn friction in the fabric. The fabric shear hysteresis occurs mainly due to frictional effects between the yarns at cross-over points. Shear stress reduces by setting due to decrease in the normal pressure between the yarns. A typical shear stress–strain curve for the fabric is shown in Fig. 18.2. Shear rigidity of a fabric is calculated as the average slope of linear section at the start of the applied shear force. The shear hysteresis 2HG and 2HG5 corresponds to shear angles 0.5° and 5°.

18.3.3 Bending The bending property of a fabric is an important component of hand evaluation [16]. It is closely related to complex fabric properties and performance

2HG5

Fs(gf/cm)

2HG

tan–1G

tan–1G 0.5

2.5

5.0

F°

2HG 2HG5

18.2 Shear behavior at low deformation G, slope between 0.5° and 2.5° shear angle 2HG, hysteresis at 0.5° shear angle.

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Woven textile structure

characteristics such as drape, buckling, handle, wrinkling, formability, shape retention properties and resistance to creasing [14]. Fiber fineness, yarn twist and yarn and fabric structure significantly influence the bending behavior of a fabric. Olofsson [17] concluded that inter-yarn forces affect clustering ratio of fibers within the yarn and thereby increases yarn bending rigidity, which influences the fabric bending rigidity. Grosberg [18] reported a correlation between the inter-yarn forces and the fabric bending rigidity. The bending property of fabric is characterized by two important parameters, namely bending rigidity and coercive couple. Bending rigidity is calculated as the average slope of linear section at the start of the applied bending moment as shown in the Fig. 18.3. The bending rigidity is attributed to elastic property of the material and coercive couple is thought to arise from inter-fiber and

N (gf  cm/cm)

tan–1B

–2

–1

2HB

0

1

2HB

2

1/s cm–1

tan–1B

m) 2–20 cm

S(c

S M

18.3 Bending behavior at low deformation B, slope between 0.5 and 1.5 cm–1 curvature 2HB, hysteresis at 1 cm–1 curvature.

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315

inter-yarn friction. The characteristic bending parameters B and 2HB obtained from the bending hysteresis curve are shown in Fig. 18.3.

B = slope between 0.5 and 1.5 cm–1 curvature



2HB = hysteresis at 1 cm–1 curvature

18.3.4 Compression The compressional property is one of the most important basic low stress mechanical properties of fabric, which is closely related to fabric handle [19]. Further, the compressional property is related to fabric structure, surface properties of fibers and/or yarn and lateral compressional properties of fibers and/or yarns. The characteristic values of compressional properties, which are concerned with fabric handle are proposed by Kawabata and Niwa [16], as LC (linearity of compression); WC (compressional energy); RC (compressional resilience); T0 (fabric thickness at 0.5 gf/cm2) and Tm (fabric thickness at 50 gf/cm2). The compressional energy (WC) is a function of mass of fibers in the surface layer, Young’s modulus of constituent yarns and density of the fibers and also packing fraction of the yarns. The value of LT is directly proportional to WC and inversely proportional to surface thickness (T0–Tm) of the fabric. RT is mainly dependent on the fiber crimp and Young’s modulus of the fiber in the fabric. Compressional properties are influenced by various fiber characteristics such as diameter, crimp and yarn structure. The compressional parameters are calculated using equations 18.5–18.7 derived from Fig. 18.4:

P, (gf/cm2)

Pm = 50

Æ

P

¨

P

0.5 T0

Tm

Thickness, T (mm)

18.4 Compressibility test.

0

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Woven textile structure T0





ÚT P dT

LC =

18.5

m

0.5(Tm – T0 )Pm T  WC = Ú P dT T T  ÚT P dT RC = e  ¥ 100 P dT Ú

18.6

0



m

0

m

18.7

m



Tm



18.3.5 Surface properties The fabric surface properties such as coefficient of friction and surface roughness are a measure of smoothness of the fabric. These properties are governed by surface properties of fiber and yarn, fabric construction such as thread density and weave [20,21]. The frictional properties are also significantly altered by yarn mechanical properties such as compression and surface treatments [22,23]. The differences between static and kinetic frictional forces are strongly correlated with fabric handle [20]. The characteristic values of surface properties concerned with fabric handle [16] are MIU (mean coefficient of friction), MMD (mean deviation of frictional coefficient) and SMD (surface roughness) given in equations 18.8–18.10 derived from Fig. 18.5:

MIU = (1/X )

X

Ú0 u dX

MMD = (1/X ) SMD = (1/X )

X

Ú0 X

Ú0

|u – u | dX | T – T | dX

18.8



18.9 18.10

The coefficient of friction (m) is defined as the ratio of the frictional force to normal load by which the probe is pressed on the fabric surface. The m value fluctuates during the sweep of the fabric surface; MIU and MMD are calculated from the obtained data. The vertical displacement, Z, of surface roughness probe from the arbitrary standard position gives mean deviation of surface contour (SMD).

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317

Thickness T (cm)

SMD = hatched area/x

z

Coffiecient of friction, µ

0

x

R

MMD = hatched area/x Y

MIU

R

x

18.5 Surface behaviour at low deformation (KES-4FB).

18.4

Primary and total fabric handle

18.4.1 Primary handle values (HV) The HESC was formed with the involvement of Japanese clothing industry. The main objectives of the committee were to standardize the terminology and procedures used in the subjective handle evaluations, relate subjective handle expressions to fabric mechanical properties such as Koshi (stiffness), Numeri (smoothness), Shari (crispness), Hari (anti-drape stiffness) and Fukurami (fullness and softness) and develop a concept of total handle value (THV) based on these primary handle values given in Tables 18.1 and 18.2 respectively. The KES has basic design for investigation of six major characteristic aspects related to fabric hand. These are tensile and shear properties, pure bending, compression, surface friction and surface roughness. Taking measurements for the above six characteristics over many years Kawabata in Postle [24] chose 17 different parameters as the objective features influencing fabric handle (Table 18.3). All or some of these parameters can be used to define the behavior of a fabric as it affects the quality and performance of a fabric.

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Table 18.1 Definition of primary handle values: men’s winter suit fabric

Handle

Japanese

English

Definition

Koshi

Stiffness

Numeri

Smoothness

Fukurami

Fullness and softness

A feeling related mainly to bending stiffness. A springy property promotes this feeling. A fabric having a compact weave density and made from elastic yarn gives high value. A mixed feeling coming from a combination of smooth, supple, and soft feelings. A fabric woven from a cashmere fibre gives a high value. A feeling coming from a combination of bulky, rich and well formed impressions. A springy property in compression and thickness is closely related with this property.

Table 18.2 Definition of primary handle values: men’s summer suit fabric

Handle

Japanese

English

Koshi Shari

Stiffness Crispness

Hari

Anti-drape

Fukurami

Fullness and softness

Same as Koshi in men’s winter suit fabric. The crisp and rough surface of fabric is due to the hard and strongly twisted yarn. This feeling results in a cooling feeling. Anti-drape stiffness, regardless of whether the fabric is springy or not. Same as Fukurami in men’s winter suit fabric.

Subsequently, the objectively measured values of selected fabric properties have been translated through a series of regression equations to equate with the subjectively assigned primary handle values for each primary handle expressions and named as Koshi, Numeri, Shari, Hari and Fukurami as given in Tables 18.1 and 18.2. The experimental handle value is evaluated by expert by hand and the 17 parameters are correlated to give the linear equation as: 17



Yk1 = C0 + ∑ Ci Xi i =1



18.11

where Yk1 is the primary handle value, C0 and Ci (i = 1,2,…,17) are constants and xi is deviation of the value of mechanical parameter from the population mean, normalized by standard deviation, namely:

xi =

Xi – Xi si

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Table 18.3 Fabric mechanical and surface parameters Parameters

Symbol

Tensile 1. 2. 3. 4.

LT WT RT EM

Description

Unit

Linearity of load/extension curve Tensile energy Tensile resilience Extensibility, strain at 500 gf/cm of tensile load

None gf cm/cm2 % None gf cm2/cm gf cm/cm

Bending

5. B 6. 2HB

Bending rigidity Hysteresis of bending moment

Shearing

7. G 8. 2HG 9. 2HG5

Shear stiffness gf cm/degree Hysteresis of shear force at 0.5° shear angle gf/cm Hysteresis of shear force at 5° shear angle gf/cm

Compression 10. LC 11. WC 12. RC

Linearity of compression/thickness curve Compressional energy Compressional resilience

None gf cm/cm2 %

Surface

13. MIU Coefficient of friction 14. MMD Mean deviation of MIU 15. SMD Geometrical roughness

None None µm

Thickness

16. T

Fabric thickness

mm

Weight

17. W

Fabric weight

mg/cm2

where Xi is the absolute value of the parameter, Mi is the mean value of Xi for the population of N fabrics and si is the standard deviation of Xi. A stepwise block-regression method was developed as follows. Kawabata has six blocks of mechanical properties, i.e. tensile, shear, etc. and each of these blocks consists of two or more variables. Initially the regression equation is formulated between Yk and each of the blocks to find the block which gives the best prediction for Y. The best equation becomes the first regression equation, for example,

Y = C0¢ + C5 X5 + C7 X7 (bending property block) (1st equation)

where Y = predicted value by the first equation, C0¢ is a constant. Secondly, the residuals Yk – Yk are correlated with each of the remaining blocks to find the best prediction of Y to obtain: Y – Y = C0≤ + C7 X7 + C8 X8 + C9 X9 (shear property block) (2nd equation) Thus the second equation can be rewritten as follows:

Y = C0¢≤ + C5 X5 + C6 X6 + C7 X7 + C8 X8 + C9 X9 (3rd equation)

where

C0¢≤ = C0¢ + C0≤

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Woven textile structure

Repeating this procedure, we can complete: 17



Yk1 = C0 + ∑ Ci Xi i =1



18.12

The accuracy of the prediction increases with increasing number of blocks but, in many cases, the accuracy almost saturates after three or four steps. By this stepwise method, one can compose the terms of linear equation in order of importance for predicting Y without strong effects coming from the correlation between variables Similarly equations for each primary hand expression can be derived. Kawabata in Postle et al. [24] worked out the importance of various low stress mechanical parameters in order to determine the contribution of each parameter in determining the primary handle values. Each primary handle value is influenced by some of selective low stress mechanical parameters. Therefore, a small change in low stress mechanical properties may cause a change in the primary handle value of the fabric. For example, a slight variation in MMD value makes a large change to the numeric value of the fabric.

18.4.2 Total handle values The THV represents an assessment of the over all quality of the fabric, which is a measure of its value in the market and varies with the end-use application. Then, THV is evaluated from primary handle values using following equation: 3



THV = C0 + ∑ Zk i=k



18.13

where

Z k = C k1

Yk – M k1 Y – M k2 + Ck 2 k 2 s k1 s k1

where Yk = hand value of kth primary hand value; Mk1 = mean value of Yk for population of N fabrics; sk1 = standard deviation of Yk; Mk2 = mean value of Yk2; sk2 = standard deviation of Yk2; and CkI and Ck2 are constant coefficients. The THV of the same fabric calculated from primary handle values are different for different kinds of end-use applications such as men’s suits, jackets and slacks. The influence of higher numeric value on THV is remarkable for suiting and slacks application and it causes an increase in THV significantly. The Koshi and Fukurami have the optimum zone around HV ~ 6. From a

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fabric engineering viewpoint, the objective measurement technique using KES system provides suitable information in terms of various low stress mechanical parameters and handle values. The objective measurement of the low stress mechanical properties of fabric either by the KES system or the FAST system is a basic tool for designing the product as per the customer’s need. The objective evaluation system will help in designing a new product by controlling and assessing the process at each step. In textiles, the new products are new type of fabrics with very high THV and excellent comfort values. These systems are able to measure the main constituents of THV up to a very fine level precisely. In fact, it is realized that fabric objective measurement technology provides a scientific basis for the application of engineering principles to the design and manufacture of apparel fabrics to meet the requirements of consumers and clothing manufacturers in terms of fabric quality and performance characteristics. Suppose we want to develop bedding for premature children than the level of handle should be extreme and the level of required comfort be very high. After development, the objective evaluation will performed by scientific means such as KESF or FAST and then result will be scrutinized to assure the achievement of prefix targets. In order to produce a good 3-D clothing structure by stitching, the operator’s technique for overfeed operation are not the only important factor but also the mechanical properties of the fabrics [25]. Lindberg et al. [26] coined term ‘formability’ to describe the relation between mechanical properties of fabric and its processing ability to form a garment:

F = C ¥ B

18.14

where F = formability, C = fabric compressional compliance in plane and B = fabric bending rigidity.

18.5

Factors affecting fabric handle

The low stress mechanical properties and handle values of a fabric mainly depend on the type, shape and structure of the fiber used in the manufacturing of the fabric. The spinning system and conditions used for manufacturing the yarn also significantly influence yarn structure and its properties, which in turn affect the low stress mechanical properties and fabric handle. Apart from these factors, fabric construction parameter that is weave structure, fabric sett, areal density and wet processing conditions used during the finishing of the fabric also influence the low stress mechanical properties and handle values of fabric [27–29].

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Woven textile structure

18.5.1 Fiber structure and properties Fiber is considered as the unit cell of textile material. Among various fiber characteristics the fineness, diameter, crimp, cross-sectional shape, surface roughness and all mechanical properties of fiber contribute to fabric mechanical property. Wool being a natural fiber, the variation of diameter significantly influences fabric properties. The fiber diameter has a main effect on the fabric stiffness and handle [30,31]. Hunter et al. [30] reported that an increase in mean fiber diameter increased the Koshi, Hari and Shari but decreased the Fukurami of the fabric. It has also been reported that the coefficient of friction of the fabric decreased with an increase in mean fiber diameter whereas mean deviation of coefficient of friction of fabric surface (MMD) increased. Among various compressional characteristics resiliency of compression (RC) is reported to be increased with increase in fiber diameter. The fine wool imparts distinctively higher smoothness, fullness and softness, which results in higher THV of the fabric [32]. Fabric handle is considered reliable and to be determined by the crosssectional shape of fibers [19]. The fabric becomes soft and deformable with an increase in the space ratio in the fiber cross-section; however, it does become inelastic and unrecoverable [19]. It is further reported that Fukurami and Shinayakasa (flexibility with soft feel) of fabric are increased with increase in space ratio whereas Koshi and Hari are decreased. Fiber crimp and fabric quality are highly correlated. An increase in fiber crimp results in an increase in the fabric thickness and weave crimp which in turn affects Fukurami, Numeri THV [30]. The fiber crimp also influences the fabric shear rigidity and shear hysteresis. These properties are increased with an increase in the fiber crimp whereas the fabric surface properties such as MIU (coefficient of friction) and MMD (mean deviation of MIU) are decreased. A good correlation between fiber crimp and primary handle is reported by Matsudaria et al. [33]. They observed that Numeri and Fukurami are strongly related to fiber crimp. Fiber mechanical properties such as tensile, bending and compression are directly reflected in their corresponding yarn and fabric properties. Among all these properties, bending and extensibility largely influence low stress mechanical property and hence handle behavior of the fabric [30].

18.5.2 Yarn structure and spinning system The low stress mechanical properties of fabric are directly related to the structure and properties of yarn out of which it is made. These are significantly influenced by yarn linear density, twist and other process parameters. The effect of the yarn linear density on the hand value was reported by Hunter et al. [30]. They reported that both Numeri and Fukurami are increased

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considerably by spinning fibers into a finer count. Coarser yarns increased the cover factor, which results in higher stiffness of the fabrics. The hard twist in the yarn increases yarn-packing density and therefore increases the fabric stiffness significantly [30, 34]. The fiber mix in the blends also significantly influenced the low stress mechanical properties of the woven fabrics. Fabric produced from pure wool fiber gives higher THV than wool–polyester blended winter fabrics for similar construction. Yarn produced on different spinning systems has different structure especially in the fiber arrangement and twist distribution in the yarn. Owing to the change in yarn structure, the properties of yarn are varied significantly. The fiber assembly in the yarn affects the physical and mechanical properties of fabric [35–37]. Therefore, mule spun yarn has always been considered as being superior quality to ring spun yarn [35]. The properties quoted as being superior are the evenness of the yarn and its handle. The influence of ring and rotor spinning system has been studied by Subramanium and Amarvati [38]. Fabrics woven from open-end spun yarn have greater thickness than fabrics of ring-spun yarn. The value of compression energy (WC) was therefore higher. It is further reported that the coefficient of friction of fabric (MIU) increased significantly in the case of fabric woven from open-end spun yarns. Most of the primary handle values, with the exemption of Fukurami, are higher for fabric woven from open-end spun yarns than those from ring spun yarns. Fabrics produced from ring spun yarns exhibit better handle than open-end spun yarns. They further reported that the use of carded cotton with polyester fiber enhances the handle of fabrics [38]. Comparison among the fabric produced from ring, rotor and friction spun cotton yarn is reported by Behera et al. [27]. They found that fabric produced from ring yarn gives lower bending, shear rigidity and hysteresis than fabric produced from rotor and friction yarns. The fabric from ring yarn also gives best compressional behavior among the rotor and friction fabrics, which in turn produces fabric of best handle. It has also been reported that fabric from friction yarn shows highest hysteresis loss, which gives poor dimensional stability of the fabric. Radhakrishnaiah and Sawhney [39] and Sawhney et al. [40,41] reported the influences of sheath and core in covered yarn in several publications. They reported that two identically constructed cotton–polyester fabrics, one made from polyester staple-core and cotton covered yarn and other from a random blended yarn showed significant difference in low stress mechanical and surface properties [42,43]. The difference in fabric properties mostly reflected difference in the physical properties of the yarn. Fabric made from polyester-core cotton covered yarn is most resilient to tensile and compressive deformation and has higher bending rigidity, lower tensile elongation and shear modulus. The same fabric gives higher values for all four primary handle qualities and THV associated with men’s summer suit application.

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The same fabric also gives higher values for five out of six primary handle qualities for women’s thin dress application. It is further reported that the same fabric also offers a cooler contact sensation and much less variation in contact sensation along its length compared with fabric from random blended yarns. The fabric made from cotton-covered yarn have better thermal comfort value for cold and dry (winter) as well as hot and humid (summer) weather conditions. Radhakrishnaiah and Sawhney [39] reported that the core–sheath yarn showed lower values for bending rigidity, bending hysteresis, compressive resilience and tensile elongation. The same yarn also showed a higher value for compressive softness and tensile modulus. The lower tensile elongation and higher tensile modulus of core–sheath yarn is reflected in lower elongation and higher modulus of corresponding fabric. However, bending and compressional properties of core–sheath yarn are inversely related to bending and compression properties of corresponding fabrics. Cotton–polyester core yarn fabrics have a cotton feel and a appearance and luxurious full handle [42]. Core-wrap composite yarn produced by an airjet spinning system is relatively weak as well as extremely harsh in handle [37]. The airjet and friction spun composite core yarn is less hairy and bulky than the ring spun, attributable to major basic differences in their structures. The fabric made from this composite yarn has a harsher handle than those of 100% ring spun cotton fabric. A very preliminary subjective evaluation of finished fabric, however, revealed a satisfactory appearance [44].

18.5.3 Fabric structure The fabric construction parameters such as fabric sett, cover factor and weave considerably change the performance of the fabric in respect of low stress mechanical properties. Fabric stiffness increases considerably if the cover factor of the fabric increases which in turn changes the THV of the fabric. Plain weave fabrics have higher shear rigidity than other weaves because of more yarn to yarn interlacing in the fabric with smaller float [45]. The fabric produced with plain weave give compact structure resulting in lower thickness as compared to other weaves structures [45]. Behera et al. [27] reported that twill weave produces higher extensibility, smoothness and compressibility than plain weave fabrics. They also further reported that bending and shear rigidity of twill fabric is significantly lower than plain fabric. A twill fabric gives higher Fukurami and THV. The level of weave crimps influences bending property; fabrics with high crimp give lower flexural rigidity and vice versa. The twill fabric behaves differently from the plain weave fabrics because of less interference between warp and weft threads. Fabric dimensional properties such as fabric thickness and areal density play important role in deciding fabric handle, because bending,

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compression and shear properties are influenced by these two parameters. Wool being a bulkier fiber exhibits high compressibility and softer and fuller feel, improving fabric handle.

18.5.4 Finishing treatment A significant reduction in both the rigidity and hysteresis in shear and bending properties of wool fabrics has been reported after scouring [29]. During finishing processes, the pressure and steam decatizing, and dry cleaning are the most critical steps in determining the final handle of woolen fabrics, especially with regard to shear rigidity and hysteresis losses. Finnimore [32,46] reported change in shear, tensile and bending properties after wet processing of wool fabric. He observed that the shear rigidity is decreased after scouring but in some cases it is increased again after decatizing. Kopke [28] also reported a decrease in shear stiffness after setting. He further reported that shear stiffness is increased with longer cooling time after decatizing. Dhingra et al. [47] reported a significant reduction in both the rigidity and hysteresis in shear and bending properties of wool fabric after scouring. These effects are almost equally divided between scouring and heat setting of wool/polyester blended fabrics. Solvent scouring of loom state fabrics imparts the worst handle to wool fabric [48]. Solvent scouring reduces the stiffness whereas the steam press controls the smoothness, fullness and softness. They also observed that perchloroethylene treatment at an elevated temperature or in combination with a swelling agent only marginally affects the mechanical properties as compared with normal perchloroethylene treatment. The soap scouring produces fabrics of best hand with desirable aesthetic attributes. During finishing, decatizing is a critical step in determining the final handle of the fabric [49]. Decatizing makes large modification in the behavior of fabric subjected to low tensile, compressive, shearing, bending and buckling stresses [50]. Steam pressing of wool causes an increase in the primary hand value Koshi with a decrease in Fukurami and Numeri [51]. Steam pressing results in increase in hysteresis and rigidity in shear and bending due to greater contact of warp and weft threads in the fabric. However, Shiomi and Niwa [51] observed that steam pressing produced a fabric with lower Koshi value and higher Numeri and Fukurami values. Dry cleaning improves the fabric handle, with Koshi decreasing and Fukurami and Numeri increasing [49]. Dry cleaning causes stress relaxation within the fabric, leading to a reduction in hysteresis and to a lesser extent rigidity in shear and bending. Chemical setting during finishing to wool fabric gives greater rigidity as compared to the continuous wet setting process. The THV of chemically set fabric is found slightly lower than wet set fabric [52]. Wet setting process tends to relax the fabric to a greater

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extent than chemically set fabric; the values for shear and bending stress are also lower than those for the chemically set fabrics. The application of softeners considerably improves the quality of textile materials by modifying the physical and chemical nature of wool fiber surface. The cationic and amino-silicon softeners are most commonly used on wool products [53]. Finnimore [46] reported a decrease in cationic softener to Hercoset-treated wool fabric f shear and bending rigidity. The cationic and amino-silicon softeners increase the tensile resiliency, tensile work (WT), compressional energy (WC), and lower bending and shear rigidity and their hysteresis and also reduce the coefficient of friction [14,53,54].

18.6

Summary

With changes of lifestyle and taste of consumers, it has now become essential that fabric should be designed according to need. The objective measurement of the low stress mechanical properties of fabric is a basic tool for engineering the product to fulfill consumers’ need. A detailed analysis of correlation between fabric objective evaluation parameters and handle value that will give guidelines for engineering a quality fabric using new fibers, processes and structures is essential for the development of quality fabric. The knowledge of structure–property relationship of fiber, yarn and fabric in conjunction with the objective measurement techniques of low stress mechanical properties provide a powerful tool for product development.

18.7

References

1. Hari P K and Sundaresan G (1993), Garment Quality: Interrelationship with Fabric Properties, GARTEX-NIFT’93 conference, New Delhi Oct 16–17, F1–7. 2. Peirce F T (1930), The Handle of Cloth as Measurable Quantity, J. Textile Inst., 21, T377–416. 3. Postle R (1989), Fabric Objective Measurement: 1, Historical Background and Development, Text. Asia, 20(7), 64–66. 4. Postle R (1989), Fabric Objective Measurement: 1, Historical Background and Development, Text. Asia, 20, 64. 5. Kawabata S, Niwa M (1991), Objective Measurement of Fabric Mechanical Property and Quality, its Application to Textile and Clothing Manufacture, Int. J. Clothing Sci. Technol., 1, 7–18. 6. Lindberg J, Behre B and Dahlberg B (1961), Mechanical Properties of Textile Fabrics Part III: Shearing and Buckling of Various Commercial Fabrics, Text. Res. J., 31, 99. 7. Kawabata S (1982), The development of the objective measurement of fabric handle, Proc. First Japan–Australia Joint Symposium on Objective Specification of Fabric Quality, Mechanical Properties and Performance, Kyoto, Textile Machinery Society, Japan, 31–59. 8. Kawabata S (1980), The Standardization and Analysis of Hand Evaluation, 2nd

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10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

25. 26. 27. 28. 29.

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edition, Hand Evaluation and Standardization Committee, Text. Mach. Soc. Japan, Osaka. Kawabata S, Postle R and Niwa M (1982), Objective Specification of Fabric Quality, Mechanical Properties and Performance, Proc. of First Australia–Japan Bilateral Science and Technology Symposium, Kyoto, Textile Machinery Society, Japan, Osaka. Mori M (1994), Basic Testing Method for Designing Excellent Fabrics for Men’s Suits, Int. J. Clothing Sci. Technol., 6(2/3), 7. Natarajan K S and Subramanium V (1985), IIIrd Japan/Australia Joint Symp. on Objective Measurement: Application to design and process control, Text Mach Soc of Japan, Osaka, Japan, 78. Natrajan V, Thilagavathi and Sankaran V (1997), Studies on Low Stress Mechanical Properties of Suiting Fabrics, Indian J. Fiber Text. Res., 22, 99. Harlock S C (1989), Fabric Objective Measurement: 2 Principles of Measurement, Text. Asia, 20, 89. Postle R, Carnaby G A and Jong S de (1988), The Mechanism of Wool Structures, Ellis Harwood Ltd, Chichester, 17, 360, 364. Kawabata S, Niwa M and Kawai H (1973), The Finite Deformation of Plain Weave Fabrics Part III, The Shear Deformation Theory, J. Text. Inst., 64, 62. Kawabata S and Niwa M (1989), Fabric Performance in Clothing Manufacturing, J. Text. Inst., 80, 19. Olofsson B (1964), A General Model of Fabric as a Geometrical-Mechanical Structure, J. Text. Inst., 55, T541. Grosberg P (1966), Mechanical Properties of Woven Fabrics Part II, The Bending of Woven Fabrics, Text. Res. J., 36, 205. Matsudaria M, Tan Y and Kndo Y (1993), The Effect of Fiber Cross-sectional Shape on Fabric Mechanical Properties & Handle, J. Text. Inst., 84, 24. Ajayi J O (1994), An Attachment to the Constant Rate of Elongation Tester for Estimating Surface Irregularities of Fabric, Text. Res. J., 64, 475. Ajayi J O (1992), Fabric Smoothness, Friction and Handle, Text. Res. J., 62, 52. Ajayi J O and Elder H M (1997), Fabric Friction, Handle and Compression, J. Text. Inst., 88, 232. Mahar T J and Postle R (1989), Measuring and Interpreting Low Stress Fabric Mechanical and Surface Properties. Part IV: Surface Evaluation of Fabric Handle, Text. Res. J., 59, 721. Postle R (1983), Objective Evaluation of the Mechanical Properties and Performance of Fabrics and Clothing, in Objective Evaluation of Apparel Fabrics (Postle R, Kawabata S and Niwa M eds), Proc. Second Australia–Japan Symposium, Melbourne, Text. Mach. Soc. Japan, Osaka. Kawabata S. and Niwa M (1989), ‘Fabric Performance in Clothing and Clothing Manufacture,’ J. Text. Inst, 80(1), 19–50. Lindberg J, Behre B and Dehlberg B (1961), ‘Shearing and buckling of various fabrics,’ Text. Res. J., 31(2), 99–122. Behera B K, Ishtiaque S M and Chand S (1997), Comfort Properties of Fabrics Woven from Ring-, Rotor- and Friction-spun Yarns, J. Text. Inst., 88, 255. Kopke V (1970), The Role of Water in the Setting up Wool, Pt II Fabric Properties, J. Text. Inst., 61, 388. Matsui Y (1983), Fabric Finishing on the basis of objective measurement of fabric measurement of fabric measurement Properties cited in Objective Evaluation of Apparel

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30.

31. 32.

33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47.

Woven textile structure Fabric (Postle R, Kawabata S and Niwa M eds.) Proc. of Second Australia–Japan Bilateral Science and Technology Symposium, Kyoto, Text. Mach. Soc., Japan, Osaka, 31. Hunter L, Kawabata S, Gee E and Niwa M (1982), The Effect of Wool Fiber Diameter and Crimp on Objectively Measured Handle of Wool Fabrics (Postle R, kawatata s and Miwa N eds). Proc. of Second Australia–Japan Bilateral Sci. and Tech. Symp., Kyoto, Text. Mach. Soc., Japan, Osaka, 161. Jong S De, Mahar T J, Dhingra R C and Postle R (1985), The Objective Specification of Mechanical Properties of Woven Wool and Wool Blended fabrics, Proc. of 5th Int. Wool Text. Res. Conf., Tokyo, Vol III, 229. Finnimoree E (1982), ‘The DWI’s Experience in Objective Handle Measurement’ in Objective Specification of Fabric Quality, Mechanical Properties and Performance, Proc. of First Australia–Japan Symp., Kyoto, Text. Mach. Soc., Japan, Osaka, 273. Matsudaria M, Kawabata S, Gee E and Niwa M (1984), The Effect of Fiber Crimp on Fabric Quality, J. Text. Inst., 85, 273. Ly N G and Denby E F (1984), Bending Rigidity and Hysteresis of Wool Worsted Yarns, Text. Res. J., 54, 180. Cassidy T, Weedal P J and Harwood R (1989), An Evolution of the Effect of Different Yarn Spinning Systems on the Handle of Fabrics Part II A Comparison of Ring spun & Mule Spun Woolen Yarns, J. Text. Inst., 80, 537. Grosberg P, Hubbard T P, Mc Manana A B and Nissan A H (1965), An Examination of Woolen Drafting as Pre-formed on a False Twister form, J. Text. Inst., 56, T49. Lord P R (1987), Air Jet and Friction Spinning, Text. Horizon, 7, 20. Subramanium V and Amarvati T B C (1994), The Effect of Fiber Linear Density and Type of Cotton on the Handle and Appearance of Polyester Fabric Produced from Ring Spun and Open End Spun Yarns, J. Text. Inst., 85, 24. Radhakrishnaiah P and Sawhney A P S (1966), Handle and Comfort Property of Woven Fabric Made from Random Blend and Cotton Covered Cotton/Polyester Yarns, Text. Res. J., 63, 573. Sawhney A P S, Harper R J, Ruppenicker G F and Robert K Q (1991), Comparison of fabric Made With Cotton Covered Polyester Staple-Core Yarn and 100% Cotton Yarns, Text. Res. J., 61, 71. Sawhney A P S, Robert K Q, Ruppenicker G F and Kimmel L B (1992), Improved Method of Producing Cotton Covered/Polyesters Staple Core Yarn on Ring Spinning Systems, Text. Res. J., 62, 62. Sawhney A P S, Kimmel L B, Ruppenicker G F and Thiboneaux D R A (1993), Unique Staple Core Cotton Wrap Yarn Made on a Tandem Spinning System, Text. Res. J., 63, 764. Radhakrishnaiah P and Sawhney A P S (1966), Low Stress Mechanical Behavior of Cotton Yarns and Fabrics in Relation to Fiber Distribution within the Yarn, Text. Res. J., 66, 99. Tzanov T, Betcheva R, Hardalov I and Hes L (1998), Quality Control of Silicone of Silicone Softener Application, Text. Res. J., 68, 749. Fan J and Hunter L (1998), A Worst Fabric Export System, Part I, System Development, Text. Res. J., 68, 680. Finnimore E (1985), Objective Evaluation of the Effects of Finishing on Wool Fabric Handle, Proc. of 7th Int. Wool Text. Res. Conf., Tokyo, Vol. III, 80. Dhingra R C, Lia D and Postle R (1989), Measuring and Interpreting Low Stress

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Fabric Mechanical and Surface Properties, Part II, Application to Finishing, Dry Cleaning and Photo Gradation of Wool Fabrics, Text. Res. J., 59, 357. Carr C M and Weedall P J (1989), Effect of Solvent Treatment on the Handle of Wool Fabrics, Text. Res. J., 59, 45. Okamoto Y and Niwa M (1982), Changes of Mechanical Properties and Handle of Fabrics for Men’s Suit’s by Dry Cleaning, J. Japan Res. Assn. Text. Ends Users, 23, 293. Dhingra R C, Mahar T J and Postle R (1985), Subjective Assessment and Objective Measurement of Wool and Wool Rich Fabric Handle and Associated Quality Attributes, Proc. of 7th Int. Wool Text. Res. Conf., Tokyo, Vol. III, 61. Shiomi S and Niwa M (1983), Changes in Mechanical Properties and Handle of Woven Fabrics Caused by Steam Pressing, Text. Mach. Soc. Japan, 33, 40. Mazzuchetti G and Demichelis R (1993), The Process of Chemical Setting of Wool Fabrics and its Influence on their Physical Character, J. Text. Inst., 84, 645. Rushforth M (1991), Soft Handle Treatment for Wool, Wool Sci. Rev., 67, 1. Joynar N M (1989), A New Class of Silicone Softeners, Text. Asia, 6, 55.

19

Assessing the comfort of woven fabrics: thermal properties

Abstract: This chapter first discusses the way body and brain mechanisms achieve comfort by the control of temperature, and how moisture plays an important role in this process. Measurement techniques for fabric heat and moisture transmission behavior are also described which allow the user to make an informed choice of fiber type and processing to provide the optimum comfort level achievable. Key words: fabric comfort, heat and moisture transmission, measurement techniques.

19.1

Introduction

Comfort is arguably the most important human attribute because every single member of the species from before birth to death is constantly striving to reach an optimum level of comfort. The effort may be conscious or subconscious and it continues whether one is awake or asleep. The comfort sought may be physiological, psychological or physical in nature; the body and mind are constantly working in unison to provide it. Textile materials are a major source of help in this search. Their contribution to psychological comfort lies in their ability to enhance the expression of one’s personality; provide concealment for the sake of modesty or to display status and wealth. Fashion, with its emphasis on color, style and texture, depends almost exclusively on textiles for success and is primarily aimed at mental comfort. The most significant contribution of textile goods to comfort is relevant for physiological and physical needs. The ability to survive in extreme climate against the elements is an important protective function provided by textiles that is most widely appreciated. The protective abilities of textile goods in providing a thermal barrier are most prevalent. It should be noted that the function of maintaining warmth in cold weather is not the only means by which textiles contribute to thermal comfort. To appreciate their total effect, it is necessary to consider how the mind and body interact to maximize comfort for any human being. Only then one can appreciate the complexity of what is actually happening and how clothing or other textile goods can aid in the process [1]. This chapter first discusses the way body and brain mechanisms achieve comfort for the attainment of thermal equilibrium. We shall then examine 330

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how these mechanisms operate in providing protection from being too hot or too cold, including the important role that moisture plays in this process. Finally, attention will rest on textiles, examining their important properties and ability to enhance thermal comfort, so that the user is able to make an informed choice of fiber type, construction factors and treatment mode in selecting a material to provide the optimum comfort level achievable. ISO 7730 defines thermal comfort as the condition of mind which expresses satisfaction with the thermal environment. This is achieved when there is a balance between the energy produced by a human being and the energy lost to the environment. The zone in which the temperature, moisture and air circulation are properly matched to maintain thermal and moisture balance is called the comfort zone. Moisture transfer from the skin through clothing is ideally in vapor form for necessary comfort. Fabric comfort is visualized in terms of tactile (sensorial), handle (hand-value) and thermal (feeling of hot or cold) transmission behavior (air permeability, water and moisture transfer, and heat transfer).

19.2

Thermal comfort in humans

The definition for any type of comfort is difficult to establish, simply because comfort is detected only in its absence. Comfort can be regarded empirically as a pleasant state of physiological, psychological and physical harmony between a human being and the environment; thermal comfort then becomes the manifestation of this harmony by any manner in which temperature or heat makes a significant contribution [2]. The way in which thermal comfort is achieved or enhanced by the body is complex, involving the brain, the central nervous system, the muscles and even the skeleton. To understand how it occurs, it is necessary to examine the way in which all these areas of human physiology function in collaboration to achieve the desired aim. The central control unit for all comfort sensations is the hypothalamus, a small organ located near the brain stem. This unit serves as the device setting all control points for body mechanisms and acts as a comparative unit to ensure that these mechanisms are operating at the correct level. Signals brought to it from all regions of the body are compared with the set point and adjustments made to restore the body’s operation to a harmonious state. The signals are derived from sensors located around the body and connected to the brain by the central nervous system. The sensors are of several kinds, including those which detect thermal changes, mechanical force (such as touch or pressure) and pain. An electrical signal in the form of a sharp spike is generated and passed to the brain through connecting sensory organs. It is received by the hypothalamus, which detects the signal and analyzes it to determine the state of the sensor’s environment. If this

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is unsatisfactory, a correction is applied via another network, the set of motor nerves controlling muscles which operate to apply the needed correction. The type of sensor and correction differs for each detection mechanism. In the present context, it is only important to consider two of them, the detection of thermal changes or pain. Thermal changes of a normal kind are involved in the process of thermoregulation, while pain occurs when burns are experienced. In both cases, the existence of a signal (temperature difference or imbalance between the sensor and the ambient conditions) is detected by the sensor, as discussed above. As the level of stimulus is increased, more signal spikes are passed along the nerve fiber, indicating to the brain that the deviation from an ideal state is increasing. The amplitude of the spike signal appears to be invariable, with only the frequency of spike generation increasing until a saturation point is reached. If the sensation increases still further, then more sensors in that locality begin to pass signals to the brain, warning of a potentially dangerous situation requiring correction in an urgent manner. It is the manner in which corrections are applied for this signal that distinguishes the various types of control mechanism [3–5].

19.3

The function of textiles in enhancing thermal comfort

The main purpose of textiles is to provide protection to the people using or wearing them. They should contribute as much aid as possible in preventing any change taking place in the body core temperature and in eliminating the possibility of skin burning. It is important to realize that the protection may be needed against both low and high ambient temperatures. Clothing may be needed to keep the body cool as well as warm and to prevent contact with an extreme environment that is too cold or too hot. Two types of application may be envisaged, one dealing with the usual conditions encountered in the expected variations of climate, and one where the temperature differences between the body and environment are abnormally high. The textiles needed for these two applications may generally be classed respectively as standard clothing or as specialist protective clothing, through there may be some overlap between the two in, for example, clothing to guard against sunburn. The most obvious function of standard clothing (which may include hats, gloves, scarves or other accessories as well as more familiar garments) is to cover the body to prevent the loss of too much heat on cold days or damage from sunburn when this is a hazard. For this purpose, thermal insulation is needed and clothing is ideally suited to provide it by forming a thermally insulating barrier. For the converse effect, where heat loss is required, a

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slightly different attribute, the ability to allow heat to be dissipated rapidly from the body, is necessary; some kind of enhanced airflow by garment design is more important in this case. In the case of thermally protective clothing, a more urgent need is to provide a flame-resistant barrier as well as contributing a more effective heat insulation layer to protect the body’s pain sensors from being affected or, ultimately, to prevent skin or underlying flesh from being burnt. Protection against the burn resulting from too rapid a flow of heat to the body, and from skin contact with an extremely cold surface should not be forgotten, though there is usually little possibility of major burns to underlying flesh being caused in such conditions because the temperature difference is so much lower than it is when the burn from a hot source is involved. It is obvious that the nature of a textile material will influence its thermal comfort properties drastically. The effect will be a complex one, combining factors controlled by fibers, yarns, fabrics and finishing treatments and their individual contributions will be difficult to identify. Nevertheless, general inferences can be drawn about the part each level of relevance in the process of modifying thermal comfort can be specified quite easily by consideration of characteristics of fibers, yarns, fabrics and garment assemblies. The heat transfer from body skin to the environment is affected by the fit of the garment, proportion of body surface area covered, geometry of human body and body movements. However, the thermal resistance of clothing plays a significant role. Clothing consists of a number of fabric layers and the air is trapped between additional layers of the fabrics. However, the boundary layer of air over the outer surface of clothing also plays a significant role. It must be remembered that the thermal resistance of a combination of garments is more than the sum of the thermal resistance of individual components.

19.4

Heat transfer through woven fabrics

Dry heat transfer takes place by conduction, convection and radiation. Another mode, evaporative heat transfer, is facilitated by moisture and vapor transmission. Heat transfer is affected by environmental factors such as air temperature, mean radiant temperature and mean relative air velocity and ambient humidity. Wind induces a reduction in thermal insulation of fabrics. In cold temperatures, wind causes rapid cooling of skin temperature known as the wind chill effect. Thermal resistance R is defined as the temperature differential across the body per unit heat flux density, (see Fig. 19.1):

R = DT/F

19.1

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Woven textile structure F d

T1

T2 (T1 > T2)

19.1 Thermal resistance model.

where T is the mean temperature of measurement and F is heat flux density. The SI unit of thermal resistance K .m2/W; tog is 1/10th of SI unit and clo ~ 1.55 togs. The most important factors which influence the dry thermal resistance of a fabric are thickness, cover factor, surface roughness and finishing or coating materials used on the fabric. Heat flows through materials differently depending on their thermal conductivity. It might be thought that the fiber content may have a major influence on thermal insulation, but this is not the case for two reasons. The first one is the fact that most textile fibers have similar values of thermal conductivity. The second is the far greater influence of textile structures on thermal insulation. Insulation is governed by the bulk structure of a fabric rather than by any of its individual parts, and air has a much higher insulation value than fibers. Thermal insulation is governed predominantly by the amount of entrapped air within a structure. Fibers which have an irregular surface, a non-circular cross-section, high levels of unevenness or a convoluted form will produce materials with better insulation than otherwise. Yarns which are loosely twisted, irregular, hairy and fancy will be better insulators. Fabrics loose in structure, soft, thick, porous or textured will generally insulate better than those which are flat, thin or level-surfaced. A clothing system is more effective in retaining heat if it consists of many garments layered over each other than if it is a single-layer garment of the same total thickness and weight, because of the presence of additional air zones between the garment layers. Garment design can also be used to improve heat retention, by taking care to ensure that air flow is restricted. The absence of any gaps between the clothing and the body at the places where the garment ends (such as the neck or wrists) and the tightening of the region near the waist by means of a belt will prevent air from circulating through the clothing to remove heat by convection from the surface of the body. When the body needs to be cooled to prevent overheating or minimum retention of heat is required, one can choose straight, uniform, even fibers

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and yarns to make thin, flat, open fabrics and use a single thin layer in garment to allow heat to escape efficiently. Garment design also has an effect: ample ventilation to permit the free movement of air over the surface of the body will allow convection currents to flow over the skin, removing heat more rapidly. The way in which the air is enclosed is critical. If it can leak out from the structure easily, its insulation value is lost. For this reason, loose fabrics will be poorer insulators than tight ones in windy conditions where a current of air impinges on the fabric. Conversely, if air cannot easily escape, then it will retain its insulation value and provide an additional barrier against heat loss by conduction. This factor accounts for the high insulation values of foam materials, which have totally enclosed air spaces in a closed-cell structure, in comparison with permeable materials with open-cell arrangements. There can be vastly different insulation values in a garment depending on its construction. If a fabric in which yarns are hairy or uneven is used to make a garment, then it will tend to have higher insulation than one from smooth, regular yarns. Similarly, a fabric made from loosely twisted yarns may be a better insulator than the one made from tightly twisted ones if the air remains entrapped; but will be a poorer one if the air flow through the structure takes place. A knitted structure will be able to resist heat flow in still air conditions better than a woven one, but the converse will be true if air flow occurs. It is for these reasons a knitted garment, made from hairy fibers loosely twisted into bulky yarns is warmer than a woven one indoors, but colder when the wearer is walking rapidly or encounters windy condition outdoors.

19.5

Moisture vapor transfer through woven fabrics

Water vapor is constantly being released by the skin. For comfort, this vapor should be able to escape easily from within the clothing microclimate to the outside through the fabric. Vapor transmission takes place by diffusion. In general, fabrics with high vapor permeability have low resistance to air flow and rainwater. Breathable fabrics enable water vapor transmission. The rate at which water vapor passes through a fiber depends on the nature of the fiber. Hydrophilicity of the fiber becomes an important criterion in case of dense fabric construction. Wicking behavior of fabric is also important in the moisture management of clothing. The transfer of moisture vapor through fabrics may not at first seem to be a comfort property related to thermal behavior, but a consideration of the body mechanisms discussed earlier conform that it is indeed a vital part of thermal comfort. Thermo-physiological comfort of a human being is mainly influenced by moisture transmission through clothing maintained by

336

Woven textile structure

perspiration both in vapor and liquid form. Moisture transmission through textiles plays a decisive role in the performance of sportswear, casual wear and protective textiles from a comfort point of view, textile processing and many other areas. Water vapor transmission through textiles is governed by Ficks Law [6]:

J Ax = – DAB

dC A dx

19.2

Where JAx is the rate of moisture flux; dCA/dx is the concentration gradient in the x direction; and DAB is the diffusion coefficient or mass diffusivity of component A (water vapor) diffusing through component B (porous vapor) diffusing through component B (porous media). Mass diffusivity of a particular fluid at a specific atmospheric condition depends on the nature of the porous media, such as its moisture regain and porosity. Liquid moisture flow through textile materials is controlled by two processes; wetting and wicking. Wetting is the initial process, involved in fluid spreading. It is controlled by the surface energies of the involved solid and liquid. In textiles, as water wets the fiber, the water enters the inter fiber capillary channel and is dragged along by capillary pressure. The magnitude of the capillary pressure is given by the following Laplace equation [6]:

P=

2g LV cosq Rc

19.3

where P is the pressure developed in the capillary channel, Rc is the radius of the capillary formed in the fibrous structure, g represents the surface tension at the interface between the various combinations of fiber (S), liquid (L) and air (V), and q is the contact angle between the liquid drop and fiber surface. gLVcosq is the resultant surface tension between fiber and liquid interface. The simplified forms of the above equation is known as Young-Dupre’s equation as given in equation 19.4:

P = g LV cosq

perimeter of capillary area of tge capillary

19.4

call the perimeter of capillary/area of the capillary ratio y where

gLVcosq = gSV – gSL

19.5

Absorption-desorption, diffusion and convection of vapor perspiration integrally with wetting and wicking of liquid perspiration are the prime parameters to maintain the thermo-physiological comfort index. The

Assessing the comfort of woven fabrics: thermal properties

337

perspiration of human body should be transferred to the atmosphere in order to maintain the thermal balance of the human body. The moisture vapor transmission rate (MVTR) through any clothing item will depend on the moisture content of the fabric, type of material used, the perspiration rate and atmospheric stimuli such as temperature, wind speed and relative humidity.

19.5.1 Moisture vapor transfer mechanism In some respects, a similar effect is evident when moisture vapor transfer is considered, since the molecules of air and moisture vapor are similar in size and subjected to the same type of mechanism regarding their movement through the structure. An important difference in this case is the fact that moisture can enter into a physicochemical reaction with some textile materials. Thus the movement of moisture away from the body may take place readily through a garment system consisting of loosely twisted yarns in either a knitted or a woven structure as long as a free path is available. A ‘breathable’ raincoat made from Gore-tex or Sympatex and worn in a light rain shower may allow moisture vapor to escape after passing through the garments worn beneath it, since these fabrics are reasonably permeable to moisture vapor. In a heavy storm when the outer surface of the fabric gets very wet and the wearer is producing large quantities of heat by battling against the elements, then the rate of perspiration production may well exceed the capacity of the raincoat to transmit moisture vapor against the resistance of wetted outer surface. In this case, the perspiration can no longer escape and the discomfort level rises drastically [7]. The complicating factor of potential reactions between water and the fibers from which the garment system is constructed may now exert an effect. If they are absorbent like most natural fibers, then there is a possibility of disturbing the water load to some extent, thus delaying the onset of sensible perspiration, unlike most synthetic fibers which are not absorbent. In the former case, the moisture is absorbed into the fiber and then distributed for evaporation over a wide area, rather than liquefying locally in one region, so the wearer’s awareness of any wetting from the extra heat load is delayed and there may never be noticeable perspiration wetting inside the system. There are equivalent compensating effects that can come into play due to structural variations when synthetic fibers are used. A yarn with medium twist may allow the process of wicking between fibers to occur better than one with loose twist (with little surface tension flow from contact between adjacent fibers) or with tight twist (preventing movement by making interfiber pore spaces too small to allow water flow). Similarly, the outer fabric structure of the raincoat can affect moisture flow. If it is made from too tight

338

Woven textile structure

a weave, moisture vapor transmission may be hindered so that perspiration wetness occurs quickly. Conversely, if the fabric is made more open to reduce the likelihood of this sequence of events, then liquid water may be able to enter into the structure in heavy rainfall conditions and prevent the escape of moisture vapor to cause discomfort wetness. The presence of water-resistant finishes, often used to prevent ingress from occurring, may reduce the pore size or interfere with the absorption or wicking behavior to change the moisture escape mechanism. The finish may be destroyed after extended use and its effectiveness is lost without the wearer being aware until a heavy rain storm reveals it.

19.5.2 Moisture loss from the body When perspiration takes place to cool the body, the water exuded through the skin appears initially as liquid which evaporates at once in comfortable situations and forms moisture vapor. This vapor is then removed from the vicinity of the body, either by convection or through the clothing worn on the person, carrying heat away with it. This second mode of loss, represented by transfer through clothing, needs to be examined in detail. When the moisture vapor reaches the inner surface of the fabric, several events can take place. The vapor may pass through the fabric system to the outermost surface to be carried away by the air. At the other extreme, it may be prevented from escaping through the fabric system if a component of the latter is impermeable, and will condense at some position in the system. The transfer of additional moisture vapor through the system will then be impeded by the liquid water layer so formed. The plane of condensation will gradually move inwards from the impermeable barrier until eventually condensation takes place at the inner layer of the system and at the surface of the body, marking the onset of sensible perspiration. The mechanism by which moisture, in liquid or vapor form, moves through the textile material will thus exert a great influence on comfort. Moisture vapor molecules move from the inner to the outer surface by a series of molecular collisions, either with the molecules of the textile structure or with the molecules of air or other moisture vapor. As long as the collisions take place relatively infrequently, there is time for the molecules to reach the outer surface and be lost, so the presence of moisture is never detected by person wearing textiles. If the collisions occur so frequently that there is no time for the molecule to escape before becoming trapped in a location where it is continually being bombarded by other newly arriving molecules. The vapor pressure in that region will increase until it is eventually greater than that associated with the evaporation of water and condensation to liquid water will take place.

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The flow now takes on an entirely different form. Liquid water moves by means of surface tension or wicking in the form of large aggregates of molecules. The rate is much slower and the presence of the liquid water can block the pores between the elements of the textile material unlike the situation with vapor which escape without any blockage. Once liquid water is present then the condensation process will increase since no vapor can escape through the blocked pores and the discomfort of the situation can only increase.

19.5.3 Air transmission Backer [8] reported that fabric interstices are related to cloth structure. Other parameters which influence the pore size distribution are yarn crimp, yarn ballooning and yarn flattening. He classified the primary and secondary features of woven fabrics in the design of material which must satisfy air permeability requirements. The air permeability of a fabric increases with increase in synthetic fiber content in blended yarns. The fabric comfort is not affected adversely by the addition of synthetic fibers to the blend [9]. Kullman et al. [10] studied the air transmission behavior of fabrics having different yarn types such as ring spun, open end yarn, core-spun with filament yarn and zero-twist filament yarn, and compared in grey and bleached states. They added that air permeability of yarn is higher with externally wrapped filament. For the core spun with twistless core, with higher bulk provides greater cover the yarn with a twisted core. The level of yarn twist is directly proportional to air permeability. Crimp did not add a trend but zero twist yarn showed low air permeability with least crimp. The flat yarns greatly reduce air permeability. Rainford [11] studied air permeability of fabrics and defined the intrinsic permeability and its utility to calculate air permeability of a fabric at given pressure. Fiber fineness improves the available surface area per unit fabric area, and consequently resistance against air transmission rate increases [12]. The air flow through a fibrous plug under small pressure gradient is described by Kozeny’s equation:



Ê ˆÊ 3 ˆ Q = 1 Á A2DP ˜ Á e 3˜ k Ë S m L¯ Ë1 – e ¯



19.6

where Q is the volume rate of flow through the plug, k is the proportionality factor depend on the cross-sectional shape of the fiber and on their orientation with respect to direction of air flow an A is the cross-sectional area of the plug. The porosity of the plug of fibers is given by

340

Woven textile structure



e =1– m rAL

where m is the total mass of the plug and r is density of the fiber. The flow equation can therefore be rewritten to give a resistance to air flow, R, as

kmm 2 rS 2 L2 R = DP = Q (ral – m )3

19.7

If the plug consist a fixed mass of fiber uniformly compressed in cylinder of fixed dimension then for a given fiber type A, L, m and P are constant over a range of normal room temperature. Thus for a fixed pressure drop, DP is part of the experimental conditions and provided that k can also be maintained constant. Q is inversely proportional to the square of the specific surface S [13].

19.6

Measuring thermal comfort

A method for predicting the thermal comfort of fabric comprises the provision of (i) a perspiring hot plate to simulate the skin thermoregulatory responses of a human, (ii) fluid flow through the fluid input source and a power flux through the thermal input source to correspond to human perspiring and thermal output level, and (iii) placing a fabric on top of the perspiring hot plate. The temperature of the top surface of the plate as the temperature changes to simulate the skin surface thermoregulatory responses can be observed. The temperature profile is analyzed and the comfort level of the fabric from the results is determined [14]. Properties which determine the comfort of garments, for example, thermal retention or transmission, moisture vapor permeability and water resistance, are examined. Fiber content, yarn structure and fabric construction are related to garment comfort. Potential effects of methods for measuring these parameters are outlined in a research paper [7]. Suitable temperature and humidity values are proposed as applied indices of thermal-wet comfort of textiles based on the human body clothing environment system. Through physical measurement of some layers of fabric and wear tests of the corresponding apparel, it can be known that wearing apparel is fundamentally in accordance with the proposed indices of thermal-wet comfort state. The thermal insulation of an apparel system which the human body needs can be estimated in terms of the clo value: 1 clo is the thermal insulation to withstand a temperature difference of 4°C between two sides of fabric, when the moisture transmission occurs through the textile material [15–17]

Assessing the comfort of woven fabrics: thermal properties

341

The thermal-wet comfort properties of textiles under the reverse temperature field when the environment temperature is higher than that of human body is also an appropriate consideration. Four quantities, i.e. equivalent thermal resistance, thermal resistance, resistance to water vapor transmission and air permeability, are physical indices of thermal-wet comfort properties of textiles under this condition. The Clothing Microclimate Testing Meter is used to determine the indices of textiles. The statistical analysis helps to discover the relationship between these indices and the results from wearing-clothing test [18,19]. The comfort of a fabric cannot be expressed by a mathematical equation. The assessment of comfort is based on parameters which can be determined objectively and also some factors which are quite subjective. The areas in which textile comfort is of most concern are underwear, sportswear and individual protection. EU standards and test methods associated with the textile comfort parameters such as water resistance, wind resistance, breathability and thermal properties, anti-UV properties, antimicrobial properties, and electrostatic properties are available [20].

19.7

References

1. Slater K (1985), Human Comfort Charles C Thomas, Springfield IL. 2. Kothari V K (1999), Testing and Quality Management, IAFL Publication, New Delhi. 3. Hoffmeyer F and Slater K (1981), J. Text. Inst., 72, 183. 4. Willard J J and Wondra R E (1970), Text. Res. J., 40, 203. 5. Fahmy S M A and Slater K (1976), J. Text. Inst., 67, 273. 6. Das B, Das A, Kothari V K, Fanguiero R and Araujo M de (2008), Fibers and Polymers, 9(2), 225–231. 7. Arora H (2006), Development of pathogen protective surgical gown, M. Tech. Thesis, I.I.T. Delhi. 8. Backer S (1951), Text. Res. J., 21, 52–69. 9. Knight B A, Hersh S P and Brown P (1970), Text. Res. J., 40(9), 843–852. 10. Kullaman R M H, Graham C O, and Ruppenicker G F (1981), Text. Res. J., 51, 781–786. 11. Rainford LW (1946), Text. Res. J., 16(10), 473. 12. Lee S and Ovendor F (2007) SK ‘Transport properties of layered fabric systems based on electrospun nanofibers’, Fib & Polym. 8(5) p501–506. 13. Morton W E and Hearle J W S (2008), ‘Fiber fineness in transverse direction’, in Physical Properties of Textile Fibers, Woodhead Publications/CRC Press, 4th ed., p115–116. 14. Hamouda H (1998), Modeling of thermal protection outfits for fire exposure of human skin and related method for predicting fabric comfort level, US Patent 7216068 – Digitized thermal functional design of textiles and clothing. 15. Slater K (1977), Text. Prog., 9(4). 16. Gibson P W (1993), Text. Res. J., 63(12), 49–764. 17. Shi F (2000), Text. Res. J., 70, 247−255.

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18. Yao B G, Li Y, Hu J Y, Kwok Y L and Yeung K W (2001), The Sixth Asian Textile Conference, Hong Kong, China. 19. Yao B G, Li Y, Hu J Y, Kwok Y L and Yeung K W (2001), Text. Res. J., 71(12), 1033–1045. 20. Alimaa D, Matsuo T, Nakajima M and Takahashi M (2000), Text. Rese. J., 70(11), 985–990.

20

Modeling woven fabric drape

Abstract: Fabric drape is one of the many attributes that influences the aesthetic appearance of a fabric. This chapter discusses various aspects of drape including classification, measurement techniques and its relationship with fabric mechanical properties. The relationship between fabric low stress mechanical properties and drapeability is also described. Methods for prediction of drapeability of woven fabrics are discussed. Prediction of drape using artificial neural network (ANN) modeling is also discussed. Key words: fabric drape, drape measurement, predicting drape.

20.1

Introduction

Drape refers to the falling behavior of the cloth along a curvilinear track. The cloth drapes and compresses internally owing to gravity, resulting in a flared shape [1]. It is one of the most important low stress mechanical properties of the fabric that determines many practical qualities of clothing. When a fabric is draped, certain parts of it form curves in more than one direction. This property enables a fabric to be molded into desirable shape and produce a smooth flowing form under its own weight. This unique characteristic provides a sense of fullness and a graceful appearance, which distinguishes fabrics from other sheet materials. Fabric drape is also one of the many attributes that influence the aesthetic appearance of a fabric and has an outstanding effect on the formal beauty of the cloth. Drape is important for the selection and development of textile material for apparel industries. Thus, the investigation of fabric drape has attracted much attention.

20.2

Two-dimensional and three-dimensional drape

Drape can generally be classified into two categories, namely 2-D drape and 3-D drape. In 2-D drape a fabric bends under its own weight in one plane while 3-D drape allows a fabric to be deformed into folds in more than one plane under its own weight.

20.2.1 2-D drape Peirce developed the ‘cantilever method’ for measurement of fabric bending properties and used bending as a measure of fabric drape [2]. The Peirce 343

344

Woven textile structure

cantilever test is performed on the commercially available Shirley stiffness tester in which a rectangular strip of fabric is allowed to bend under its own weight to a fixed angle of 41.5° when projected as a cantilever. A stiffer fabric needs a longer projected length. To measure bending length, a fabric sample is placed under a metal ruler and slowly moved forward until the tip of the specimen viewed in the mirror cuts both the index lines and then the bending length is read. The mean value for the bending length is calculated by testing the specimen four times on each end and again with the strip turned over. Using the average value of bending length c, flexural rigidity G and bending modulus q of the fabric can be estimated by equations 20.3 or 20.4 and 20.5 or 20.6 respectively [3]. From the fabric length (l) and angle (q), bending length (c) can be calculated using Equations 20.1 and 20.2. Flexural rigidity of the fabric can be calculated from the bending length c and fabric weight using the equation 20.3 or equation 20.4 where w1 is the cloth weight in ounces per square yard, and w2 is the cloth weight in gram per square centimeter. Bending modulus q is calculated by using equation 20.5 or equation 20.6 considering g1 is the fabric thickness in thousandths of an inch, or g2 is the fabric thickness in centimeters respectively.

c = l f1 (q)

20.1 1/3



Ècos 1 q ˘ 2 ˙ f1 (q ) = Í Í 8 tanq ˙ ÍÎ ˙˚

20.2



G = 3.39 ¥ w1c3 mg/cm

20.3



G = w2c3 ¥ 103 mg/cm

20.4



q = (732G)g13 kg/cm2

20.5



q = (12G ¥ 10–6)g23 kg/cm2

20.6

Theories of fabric cantilever with different weight distributions Differential equations are used to describe the drape profile of fabric cantilevers having distributed or concentrated weight at the tip. Peirce’s cantilever method is based on the concept of the classical beam theory using the Bernoulli-Euler law. The Euler law states that the bending moment of a beam is proportional to the radius of curvature as shown in equation 20.7. The applied bending moment of the beam is equal to the product of the applied load on the cantilever to the perpendicular distance of the line of action. Two assumptions are made that the curvature is evaluated by the

Modeling woven fabric drape

345

approximate equation and the change in length of moment arm during beam deflection is ignored [4,5]. Since /l/R ≈ d2y/dx2 (R is the radius of curvature of the beam)

M = Bd2y/dx2

20.7

Two cases of applied loading are considered; one with distributed weight and the other with the concentrated weight. Fabric cantilever with concentrated weight In this case the applied load W is acting on the free tip end of the cantilever as shown in Fig. 20.1, and equation 20.8 is developed:

M = Bd2y/dx2 = –Wx

20.8

where M is bending moment and B is bending rigidity. Double integration with the boundary condition gives equation 20.8. Bending rigidity of the beam can be found from the deflection angle:

tanq = wl3/3B

20.9

Peirce modified this equation by multiplying with a factor cos0.938q based on results from his experiments, as shown in equation 20.10:

B/wl3 = cos0.938q/3tanq

20.10

Fabric cantilever with distributed weight The deflection of a cantilever due to the distributed load under its own weight is shown in Fig. 20.2. A uniformly distributed weight W is applied along the length of the cantilever and thus equation 20.9 can be rewritten to form equation 20.11: l B

ymax

w

20.1 Cantilever beam with concentrated load.

346

Woven textile structure l B

W/unit length

ymax

20.2 Cantilever beam with uniformly distributed load.

M =B

2 d2y = – Wx 2 2 dx

20.11 Double integration with the boundary conditions gives equation 20.12. Bending rigidity of the beam can be obtained from the deflection angle.

tanq = wl3/8B

20.12

Peirce modified this result by multiplying with a factor of cosq/2, based on his experimental studies as shown in equation 20.13:

B = cos(q /2) 8tanq Wl 3



c3 = B/W



c3 = l 3

cos(q /2) 8tanq

20.13

20.14

Peirce defined the term B/w equal to the cube of the bending length c which is a quantitative value and a measure of strip’s drapeability in two dimensions. Substituting the value for B/w equation 20.13 results in equation 20.14, from which bending length can be evaluated from the extended fabric length l that bends to an angle q under its own weight. Peirce’s cantilever formula (equation 20.14) is extensively used to describe the characteristics of fabric stiffness and fabric drape in two dimensions.

20.2.2 3-D drape Chu et al. studied 3-D fabric drape using the FRL drape meter [6]. He quantified the drapeability of a fabric into a dimensionless value drape coefficient. Cusick re-investigated this experimental method by using a parallel light source which reflects the drape shadow of a circular specimen

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347

from a hanging disc onto a paper ring [7]. He also modified the calibration of Chu’s drape coefficient in terms of paper-weighing method. In recent years, the emphasis has been on improving the efficiency and accuracy of Cusick’s drapemeter by using digital readout of the drape shadow using photovoltaic cells [8], and computerized image analysis [9, 10]. A digital display gives the amount of light being absorbed by the photovoltaic cells, which is related to the amount of drape of the fabric specimen. The method is more convenient and accurate than the paper tracing method. The image processing measurement technique and advantages of this method are discussed in Section 20.4.

20.3

Subjective and objective measurement of drape

Drapeability of a fabric is primarily concerned with aesthetic appearance of the garment. It is therefore affected by psychological factors which relate to human perception and fashion. Subjective evaluation of fabric drape is an investigation aimed at understanding the human perception of drape of fabrics. Subjective evaluation of the drape of a fabric involves the rating of drapeability on a garment such as a skirt. The numerical value of the drape coefficient calculated from the drape measurement is not sufficient to represent drape behavior. Drape is differentiated even when fabrics have the same value of drape coefficient percentage. Cusick [11] mounted semicircular cotton and rayon fabrics in the shape of a skirt on a model. The model was rated to see which skirt could drape best. The results indicated that a good drape assessed by objective measurement almost matches one assessed by the subjective selection. However, the subjective rating of fabric drape is rather inconsistent; the best drape fabric may not be the preferred one. Collier et al. [12] reported that subjective drape is affected by the length of draping fabric on the pedestal. Cusik [7] calculated the drape coefficient (DC) as: Ad – A1 20.15 ¥ 100 A2 – A1 where Ad is the area of draped shadow, A1 is the area of the disc and A2 is the area of the fabric. It was later modified and the new drape coefficient is defined as the ratio of paper weight of the drape shadow W2 to that of the specimen W1: DC(%) =

W2 20.16 ¥ 100 W1 This formula is shown in dimensionless quantity. The drape coefficient percentage is high for stiff fabrics but low for limp fabrics. These methods have several disadvantages; testing is time consuming, tracing of the pattern DC(%) =

348

Woven textile structure

by hand is highly dependent on the skill of the operator, the light source needed is of special type, the mass variation in the paper may cause error in the calculation of the drape coefficient. The drape coefficient does not sufficiently describe the aesthetic appearance. It may be influenced by geometrical factors such as number of nodes and curvature of the draped fabric [12]. Equivalent drape coefficient is possible for two different fabrics. Thus it may be better to use the distribution of number of nodes with the drape values to describe the aesthetic appearance. In view of these constraints and also with the advent of much convenient image processing technology, objective evaluation of drape came into existence. Objective evaluation of fabric drape involves the measurement of the drapeability in terms of drape coefficient, drape profile and node analysis from Cusick’s drapemeter with the help of digital image processing technique [13].

20.4

Drape measurement by digital image processing

The measurement of drape parameters based on digital image processing technique is shown in Figs 20.3 and 20.4. In this image analysis system, the shadow projected from the fabric is quantified into a binary image after being digitized. The threshold value that sets the criteria for converting a gray scale image into a black and white image is controlled at the user interface of the system. For this reason, this image analysis method is not influenced by the fabric color. The digitized binary image is processed with a closing operation which removes noise and segmentizes the shadow image of the draped fabric from the background image. The closing operation is a dilation operation followed by an erosion operation. This operation fills in single pixel object abnormalities. After digitizing the image of the draped A B

C D E A Image acquisition chamber B Camera C Lighting arrangement D Fabric sample E Processor F Display

20.3 Digital drape meter.

F

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349

20.4 Draped fabric image.

fabric, the image analysis system searches the boundary between the fabric shadow and the central disk on the drape meter and the boundary between the fabric shadow and the outer region of the fabric shadow. Then it calculates the radius of the boundary point at an interval of 1°. So it calculates 360 radii (n = 360). By using this boundary description, the software calculates the different drape parameters such as drape coefficient drape distance ratio, fold depth index, amplitude and number of nodes from the model diagram shown in Fig. 20.5. A suitable code is developed to find the center of the image and distances to the edge of the fabric are obtained by rotating the image by 1°. Repeated measurements gave less variation than the conventional manual method. The image analysis system makes it quite easy to take multiple measurements [14,15].

20.4.1 Drape parameters A drape profile obtained from digital image processing-based drape image is shown in Fig. 20.5 from where the polar coordinates of the profile image can be obtained by using following equations:

Xi = ri cos qi



Yi = ri sin qi



average radius Ravg = (1/n)∑ri

In image processing method, apart from drape coefficient a number of other important drape parameters can be determined for a complete analysis of drape

350

Woven textile structure Y

(xi, yi) ri

qi X

20.5 Schematic diagram of a drape profile.

profile. These parameters are obtained by processing a 2-D drape shadow image by properly developed software and the results of these parameters are given in Table 20.1. These drape parameters are defined below. Drape coefficient, DC Drape coefficient is the percentage of the area from an annular ring of fabric covered by a vertical projection of the draped area. It depicts the fabric falling behavior when supported partially like a garment on the body of the wearer. It is denoted by: As – A1 20.17 A 2 – A1 where AS is the area of the draped fabric image, A1 is area of the fabric supporting disc and A2 is the area of the undraped fabric sample. DC =

Drape distance ratio (DDR) Drape distance ratio is the corresponding ratio of the draped and undraped fabric annular radii. It helps garment designer for accurate modeling of the drape profile of the fabric. The drape distance ratio is expressed by: r2 – rs 20.18 ¥ 100% r2 – r1 where rs is radius of the draped fabric image, r1 is radius of the fabric supporting disc and r2 is radius of the undraped fabric sample. DDR =

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Table 20.1 Data from the analysis of standardized residuals Drape parameters

Mean

SD

N

AD

p

DC DDR FDI Amplitude N

64.68 27.21 18.46 12.30 4.6

8.756 8.242 9.462 8.245 1.916

65 65 65 65 65

0.424 0.454 0.461 0.398 0.384

0.310 0.262 0.215 0.168 0.209

Fold depth index (FDI) Fold depth index is the ratio of difference between maximum and minimum radii of the fabric draped image to the annular radius between support disc and undraped fabric. This is an index showing the depth of the folds generated with reference to undraped fabric.

FDI =

rmax – rmin ¥ 100% r2 – r1

20.19

Amplitude Amplitude (A) is half the difference between maximum and minimum radii. It gives the depth of the drape profile with respect to the radius of draped fabric image:

amplitude = (rmax – rmin)/2

20.20

where rmax is the maximum radius of the draped fabric image profile, rmin is the minimum radius of the draped fabric image profile and ravg is the average radius of the draped fabric image profile. Number of nodes, (N) N is the number of peaks in the draped shadow and gives an idea about the formation of folds during actual wearing conditions. During drape test, the fabric sample actually bends at the edges of the supporting disc in order to get the folds. A higher bending rigidity prevents the folds being formed and thus the fabric remains more towards the flattened state, thereby having a higher drape coefficient, drape distance ratio, amplitude and fold depth index. Lower bending rigidity offers less resistance to formation of folds and a smaller shadow is generated, giving low coefficient value with more nodes. Nodes in the draped fabric shadow are basically the folded apexes formed due to the fabric being hung from the supporting disc or platform. However, a higher drape coefficient value may not always be supported by fewer nodes.

352

Woven textile structure

Besides the above analysis, the image processing system saves both time and paper. The drape coefficient along with other drape parameters can be evaluated accurately within a few seconds. The measuring system is timeefficient and change of drape can be measured and comparisons made within a short time [16].

20.5

The relationship between drape and the mechanical properties of woven fabrics

The drape coefficient provides an objective description of drape deformation in three dimensions, but the study of 3-D fabric drape is not independent. In general, fabric drape is closely related to fabric stiffness [17]. Very stiff fabrics have drape coefficients approaching 100%; very limp fabrics have drape coefficients of about 30%. Drape coefficient is about 90% for starched cotton gingham. In other words, the study of 3-D drape in terms of drape coefficient percent is empirically related to 2-D drape in terms of bending properties. Chu et al. found that drapeability is dependent on three basic fabric parameters: Young’s modulus Y, the cross-sectional moment of inertia I, and fabric weight W. Yamada et al. [18] also reported that when bending rigidity (B) per unit weight (YI/W) of fabric is similar to each other, drape coefficient percent and deflection angle also give similar values [19]. Cusick proved by statistical inference that the fabric drape involves curvature in more than one direction, and the deformation is dependent on the shear angle (A) in addition to bending length c [20]. He used 130 fabric samples for a multiple regression analysis and developed an equation (20.21) to establish relationship between drape coefficient, bending length (c) and shear angle (A).

DC = 35.6c –3.6lc2 –2.59A + 0.0461A2 + 17

20.21

For this equation, residual sum of squares of the regression is the smallest when ‘c’ and ‘A’ are both considered to be the main factors influencing the drape coefficient percent. Mooraka and Niwa generated an equation to predict fabric drape using data from the KES system and concluded that fabric weight and bending rigidity were the most important factors. In their study, drape coefficient percent is found by (B/W)l/3. The correlation coefficient r between drape coefficient percent and (B/W)l/3 is 0.767, which is greater than the coefficient value of 0.686 between drape coefficient percent and B only. The use of bending rigidity from the warp, weft and bias direction on a regression equation allows for better prediction of drape coefficient percent than by using a mean bending rigidity. Physical properties which contribute greatly to the drape coefficient percent are bending properties followed by weight,

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353

thickness, and shear properties. When bending and shearing hysteresis are large, drape coefficient percentage would be large and unstable [21]. Niwa and Seto published a paper concerned with the relationship between drapeability and mechanical properties of fabrics. They used mechanical parameters (B/W)1/3, (2HB/W)1/3, (G/W)l/3 and (2HG/W)l/3 as independent variables, where B, 2HB, W, G and 2HG are bending rigidity, bending hysteresis, weight per unit area, shear stiffness and shear hysteresis respectively. These parameters were derived from the analysis of the bending of a fabric cantilever having hysteresis in bending and shear by applying the elastic theory [22]. It is concluded that 3-D drape in terms of drape coefficient percentage is closely associated with 2-D drape in terms of bending length and bending rigidity. Nevertheless, drape coefficient percentage from 3-D drape study is also influenced by other fabric physical properties which include shear and tensile properties as well as fabric weight and fabric thickness [23,24]. Although 2-D drape study is only a partial measure of drape behavior, yet it is the most important index for predicting 3-D drape behavior. Many researchers have used the 2-D drape of a fabric cantilever to verify mechanics models, the results of numerical and theoretical investigations and the accuracy of soft computing.

20.6

Low stress mechanical properties of woven fabrics and drapeability

Drape is an essential parameter to decide both appearance and handle of fabrics. It is a secondary determinant of fabric mechanical properties and influenced by the low stress mechanical properties such as bending rigidity, formability, tensile, shear properties and compressibility of the fabric [25]. Fabric drapeability is expected to be influenced significantly with the change in fiber composition, fabric construction and aerial density as these parameters influence low stress mechanical properties of fabric. The fabric becomes more flexible and may lose structural stability with decrease in fabric aerial density. Therefore an understanding of the relationship between drape parameters such as number of folds, depth of folds, evenness of folds together with the drape coefficient with fabric low stress mechanical properties would help the fabric manufacturer to set construction parameters during weaving process. There is strong correlation between fabric bending rigidity and drape parameters. Bending rigidity is related to the tensile properties as:

G = E ¥ I

20.22

where G is bending rigidity, E is Young’s modulus and I is moment of inertia, which for a circular cross-section is equal to p r4.

354

Woven textile structure

Since drapeability is directly related to bending rigidity, it is obvious that it should be influenced by the tensile properties of the fabric, particularly at low stress levels. Among the low stress tensile parameters, tensile energy is reported to have strong correlation with drapeability. A good correlation between tensile energy and drape parameters suggests that a fabric with higher tensile energy is less susceptible to draping or falling from the edge of a contour. Tensile energy is analogous to initial modulus of the fabric and this actually enables the fabric to overcome tensile deformations. Draping under gravitation is also a tensile phenomenon against this energy. Thus a higher tensile energy means less tensile deformation under gravity. This enables the fabric to remain towards the flatter side. Thus a higher drape coefficient value is obtained. The correlation between low stress extensibility and drape parameters is negative. A higher extensibility always favors the folding and hanging of fabric at the edges of the platform and thus a smaller shadow is formed, giving lower drape coefficient. Shear refers to the movement of yarns in the fabric relative to each other. Shear deformation in a fabric is more relevant in predicting the end-use performance in real life as the fabric is subjected to stresses in all possible directions. The shear rigidity of fabrics at low stress levels gives very good correlation with the drape parameters. When the fabric sample is supported on the disc, it hangs down from the edges at all possible points of deformation. Inter-yarn movement in the fabric allows deformation in all directions. Higher shear rigidity prevents folding or hanging and thus a high drape coefficient is obtained. When a fabric is draped on the edges of a contour, there is a compressional deformation at the point of bending. Thus fabric compressibility is another low stress mechanical property which influences the drape behavior of a fabric. The correlation shows that fabrics with higher compressional energy give higher drape parameters. A highly compressible fabric does have high compressional energy and can absorb and withstand compressive forces to a greater extent at the deforming points. This prevents the folding at the deforming points and a higher drape coefficient results.

20.7

Modeling of woven fabric drape

Conventional analysis of drape does not help to characterize the fabric appearance in true usage. There is a need to determine the complete drape profile in three-dimensional views to have a realistic appreciation of fabric aesthetic properties. This approach would help to develop new products to fulfill the requirement in terms of functionality and aesthetic characteristics. In this context simulation and modeling of textile products appear to be a practical proposition in which both properties and performance of the fabric can be assessed using the basic raw material, yarn and fabric structure as input parameters. Warp and weft yarns of woven fabrics and garments undergo

Modeling woven fabric drape

355

large displacements under their own weight during drape deformations. In general, drape deformations are large but the resulting strains are small. During use, fabrics and garments usually come into contact with human bodies, forming complicated final shapes with various double-curved folds. Furthermore, fabrics exhibit material anisotropy as their mechanical properties in the warp and weft directions differ. Many modeling tools are now being used for predicting drape behavior of apparel fabric [26–30]. In order to compare the predictability of various models fabric samples were tested for their drape parameters. Fabric constructional details are used as input parameters of the models and drape parameters were predicted by using three different models such as statistical model, finite element analysis (FEA) and polar coordinate technique for comparison.

20.7.1 Drape prediction by statistical method In order to determine the combined effect of fabric low stress mechanical properties on drape parameters and the contribution of individual properties in deciding the falling behavior, a multiple correlation is exercised and regression equations are derived with respect to all drape parameters discussed above. These regression equations are used to predict drape parameters and the results are compared with the drape value obtained from image processing method. The interdependence between drape parameters and the mechanical properties of fabrics are also studied. Before constructing a predictive model using multivariate analysis, the relationship of the variables must be assessed using a matrix plot as shown in Fig. 20.6. It is assumed that the fabric mechanical properties are linearly associated with the drape parameters and all input parameters follow normal distributions. A linear regression model as given in equation 20.23 is used [31].

Y = a + b1 ¥ X1 + b2 ¥ X2 + ... + bn ¥ Xn

20.23

where X1…n are the fabric mechanical properties, a and b1…n are the constants, and Y is one of the drape parameters. To construct a reliable and simple predictive equation, the backward elimination method is used, in which the starting point is the model with all of the available variables for the model construction. Then the insignificant variables are deleted by using the a (confidence interval) and p value at each testing stage. This process stops when all variables in the model have values that are less than or equal to the specified a value (0.05). Minitab 15 software was used to develop the regression model. Alpha (a) is the maximum acceptable level of risk for rejecting a true null hypothesis (type 1 error) and is expressed as a probability ranging between 0 and 1. Alpha is frequently referred to as the level of significance. Alpha is set before beginning the analysis then the p

356

Woven textile structure

20.6 Matrix plot for fabric low stress mechanical properties.

values are compared with alpha to determine significance. If the value of p is less than or equal to a level, the null hypothesis is rejected in favor of the alternative hypothesis. If p is greater than a, the null hypothesis cannot be rejected. The predictive equations for different drape parameters are given in Equations 20.24 to 20.28. The symbols used in Fig. 20.6 and in equations 20.24–20.28 are the 17 parameters which describe low stress mechanical properties of the fabric obtained from KES instrument [32].

DC% = 57.47 + 0.47 ¥ WT + 97 ¥ B + 118 ¥ HB – 1.42



¥ G – 0.44 ¥ 2G5 (R2 = 0.76)

20.25

DDR = 12.8 – 0.170 ¥ RT + 5.1 ¥ B – 6.4 ¥ 2HB



+ 13.7 ¥ G + 1.23 ¥ 2HG – 0.5 ¥ 2HG5



+ 32 ¥ W (R2 = 0.78)



20.24

N = 7.569 + 0.044 ¥ RT– 41.1 ¥ B + 10.4 ¥ 2HB – 1.67



¥ G – 90 ¥ W (R2 = 0.82)

20.26

FDI = 2.103 – 0.89 ¥ EM – 0.28 ¥ RT + 74 ¥ B – 59



¥ 2HB + 21.2 ¥ G – 1.06 ¥ 2HG5 (R2 = 0.76)

20.27

Modeling woven fabric drape

357

amplitude = 1.579 + 82.7 ¥ B – 0.4 ¥ 2HG



+ 0.39 ¥ 2HG5 + 0.054 ¥ RC (R2 = 0.74)



20.28

The above equations demonstrate that bending, shear property and fabric weight influence the drape parameters most, whereas tensile and compressional properties have less influence. The assumption of normality was checked by constructing normal probability plots of the standardized residuals and these plots are presented in Figs 20.7–20.11. These plots show that the data follow normal distribution, as the indicated p value for the Anderson–Darling (AD) normality test is far in excess of 0.05. The p values and the Anderson–Darling (AD) values are shown in Table 20.2. The Anderson–Darling statistic was used to measures how well the data follow a normal distribution. The better the distribution fits the data, the smaller this statistic will be. The hypotheses made for the Anderson-Darling test were:

H0: The data follow a normal distribution



H1: The data do not follow a normal distribution

20.7.2 Drape prediction by FEA The finite element method (FEM) is a numerical method used to solve real world problems that involve complicated physics, geometry and/or boundary

99.9 99

Percent

95 90 80 70 60 50 40 30 20 10 5 1 0.1 30

40

50 60 70 Standardized residuals of DC

80

90

20.7 Probability plot of standardized residuals of drape coefficient.

358

Woven textile structure 99.9 99

Percent

95 90 80 70 60 50 40 30 20 10 5 1 0.1 0

10

20 30 40 Standardized residuals of DDR

50

60

20.8 Probability plot of standardized residuals of drape distance ratio. 99.9 99

Percent

95 90 80 70 60 50 40 30 20 10 5 1 0.1 –10

0

10 20 30 Standardized residuals of FDI

40

50

20.9 Probability plot of standardized residuals of fold depth index.

conditions. In FEM, a given domain is viewed as a collection of sub-domains, and over each sub-domain the governing equation is approximated by any of the traditional varitaional methods. The main reason behind seeking the approximate solution on a collection of sub-domains is that it is easier to

Modeling woven fabric drape

359

99.9 99

Percent

95 90 80 70 60 50 40 30 20 10 5 1 0.1 0 5 10 15 20 25 Standardized residuals of amplitude to average radius value (ARR)

20.10 Probability plot of standardized residuals of amplitude. 99.9 99

Percent

95 90 80 70 60 50 40 30 20 10 5 1 0.1 –4

–2

0 2 4 6 Standardized residuals of N

8

10

20.11 Probability plot of standardized residuals of N.

represent a complicated function as collection of simple polynomials. In this study ABAQUS 6.6 was used for the simulation and analysis of the fabrics [33].

360

Woven textile structure

Table 20.2 Drape parameters of the fabrics Sample no.

DC (%)

DDR (%)

FDI (%)

Amplitude (cm)

N

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10

72.54 73.51 71.32 69.37 73.83 68.58 64.37 63.71 59.95 58.91

47.65 51.54 56.53 55.59 69.62 65.53 73.28 77.76 67.52 72.36

53.56 62.27 61.45 59.83 70.72 68.61 79.74 72.88 83.52 74.39

1.15 1.23 1.33 1.29 1.24 1.52 1.41 1.34 1.786 1.86

5 4 3 5 4 5 4 5 4 4

Domain discretization In this step, the complex fabric domain is represented as a collection of simple sub-domains or elements. These elements are the cross-over points of the warp and weft. Each finite element is viewed as an independent domain by itself. The discretization of the fabric is illustrated in Fig. 20.12. The elements are connected to each other point called nodes and in this case it is 4 with 24 degrees of freedom. The domain is assumed to be a uniform mess. Constitutive equations In formulating FEM equations for elements, a local coordinate system is used in reference to global coordinate system that is defined for the entire structure. In this study, the model is assumed to be a linear elastic model. So the total stress is defined from the total elastic strain as shown in equation 20.29:

s = Deleel

20.29

where s is the total stress, Del is the fourth-order elasticity tensor and eel is the total elastic strain. To define the material properties, the fabric is considered to be an orthotropic material which has two principal directions, warp and weft and the fabric is discretized to quadrilateral shell elements. In this study E1 (Young’s modulus in warp direction), E2 (Youngs modulus in weft direction), n12 (Poisson ratio in bias direction), G12 (shear modulus in X–Y direction), G13 (shear modulus in X–Z direction) and G23 (shear modulus in Y–Z direction) are used to define the orthotropic material. In this study (1,2) surface is the surface of plane stress, so that the plane stress condition is s33 = 0. The shear moduli G13 and G23 are included because as they are required for modeling of transverse shear deformation in the shell [34].

Modeling woven fabric drape

361

D C

O

A

B

20.12 A typical grid-point ‘O’ and its four neighborhoods in the fabric mesh.

In this case the stress–strain relationship is expressed as shown in equation 20.30: Ï s 11 Ô Ô s 22 ÔÔ s 33 Ì Ô s 12 Ô s 13 Ô ÔÓ s 23

¸ Ê D1111 D1122 D1133 0 0 0 ˆ Ï e11 Ô Á ˜Ô 0 0 ˜ Ô e12 Ô Á 0 D2222 D2233 0 ÔÔ Á 0 0 D3333 0 0 0 ˜ ÔÔ e 33 ˜Ì ˝=Á 0 0 D1212 0 0 ˜ Ô e12 Ô Á 0 Ô Á 0 0 0 0 D1313 0 ˜ Ô e13 ˜Ô Ô Á 0 0 0 0 D2323 ˜¯ Ô e 23 Ô˛ ÁË 0 Ó



¸ Ï e11 Ô Ô Ô Ô e12 ÔÔ Ôe el Ô 33 ˝ = [D ] Ì Ô Ô e12 Ô Ô e13 Ô Ô Ô˛ ÔÓ e 23

¸ Ô Ô ÔÔ ˝ Ô Ô Ô Ô˛

20.30

For an orthotropic material the engineering constants define the D matrix as shown in equations 20.31 to 20.39:

D1111 = E1(1 – J23J32)g

20.31



D2222 = E2(1 – J13J31)g

20.32



D3333 = E3(1 – J12J21)g

20.33



D1122 = E1(J21 + J31J23)g

20.34



D1133 = E1(J31 + J21J32)g

20.35



D2233 = E2(J32 + J12J31)

20.36



D1212 = G12

20.37



D1313 = G13

20.38



g =

1 1 – J12 J 21 – J 23J 32 – J 31J13 – 2J 31J 32 J13

20.39

The restrictions on the elastic constants due to the material stability are shown in equations 20.40 to 20.44:

362

Woven textile structure



D1111, D2222, D3333, D1212, D1313, D2323 > 0

20.40



| D1122 | < (D1111D2222)1/2

20.41



| D1133 | < (D1111D3333)1/2

20.42



| D2233 | < (D2222D3333)1/2

20.43



det (Del) > 0

20.44

That last relation turns to equation 20.45:

D1111D2222D3333 + 2D1122D1133D2233 – D2222 D21133



– D1111 D22233 – D3333 D21122> 0

20.45

These restrictions in terms of the elastic stiffness are equivalent to the restrictions in terms of the engineering constants. The final equilibrium equation is formed using the principle of total potential energy, which is the sum of the total strain energy and work done due to gravitational forces. The nonlinearity of the final equation was approximated using the Newton–Raphson method. The input to the ABAQUS software is D matrix which can be calculated from above cited equations from the Young’s modulus (E), shear modulus (G) and the Poisson ratio (n) of the fabric. The other inputs are thickness of the fabric and for the boundary condition the diameter of the fabric (24 cm) was applied. The Poisson ratio (n) for all the fabrics is assumed to be 0.3. So these properties are considered for the input parameters for the finite element analysis. These parameters are listed in Table 20.3 and the virtual draped images obtained from FEA are given in Fig. 20.13. The result obtained from this method is tabulated in Table 20.4 after these draped images have been fed to the image processing software to get the drape parameters. Table 20.3 Input parameters used for finite element analysis Sample Thickness gsm no. (mm)

E1(e7) (g/cm2)

E2(e7) (g/cm2)

E3(e7) (g/cm2)

G12(e3) (g/cm2)

G13(e3) (g/cm2)

v

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10

4.8 4.1 4.6 3.8 3.5 2.8 2.4 1.8 1.9 1.6

4.36 4.00 4.10 4.24 3.51 3.21 3.65 2.89 2.74 2.14

4.57 4.10 4.34 4.00 3.50 3.00 3.00 2.28 2.28 1.85

1.36 1.58 1.27 1.13 1.19 1.52 1.41 1.16 1.17 0.98

1.36 1.23 1.18 1.12 1.15 1.16 1.09 1.11 1.02 0.97

0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

0.64 0.71 0.73 0.78 0.80 0.40 0.43 0.47 0.53 0.59

190 200 215 226 240 190 210 230 240 255

Modeling woven fabric drape

363

Table 20.4 Drape parameters measured by finite element analysis Sample no.

DC

DDR

FDI

Amplitude

N

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10

73.81 72.24 71.76 67.79 66.89 62.28 61.56 60.58 53.12 59.28

47.65 51.12 52.71 60.23 63.04 66.34 71.68 70.2 75.24 74.67

56.28 54.32 60.69 65.49 68.52 72.64 73.09 76.38 80.59 81.79

1.15 1.25 1.30 1.2 1.4 1.25 1.75 1.5 1.65 1.8

6 5 6 6 5 6 5 6 5 5

S1

S2

S5

S6

S9

S3

S7

S4

S8

S10

20.13 Virtual draped images of fabric samples.

20.7.3 Drape prediction by polar coordinate technique A fabric drape profile can be captured in a two-dimensional image projected from a 3-D draped fabric sample by a digital camera and the image can be transferred to the computer for observation [35]. Software was developed using Matlab 7.0 to estimate the drape parameters. The input parameters of the software are the boundary coordinates of the draped profile. The algorithm used to determine the drape parameters are image captured by a digital camera followed by conversion of the image into a binary image (from an intensity-based luminance threshold). The centroid and the boundary of the binary image were traced by eight connected neighbored principles. After boundary tracing, the radii of the drape profile were measured using equation 20.46 from the drape profile. In the last step drape profile was plotted in the form of a polar diagram.

364



Woven textile structure

ri = (xi – xc )2 + (yi – yc )2

20.46



where ri are the radius of the drape profile at 1° interval, i.e. i varies from 1 to 360°, xi and yi are the Cartesian coordinates of the boundary of the drape profile at 1° interval. xc and yc are the Cartesian coordinates of the center of the drape profile. 360

∑ rn

n =1

r= 360 is the average radius of the drape profile. This r value is in terms of pixels. For conversion of pixels to centimeters, the supporting disc image was captured and then it was transformed into centimeter scale by counting the number of pixels in radial direction and then changed to the centimeter scale. The drape parameters can be estimated by the formulae stated in equations 20.18–20.20 except for drape coefficient percentage which is derived in equation 20.47:

2 DC% = r – 6.25 ¥ 100 = 4(r 2 – 6.25) 25

20.47

as As = pr2, A1 = p2.252 and A2 = p52 where 5 and 10 are the diameters of the supporting disc and the undraped fabric in inches. The drape parameters measured by polar coordinate technique are listed in the Table 20.5 and the predicted images are shown in Fig. 20.14.

20.7.4 Comparison of drape prediction methods The drape parameters predicted by the above modeling methods are compared with the drape parameters measured by digital image processing (DIP) Table 20.5 Drape parameters measured by the polar coordinate technique Sample no.

DC%

DDR

FDI

Amplitude

N

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10

73.25 69.37 63.25 61.46 74.29 59.38 56.03 59.25 53.86 54.19

48.47 53.35 49.97 63.26 61.65 62.08 71.68 73.55 78.78 72.19

54.37 56.72 63.09 68.57 71.36 69.97 72.05 73.19 78.29 83.76

1.39 1.45 1.17 1.22 1.45 1.29 1.73 1.51 1.45 1.80

6 5 6 6 5 6 5 6 5 5

Modeling woven fabric drape S2

S1

S4

S3

S5

S6

S9

S10

365

S7

S8

20.14 Predicted draped images of fabric samples using the polar coordinate technique.

method. The results are shown in Fig. 20.15 which shows that there is a good correlation between drape coefficient measured from the digital image processing with FEA and polar coordinate methods [36].

20.8

Predicting drape using artificial neural network (ANN) modeling

The relationship between the measured drape attributes and the subjective drape grades is a non-linear phenomenon. Of late, artificial neural neural networks (ANNs) have been used to predict the drape coefficient and circularity (CIR) given in equations 20.48 and 20.49 respectively. The neural network models used are the multilayer perceptron using back-propagation (BP) and the radial basis function (RBF) neural network. Ê A – Ac ˆ DC = 100 Á d Ë A0 – Ac ˜¯

20.48 where Ad is the area inside the drape curve, Ac is the area of the inner circle, and A0 is the area of the undraped fabric. ÊA ˆ CIR = 4p Á d2 ˜ ËP ¯

20.49 where P is the perimeter of the drape curve. Digital image analysis algorithms

80 75 70 65 60 55 50 50

R2 = 0.9393

50

55 60 70 75 80 DC% measured by DIP

R2 = 0.8864

55 60 70 75 80 DC% measured by DIP

DC% predicted by stat. method

80 75 70 65 60 55 50

DC% measured by polar coordinate

DC% measured by cusick method

Woven textile structure

DC% predicted by FEA

366

80 75 70 65 60 55 50 50

80 75 70 65 60 55 50 50

R2 = 0.6608

55 60 70 75 80 DC% measured by DIP

R2 = 0.9109

55 60 70 75 80 DC% measured by DIP

20.15 Correlation of DC% by different modeling methods.

were written to calculate these two values from all the images acquired for the fabrics used for constructing the training and testing sets.

20.8.1 Neural network model In order to take into account the nonlinearity existing between the inputs and the outputs, a feed-forward network is used and the network is trained with back-propagation, with a set of input vectors (p) and a set of associated desired output vectors called target vectors [37]. The network response is analyzed where the entire data set is supplied to the network (training, validation and test) and a linear regression between the network outputs and the corresponding targets were performed. The results are shown in Fig. 20.16. In this figure, there are four outputs and the first three regressions (training, testing and validation) seem to track the targets reasonably well, and the R values are above 0.9. The fourth regression plot shows the overall correlation coefficient of the entire data set. Drape variables measured by the statistical method and Ann were taken for the comparison study. The comparison was made in terms of the error which is defined in equation 20.50: predicted value – actual valuue ¥ 100 20.50 actual value From the error percentage of these samples, ANN gives a better prediction value than its statistical counterpart shown in Fig. 20.17. It is observed that the neural networks take into account the interactions and nonlinearity error percentage =

Modeling woven fabric drape

Output~=0.9* Target + –0.058

Data Fit Y=T

1 0.5 0 –0.5 –1 –1

Output~=0.83* Target + –0.03

Validation: R = 0.906 19

–0.5

0 Target

0.5

1

1.5 1

Data Fit Y=T

0.5 0 –0.5 –1 –05 –1.5

–1 –0.5 0 0.5 Target

Training: R = 0.906 47

1

Data Fit Y=T

0.8 0.6 0.4 0.2 0 –0.2 –0.4 –0.6 –0.8 –1 –1

–0.5

0 Target

0.5

1

1.5

Training: R = 0.906 47 Output~=0.9* Target + –0.024

Output~=0.93* Target + –0.097

Training: R = 0.966 33

367

1

1.5 1

Data Fit Y=T

0.5 0 –0.5 –1 –05 –1.5

–1 –0.5 0 0.5 Target

1

1.5

20.16 Network outputs of drape parameters.

existing between the inputs and the outputs unknown by the statistical model, hence its results are more accurate. In a neural network, the calculated output is compared with the actual output, and mean square errors (mse) are calculated. The error value is propagated backwards through the network, and small changes are made to the weights and biases in each layer. The cycle is repeated until the overall error value drops below the predetermined threshold.

20.9

Modeling dynamic drape

In actual use of a cloth, an element of movement is frequently involved in garment drape. It has been realized that although the drapebility of a fabric under known static conditions is important, fabric drapeability under dynamic conditions, for example under the influence of air twirling, should

368

Woven textile structure

9 8 7

Error%

6 5

Statistical model Neural network model

4 3 2 1 N

de

Am

pl

itu

I FD

DD R

DC

0

20.17 Comparison of a statistical model with a neural network model.

be determined, especially when garments are made with lightweight fabrics. In the case of dynamic drape, it is generally accepted that the apparel articles float outwards (twirls) under the centrifugal acceleration, reversal, or other conditions imposed on it by the wearer or by the external forces such as air. Under these conditions, the ability to float gracefully is regarded as an important ability of the dynamic drape of the fabric. Yang and Mastudaira [38] derived the dynamic drape coefficient (Dd), with swinging motion, which more closely related to human motion in walking: 20.51 Dd = 90.217 + 0.1183W – 720.73s B – 41.3s G w w where Dd is the dynamic drape coefficient, B is the bending rigidity of the sample fabric (mN m2/m), G is the shear rigidity of the sample fabric (N m/ rad) and W is the areal density (g/m2). To predict the drape parameters at a particular rotational speed, Behera and Pattanayakak [39] fitted the drape parameter values with different rotational speeds. They selected both linear and nonlinear-type functions to fit drape parameters and solved the problem with Matlab 7.6. The criteria for choosing the best model was taken as SSE and R2. The SSE (sum of squares due to error) is defined as:

SSE = ∑ (y – yˆ )2

where y is the experimental value and yˆ is the predicted value. The best model equations chosen from the study are shown in equations 20.52 to 20.55:

DC(x) = – 0.000 002x3 + 0.006x2 – 0.095x + 29.95

20.52

Modeling woven fabric drape



Ê x – 325ˆ 157.9 ˜¯

DDR(x ) = – 962.6e –ÁË

2

A(x ) =

Ê x – 102.9ˆ – 1.092e ËÁ 37.66 ¯˜

N (x ) =

Ê x – 102.9ˆ – 1.092e ÁË 37.66 ˜¯

2

Ê x – 54.1ˆ 88.82 ˜¯

+ 29.39e –ÁË

2

+

Ê x – 18.95ˆ – 6.255e ËÁ 75.62 ¯˜

+

Ê x – 18.95ˆ – 6.255e ÁË 75.62 ˜¯

2

2



2



369

20.53 20.54 20.55

In this study, a trial was made to predict the dynamic drape parameters of cotton woven fabrics with the rotational speed of the supporting disc. The drape parameters were measured by a specially designed apparatus with image processing technique.

20.10 References 1. BS 5058: 1973 (1974), ‘The assessment of drape of fabrics’, BS Handbook 11: British Standards Institution, Vol. 4, 29–31. 2. Peirce F T (1930), ‘The handle of cloth as a measurable quantity’, Journal of the Textile Institute, 21, T377–T416. 3. Booth J E (1969), Principles of Textile Testing – An Introduction to Physical Methods of Testing Textile Fibers, 3rd ed., Chemical Publishing Company, Inc., New York, Chapter 7, 282–288. 4. Potluri P, Atkinson J and Porat I (1996), ‘Towards automated testing of fabrics’. Journal of the Textile Institute, 87, Part 1 (1), 129–151. 5. Hu J (2000), ‘Structure and Mechanics of Woven Fabrics’, Woodhead Publishing Limited, England, Chapter 7, 187–198. 6. Chu C C, Cummings C L and Teixeira N A (1950), ‘Mechanics of elastic performance of textile materials. Part V: A study of the factors affecting the drape of fabrics – the development of a drape meter’, Textile Research Journal, 20 (8), 539–548. 7. Cusick G E (1968), ‘The measurement of fabric drape’, Journal of the Textile Institute, 59, 253–260. 8. Collier B J (1991), ‘Measurement of fabric drape and its relation to fabric mechanical properties and subjective evaluation’, Clothing and Textile Research Journal, 10 (1), 46–52. 9. Behera B K and Pangadiya A (2003), ‘Drape measurement by digital image processing’, Textile Asia, 34 (11), 45–50. 10. Vangheluwe L and Kiekens P (1993), ‘Time dependence of the drape coefficient of fabrics’, International Journal of Clothing Science and Technology, 5 (5), 5–8. 11. Cusick G E (1961), ‘The resistance of fabrics to shearing forces’, Journal of the Textile Institute, 52, 395–406. 12. Collier B J, Collier J R, Scarberry H and Swearingen A (1988), ‘Development of digital drape tester’, ACPTC Combined Proceedings, 35. 13. Yang M and Matsudaira M (1997), ‘Measurement of drape coefficients of fabrics and description of those hanging shapes’, Journal of Textile Machinery Society of Japan, 50 (9), T242–250.

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14. Behera B K and Mishra R (2006), ‘Objective measurement of fabric appearance using digital image processing’, Journal of the Textile Institute, 97 (2), 142–153. 15. Pangadiya A (2003), ‘Drape Measurement by Digital Image Processing’, M.Tech. Thesis, IIT–Delhi. 16. Stylos G K and Wan T R (1999), ‘The concept of virtual measurement – 3D fabric drapeability’, International Journal of Clothing Science and Technology, 11 (1), 10–18. 17. Hearle J W S and Amirbayat J (1986), ‘Analysis of drape by means of dimensionless groups’, Textile Research Journal, 56, 727–33. 18. Yamada T, Nakazato Y, Akami H and Suh J (1995), ‘Flexural rigidity and drapability of fabrics, J. Jpn. Res. Ass. Textile End-Uses, 36 (7), 495–501. 19. Chu C C, Platt M M, and Hamburger W J (1960), ‘Investigation of factors affecting the drapeability of fabrics’, Textile Research Journal, 30 (1), 66–67. 20. Cusick G E (1965), ‘The dependence of fabric drape on bending and shear stiffness’, Journal of the Textile Institute, 56, T596–T606. 21. Morooka H and Niwa M (1976), ‘Relation between drape coefficients and mechanical properties of fabrics’, Journal of Textile Machinery Society of Japan, 22 (3), 67–73. 22. Niwa M and Seto F (1986), ‘Relationship between drapeability and mechanical properties of fabrics’, Journal of Textile Machinery Society of Japan, 39 (11), 161–168. 23. Hu J and Chan Y F (1998), ‘Effect of fabric mechanical properties on drape’, Textile Research Journal, 68 (1), 57–64. 24. Tanbe H, Akamatsu A, Niwa M and Furusato K, (1975), ‘Determination of a drape coefficient from the basic mechanical properties of fabrics’, Journal of Japan Association Textile End-uses, 16 (4), 116–120. 25. Behera B K and Pattanayak A K (2008), ‘Measurement and modeling of drape using digital image processing’, Indian Journal of Fiber & Textile Research, Special Issue, September. 26. Chen B and Govindraj M (1995), ‘A physically based model of fabric drape using flexible shell theory’, Textile Research Journal, 65 (6), 324–330. 27. Chen S F, Hu J L and Teng J G (2001), ‘A finite volume method for contact drape simulation of woven fabrics and garments’, Finite Element in Analysis & Design, 37, 513–531. 28. Collier R, Collier B J, Toole J O and Sargand S M (1991), ‘Drape prediction by means of finite element analysis’, Journal of the Textile Institute, 82 (1), 96–107. 29. 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. 30. Gaucher M L, King M W and Johnston B (1983), ‘Predicting the drape coefficient of knitted fabrics’, Textile Research Journal, 53, 297–303. 31. Pattanayak A K (2009), ‘Modelling and analysis of drape profile of woven fabrics under static and dynamic conditions’, Ph.D. Thesis, IIT Delhi (India). 32. Kawabata S (2000), ‘Fabric quality desubjectivised’, Textile Asia, 31 (7), 30–32. 33. Behera B K and Pattanayak A K (2208), ‘Prediction of fabric drape behavior using finite element method’, Journal of Textile Engineering, Special Issue, September. 34. Bhatti M A (2006), Advanced Topics in Finite Element Analysis of Structures, John Wiley and Sons Inc., Hoboken, NJ, Chapter 6, 331–336. 35. Hu J L (2002), ‘Modeling a fabric drape profile’, Textile Research Journal, 72 (5), 454–463.

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36. Pattanayak A K and Behera B K (2008), ‘Comparative Analysis of Theoretical Modeling for Drapability of Apparel Fabrics’, AUTEX Conference Proceedings, Italy, 24–26 June, 2008. 37. Rumelhart D E, and Mccelland J (1986), Parallel Data Processing, Vol. 1. The MIT Press, Cambridge, MA, Chapter 8, pp. 318–362. 38. M., Yang, Matsudaira, M (1997), ‘Measurement of drape coefficients of fabrics and description of those hanging shapes’, Journal of Textile Machinery Society of Japan, 50(9), T242–50. 39. Behera B K and Pattanayak A K (2009), ‘Modeling and Analysis of Drape Profile of Woven Fabrics Under Dynamic Conditions’, AUTEX Conference Proceedings, Turkey, 26–29 May 2009.

21

Modeling woven fabric behavior during the making-up of garments

Abstract: This chapter describes fabric properties required for the smooth working of the apparel manufacturing process. The low stress fabric mechanical properties relevant in this context are explained, together with the parameters that affect sewability. The mechanisms determining seam pucker and seam slippage are discussed. Key words: garment making-up, fabric mechanical properties, sewability, seam pucker, seam slippage.

21.1

Introduction

Fabric is the basic raw material of clothing industry. The quality of fabric influences not only the quality of the garment but also the ease with which a shell structure can be produced out of flat fabric. The selection of an appropriate fabric is one of the most difficult tasks for the clothing manufacturer. The specifications of fabrics for apparel manufacturing can be considered in terms of primary and secondary characteristics. The primary characteristics are static physical dimensions and secondary characteristics are the reactions of the fabric to an applied force. The apparel manufacturer is primarily interested in the secondary characteristics of the fabric. The consumer is mainly interested in appearance, comfort and wearability of fabric. The production of garments from high quality fabrics not only give comfort to the wearer but also help in the smooth working of manufacturing processes and leads to defect-free garments [1,2]. With the advent of high speed automatic production line systems the interrelationship between fabric mechanical properties and fabric processability in tailoring has become very important. The selection of manufacturing processes requires selection of machine and process variables based on the specific properties of the fabric being processed. Therefore it is essential and logical to study various fabric characteristics influencing directly or indirectly the apparel making-up process and finished clothing product performance. This chapter deals with the relationship between some important fabric properties and the making-up process for apparel. The importance of low stress mechanical properties and fabric formability are also discussed in the context of tailorability. 372

Modeling woven fabric behavior during the making-up of garments

21.2

373

Fabric properties and apparel performance

Key dimensional parameters for fabrics include thread linear density, ends and picks per cm in woven fabric or course and wales per cm in knitted fabric, areal density (fabric mass g/m2), length and width, weave, fabric cover and dimensional stability (to washing and dry cleaning). Other mandatory tests are colorfastness (washing and dry cleaning, light, perspiration, rubbing). The blend percentage of component fibers is determined for blends. Sometimes flammability and presence of certain hazardous chemicals are determined, depending on the end use and buyer’s requirement. Fabric thickness, fabric density, crimp in warp and weft yarns, and moisture regain value are determined for detailed characterization of fabric quality depending on the requirement. Bow and skewness measurements are carried out, particularly in the case of checked and striped design fabrics. The mechanical properties of apparel fabrics are important from the point of view of stresses applied to the fabrics in making-up as well as the physical changes in the fabric which result from application of forces in a garment during its use. Bending, tensile compression and shear properties are considered important from the point of view of garment make-up. These properties influence both sewability and shape of the sewn fabrics. Other mechanical properties such as drape, tear strength, abrasion resistance, wrinkle and crease recovery, and pilling behavior of fabric are evaluated from performance point of view. Some special tests such as bursting strength, elastic modulus, stretchability, drying speed, light reflectance, weather resistance, moth resistance, size content, resin content, oily and fatty matter, solvent extract, scouring loss, degumming loss, glossiness, color index, foreign matter and nets are also evaluated. From the comfort point of view, water absorbency, air permeability and thermal insulation are also tested. Under eco-testing, ph values of extracted liquid, barium activity number and free formaldehyde content are examined. In the tailoring process, an initially flat fabric is converted into a 3-D garment. This conversion requires complex mechanical deformation of the fabric at very low loads. Formability, the ability of a fabric to be converted into a 3-D shape to fit a 3-D surface is dependent on a number of mechanical parameters such as tensile, bending, shear, compression and surface properties. At the same time, it is also dependent on the techniques of garment manufacture, particularly on the amount of overfeeding adopted in certain operations. The fabric must meet the following requirements demanded by a garment [3,4]: ∑ ∑

Utility performance to provide the individual with an adequate physiological protection. Comfort performance to ensure a sufficient degree of wearing comfort such as fitting to the human body.

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∑ ∑

Woven textile structure

Aesthetic performance to improve the aesthetic appearance of the wearer, highlighting certain anatomical particulars and concealing other. Fabric performance for engineering of clothing manufacture as clothing material.

Textile fabrics as clothing materials provide protection of the human body from injury to the skin caused by mechanical contact with outer bodies and protection from cold or hot environments. In addition, high quality fabrics must be comfortable mechanically and, thermally, and have a good aesthetic appearance.

21.3

The garment making-up process and fabric properties

The main task for clothing manufacturers is to produce shell structures out of flat fabrics to match the shape of the human body. The overall scheme of the garment manufacturing process is illustrated in Fig. 21.1. In all shapproducing methods there will be an interaction between particular method used and various physical properties of the fabric. Some of the interactions between various major manufacturing processes and fabric properties are discussed below [5,6].

21.3.1 Pattern grading The first step in manufacturing a garment is the creation of design and construction of patterns for the components of design. This requires determination of geometrical shape of the body surface in order that appropriate shell structures can be produced. For pattern grading, anthropometric data Design style Pattern grading

Interlining

Fabric Laying

Cutting

Edge seaming

Sewing Pressing Transport Consumer

21.1 The garment manufacturing process.

Fusing

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should be available for the market in which the garment is to be sold. Pattern grading is a process of enlarging or reducing a style pattern, making it possible to obtain a good fit for all sizes without changing the garment master patterns for a given compilation of anthropometric measurements which are suitable for a person whose body measurements lie within certain tolerance limits of the garment size measurements. The shape and size of the garment relative to the shape of the body, known as the fit, will be strongly influenced by physical and mechanical properties such as tendency of the fabric to stretch, shrink, distort and drape due to stresses induced during use under static and dynamic situations which must be taken into account when drafting a pattern for a garment.

21.3.2 Laying-up cutting In laying and cutting procedures, layers of fabrics are superposed on a table to be cut simultaneously into garment components for further processing. During these operations, it is essential that each layer of fabric is laid in an unrestrained state in order that the dimensions to which various parts of the garments are cut are stable dimensions of the fabric. The following properties govern this: ∑ ∑

∑

Extensibility in laying direction decides the ease with which the fabric can be laid in an unrestrained state; it is essential that the fabric should not be too extensible at low loads. The coefficient of friction helps to make multiple layers more or less stable. Stretch in fabric layers produced by in-plane or lateral stresses on superposed fabric layers will affect the stress free dimensions of the garment patterns. Building up multilayered structures in certain elements is often a necessary processing step in order to fulfill various functional requirements. Examples of such garment elements are jacket fronts, waistbands in trousers and skirts, and collar and cuffs in shirts. Multilayered structures should produce desirable bending stiffness, drape and extension. The use of fusible interlinings for this purpose is an established practice.

3-D shapes in flat apparel fabrics can be achieved by either cutting or sewing processes or by shaping using steam pressing and moulding techniques. The former goal is met by appropriate pattern drafting of garment component, for example the shoulder part of the sleeve, and by cutting drafts in the fabrics, components, for example ladies dresses, which after application of stitches gives the desired shape or form. The resulting form will be strongly influenced by certain fabric properties. During the cutting of multiple layers of fabrics, which is normally done by the action of a reciprocating blade, a minimum level of stability of fabric dimension is necessary. To be more

376

Woven textile structure

specific, a certain level of tensile rigidity both in warp and weft directions and some amount of surface friction are necessary for this process.

21.3.3 Seaming During this operation, the fabric should be kept under the control of the operator and the sewing machine feed dog. This requires a degree of inplane fabric stability. Adequate tensile, shear rigidities and fabric to metal coefficient of friction are basic requirements for seaming. The incorporation of sewing thread into the fabric structure while maintaining a flat fabric surface requires some rearrangement of the yarns within the fabric. In order to avoid puckering of the seam, it is necessary that shear rigidity be quite low to permit interlaced yarns in the fabrics to rotate and accommodate the sewing thread; however, bending rigidity should be high enough to counteract internal forces necessary to bend the fabric out of its plane.

21.3.4 Pressing The pressing or molding process produces a varied shape by application of one or more of: heat, moisture and pressure. Again the ease and stability of the resulting shape will be strongly influenced by certain fiber and fabric properties. The aim of fabric pressing is to remove distortions in the fabric surface, for example wrinkles in the zone of the seam, which depend on the buckling behavior partially related to bending rigidity. The maximum pressure that can be exerted during pressing is limited by the need to maintain the appearance of the fabric surface. The relevant mechanical properties in this case are fabric surface compressibility and resilience.

21.4

Low stress fabric mechanical properties and the garment making-up process

Low stress mechanical properties of the fabrics have established themselves as an objective measure of quality and performance of garment. There are two major reasons why low stress fabric mechanical properties are important in tailoring [7–12]. The first is that fabrics are more extensible in the low load region. The property in this region is closely related to the tailoring process and the comfort of a wearer. In the tailoring process, an initially flat fabric is formed into stable, complex 3-D garment shapes. The conformation of a flat fabric to any 3-D surface requires complex mechanical deformation of the fabric such as bending, extension, longitudinal compression and shearing in the fabric at very low loads. Garment patterns often require different lengths

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377

of fabric to be sewn together by overfeeding the longer of the two fabrics to form a seam of intermediate length as a means of imparting a 3-D character to the garment; the seams being inserted either in the warp or weft direction or at some angle. In this case, the shorter length is extended and the longer length is compressed longitudinally. The second reason is that fabric extensibility at low loads causes difficulty in the handling of fabrics during the cutting and sewing processes. Fabrics having high extensibility cause dimensional distortion. Thus the fabric tensile, longitudinal compressive and shear properties are the main mechanical properties relevant to the tailoring performance. Line production of garments and high quality requirement is now a major issue facing the apparel industry. Objective measurement of fabric mechanical properties is being used as an aid to the process and buying control of fabrics in the apparel industry. Fabric mechanical properties given in Table 21.1 are measured under low loads so that conditions similar to actual fabric deformation in use are taken. The hysteresis behavior in tensile, shear, bending and compression is measured to determine the fabric resilience or springiness. The fabric surface properties are also measured to detect the roughness by human senses.

21.4.1 Tensile property ∑ ∑ ∑

LT, the linearity of load elongation affects fabric extensibility in the initial strain range; low values of LT give high extensibility but fabric dimensional stability is reduced. RT, the tensile resilience; high value makes the fabric more elastic. EM, the tensile strain; larger values of EM in warp cause many problems in tailoring due to distortion of fabric during sewing but are important in weft for comfort in wearing and easier tailoring.

21.4.2 Shear property ∑ ∑

G, the shear rigidity; high values cause difficulty in tailoring and discomfort in wearing. 2HG5, the hysteresis of shear force at higher shear angle (5°); high values give distortion in tailoring and wrinkling during wear.

21.4.3 Bending property The bending property influences the product’s fabric bending rigidity and the longitudinal compressibility of the fabric prior to buckling. Bending rigidity is one of the basic fabric mechanical properties; it also affects puckering

378

Woven textile structure

Table 21.1 Low stress mechanical properties of fabric Symbols Property

Unit

Tensile property LT Linearity of load None elongation curve WT Tensile energy gf cm/cm2

RT

Tensile resilience

%

EM

Extensibility

%

B

Bending rigidity

gf cm2/cm

2HB

Hysteresis of gf cm/cm bending moment

Remarks LT = 1 completely linear and LT = 0 extremely non linear Higher value of WT corresponds to higher extensibility (Note: this is not a general rule as WT must be interpreted in conjunction with WT) RT = 100% elastic and RT = 0% completely inelastic Strain at maximum load (500 gf/ cm) Bending rigidity per unit width of fabric Hysteresis of bending moment observed in the bending moment–curvature relationship. A larger value of 2HB means a greater fabric inelasticity

Bending property G Shear stiffness gf/cm.degree 2HG Hysteresis of shear force gf /cm at 0.5° of shear angle 2HG5 Hysteresis of shear force gf/cm at 5° of shear angle Shearing LC WC RC

property Linearity of compression– none thickness curve Compressional energy gf/cm/cm2 Compressional resilience %

Compression property MIU Coefficient of friction

None

MMD

Mean deviation of MIU

None

SMD

Geometrical roughness

μm

Areal density and thickness W Fabric weight mg/cm2 T0 Fabric thickness mm Tm Fabric thickness mm

LC = 1 completely linear and LC = 0 extremely non linear Higher value of WC corresponds to higher compressibility RC = 100% elastic and RC = 0% completely inelastic Higher value corresponds to higher friction Higher value corresponds to larger variation of friction Higher value corresponds to geometrically rough surface

Thickness at pressure of 0.5 gf/cm Thickness at pressure of 50 gf/cm

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and fabric cutting. Fabric surface property and thickness influence cutting and sewing operations.

21.5

Measuring fabric suitability for the garment making-up process

The tailoring control chart developed in Japan is shown Fig. 21.2. If all the properties of a fabric fall inside the ‘non-control’ zone, the tailoring of this fabric is easy and there will be no defects in its appearance. However, if it was found that the properties of the fabrics providing good handle are not necessarily in the ‘non-control’ zone, the fabric might not be suitable for tailoring. The dots and horizontal lines show the mean value and the range of distribution of fabric properties. Fabrics are separated into two groups: where online control is necessary and where no control is required. If all the fabric mechanical properties and shrinkage parameters fall into the central non-control zone, no special control of the tailoring process is required. If one or more than one parameter falls out of the non-control zone, then control in tailoring process is required for the parameter concerned. Control zone

Non control zone

Control zone

The Fabric LT R

EM1

0.5

0.5

5

5

3

EM2

0.5 0.

3.

3

2

G

2HG5

6

6 7

4

4.

5

5.

6

8

10

1

0.

0.

1.

0.

6

4

EM1/EM2

0.6

0.

1.

2.

High total hand value (THV), Total appearance value (TAV), Comfort zone

21.2 Tailoring process control chart.

6

15

3

2

0.

7

0.

0.

1.

2.

3.

3.

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Woven textile structure

As an example, the difference in the smoothness of the seam line comes from the mechanical properties of the constituent fabric. The mechanical property related to seam smoothness is mainly fabric bending property in the weft direction. Simple criteria for fabric properties consistent with the tailoring of suits are given in Table 21.2. Other important properties of fabric for processing include fabric shrinkage caused by steam pressing process in the production line system of suits. The inspection of fabric properties before tailoring is necessary to decide a fabric’s suitability The ranges of rejection values of fabric properties for tailoring are given in Table 21.2 [3,13]. ∑ ∑ ∑ ∑ ∑

These values take into account such factors as: whether fabric extensibility is abnormal (too high or low); fabric properties which present puckering during the sewing process; distortion during spreading of fabric in cutting or grading process and in steam pressing; pressing pressure and amount of steam in steam pressing to minimize fabric distortion; whether fabric tensile resilience and shear hysteresis are abnormal: when a fabric is too elastic, control of shape is very difficult in both sewing and steam pressing.

Suitable fabrics are sent to suit manufacturers from textile factories. Pieces of the same fabrics are sent for objective measurement and to retail showrooms. The customer selects the fabric and style of suit at the shop. His selection and statistics are sent to the factory and test house. The objective measurement data is also sent to the factory. The features of this system is that number Table 21.2 The range of rejection for tailoring Mechanical property and its rejection range

Remark

EM1 > 8

Not suitable for business suits from the shape retention; unstable in processing Not suitable for all types of suits Difficulty in overfeed (over action of overfeed) Too deformable and causes difficulty in tailoring; suit shape retention problem Wrinkle problem; too stiff for suit, difficulty for overfeed operation Dimensional instability problem during tailoring Dimensional change of fabric during wearing of suit Difficulty in predicting fabric dimensional change after steam pressing

EM1 > 10 EM2 < 4 2HG5 < 0.8 2HG5 > 3.5 S2 > 1.5* S4 > 1.0* Q < 30 and/or Q > 100

S2 = the shrinkage-offset in % in equilibrium after steam pressing S4 = the relaxation shrinkage in % after steam pressing Q = rate of the shrinkage recovery in % in the period of 2 hours after steam pressing

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of online control points are reduced by strict buying control of fabric from textile mills based on mechanical properties. In the tailoring process, an initially flat fabric is formed into a complex 3-D garment shape. The conformation of a flat fabric to any 3-D surface requires complex mechanical deformation of the fabric such as bending, extension, longitudinal compression and shearing in the fabric plane at very low loads. Garment patterns often require different length of fabrics to be sewn together by overfeeding the longer of the two fabrics to form a seam of intermediate length as a means of imparting a 3-D character to the garment. The seam is inserted either in the warp or weft direction or at some angle. Higher fabric extensibility in the initial region causes difficulty in the handling of fabrics during the cutting and sewing processes, e.g. fabrics having high extensibility cause dimensional distortion. Thus the fabric tensile, longitudinal compressional and shear properties are the main mechanical properties relevant to the tailoring performance.

21.6

Fabric buckling and tailorability of garments

Tailorability is the ease with which fabric components can be sewn together to form a garment. It mainly depends on the fabric characteristics of formability and sewability. Formability is a measure of the ability of a fabric to absorb compression in its own plane without buckling. Sewability refers to ease of formation of shell structure and styles, absence of fabric distortion and seam damage, achieving acceptable seam slippage and seam strength. Researchers use the terms sewability and tailorability interchangeably. However tailorability covers a broader issue of garment appearance [1,5,14]. Buckling has considerable importance in a typical situation which occurs when, for example, the shoulder of a suit must be tailored by partially overlapping, curving and sewing together two surfaces of a fabric which are initially flat. The fabric which is overfed to follow the new configuration is subjected to compression in a longitudinal direction. Fabric can be compared to a column, and buckling can quite easily occur. Sudden yielding of fabric during buckling results in the appearance of wrinkles which affect the appearance of a tailored garment. The critical load Pcr required for buckling is obtained by using Euler’s formula:

Pcr = p E I/L2

where E is Young’s modulus, I is the moment of inertia of the section and L is the length of column. Alternatively

Pcr = KEI = KB

Compressibility of the fabric in longitudinal direction is given by:

C = e/P

382

Woven textile structure

where e is deformation and P is applied load e = PC = KBC = KF where F is formability. Lindberg et al. [14] were the first to apply the theory of buckling to textile fabrics in garment technology and defined the fabric formability as the degree of longitudinal compression sustainable by a fabric in a certain direction before the fabric buckles. The formability signifies the conformant of a particular shape during tailoring and this is achieved by forcing a 2-D fabric to take on a simple or complex 3-D shape. In practice this type of compression is imposed upon the fabric by a combination of thread size, needle size, thread tension and stitch rate. A fabric which buckles easily under these forces will form puckered seams. Formability is a direct indicator of the likelihood of seam pucker occurring either during or after sewing. It can be calculated by using values from FAST 2 and FAST 3 [15] instruments. For a lightweight fabric if F < 0.25 mm2, the fabric is likely to pucker. Normally F varies between 0.25 and 0.75 mm2. Some derived properties produced by FAST are not measured directly but are calculated using values from different FAST instruments, such as bending rigidity and shear rigidity.

21.7

Measuring sewability: seam strength

Sewability is the ability and ease with which the fabric components can be qualitatively and quantitatively seamed together to convert a 2-D fabric into a 3-D garment. The quality and serviceability of a garment depend not only on the quality of the fabric, but also on the quality of its sewing. The quality of sewing is affected by the machine parameters, the sewing thread parameters and the fabric to be sewn [1,11,16–19]. The quality of a seam depends on its strength, elasticity, durability, stability and appearance. These characteristics can be measured by seam parameters such as seam strength, seam pucker, seam slippage, seam appearance and seam damage. Each of these parameters are influenced by various material and machine variables and can be quantitatively measured. The strength of the seam should be equal to that of the material it joins in order to have a balanced construction that will withstand the forces encountered during use. The transverse strength of a seam is determined by a number of factors such as stitch type, stitch density, thread strength, thread tension, and needle size and type. It will be observed that the seam failure in a garment can occur because of: ∑ ∑ ∑

failure of the sewing threads, leaving the fabric intact; fabric ruptures leaving the seam intact; both fabric and seam breaking at the same time.

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It is desirable that the sewing thread rather than the fabric yarns should break because the seam can be restitched. The durability of a seam depends largely on its strength and the elasiticity of the material and it is expressed in terms of seam efficiency: Seam efficiency(%) =



seam tensile strength ¥ 100 fabricc tensile strength

It generally ranges between 85% and 90%. Seam efficiency depends on strength, count and ply of sewing thread; it correlates well with the toughness index of sewing thread. The thread loop strength relates well with the measured strength of seam in which thread breakage occurs. The reduction in the strength of sewing thread depends on [19]: ∑ ∑ ∑

shape and type of needle; fabric thread density, hardness of yarns, number of plies to be sewn; number of passages of the thread through the needle eye and the fabric before it is incorporated into the seam.

The loss in strength due to abrasion in the sewing machine is 25% for the upper and 15% for the lower threads in single and double thread chain stitch machines. During sewing, the thread is subjected to mechanical and thermal stresses resulting in severe thread deformations. These deformations cause structural and mechanical damage to the thread and the fibers.

21.8

Measuring sewability: seam puckering

Puckering is a disruption in the original surface area of a sewn fabric and gives a swollen and wrinkled effect along the line of the seam in an otherwise smooth fabric. Seam pucker is a differential contraction along the line of a seam and is in most cases caused by the tension from the thread of the seam or the yarns of the fabric [19]. The sewing thread displaces the yarns of the fabric into new position and prevents them from recovering by the stitch bulk. A resulting crowding and compressive situation then exists around each stitch. The severity of this condition depends on the yarn and fabric density and the closeness of the weave [19]. Its severity is also directly related to the thickness of the thread and the number of stitches per inch. Another important cause of pucker is the high thread tension imposed during sewing. When a seam is made the thread is stitched into the fabric under a certain amount of tension in order to form a good stitch. Pucker can actually happen either during the stitch formation or after stitching due to relaxation of the sewing thread. During stitching, the needle along with the thread enters in the space between two consecutive picks (yarns perpendicular to the seam). The extent

384

Woven textile structure

of deformation of the weft yarns will take place depending on the spacing between these two picks and the diameter of the sewing thread. When the needle enters the fabric, owing to its impulsive action, deformation of the weft will be maximum but when it comes out, this deformation may get reduced due to the readjustments in the fabric structure. The fabric structure plays a crucial role because the actual pucker in a fabric depends on its mechanical properties; that is how and to what extent the deformation is caused and absorbed by the fabric structure. Therefore, for a better understanding of the seam pucker behavior of fabrics the role of physical and mechanical properties of the fabrics in causing and preventing pucker is needed. The sewing thread forms the seam so its contribution towards pucker is required. The study of seam pucker formation by sewing threads of different tensile properties would help in better understanding of the pucker mechanism but also in the selection of the suitable sewing thread for fabric having specific physical and mechanical properties. Analysis of mechanism of seam pucker relates the cause of seam pucker to the compressive forces on the fabric generated during sewing by thread and interaction between the thread, fabric and feed mechanism. Seam puckering depends on sewing thread properties, stitch length type, thread tension, sewing speed, presser foot pressure, needle size, and frictional properties of fabric and its constituent yarns. The seam pucker can be quantified by thickness strain [19] as given below: thickness strain (%) =



t s – 2t ¥ 100 2t

where ts is seam thickness and t is fabric thickness. In order to visualize the development of pucker, a model. Figs 21.3 and 21.4) is shown to understand the deformation of fabric structure due to the insertion of a seam in it. This stitching line or a seam has to find a position on and in the plane of the fabric. In order to accommodate the bulk of stitch the fabric yarn in both the directions get displaced around this juncture. Depending on the physical and mechanical properties of the fabric the sewing thread Fabric

Seam line

21.3 Seam pucker model.

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21.4 Force distribution on threads in a stitch.

may have no resistance from the fabric and would manifest in different types of yarn movements (distortions) in the fabric structure; otherwise, owing to resistance from the fabric, only compression of the thread and fabric yarn may take place. The former causes severe pucker and the latter little or no pucker. It is either the yarns parallel to the seam or the ones perpendicular to the seam which absorb the longitudinal and lateral compressive forces, supposedly leading to a ripple effect in the body of the fabric. If the fabric bulk and properties are such that these forces get absorbed or diluted by the movement of the yarn around the stitch, then low pucker will result, but if the fabric properties allow the transfer of this deformation, maximum dislocation around the stitch would appear as severe pucker. The generation of forces also depends upon the tensile properties of the sewing thread. The different threads may give rise to a different extent of pucker in the same fabric due to different tensions developed in them. The physical movement of the fabric yarn may offer differential resistance depending upon the fabric properties such as cover factor, tensile extensibility, bending and shear rigidity, frictional hysteresis, thickness and lateral compressibility. However, the extent of pucker would depend upon the amount of resistance to the yarn offered by the fabric properties and the tension developed in the sewing thread.

21.8.1 The process of pucker formation The introduction of the sewing thread in the structure of the fabric triggers off deformations which may be dissipated into the bulk of the fabric or result in the development of the pucker. The factors which would come into play are the physical and mechanical properties of the fabric, tensile properties of the sewing thread and some sewing machine parameters. Initial pucker Initial pucker is dependent upon the size of the sewing thread, needle and the physical and mechanical properties of the fabric. The diameter of sewing thread and needle during stitch formation initiates dislocation of fabric

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Woven textile structure

yarn. If the adjacent warp and filling yarns have enough free space for the physical presence of a stitch then no change in the fabric plane occurs and no pucker is formed; otherwise, owing to the impulsive action, force is generated to push these aside to make space for the needle and the sewing threads. Yarn mobility can be unidirectional or multidirectional depending upon the inter-yarn space available; the latter dilutes the impact so low pucker is initiated but the former, because of clustering, bunching or overlapping, gives higher pucker. The extent of yarn mobility is determined by the properties of the fabric and the sewing thread. The yarns around the insertion may slide, rotate or deform depending on the fabric’s mechanical properties. Subsequent pucker The sewing threads when they enter the fabric are under tension and a movement is caused in the yarns of the fabric. The type and extent of movement (pucker) are dependent upon the amount of tension in the sewing thread (high modulus, low extension thread would have higher tension than low modulus, high extension). The interaction between the horizontal component of the thread tension and the nature of the longitudinal fabric compression decides the extent of deformation. High thread tension and unfavorable fabric properties give very little yarn mobility so the seam remains under tension until time-dependent stress relaxation. Therefore the initial pucker and the resultant pucker will be the same. The thread tension will be in equilibrium with the reaction from the yarns of the fabric and will decay as a function of time. High thread tension and favorable fabric properties increase initial pucker in thin fabrics due to low fabric cover. Initial pucker decreases due to dissipation in thick fabrics (into the bulk of the fabric) by yarn compression and does not cause physical yarn movement. Low thread tension and unfavorable fabric properties do not affect yarn mobility so initial pucker will not change. The possible yarn movements in the fabric deformations are as follows: ∑

∑

Yarn sliding would happen when bending rigidity is high but its frictional hysteresis is low; shear rigidity and its frictional hysteresis are high. The extent of yarn movement under these conditions will depends upon the cover factor; especially that of the filling, so: very low cover Æ no yarn bunching Æ very low pucker low cover Æ yarn bunching Æ high pucker moderate cover Æ some yarn bunching Æ medium pucker high cover Æ sewing thread is embedded Æ low pucker Yarn rotation takes place when bending rigidity and its frictional hysteresis are high but shear rigidity and its frictional hysteresis are low. The

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∑



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final pucker in this case would depend upon the extent of cover factor; especially the filling. So: low cover Æ high pucker medium cover Æ medium pucker high cover Æ low pucker Yarn bending takes place when the bending rigidity and its frictional hysteresis is low or moderate; shear rigidity and its frictional component are moderate. Under these conditions the actual pucker will depend on fabric cover factor; filling in particular. So: low cover Æ low pucker high cover Æ high pucker

21.8.2 Sewing thread properties and pucker The relevant thread properties affect the appearance and performance of a seam based on their interaction with the fabric properties. Thus the important thread properties from that point of view are discussed below: Initial tensile modulus During sewing, the needle and bobbin thread, under certain tension, deform the fabric for stitch formation. High modulus, low extension threads develop more tension than the low modulus, high extension sewing threads when stitched at the same static tension. Figure 21.4 shows that the sewing thread exerts force perpendicular and longitudinal to the fabric for lateral and longitudinal fabric compression respectively. Thus a high modulus, low extension sewing thread would have more lateral force to compress, thereby helping to reduce the extent of pucker. However, the fabric response to longitudinal compression induced by the horizontal force exerted by the sewing thread depends upon the fabric properties such as bending and shear rigidities (along with their frictional hysteresis), extensibility and cover factor. If these properties are favorable than their reaction to the horizontal force will determine the extent of pucker. Tensile modulus and extension are the most important properties from the point of view of seam puckering. Diameter When the sewing thread and the needle enter the fabric for stitch formation they cause localized deformation of the warp and filling yarns around it because actual physical space is required for two diameters of the sewing thread even after the needle pulls out. Bigger thread diameter needs more space for its in situ deposition resulting in greater deformation; higher level of pucker depending on the fabric cover.

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Woven textile structure

Yarn diameter compressibility If the fabric properties are such that very little movement of the yarn takes place (high fabric cover) due to the insertion of sewing thread then the sewing thread and the adjoining yarns of the fabric are compressed. Therefore, a sewing thread which has greater compressibility will tend to cause less fabric yarn deformation and subsequently less pucker. Fiber density Sewing threads spun from low density fibers will have a bigger diameter. Polyester fiber has a lower density than cotton.

21.8.3 Compressional behavior of fabrics and pucker The sewing thread develops tension during stitching on the sewing machine, after which it tends to relax by shortening the thread path in a stitch. This can be achieved in two ways. Lateral compression When force is applied perpendicular to the plane of the fabric, a certain amount of fabric compression takes place, decreasing its thickness. These fabric properties are compressional energy and actual thickness compression. The extent of compression depends upon factors such as the original fabric thickness, fabric construction (weave or sett), crimp, and fiber content. The sewing thread under tension compresses the fabric laterally in order to reduce the thread stretch and hence relaxes the tension developed during sewing. If the fabric has a higher capacity to compress and it is stitched with a sewing thread which develops high tension it increases the compression of the fabric and smoothen the pucker. Thus the fabrics with high degree of compression (usually thicker fabrics) are less vulnerable to pucker especially when stitched with high modulus sewing thread. Longitudinal compression The sewing thread under tension also compress the fabric in its plane. At each stitch juncture, the longitudinal force cause in-plane compression of the yarns perpendicular to the seam, in a stitch, is resulting in its deformation (bending). The resistance to movement and deformation (bending and shear) is due to frictional resistance at the cross-over points due to inter-yarn force. Therefore fabrics respond differently depending on the fabric sett, yarn count and the degree of setting which depends on the finishing treatment

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given to the fabric. The deformation is facilitated by low values of shear and bending and higher values of extensibility. Owing to crimp interchange, thickness within and around the stitch may increase. Thus the extent and nature of longitudinal compression will depend on the fabric structure and the compressive force applied. If the fabric properties favor longitudinal compression then during the insertion of the needle and the sewing thread, the fabric yarn (warp and filling) will be pushed aside easily and may lead to bunching or clustering of yarn, leading to increase in pucker. This is more likely in thin multifilament fabrics. Further, the horizontal component of the tension in the sewing thread would tend to compress them more to further increase pucker or its inability to compress longitudinally may either lead to an increase in pucker due to buckling as very thin fabrics have low bending rigidity or in thick fabrics help in dissipating the pucker into the bulk of the fabric.

21.8.4 Correlation coefficients Thus to get a better understanding of the pucker mechanism, the correlation coefficient between fabric properties and the thickness strain values were obtained. By taking one fabric property at a time with thickness strain values it was possible to find out the contribution of each fabric parameter. These fabric properties were fabric mass, thickness compression, bending rigidity, shear stiffness, extensibility, cover factor and formability in the warp and filling direction. Most of the fabric properties gave insignificant correlation except fabric thickness. It gave fairly high correlation coefficients (–0.751 to –0.810) for cotton and polyester sewing threads. Fabric thickness alone gave a good correlation with the thickness strain values indicating the maximum contribution of this property. Since the other fabric properties were having an insignificant effect, though they were important for the actual deformation of the yarns within and around a stitch, it is logical to expect that these fabric properties may have an indirect effect through interactions with the fabric thickness. Correlation coefficients were calculated by combining each of the other fabric properties with fabric thickness to examine their interaction. Interestingly, there was a considerable increase in the correlation coefficient values. This clearly indicates that pucker formation, a very complex phenomenon is directly as well as indirectly dependent upon various fabric properties. The decrease in initial tensile modulus of the sewing thread gave higher correlation coefficients, indicating the interaction of sewing thread differently with the fabric properties. The correlation values improved significantly when the effect of the secondary fabric properties along with fabric thickness was considered (0.943 to 0.965). These secondary fabric properties contribute

390

Woven textile structure

indirectly through the primary fabric properties to affect pucker. The cotton fabrics even with low thickness give low to medium pucker. Synthetic filament fabrics (polyester and viscose) give high pucker but synthetic spun fabrics gave low pucker owing to more thickness and higher level of surface friction. Blends as a group give low to medium pucker. Cotton sewing threads are more suitable for cotton and blended fabrics and polyester sewing threads are better for synthetic fiber fabrics.

21.9

Measuring sewability: seam slippage

When the seam is under some transverse strain, then displacement of the stitch relative to one or more of the fabrics can occur. This is called seam slippage. The stitch displacement produces some displacement of one yarn system in the fabric against the other, which causes opening in the fabric. This phenomenon is an adverse feature of some woven fabrics and it decreases the range of possible end uses and problems in garments. The amount of seam slippage or the fabric resistance to seam slippage depends on: ∑ ∑ ∑ ∑

yarn to yarn friction; contact angle between threads; stitch density; yarn flexural rigidity.

An increase in the values of the above increases the fabric resistance to seam slippage. Seam slippage depends on weave, fabric raw material, type of seam, stitch density and sewing thread tension.

21.9.1 Understanding the seam slippage mechanism Consider two fabrics sewn together parallel to a yarn system; if the seam is opened by applying some tension transverse to the seam axis, this tension imposes strain on the seam. The tension in the sewing thread in the seam depends on thread tension during sewing, fabric tension and stitch density. The tension applied to the fabric through the seam creates a pushing force on the threads transverse to the seam axis. This causes deformation of stitch geometry, displacement of threads along the seam. Seam slippage is basically a consequence of the tensile elongation. Seams in the garments are constantly being subjected to stresses in various directions among which those perpendicular to the seams are most common. When two pieces of woven fabric are joined by a seam and an increasing force is applied to the assembly at right angles to the seam line, rupture ultimately occurs at or near the seam line and at a load usually less than that required to break the unsewn fabric [19]. The set of yarns being pulled slip out of the

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seam assembly, overcoming the frictional resistance due to inter-yarn forces. In addition, the extent of slippage is also determined by fabric mechanical properties and the tensile behavior of the sewing thread. The severity of seam slippage is generally observed in tight fitted women’s garments which are made from either lightweight or medium-weight fabrics. By and large these smooth fabrics are made from synthetic filaments. The stretch on the seams in the perpendicular direction leads to a change in the basic structure of the fabric due to the extension of yarns in the direction of the pull. This extension in one direction would most certainly lead to changes in the fabric geometry of the opposite side. How much change takes place and with what consequences would depend upon the physical and mechanical properties of the fabric. The presence of a stitch line (seam) acts like a barrier in the load elongation behavior of a seamed fabric. When the fabrics are stretched or load is applied some changes are expected in the structure of the fabric which is dependent not only upon the tensile properties of the fabric but also upon other mechanical properties such as bending, shear (along with their frictional hysteresis) and surface coefficient of friction and roughness. In addition, the physical properties of the fabrics are also important in facilitating the mechanical properties to interact effectively. As a load is applied to stretch the fabric, at first the crimp is straightened and then the yarn extends and overcomes inter-yarn friction. The higher cover factor in the cross-direction gives a greater number of cross-over points. Therefore the yarns slippage of such a fabric will be more difficult. Another important consideration is that decreases in crimp in the direction of the pull increases crimp in the opposite direction. Therefore fabric elongation becomes more difficult due to increase in the frictional resistance due to increase in contact area between yarns. When force is applied perpendicular to a seam joining two pieces of fabric some of the above movements would take place but with a difference. The stitching line acts like a clamp which is flexible. Its flexibility would therefore determine the load-elongation behavior of a seamed fabric.

21.9.2 The process of seam slippage When tensile load is applied to a fabric seam it has to overcome two types of frictional forces: the inter-yarn frictional forces within a fabric and the frictional force of the stitch assembly. The former is dependent upon the crimp, yarn diameter, fiber content and, number of cross-over points. The latter is, however, dependent upon the fabric properties such as fiber content, type of yarn (spun or filament), thickness and its lateral compression, cover factor (threads per cm), bending, shear, tensile and surface roughness and coefficient of friction. It is also dependent upon the properties of the sewing

392

Woven textile structure

thread such as fiber content, diameter, coefficient of friction, initial modulus and extensibility. All these properties, together with the machine variables such as needle and bobbin thread tension and the stitch length, make up the frictional force of the stitch assembly. Thus different combinations of these would be expected to provide different frictional resistance and hence different loads at which seam slippage may take place. This stitch assembly acts like a clamp for the fabric and as long as the pulling force is less than the frictional resistance of the stitch assembly the strain is shared by the fabric and the stitch assembly. However, as soon as the pulling force exceeds the frictional resistance of the stitch assembly, the fabric yarn slips and the load is transferred indirectly through the cross-yarn to the stitch assembly. Thereafter depending upon the fabric characteristics, the yarns slip out or, if that is not possible, then the force gets shared by the fabric yarn and the sewing thread. A more extensible sewing thread may break at a higher load in comparison to a less extensible one. The correlation of resistance to seam slippage per thread (RSST) value with each fabric property individually so that the interaction or influence of each fabric property or variable (primary properties) on the seam slippage behavior of the fabric is known.

21.10 References 1. Behera B K (1999), Testing and Quality Management, Vol 1, IAFL Publication, 386–402. 2. Behera B K and Hari P K Sep (1990), Indian J Fiber Textile Res, 19, 168. 3. Kawabata S and Niwa M (1989), J. Text. Inst. 8, 1, 19. 4. Masukuni M (1994), Int J Clothing Sci Technol, 16, 2/3, 7. 5. Harlock S C (1989), Textile Asia, July, 89. 6. Postle R (1990), Int J of Clothing Sci Technol, 2, 3, 7–17. 7. Kawabata S, Niwa M and It K (1992), J. Text. Inst., 83, 3, 361–373. 8. Stylios G and Liods D W (1990), Int J Clothing Sci Technol, 6, 4, 6. 9. Kawabata S and Niwa M (1994), Int J Clothing Sci Technol, 6, 5, p14–27. 10. Shishoo R L Feb (1989), Textile Asia, 20, 2, 64. 11. Behera B K and Chand S (1997), Int J Clothing Sci Technol, 9, 2/3, 128. 12. Potluri P, Porat I and Atkinson J (1996), Int J Clothing Sci Technol, 8, 12, 12. 13. Hari P K and Sundaresan G (1993), Garment Quality: Interrelationship with Fabric Properties, GARTEX-NIFT’93 Conference New Delhi Oct 16–17, F1-7. 14. Lindberg J, Waertraberg L and Svenson R (1960), J. Text. Inst. 51, T1475. 15. FAST Manuals, Published by CSIRO Research Centre, Australia. 16. Mehta P V (1992), An Introduction to Quality for Apparel Industry, ASQC Quality Press, Wisconsin. 17. Stylios G and Sotomi J O (1993), J. Text. Inst. 84, 4, 601. 18. Sundaresan G (1996), Studies on the Performance of Sewing Threads During High Speed Sewing in an Industrial: Lock stitch Machine, Phd Thesis, IIT Delhi, India. 19. Chopra K (1997), Seam Behavior of Woven Fabrics, Phd Thesis, IIT Delhi, India.

22

Modeling three-dimensional (3-D) woven fabric structures

Abstract: This chapter starts with definition of three-dimensional (3-D) fabrics and also explains how they are different from 2-D fabrics in terms of manufacturing technique and structure. A systematic classification of 3-D fabrics is also given. Applications of 3-D fabrics particularly in textile composites are discussed. Some examples of structure–property relationships of 3-D fabrics are also given. Key words: 3-D fabrics, structure–property relationships.

22.1

Introduction: 3-D fabrics

Textile structures are normally fibrous, flexible and soft. Conventionally fiber and yarn are considered as one dimensional as their longitudinal dimension is many times larger than the transverse dimension. Fabrics made from fiber and yarns are often regarded as two-dimensional materials, whereas garments made out of 2-D fabric are considered as 3-D structures. However, all these materials are three dimensional. Woven fabrics are also classified into three groups according to their dimensions: ∑ 2-D fabric: fabric in which the constituent yarns are disposed in one plane. ∑ 2.5-D fabric: fabric in which the constituent yarns are disposed in a two mutually perpendicular planes. ∑ 3-D fabric: fabric in which the constituent yarns are disposed in a three mutually perpendicular planes. 3-D fabrics can be defined as ‘a single-fabric system, the constituent yarns of which are supposedly disposed in a three mutually perpendicular plane relationship’. There are mainly three types of manufacturing systems to produce woven 3-D fabrics. They are 2-D weaving, 3-D weaving and a non-interlacing method called noobing. A conventional 2-D weaving device is employed to produce interlaced 3-D fabric comprising two sets of yarns. In producing interlaced 3-D fabric, three sets of yarns are interwoven. The use of the words ‘three dimensional’ in connection with these structures means that they have substantial measurements in three dimensions, as compared with, say, conventional textile fabrics having substantial measurements in two dimensions only as shown in Fig. 22.1. [1] 393

394

Woven textile structure Y

Z X

(a)

(b)

22.1 Representation of (a) 2-D and (b) 3-D fabrics.

3-D fabrics can also be defined as thick planar sheets or shaped solid forms with multiple layers of yarns, hollow structures and thin 3-D shells. Some have been part of the long history of textiles. An example of a 3-D woven fabric is a forming fabric used in papermaking with two or three interwoven layers. Velvets are made as two-layer fabrics with linking threads, which are then cut to give the fabric pile. A hand-knitted sock is an old form of a 3-D shell structure. [2]

22.2

2-D and 3-D fabric weaving

Figure 22.2 represents 2-D and 3-D weaving processes. These can be differentiated on the following bases: ∑ Pick insertion per loom cycle. In 2-D weaving there is only one pick insertion per loom cycle, while in 3-D weaving there are multiple pick insertions per loom cycle [3]. ∑ Crimp in the fabric. In 2-D weaving there will be unavoidable crimp in the fabric formed, while in the 3-D weaving there will not be any internal crimp in the fabric formed. The higher impact resistance of 3-D fabrics over that of 2-D fabrics is mainly due to the crimpless structure of 3-D fabrics [3]. ∑ Thickness of the fabric. 3-D woven fabrics are thicker than 2-D fabrics. Because of this, 2-D fabric is used in the normal clothing while 3-D fabrics are used in protective clothing [3]. ∑ Production speed. The production speed of 2-D weaving process is much high than that of 3-D weaving process [3].

22.3

Classifying of 3-D woven fabrics

There are two ways to classify 3-D fabrics: ∑ on the basis of geometrical structure; ∑ on the basis of manufacturing method [4].

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Interlaced 3-D fabric

Shedding Picking

Interlaced 2-D fabric Vertical binder yarn (a)

(b)

22.2 Representation of (a) 2-D weaving and (b) 3-D weaving processes [1].

22.3.1 Classification on the basis of geometrical structure According to geometrical details 3-D woven architectures can be classified as: ∑ ∑ ∑ ∑

3-D 3-D 3-D 3-D

solid hollow domes nodal.

3-D solid structures 3-D solids refer to those woven architectures that have solid cross-sections either in a broad panel or in a net-shaped preform.There are a number of different ways to form 3-D solid architectures; each having its own features structurally and mechanically. 3-D solid architecture can be made based on the multilayer principle, orthogonal principle and by angle-interlock principle as shown in Fig. 22.3(a), (b) and (c) respectively [4]. 3-D hollow structures 3-D hollow architectures in this context refer to those having tunnels running in warp, weft, or any diagonal directions in the thickness of the 3-D architecture. There are two different types of 3-D hollow architectures – one with flat surfaces and the other with uneven surfaces. 3-D hollow architectures are generally based on the multilayer weaving principle to join and separate fabric layers in places as needed. 3-D dome structures 3-D dome architecture can be achieved by weave combination, discrete take-up and molding with fabrics of low shear rigidity.

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Woven textile structure

(a)

(b)

(c)

22.3 Cross-sectional views of 3-D solid architectures [4].

3-D nodal structures 3-D nodal architectures basically refer to woven tubes, which are joined together. Smooth opening-up of all joining tubes must be achieved.

22.3.2 Classification on the basis of manufacturing method On the basis of manufacturing method, 3-D fabrics can be classified as: ∑ ∑ ∑ ∑ ∑

multilayer principle; orthogonal principle; angle interlock principle; dual direction shedding method; stitching operation.

Multilayer principle In the multilayer principle, there are multiple layers of distinctive woven fabrics being stitched during the weaving process as shown in Fig. 22.4. 3-D weaving of multilayer preforms is done on conventional weaving machines equipped with an electronic dobby or a jacquard system: this is a well-established textile technology and very cost-effective [4]. As most 3-D composites are produced from high performance yarns (carbon, glass, ceramic, etc.) standard textile tensioning rollers are unsuitable and tension control on the individual yarns during the weaving is critical in obtaining a consistent preform quality. This is generally accomplished through springloaded or frictional tension devices on the creel or through hanging small weights on the yarns before entering the lifting device. Jacquard lifting mechanisms tend to be used more frequently as their greater control over individual warp yarns offers more flexibility in the weave patterns produced. The weft insertion is accomplished with standard technology (generally a rapier mechanism) inserting individual

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22.4 Multilayer fabric.

wefts between the selected warp layers. Variations in the lifting and weft insertion mechanisms to allow multiple sheds to be formed and thus multiple simultaneous weft insertions have also been developed and would allow a faster preform production rate [5]. This type of 3-D architecture has the following features: ∑ Each fabric layer can be given a different weave to facilitate ‘hybrid’ properties through the thickness of the composite. ∑ All warp and weft yarns in the 3-D solid textile architectures can be crimped to specified extents to suit the property requirements of the composite. ∑ The required amount of vertical stitching can be arranged between any layers of fabrics in the preform to enhance the through-thickness property. ∑ Adding straight wadding yarns to any adjacent fabric layer in either warp or weft or both directions can further strengthen the architecture [4]. Orthogonal principle The manufacturing method of orthogonal 3-D fabric is shown in Fig. 22.5. The features of orthogonal principle-based 3-D fabrics are as follows: ∑ All yarns in the three principal directions are laid straight, therefore they are able to take on the load directly and most effectively. ∑ Required amount of vertical yarns can be arranged by the binding weave specification. ∑ The interlinking depth can be altered easily within the same preform, leading to variable preform thickness.

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Woven textile structure

22.5 Manufacturing method for orthogonal 3-D fabric.

∑ Structure can be either isotropic or anisotropic. ∑ Fiber volume fraction is 45–55% [4]. 3-D orthogonal woven fabric is manufactured with a multi-warp yarn system. The main concept of the fabric is to bind straight warp yarns and weft yarns (along 1- and 2-direction) together using binder yarns (along 3-direction). The warp and weft yarns provide high in-plane stiffness and strength, and the binder yarns run through the thickness direction to stabilize the woven structure. 3-D orthogonal woven composites have higher interlaminar fracture toughness and impact damage resistance than laminated composites [5,6]. Angle interlock principle Multilayer interlocked fabrics are a quite distinctive class of preforms, which have been scantily explored to achieve interlocking of fabric layers during the weaving stage. They provide the advantage of cost-effective preform manufacture with control over layer interlocking density based on weave variations apart from imparting higher impact and delamination resistance to the fiber reinforced composites [3]. Woven preforms have two sets of yarns perpendicular to each other interlaced by weaving process. Tensile, bending and permeability properties in either direction of the woven reinforcement is primarily a function of the yarn property, but are also influenced by the fabric weave. Figure 22.6 shows the cross-sectional view of angle interlock 3-D fabric. Some of the features of angle interlock 3-D fabrics are: ∑ it is a multilayer fabric used for flat panel reinforcement; ∑ it is normally woven on a shuttle loom;

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22.6 Cross-sectional view of angle interlock 3-D fabric.

∑ warp yarns are taken directly from the creel; ∑ warp yarns are used to bind several layers of weft yarns together or vice versa; ∑ stuffer yarns can be used to increase fiber volume fraction and in-plane strength. Dual direction shedding method The defining feature of this 3-D weaving process is the dual directional shedding operation. There are two different types of dual directional shedding systems available: linear–linear and linear–angular. No earlier weaving process incorporating a dual directional shedding operation has been known in 5000 years of weaving history. The linear–linear dual directional shedding operation alternately displaces the grid-like arranged warp yarns Z (disposed in accordance with cross-sectional profile needes) to enable creation of multiple sheds in the fabric–thickness and fabric–width directions. Consequently, two mutually perpendicular sets of corresponding wefts Y and X can be inserted into the created sheds. The warps (Z) therefore interlace with the sets of vertical (Y) and horizontal (X) wefts creating an interlaced woven 3-D fabric shown in Fig. 22.7 [3,6,7]. Existing conventional 2-D weaving equipment and its components can be neither used nor modified to carry out this type of 3-D weaving. The main features of this 3-D weaving equipment are: ∑ incorporates linear–linear type of dual directional system; ∑ designed to process a maximum of nearly 3600 warp yarns in a grid arrangement; ∑ stuffer warp yarns can be included between any four adjacently occurring warp yarns; ∑ capable of producing 60 sheds in vertical (fabric thickness) and 60 in horizontal (fabric width) directions;

400

Woven textile structure Y

Z

Warp level

Horizontal shedding

Z

Vertical picking

Y

Interlacing X

X

Z

Interlaced 3-D fabric Warp level

Vertical shedding

Horizontal picking

Interlacing

22.7 Dual direction shedding operation and 3-D fabric formed.

∑ capable of generating a variety of weave patterns in vertical and horizontal directions; ∑ incorporates 60 shuttles in vertical and 60 in horizontal directions; ∑ achieves direct integration of structure in both vertical and horizontal directions; ∑ beating-up operation performed during weft insertion sequence; ∑ standard lengths of up to 3 m produced linearly; ∑ direct production of profiled cross-sections of up to 70 ¥ 70 mm2; ∑ direct production of shell, solid and tubular types of profiled 3-D fabrics; ∑ ensures gentle treatment of fibers and control over dimensional tolerances. As can now be understood, the shells, solid and tubular types of profiled 3-D fabrics are produced directly by arranging the supply of the warp yarns in accordance with the cross-sectional profile to be created. Use of stuffer warp yarns allows direct control over fiber volume fraction. Depending on the cross-section of the profile, the sheds in each direction can be created simultaneously or as required. The weave pattern can be freely varied, if required, between each column and row of warp yarns to meet particular performance demands [6,7]. Shuttle traversal can be activated as and when desired. A direct fabric integration method enables easy profile generation. The beating-up operation during the weft insertion sequence renders the process highly efficient and gentle. Lengths of profiled materials longer than 3 m can be produced. A product combining shell, solid and tubular types in different sections can be produced directly as well, depending on the profile geometry.

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Stitching operation to produce 3-D fabric Basically the stitching process consists of inserting a needle, carrying the stitch thread, through a stack of fabric layers to form a 3-D structure (see Fig. 22.8). Standard textile industry stitching equipment is capable of stitching preforms of glass and carbon fabrics and there are many high performance yarns that can be used as stitching threads. Aramid yarns have been the most commonly used for stitched composites as they are relatively easy to use in stitching machines and are more resistant to rough handling than glass and carbon [5]. The use of aramid stitching threads can, however, cause difficulties in the final composite component due to their propensity to absorb moisture and the difficulty of bonding the aramid yarn to many standard polymer resins. The manufacturer must therefore be aware that these problems may lead to a reduction in the mechanical performance of the component in certain situations. Glass and carbon yarn do not have the problems of moisture absorption and weak interfaces that aramid yarn has, but they are significantly more difficult to use in stitching machines. This is due to their inherent brittleness, which can lead to yarn breakage when stitch knots are being formed, and fraying of the yarn in its passage through the stitching machine. Apart from trying to minimize the potential fraying on the stitch thread the main requirement for a suitable stitching machine is that the needle be capable of penetrating the number of fabric layers to be stitched together in a precise and controlled manner. Stitching has a number of advantages over other textile processes. Firstly, it is possible to stitch both dry and prepreg fabric, although the tackiness of the prepreg makes the process difficult and generally creates more damage within the prepreg material than in the dry fabric. Stitching also utilizes the standard 2-D fabrics that are commonly in use within the composite industry, and therefore there is a sense of familiarity concerning the material systems. The use of standard fabric also allows a greater degree of flexibility Needle thread

Bobbin thread

22.8 Illustration of a stitch pattern through a composite laminate [5].

402

Woven textile structure

in the fabric lay-up of the component than is possible with the other textile processes, which have restrictions on the fiber orientations that can be produced. Through the use of robotic mechanisms, it is also possible to automate the stitching of the fabric and thus create a highly automated and economical production process [5]. Stitching is not restricted to a ‘global’ stitching of the complete component. If required, stitches can be placed only in areas which would benefit from through thickness reinforcement, such as along the edge of the component or around holes. The density, stitch pattern and thread material can also be varied as required across the component therefore this technique has a great deal of flexibility in the arrangement of the through-thickness reinforcement. Stitching can also be used to construct complex 3-D shapes by stitching a number of separate components together as shown in Fig. 22.9. This not only increases the through-thickness strength of the final component but also produces a net-shape preform that can be handled without fear of fabric distortion.

22.4

Modeling equations for weaving 2-D and 3-D fabrics

22.4.1 Weave equations for 2-D fabric A single-layer woven fabric is made from one set of warp yarns and one set of weft yarns. By arranging interlacement between warp and weft yarns, different weave patterns can be obtained. A 2-D binary matrix has been used to represent these patterns. Figure 22.10 shows a 2-D binary matrix and the weave it represents [4].

22.9 Illustration of complex preform manufacture via stitching [5].

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1 0 0 1 Warp

0 0 1 1 0 1 1 0 1 1 0 0 Weft

22.10 Weave and weave matrix.

In order for the computer to create weaves, weaves need to be parameterized. The parameters should be the ones that are commonly used by the weave designer and engineers. Based on the nature of the weaves, weaves are classified into regular and irregular. The former refers to weaves with constant float arrangement and step number within one complete repeat, and the rest are called irregular weaves. Many commonly used weaves are regular weaves. For creating regular weaves, the input parameters are as follows: Nf – the number of floats; Fi (i = 1, 2, 3, …, Nf) – the lengths of the ith float. If i is an odd number, Fi represents a warp-up float; and if i is an even number, it represents a warp-down float; S – the step number of the weave. The weft repeat Rp of a regular weave can be obtained using the following equation [4]: Nf



Rp = ∑ Fi i =1

The step numbers, denoted by S, may be specified either in the warp or the weft direction. The warp repeat, Re, of a regular weave can be calculated by:



ÏÔ Rp /|S| if Rp mod |S| = 0 Re = Ì if Rp mod |S| ≠ 0 ÔÓ Rp

The operator ‘mod’ in the above equation is the remainder operator. This operation returns only the remainder as the result. S must be the smaller one between the absolute value of positive step number in the z direction

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Woven textile structure

of twill line (| Sp | ) and the absolute value of negative step number in the s direction of twill line ( | Sn | ). The parameters needed for the construction of a regular weave are the number of floats, float length Fi where i is an integer such that (1 ≤ i ≤ Nf), and the step number S. A weave matrix, W, is used to represent the weave, and Wx,y is the element of this matrix at coordinate (x,y), where 1 ≤ x ≤≤ Re and 1 ≤ y ≤≤ Rp. The first column of the weave matrix is to be created first using the following equation:



ÏÔ 1 if i is odd integer W1,y = Ì 0 if i is even integerr ÓÔ

where



i Ê i ˆ y = Á ∑ Fj – Fj + 1˜ to ∑ Fj and 1 £ i £ N f Ëj=1 ¯ j=1

The values of the rest of the matrix elements are determined as below:

Wx,z = W1,y

where



Ï y + [S ¥ (x – 1)] + Rp if {y + [S ¥ (x – 1)]} < 1 ÔÔ if 1 £ {y + [S ¥ (x – 1)]} £ Rp z = Ì y + [S ¥ (x – 1)] Ô y + [S ¥ (x – 1)] + E if {y + [S ¥ (x – 1)]} > R p p ÔÓ

2 ≤ x ≤ Re; and 1 ≤ y ≤ Rp.

22.4.2 Weave equations for 3-D fabric In any orthogonal architecture, the relationship between the number of layers of straight warp, Nw, and number of layers of straight weft, Nf, can be explained as follows:

Nf = Nw + 1

Warp and weft repeats of an orthogonal structure can be calculated according to the numbers of layers of straight wrap and weft and the binding weave repeat:

Re = (Nw + 1) ¥ Be



Rp = Nf ¥ Bp

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where Re = warp repeat of the orthogonal structure, Rp = weft repeat of the orthogonal structure, Be = warp repeat of the binding weave and Bp = weft repeat of the binding weave. Therefore, in order to generate an orthogonal weave, it is necessary to provide the number of the straight warp layers (Nw) or straight weft layers (Nf), and the binding weave. Based on the provision of these parameters, the matrix for the noninterlaced body structure is generated as follows [4]: if (x – 1) mod Nw < (y – 1) mod Nf and 1 ≤ x ≤≤ Nw ¥ Be and 1 ≤ y ≤ Rp,

W nix,y = 1

otherwise

W nix,y = 0

where W ni is the weave matrix for the non-interlaced body structure; W nix,y is the element of matrix W ni at the xth warp and the yth weft. The binding weave is introduced to integrate the non-interlaced body structure. Weft repeats of the binding weave must be expanded to suit the straight weft repeat before the introduction using equation:

Wbex,y = Wbx,j for 1 ≤ x ≤ Be and 1 ≤ y ≤ Rp

where Wbex,y is extended binding weave matrix. Wbx,j is the binding weave matrix:

j = [(y – 1)\Nf] + 1

‘\’ is the integral division operator used for dividing two numbers. The result is rounded down and the operation returns an integer. For example, in the expression of a = 17\3, a is equal to 5. Then, the extended binding weave will be inserted into the non-interlaced body structure [4]:

where

Ï W ni if(x – 1) mod (N + 1) > 0 w Ô a,y Wx,y = Ì be ÔÓ Wb,y if(x – 1) mod (N w + 1) = 0



a = {[(x – 1)\(Nw + 1)] ¥ Nw} + [(x – 1) mod (Nw + 1)]



b = [(x – 1)\(Nw + 1)] + 1

22.5

The use of 2-D and 3-D textiles in composites

Textile composite performs are made of two or more fiber and/or fabric layers bonded together. The performance properties of laminate composites depend on the selection, composition and orientation of the individual layers. Laminate construction can be quasi-isotropic or anisotropic (i.e.

406

Woven textile structure

property depends on direction). Each individual layer may be of the same or a different material performing a separate and distinct function. Fabric layers may or may not be stitched together. Laminar composites made of unstitched layers are prone to delamination. Stitching the layers together can be done on-loom or off-loom. Angle interlock structure is an example of on-loom stitching. Layers can be sewn together with a sewing machine that can do off-loom stitching. Laminate composites have good strength, low material and labor costs and are easier to manufacture. Although stitching improves delamination resistance, 3-D performs of stitched layers are not as strong as 3-D woven performs because the amount of yarn in thickness direction (stitch yarn) is relatively small.

22.5.1 Properties of textile reinforced composites Rule of mixture As stated earlier, the primary purpose of composites is to obtain properties that are not possible by any of the constituent materials alone. Continuous fibers, which have a higher aspect ratio (l/d), give the best composite properties in terms of stiffness and strength. Discontinuous fibers with a large aspect ratio are also preferred. As volume fraction of fibers (VF) increases, strength and stiffness also increase. The upper limit of VF is approximately 80%, which is determined by the geometry of the assembly. Process capability to surround the fibers with the matrix materials should also be considered when determining the VF during design stage. In general, the rule of mixtures states that the value of the descriptive parameter of a fibrous composite denoted by Pc is given by: n



pc = ∑ fi Pc = f1P1 + f2P2 + … + fnPn i =1

where, n is the number of components in the composite, fi is the fraction of a component and Pi is the value of the same descriptive parameter for the individual component. If the fiber alignment is in more than one direction, the rule of mixture does not apply. Since textile structural composites are usually made of two components, i.e. fiber reinforcement and resin, n = 2. Therefore some properties of fiber reinforced composites can be roughly estimated as follows. Tensile strength According to the rule of mixture, total stress in a continuous fiber composite is equal to the sum of the stresses in its constituents. For textile structural

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407

composites, the strength of the composite depends on the stress transfer from matrix to the fibers. The fiber length and the alignment of fibers with respect to the loading direction affect the amount of stress transferred. As the angle between the fiber axis and loading direction increases, the strength of the short fiber composite decreases. The strength of the textile structural composite can be calculated as: l s c = ff ÊÁ1 – f ˆ˜ s f + fms m Ë 2l ¯

where sc is the ultimate tensile strength of composite, ff is the volume fraction of fiber, lf is the critical fiber length, sf is the fiber tensile strength, fm is the matrix volume fraction and sm is the matrix tensile strength. This equation is valid when l ≥ lf. The critical fiber length is defined as the length at which fibers are stresses to the breaking stress and is given by:

lf = sf/2t

where t is the interfacial shear stress parallel to the fiber surface. Most of the time lf can be taken as 2000 mm. Density

Q c = f f Q f + f mQ m

where Qc, Qf and Qm are the densities of the composite, fiber and matrix materials respectively. Modulus of elasticity When the direction of loading is parallel to fibers:

E c = f fE f + f mE m

where Ec, Ef and Em are the elastic moduli of the composite, fiber and matrix, respectively. When loading direction is normal to fibers:

1 = ff + fm Ec Ef Em

22.5.2 Advantages of 3-D fabric over 2-D fabric in composite formation 3-D fabrics possess following advantages over 2-D fabrics in composite formation [5]:

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Woven textile structure

∑ 3-D fabrics are highly comfortable to complex mold shapes providing uniform part thickness and eliminating complicated darting and pinwheeling. ∑ 3-D fabrics wet out faster in both open and closed molding, improving quality, reducing molding times and facilitating migration to vacuum infusion. ∑ The higher fiber volume of 3-D fabric and straight non-crimp fibers can lead to stronger or lighter structures. ∑ 3-D fabrics have ‘Z’ fibers through the part thickness. This dramatically impact damage tolerance by suppressing delamination. ∑ 3-D fabrics can be made over 25 mm thick, as a hybrid of carbon, glass and aramid, and can be made in customer specific complex shapes. ∑ The thickness of 3-D fabrics eliminates multiple plies of 2-D and the associated costs.

22.5.3 Advantages of 3-D woven composites over 3-D braided and 3-D knitted composites Three-dimensional preforms can be made using weaving, braiding, knitting and non-woven processes. All 3D textiles have better strength in throughthickness direction, better impact resistance and smaller delamination area. However, each technology has its own strength and weakness [5]. 3-D braiding composites have the following disadvantages: ∑ 3-D braiding machines can only make preforms to be mobile in a braiding process with a relatively small cross-section. ∑ The mechanical properties of braided composites are not constant and large variation was found in tests. ∑ The in-plane modulus of braiding structure can be significantly lower than that of unidirectional composite due to the large angle between fibers and loading direction. 3-D knitted composites have the following disadvantages: ∑ Most conventional knitting machines cannot produce thick preforms. ∑ Weft knitting of non-crimp fabrics causes breakage and distortions to the in-plane fibers. ∑ Because the stretching of the fabric during fabrication will result in a structure change, knitted composites usually contain ‘soft spots’ and ‘hard spots’ [5]. Stitching is widely used in aerospace applications. However, its application is restricted by several drawbacks: ∑ Most stitching machines can only handle preforms less than 1 m wide and 5 mm thick. A large capacity sewing machine is usually very costly.

Modeling three-dimensional (3-D) woven fabric structures

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∑ The sewing machine cannot stitch curved composites or handle complex structures. ∑ Most sewing machines are limited to a vertical stitching plane. ∑ Stitching breaks the fiber in the needle path and degrades the in-plane properties of the composites [5]. 3-D woven composites were developed in the early 1970s first in the manufacturing of 3-D carbon–carbon composite for aircraft brakes. Compared with 2-D laminates, 3-D woven composites have the following advantages: ∑ 3-D weaving can produce complicated near-net-shape preforms. This capability greatly reduces the material cost and handling time. The integrated complex shaped structure tends to have better mechanical properties ∑ Through-thickness properties can be adjusted by controlling the amount of Z (warps) yarns. The variation of properties could also be achieved by hybriding. ∑ Z yarn could arrest the cracks formed during impact loading; therefore, 3-D woven composite has high ballistic impact damage resistance and low velocity impact damage resistance. A 3-D composite will also have improved post-impact mechanical properties than that of the 2-D laminates. ∑ 3-D woven composites have higher failure strain and fracture toughness than that of 2-D laminates. ∑ Woven fabrics usually exhibit good dimensional stability in the warp and weft directions. It also has highest yarn packing density and provides higher out-of-plane strength. Thus it can carry higher secondary loads and local buckling. ∑ Woven fabrics have a very low shear rigidity that gives a very good formability [5].

22.6

The tensile properties of 3-D textile composites

An understanding of the failure mechanisms of textile composites is expected to accelerate the design of improved structures, since those microstructural features that degrade performance can be eliminated from preforms, while those that enhance performance can be incorporated. A significant amount of research has been conducted on the compression and compression-afterimpact properties of 3-D woven composites. The tensile properties and failure mechanism of 3-D woven composites have been investigated since the mid-1980s, but only recently has an understanding of their tensile performance begun to emerge. Tensile studies

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Woven textile structure

have been performed on 3-D woven composites with orthogonal or interlock woven structures made of carbon, glass or Kevlar. Numerous studies have compared the tensile properties of 3-D woven composites against 2-D laminates with similar (but not always the same) fiber content, and different results are reported. Young’s modulus of some 3-D woven composites is lower than the modulus of their equivalent 2-D laminate. The difference is shown by a comparison of tensile stress–strain curves for a 2-D and 3-D woven composite in Fig. 22.11. The figure shows that Young’s modulus of the 3-D composite is about 35% lower than the 2-D composite. However, in some cases the tensile modulus of 3-D woven composites can be slightly higher than the 2-D laminate [5]. Cox [8] has outlined a significant study relating the unique microstructural features and failure mechanisms of 3-D woven composites to their tensile properties. In that work, carbon and epoxy composites with a variety of woven architectures (orthogonal, layer-to-layer angle interlock and throughthe-thickness angle interlock) were loaded to failure in the warp direction. Cox identified a number of regions on the stress–strain curve, which is shown in Fig. 22.12, that were common for all fiber architectures tested and related these features to failure mechanisms occurring in the material. Cox observed that after an initial linear region up to a strain of about 0.6%, there was a significant non-linear response, which was termed the ‘hardening phase’, which continued up to the primary load drop at a strain of 2.5–3.0%. They attributed the gradual stiffness reduction occurring in the hardening phase to ‘inelastic’ straightening of the in-plane tows. Towards the end of the hardening phase, Cox observed that the smooth stress–strain 400

2-D woven composite

Tensile stress (MPa)

350 300 3-D woven composite

250 200 150 100

Onset of plastic tow straightening

50 0 0

1

2 3 Strain (%)

4

5

22.11 Tensile stress–strain curves for 2-D and 3-D woven composites [5].

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411

1200

Stress (MPa)

1000

Elastic load line

800

Hardening phase

600 400 Pull-out phase 200 45 mm gauge 0

0

0.05

0.10 Strain

0.15

0.20

22.12 Tensile stress–strain curve for a 3-D woven carbon/epoxy composite [5].

100

Load (kg/mm2)

Abrupt failure 75

50

3-D 3-D 3-D 3-D 2-D

25

– 3A – 3A – 5A – 5A –2A

– – – –

5 7.5 5 7.5

0 0

0.4

0.8 1.2 Displacement (mm)

1.6

2.0

22.13 Load–displacement curve from a tensile test on 2-D and 3-D orthogonal composites. [5].

curve gave way to a series of jagged peaks and small load drops due to the rupture of individual tows as shown in Fig. 22.12. After the primary load drop, low loads were required to separate the specimen halves. This was

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Woven textile structure

termed the ‘pull-out phase’ and described the process of warp tows, which had ruptured randomly along their length, being gradually withdrawn from the opposing specimen half. Cox’s work was limited to a number of specific weave architectures in one carbon/epoxy material system. There are wide varieties of 3-D architectures and material systems that are of interest to the composites industry. After Cox, other authors have done some experiments [9,10,11]. to examine the tensile failure mechanism of different types of 3-D composites.

22.6.1 Load–elongation curve of 2-D and 3-D composites The load–displacement curves of 2-D and 3-D orthogonal composites are shown in Fig. 22.13.

22.7

References

1. Khokar N (2008), Second generation woven profiled 3D fabrics from 3D weaving; The first world conference on 3D fabrics and their application; 10–11 April 2008 Manchester Conference Centre, UK. 2. Hearle W S (2008), Innovation for 3D fabrics; The first world conference on 3D fabrics and their application; 10–11. 3. Khokar N (1996), 3D Fabric-forming Processes: Distinguishing Between 2D-Weaving, 3D Weaving and an Unspecified Non-interlacing Process, J. Text. Inst., 87, Part 1, 97–106. 4. Chen X (2008), CAD/CAM of 3D woven fabrics for conventional loom; The first world conference on 3D fabrics and their application; 10–11. 5. Tong L, Mouritz A P, Bannister M K (2002), 3D Fiber Reinforced Composites; Elsevier Books. 6. Mohammed M H (2008), Recent advances in 3D weaving; The first world conference on 3D fabrics and their application; 10–11. 7. Khokar N (2002), Nobbing: A Non Woven 3D Fabric Forming Process, J. Text. Inst., 93; (1), 52–74. 8. Cox B N, Dadkhah M S, Morris W L and Flintoff J G (1994), Failure mechanisms of 3D woven composites in tension, compression, and bending, Acta Metall Mater 42 (12), 3967–3984. 9. Chou S, Chen H and Chen H (1992), Effect of weave structure on mechanical fracture behavior of three dimensional carbon fiber fabric reinforced epoxy resin composites, Compos Sci Technol 45, 23–35. 10. Cox B N, Dadkhah M S and Morris W L (1996), On the tensile failure of 3D woven composites, Compos Pt A: Appl Sci Manuf 27 (6) 447–458. 11. Callus P J, Mouritz A P, Bannister M K and Leong K H (1999), Tensile properties and failure mechanisms of 3D woven GRP composites, Compos Pt A 30 1277– 1287.

23

Application of woven fabrics

Abstract: This chapter deals with the application of modeling in the area of technical textiles. The chapter reviews such examples as sportswear, medical applications, textiles for electronics and airbag construction in automotive engineering. Key words: textile modeling, technical textiles.

23.1

Introduction

The formal structure of a woven fabric is defined by weave, thread density, crimp and yarn count. The design of a fabric to meet the requirements of a particular end use is a complicated engineering problem. Theoretically, it is possible to design a fabric structure to achieve any desired characteristic, but in actual practice it is not so easy because of inherent nonlinearity and complex relationship between structure and properties of the textile materials along with their visco-elastic behavior. The factors associated with fabric design include fiber type, yarn geometry, fabric structure and finishing method. The use of different weaves alters the ability of the component threads to move relative to one another, and as a result mechanical properties such as shear characteristics and drapeability of fabric change significantly. The strength of the woven fabric is highest in the warp and weft direction, while in bias, the fabrics show lower mechanical properties, higher elasticity and lower shear resistance. The utility performance properties of speciality woven fabrics depend on the combined effect of the properties of the constituent fibers, yarn and the fabric structure. Thus, designing such a fabric consists of identifying the best combination of those variables that renders the fabric, able to meet the performance requirements. In order to enhance mechanical properties, a triaxial woven structure that consists of three systems of threads (one system for weft and two systems for warp) can be constructed. Warp threads in a basic triaxial fabric are interlaced at 60° and the structure is fairly open with a diamond-shaped center. A modification of basic triaxial fabric is basket weave that forms a closer structure with different characteristics. Woven fabrics have broad application in all segments of technical textile production. Conventional and triaxial fabrics fall into the group of 2-D fabrics. The application of woven fabrics in production of technical textile (as reinforcement in composite 413

414

Woven textile structure

production), has inflicted the need for production of 3-D fabrics, which have high mechanical properties in x, y and z directions [1]. The uniqueness and challenge of technical textiles lie in the need to understand and apply the principles of textile science and engineering to provide right solutions to the growing and widely varying demands of their applications in areas such as protective clothing, sportswear, automotive textiles, geotextiles, agricultural textiles, medical textiles and textiles for building and construction and specialty textiles for defence and military applications. Thus it is very important to have an in-depth knowledge of the principles involved in the selection of raw materials and their conversion to desired yarns and fabric structures followed by various treatments such as coating and finishing of fabrics to introduce special technical and commercial features of a wide range of specific areas of applications. High performance technical textiles should not only possess general fabric characteristics but should also satisfy the critical performance requisites. Such fabrics should be engineered with utmost precision for its performance requirements.

23.2

Fundamental aspects of woven textile structure and function

23.2.1 Configurational functions of fiber The reason why textiles are selectively used for a certain specified end use instead of the other kinds of materials is that the textile products in which some of the configurational functions of fiber are effectively utilized can become most valuable among several forms of materials such as powder and solid sheet. The configurational functions of fiber consist of the following four elements: ∑ ∑ ∑ ∑

flexibility (pliable); high ability in axial transmission of such properties as mechanical; high specific surface area; technological easiness in transformability into textile structure; materials such as woven and nonwovens.

23.2.2 Structural system of fiber assembly Fiber assembly structural systems can be summarized based on constitutional element, orientation of element, bonding manner of element and macroscopic form. ∑ ∑ ∑

uniaxial bundle of membrane hollow fiber; nonwovens; glass matt thermoplastic sheet called stampable sheet;

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∑ ∑ ∑

415

woven fabrics; knitted fabrics; braids.

23.2.3 Function system of fiber assembly structures The functions of fiber assembly structures for technical textiles are classified as mechanical bearing, shielding, removal or separation, medium transportation, axial conduction and reinforcement.

23.2.4 The maximum fiber volume fraction There is a geometrical upper limit in the fiber volume fraction which is dependent on fiber orientation and aspect ratio. It must be considered as an inevitable restrictive condition for designing assembly structure.

23.2.5 Pore size and its distribution within fiber assembly structures Pore size is an important parameter for considering such functional properties as shielding, medium transportation and removal or separation. Total fiber lengths by unit volume, inter-fiber coherence are main factors to determine pore size and its distribution.

23.2.6 Directive fiber assembly structures for required functions Directive fiber assembly structures can be roughly assigned to meet required functions using following consideration. ∑ ∑ ∑ ∑ ∑ ∑

For the mechanical functions of tensile loading, impact loading, tear resistance, ballistic resistance, oriented filament is used as constitutional element. For shielding, fiber or yarn is used as constitutional element formed into sheet. For removal or separation, there are typically two kinds of fiber assembly forms; randomly oriented fibers in sheet and uniaxially oriented bundle of membrane hollow fiber. For medium transportation the constitutional element is usually fiber, to obtain a high contact area of assembling struct with medium. For axial conduction, fiber or filament is usually uniaxially oriented. For reinforcement, there are typically two types: fiber randomly distributed within the matrix and yarn unidirectionally oriented within the matrix.

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Woven textile structure

These kinds of analysis can provide a directional systematic knowledge for designing optimum assembly structure for developing different textile products suitable for various end-use applications.

23.3

Medical textiles

Medical textiles are the products and constructions used for medical and biological applications for clinical and hygienic purposes, scaffolds for tissue culturing and a large variety of prostheses for permanent body implants. They consist of all those textile materials used in health and hygienic applications in both consumer and medical markets. A broad classification of medical textiles can be as under: ∑ ∑ ∑ ∑ ∑

Protective and healthcare textiles – surgical wear, operation dresses, staff uniforms, etc. External devices – wound dressings, bandages, pressure gauze, prosthetic aids, etc. Implantable materials – sutures, vascular grafts and artificial limbs are the products where textiles are used. Hygiene products – incontinence pads, nappies, tampons, sanitary towels, etc. Extracorporeal devices – artificial liver, artificial kidneys and artificial lung are the recent advances in medical textiles.

23.3.1 Woven medical textiles Woven medical textiles are typically used for products requiring extreme stability and; high durability over a significant number of loading cycles; or to precisely control porosity for air or fluid flow. For example, a good quality surgical gown must be made of light and comfortable, breathable fabric material, yet be tough and durable enough to withstand abrasion, ripping and puncture. Surgical gowns must act as a barrier between the sources of infection (micro-organisms such as bacteria, and viruses of different size and geometry) and the user (healthy person), and must also demonstrate good wearing comfort. The latter is important for the surgeon who often has to wear the surgical gown for several hours while doing hard work. Hydrophobic wovens from polyester are used for shorter surgical operations with a small amount of liquid, and have so far been the only reusable surgical gowns which are currently able to fulfill both these contrary demands of barrier effect and wearing comfort [2]. The barrier function of such fabrics depends on the surface structure, and also on the number and size of the continuous pores running through the fabric; the pores which run both between the filaments in the filament yarn

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417

and also between the filament yarns. When the ‘barrier’ is the feature to be evaluated, there are three measurable characteristics: ∑ ∑ ∑

resistance to dry microbial penetration; resistance to wet microbial penetration; resistance to liquid penetration.

When the mechanical resistance is the feature to be evaluated, there are four measurable characteristics: ∑ ∑ ∑ ∑

dry bursting strength (combination of air movement and mechanical action); wet bursting strength (combination of wetness, pressure and rubbing); dry tensile strength; wet tensile strength.

When the freedom from contamination or unwanted foreign matter is the feature to be evaluated, there are two measurable characteristics: ∑ ∑

microbial (not viable micro-organisms); particulate matter (freedom from particles not generated by mechanical impact).

When the release of fiber fragments or other particles, originally from the fabric itself, is the feature to be evaluated, there is one very important measurable characteristic: linting. The only obvious characteristic that is exclusively requested for the surgical drapes (but not for the surgical gowns) is adhesion for fixation for the purpose of wound isolation.

23.4

Automotive textiles

Automotive textiles are finding extensive use in the product categories of interior trims, safety devices such as seatbelts and airbags, carpets, filters, battery separators, hood liners, hoses and belt reinforcement. Textiles, which constitute approximately 20–25 kg in a car, are not only used for enhanced aesthetics of automotives but also for sensory comfort and safety. Additionally, few textile products found their application as design solutions to engineering problems in the form of composites, tyre reinforcement, sound insulation and vibration control. Apart from woven and knitted constructions, nonwovens also find applications in automotive textiles due to certain advantages served by them. The fabrics used worldwide as surface material for car interior can be woven, knitted or nonwovens. Woven fabrics represent the dominant application areas in seat covers, headrests and door panels. Fabrics are characterized by a large variety in design, stable shape retention and high mechanical resistance.

418

Woven textile structure

23.4.1 3-D woven fabrics for automotive textiles 3-D sandwich woven fabrics are made of 100% E-glass yarns, as well as carbon fiber, basalt fiber or other high performance fibers. Two deck layers are bonded together by Z-piles to the specified height of 2–25 mm. When the fabric is impregnated with a thermoset resin, it immediately absorbs the resin and, due to the capillary forces of the Z-piles, the fabric rises to the preset height. Because the composite material is a kind of hollow integrated core sandwich structure that offers excellent mechanical properties and design versatility. The composite material is widely used for many applications in the core composites industry, such as ships, railways, automotive, aviation, wind energy, double wall tanks and construction, while offering multiple advantages (delamination, impact, etc.) against traditional sandwiches such as honeycombs, foams, balsa and more.

23.4.2 Airbags Airbags are a type of automobile safety restraint like seatbelts. They are gas-inflated cushions built into the steering wheel, dashboard, door, roof or seat of the car that use a crash sensor to trigger a rapid expansion to protect a person from the impact of an accident. The working of airbag is a precision application. Airbags should begin to inflate 0.03 seconds after a crash and should be fully inflated after 0.06 seconds. Airbags may be built into steering or in some other strategic location. Nitrogen gas is commonly used in airbags. Fabrics used for airbags must be able to withstand the force of hot gases and they must not penetrate through the fabric. Airbags are typically woven from high tenacity (HT) multifilament nylon 6,6. Nowadays, a one-piece weaving system produces an airbag directly on loom, but formerly two pieces were sewn together with suitable threads. Typically, front airbags are uncoated. The size of airbags may vary according to their position. The concept of the airbag, a soft pillow to land against in a crash, has been around for many years [3]. Airbag working Airbags inflate, or deploy quickly, faster than the blink of an eye. Imagine taking one second and splitting it into one thousand parts. In the first 15 to 20 milliseconds, airbag sensors detect the crash and then send an electrical signal to fire the airbags. Typically a squib, which is a small explosive device, ignites a propellant, usually sodium azide (NaN3). The azide reacts with potassium nitrate (KNO3) and burns with tremendous speed, generating nitrogen, which inflates the airbags. Within 45 to 55 milliseconds the airbag

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is supposed to be fully inflated. Within 75 to 80 milliseconds, the airbag is deflated and the event is over [4]. When airbags work properly, they dramatically reduce the chance of death or serious injury. However, the speed with which airbags inflate generates tremendous forces. Passengers in the way of an improperly designed airbag can be killed or significantly injured. Unnecessary injuries also occur when airbags inflate in relatively minor crashes when they are not needed. Airbag inflation The goal of an airbag is to slow the passenger’s forward motion as evenly as possible in a fraction of a second. There are three parts to an airbag that help to accomplish this feat: ∑ ∑

∑

The bag itself is made of a thin nylon fabric, which is folded into the steering wheel or dashboard or, more recently, the seat or door. The sensor is the device that tells the bag to inflate. Inflation happens when there is a collision force equal to running into a brick wall at 10 to 15 miles per hour (16 to 24 km per hour). A mechanical switch is flipped when there is a mass shift that closes an electrical contact, telling the sensors that a crash has occurred. The sensors receive information from an accelerometer built into a microchip. The inflation system which inflates the airbag through the production of nitrogen.

Airbag manufacture Airbag fabrics are made of nylon 6,6 multifilament yarns with counts from 235 to 940 tex. Airbag fabrics are generally dense which presents a challenging task to weave. Tensile strength, elongation, tear proportion resistance and weight requirement of airbag fabric are critical [5]. Air permeability of airbag fabric should be uniform across the whole width of the fabric. There are currently two principal material types which are used in the manufacture of airbags. They are uncoated nylon (polyamide 66) and coated nylon. Two types of commonly used coatings are silicone and neoprene. In general, coated materials are used for driver’s side airbags and side impact bags, while passenger side airbags are made from uncoated nylon materials [6,7]. All airbag cushions manufactured worldwide are constructed with fabric made from nylon 6,6 yarn. The key initial drivers were performance, cost and benefit. As one can imagine, the key function of the airbag cushion is to absorb the impact. Nylon 6,6 has superior capability in energy absorption. The balance between the strength and elongation gives it unmatched suitability for airbag cushion materials. The performance attributes that have

420

Woven textile structure

led to industry standardization are its breaking strength or tenacity; energy absorption capability or toughness; heat resistance; and stability over time as measured by accelerated aging tests [6]. More recently, a third selection criterion has started to come to the fore, that of proven performance or confidence. Since the airbag system forms part of the automotive supply chain there is continuous and necessary consideration of other materials such as polyester, for use in the airbag cushion. It is possible to demonstrate that all these alternatives, including polyester are significantly inferior to nylon 6,6 when measured against the key performance attributes listed above and that their use would pose a risk of failure in airbag applications. That lower performances of polyester coupled with increasing legislative and litigation activity around automotive safety and the lack of a track record in the global market for polyester have led to the conclusion that polyester is not appropriate for airbag cushion use. For comparison purpose, the key physical properties of nylon 6,6 and polyester are shown in Table 23.1. The key differences between the two polymers are density and specific heat capacity. Comparison of key properties of nylon 6.6 and polyester Although nylon 6,6 and polyester have similar melting points, the large difference in the specific heat capacity causes the amount of energy required to melt polyester to be about 30% less than that required to melt nylon 6,6. Hence in any inflation event that uses a pyrotechnic or pyrotechnic-containing inflator, cushions made from polyester yarn are far more susceptible to burn or melt through in the body of the cushion or at the seam. The second advantage of nylon 6,6 is its lower density. Lower mass has key advantages; reducing the mass of the cushion lowers the kinetic energy of impact on the occupant in out-of-position situations thus enhancing safety, while allowing the overall weight of the vehicle to be reduced. The difference in density between the two polymers leads to polyester yarns usually being of higher denier or decitex (weight per unit length) than nylon 6,6, to generate the same filament diameter. These results in reduced

Table 23.1 Key physical properties of nylon 6,6 and polyester 3

Density (kg/m ) Specific heat capacity (kJ/kg/K) Melting point (°C) Softening point (°C) Energy to melt (kJ/kg)

Nylon 6,6

Polyester

1140 1.67 260 220 589

1390 1.3 258 220 427

Application of woven fabrics

421

fabric coverage. Using polyester yarn, the cushion fabric is more open for gas permeation. This reduces thermal protection for the vehicle occupants, and makes it more difficult for the cushion designer to control the bag deployment dynamics. In addition, since seam strength is strongly dependent on cover factor, seam performance is negatively impacted. This is particularly important since seam leakage of hot gas is one of the principal concerns of the engineer and the potential for an increase in leakage combined with a reduction in thermal resistance is critical [8,9]. Coated base fabric for airbags A coated airbag base fabric made of a textile fabric that has an excellent air barrier property, high heat resistance, improved mountability, and compactness and excellent adhesion to a resin film is characterized in that at least one side of the textile fabric is coated with resin, at least part of the single yarns of the fabric are surrounded by the resin, and at least part of the single yarns of the fabric are not surrounded by the resin. An airbag is characterized by using such a coated airbag base fabric [10]. A method for manufacturing the coated airbag base fabric is characterized by applying a resin solution having a viscosity of 5–20 Pa s (5000–20 000 cP) to the textile fabric using a knife coater with a sharp-edged coating knife at the contact pressure between the coating knife and the fabric of 1–15 N/cm [11]. Laminated material for airbag A polymer film, preferably polyamide polymer film, which comprises at least one first layer and a second layer, is laminated onto a fabric. The material of the first layer has a glass transition temperature of less than 10 oC, while the material of the second layer has a glass transition temperature of less than 20 oC. Preferably, the polymeric materials contain portions of polyamide blocks. The fabric–polymer film laminate is suitable as a laminated material especially for an airbag [11].

23.5

Filter fabrics

The surface quality of a woven fabric has become an increasingly important factor which influences the property of the filter in many different ways. Surface treatments modify the functionality of the woven fabric according to the different requirements and thereby significantly increase the effectiveness of the resulting filter in a specific environment [12]. The following surface treatment technologies improve the surface property:

422

∑ ∑ ∑

Woven textile structure

wet chemical surface modification (mainly hydrophilic); low temperature plasma treatment (mainly activation, fictionalization and plasma polymer deposition); metal coating (aluminum, copper and nickel).

The selection of the appropriate fabric type and coating depends on the functionality needed for the test. The phenomenon of wetting or non-wetting of a solid by a liquid is better understood by studying contact angle of a liquid drop on a condensed surface as demonstrated in Fig. 23.1. The lower the contact angle between liquid drop and fabric surface, the better the hydrophilic action of the fabric. Woven filters are used in many acoustic devices, loudspeakers and microphones. Filters not only improve the speech and sound quality in mobile phones by adsorbing unwanted frequency peaks; they also protect the sensitive electronic equipment from moisture, dust and dirt. Hydrophobic surface treatments offer an excellent protection against moisture uptake and contamination. Acoustic fabrics are hydrophobically treated to provide optimal protection against moisture uptake and to repel dust and dirt. Hydrophobic woven fabrics protect loudspeakers and microphones from moisture, dust and dirt. In automobiles, a series of filter systems are used to protect sensitive components. High precision woven fabrics are mounted in the fuel, injection and hydraulic filter systems. Since the fuel can be contaminated with particles and dirt originating from refining, transport and storage, from the filling process or from simply the automobile tank itself, a series of security filters are installed along the fuel transport path. These filters, from the tank to the injector system, protect the mechanical parts from damage and prevent the injection nozzles from blocking. In addition, high water content is usually found in fuels, especially in diesel, which has to be removed as it may lead to corrosion. In order to enhance water removal, the fabrics used in fuel systems should be hydrophobic. Fabrics remove water from kerosene and other fuels. An airplane carries thousands of liters of fuel which must be free of particles and water to guarantee trouble-free operation of the jet engines. Jet fuel contains a certain amount of dissolved particles (approx. 60 parts per

23.1 High-contact angle, hydrophobic fabric and low-contact angle, hydrophilic fabric.

Application of woven fabrics

423

million [ppm], ca. 60 micrograms per kilogram of kerosene); free water must be removed to prevent freezing and blocking of the fuel transport system. Coalescer systems are used in the removal of water from jet fuel and others (e.g. diesel). Water droplets combine at the coalescer surface (filter medium) to form drops which by flow and or gravity move to a separator. The fuel then flows through the separator while the water drops are retained by the hydrophobic filter [13]. The surface of the separator consists of a hydrophobic woven filter medium supported by a stainless steel element.

23.6

Textiles for electronics

E-textile technology holds out the promise of truly wearable computers as well as inexpensive large-scale computational devices. To achieve these goals, e-textiles combine high volume, low cost textile manufacturing capability with discrete electronics and novel fiber technologies. Industrial weaving machines capable of inserting thousands of meters per minute of weft yarn can efficiently produce large volumes of complex woven textiles while individually controlling the position of every fiber in the design. New fibers are being created for inclusion in e-textiles, including battery fibers, conductive fibers and mechanically active fibers. Methods are being developed for attaching discrete components to e-textiles, including processors, microphones and speakers. Two broad categories of e-textile applications are envisioned, wearable and large-scale non-wearable [14]. Many specific applications in the field of wearable computing have been envisioned and realized, though most suffer bulky form factors. In the new field of large-scale non-wearable e-textiles, applications include large-scale acoustic beam-forming arrays (STRETCH), self-steering parafoils (Draper) and intelligent, inflatable decoys (DARPA). Both categories of e-textile applications share three common design goals: low cost, durability and long running. ∑

∑

∑

Low cost dictates the use of inexpensive, commercial, off-the-shelf (COTS) electronic components and yarns as well as the design of weaves and architectures that are manufacturable in current or slightly modified textile production systems. Durability dictates that the system must tolerate faults, both permanent and transient, that are inherent in the manufacture and use of the device. In addition, there is an expectation that individual components may not be repairable and that system functionality should gracefully decline as components fail. Long running dictates that the system must manage power consumption in an application-aware fashion to minimize the need for bulky batteries and/or external power recharge. Power scavenging and distributed power management are essential.

424

Woven textile structure

In the category of wearable computing, a garment that provides the user with precise location information within a building is analyzed. A large-scale, non-wearable acoustic beam-forming array is analyzed. Textiles are woven as opposed to alternative textile manufacturing techniques such as knitting, embroidering, or non-woven technologies. Woven textiles allow for stable fabrics with a high degree of precision, but impose directional limitations on the fabric, which have implications for communication within the textile. Virtually all woven e-textiles are expected to use the new fiber batteries and solar cells under development. This will lead to highly distributed, redundant power supplies for e-textiles in which some parts of the textile have more remaining power than others [15].

23.6.1 Mapper garment The mapper garment tracks the motion of the user through a structure by monitoring the user’s body position, the user’s movement, and the distance of the user from surrounding obstacles. Such a garment would allow users to be given directions in a building, maintenance workers to be automatically shown blueprints for their current room, or users to automatically map existing structures. The user’s body position is measured by a set of piezoelectric strips woven into the clothing; by measuring the deformation along tens of strips, the physical configuration of the user’s body can be detected [16]. The user’s activity, such as walking up stairs, climbing a ladder and walking on a flat surface, can be detected. The user’s movement rate can be measured by a small set of discrete accelerometers as well as a digital compass attached to the garment. The distance from obstacles is measured using ultrasonic signals. An array of approximately ten ultrasonic transmitters, also piezoelectric strips, are distributed around the garment to periodically send signals in each direction; a similar number of receiver piezoelectric strips are used to detect the reflected signals, allowing time-of-flight to be measured. The primary challenge in this application is interfacing to a large number of sensors and actuators in a reliable fashion. Simply attaching the leads of every sensor or actuator to a single processing unit and power supply would not meet the design goal of a durable e-textile. In the event of a tear in the fabric, single leads running to one collection point could lead to significant rather than graceful degradation in performance; in addition, the potentially long leads required would cause degradation in analog signal quality unless significant amplification is applied, leading to larger power consumption. The garment needs multiple points at which analog data is converted to digital data; these conversion units, likely in the microcontroller or digital signal processor (DSP) class, would need to communicate within a fault tolerant network. The sample rate at each conversion point is very low (10–100 per second) for the body position sensors and moderate (100 000 per second)

Application of woven fabrics

425

for the occasional ultrasonic reception. Once the data has been converted to a digital format, low power data transmission and coding techniques can be applied. By carefully managing the active sensors and processing units the power requirements of the system can be reduced. When determining the location of a wall, the garment must activate a transmitter in the direction desired and then sample a receiver for the return signal. This will accurately compute the distance, but gives no information on the direction in which it is located. To compute direction, the location of the transmitter on the body, the position of that part of the body relative to the torso, and the direction in which the user’s torso is pointing must be known. The location of the transmitter should be known from the manufacturing process and the digital compass can provide the torso direction. A number of techniques are available for determining the location of one part of the e-textile with respect to other parts of the e-textile; in the garment, the body position is available and acoustic beam forming could be used to determine the location of all of the ultrasonic transceiver with respect to one another. To accurately compute the body position requires the analysis of samples from a large set of sensors that have been collected at several processing elements. Due to its nature, the analysis is best done at a single processing element. To initialize the collection of the data, the processing element would send out a query to the selected elements, such as ‘give me your current reading’ or ‘give me your reading every 100 ms’. In both cases, some time stamp should be applied to both the query and the replies, though high accuracy is not required in this particular application [17].

23.6.2 Beam-forming array The beam-forming array textile gathers data from a large array of acoustic sensors and analyzes this data to determine the direction of an acoustic emitter (e.g., a moving vehicle or a human voice). Through the use of acoustic beam-forming algorithms, a set of three acoustic sensors can identify the direction of a single emitter if the sensors and the emitter are all in the same plane. Identifying the direction of multiple emitters or working in three dimensions requires data from more acoustic sensors. Further, given noise and potential miscalibrations in the acoustic data, the use of redundant acoustic sensors is advisable. If the fabric is large enough, then not only the direction, but also the location of an emitter can be found. Like the mapper garment, for reasons of robustness, the large number of sensors is not all handled by one conversion or processing node; the fabric is sprinkled with many communicating processing nodes. It is important to note that each acoustic sensor must know its location precisely with respect to the other sensors; small errors in sensor location result in increasingly larger errors as the distance to the emitter increases. Although this is not a wearable

426

Woven textile structure

textile, it is flexible and thus subject to movement; at a minimum, the initial position of each acoustic sensor must be computed. In contrast to the mapper garment, the positions of each sensor must be known quite accurately. To accomplish this, the textile is augmented with speakers that are physically co-located with a subset of the acoustic sensors; by systematically activating the speakers, the distances between the microphones can be determined. Once enough distances are known, the relative positions of all of the microphones can be computed. The frequency, direction and distance of a potential target all affect the optimal selection of a subset of sensors on which to perform beam forming. Because beam forming is fairly computationally demanding, it would be wasteful of resources, including power, to collect and analyze the data from the entire set of acoustic sensors. An efficient strategy, therefore, is to have a small active set of sensors look for emitters while the rest of the sensors sleep to conserve power. Upon the tentative identification of an emitter’s characteristics along with an assessment of remaining power at processing nodes, an optimal set of sensors can be activated. Once a set of sensors is selected, the time series data from those sensors must be collected at a single processor where the beam-forming algorithm is to be run. If multiple beams are formed, then the direction and intensity data must be combined at a single node; this is much less demanding of communication resources than the exchange of time series data. It is expected that some nodes along potential routes may be asleep, others out of power, and some broken; routes must be found in spite of these drawbacks. In addition, time series data from different nodes must be synchronized; small errors in time can lead to large errors in the computed results [17].

23.6.3 Nanotube-based e-textile Conductive woven fabrics are made by utilization of metallic conducting wires which are flexible wearable electrical circuits; the properties of nanotube-based yarns could be leveraged to produce more robust systems far lighter and more flexible than metallic wires. The applications and methods of integration of conductive yarns into clothing have been dealt with the integration of conventional integrated circuits and the utilization of fabricbased components as part of wearable computing devices. As a step in the direction of creation of nanotube-based electronic components for fabric applications, super-capacitors woven into a textile fabric as shown in Fig. 23.2 has been reported. The capacitors were shown to have capacitances and life cycles comparable to commercially available super-capacitors. Since nanotubes are also known to have effects similar to piezoelectric materials (when exposed to strains), such materials could

Application of woven fabrics

427

be integrated into structures to produce sensors that monitor the stresses in structures [18].

23.6.4 Organic field effect transistors (OFETs) By coating fibers with conducting polymer, they can join them with solid electrolyte at cross-points to form micrometer-sized organic electrochemical transistors (OECTs). They then use the OECTs as components for logic circuits, offering an alternative approach to organic field effect transistors (OFETs) commonly used in flexible electronics. The wire OECTs provide an easier route to weaving electronics directly into fabrics Fig. 23.3 [19]. Common OFETs operate like electrical valves, with the flow of current between the sources and drain electrodes controlled by the voltage of the gate electrode. Increasing the gate voltage injects charges into the conducting polymer next to the gate electrode, creating a conduction channel, through which the source-to-drain current flows. The magnitude of the voltage applied by the gate controls the size of this conduction channel. OFETs can be flexible, but printing them onto fibers is a complex process. Their successful operation depends on the accurate control of the electric field applied to the polymer by the gate electrode, which in turn requires a very thin and uniform insulating layer to be deposited between the gate and active polymer. Precise micropatterning of source drain and gate electrodes on a fiber is therefore needed. These requirements make the implementation of OFET-based knitted or woven structures very impractical. ∑

OFET on fibers; switching from the Off to the On state operates through charge accumulation in the polymer channel under the action of the electric field from the gate electrode, which increases the polymer conductivity in the conduction channel.

23.2 Woven textile super-capacitor.

428

Woven textile structure Source

Drain

Gate

Drain

Gate Insulator

Off

Off

Source

Drain

Drain

Gate

Gate

On (a)

Insulator

(b)

On

Source

Conductor Semiconductor in the low-conduction state Semiconductor in the high-conduction state Ion reservoir

23.3 Working principles of (a) organic field effect transistors (OFET) and (b) wire electrochemical transistors (WECT).

∑

∑

Wire electrochemical transistor (WECT) switching from the On to the Off state occurs when ions are depleted from the polymer semiconductor channel by electrodiffusion through the solid electrolyte under the action of the gate voltage. The WECT structure is symmetrical; the source–drain fiber and gate fiber can be interchanged, which adds flexibility to circuit design. In the OECTs the conducting channel is made by ions being injected from or removed to a solid electrolyte reservoir, which is in turn controlled by the gate electrode. This means very large conductivity changes can be easily induced, and these conductivity changes control the sourceto-drain current in the same way as the injected charges from the gate electrode in the OFET. Because of the differences in the way the devices work, the need for accurate dimensions and precise positioning of the transistor subparts is greatly relaxed in OECTs compared with OFETs. OECTs also benefit from needing very low operating voltages of the order of a couple of volts [20].

Wires are coated with conducting polymer to create cylindrical electrodes. At junctions where the wires cross each other, a drop of solid electrolyte is used both as a physical joining method and as the ion reservoir to create a transistor (WECTs). If a polymer with lower conductivity is used to

Application of woven fabrics

429

join the wires instead, a resistor is made. The logic circuits can be made using arrays of wires crossed and connected in these ways as shown in Fig. 23.4 [21]. ∑ ∑

Classical circuit diagram of an inverter, consisting of a transistor and three resistors. Illustration of how this circuit can be realized using WECT technology.

Despite all the positive features outlined, there is a major intrinsic constraint on the performance of OECTs that is highly relevant to their implementation on fibers. The rate-limiting process of OECT operation is electrodiffusion of ions within the solid electrolyte; ionic charge carriers have very low mobility, which does not allow speeds of operation comparable to either inorganic or conventional organic transistors. The long response time and the consequent low switching frequency of WECT-based logic circuits will certainly limit the dynamic characteristics of any application. Dimensional scaling to speed up operation is an option because the time characteristics of electrodiffusion

+Vdd

–Vdd

R1 Vout

Vin

R2

Vin

R3

Vout

–Vdd

Vout

Vin +Vdd (a)

(b) Coated fiber

Wect

Resistor Insulating

Low resistance High resistance

23.4 Logic circuits constructed from WECTs (a) classical circuit diagram of an inverter, consisting of a transistor and three resistors (b) illustration of how the circuit in (a) can be realized using WECT technology.

430

Woven textile structure

processes scale with the inverse square of characteristic lengths. However, other rate phenomena might be dominant, limiting operations to very low frequencies and hence confining WECT technology to quasi-static applications. This aspect needs investigation to assess the full potential of WECT woven logic in the field of e-textiles and wearable technology. Body signals with slow dynamics, such as sweat rate and composition changes, body surface temperature mapping and surface-strain field mapping for posture recognition and respiration monitoring, are therefore likely to be ideal targets in the area of wearable monitoring systems for health, sport and ergonomics using this technology [22]. Chemo-, piezo- and thermo-resistive fibers are now available in textilecompatible form, and their integration into fabrics and garments is being actively pursued [17,18]. Using simple and elegant solutions, the inganas team [23] has interwoven WECTs with passive electronic components on fibers for local signal acquisition and early conditioning in e-textiles, paving the way for a revolution in existing wearable technology [21].

23.7

Sports textiles

Sport textiles are textiles used in sports. These are sports goods and sportswear. Sportswear is clothing, including footwear, worn for sport or exercise. Typical sport-specific garments include short pants, tracksuits, T-shirts, polo shirts and trainers. Specialized garments include wet suits and salopettes. It also includes some underwear, such as the jockstrap. Sportswear is also often worn as casual fashion clothing. For most sports the athletes wear a combination of different items of clothing, e.g. sports shoes, pants and shirts. Some athletes wear personal armour such as helmets or American footbal body armour.

23.7.1 Functional considerations Almost every piece of sports clothing is designed to be lightweight so the athlete is not encumbered by its weight. The best athletic wear for some forms of exercise, for example cycling, should not create drag or be too bulky. On the other hand it should be loose enough so as not to restrict movement. Clothing worn for some other forms of exercise should not unduly restrict movement and may also have specific requirements, for example the Keikogi used in karate. It should allow freedom of movement in competition. Various physically dangerous sports require protective gear, e.g. for fencing, American football or ice-hockey. Standardized sportswear may also have the function of a uniform. In team sports the opposing sides are usually made identifiable by the colours of their clothing, while individual team members can be made recognizable by a back number on a shirt.

Application of woven fabrics

431

Garments should allow the wearer to stay cool in hot weather and warm in cold weather. In cold climates the best athletic wear should not only provide warmth but also transfer sweat away from the skin. For activities such as skiing and mountain climbing this is achieved by using layering; moisture transferring materials must be worn next to the skin, followed by an insulating layer, and wind and water resistant shell garments.

23.7.2 Moisture-transferring fabric Waterproof, breathable fabrics are designed for use in garments that provide protection from the environmental factors such as wind, rain and loss of body heat. Waterproof fabric prevents the penetration and absorption of liquid water. The term ‘breathable’ implies that the fabric is actively ventilated. Breathable fabrics passively allow water vapour to diffuse through them yet prevent the penetration of liquid water. High functional fabrics support active sportswear with importance placed on functions as well as comfort. Finally, materials with heating and or cooling property have newly attracted the interest of the market. All these materials do not pursue a single function, but different functional properties combined on a higher level. Fabrics that can convey water vapor from body perspiration out through the material while remaining impervious to external liquids such as rainwater are widely used in sportswear and similar applications. Water-resistant and moisture-permeable materials may be divided into three main categories, high density fabrics, resin-coated materials and film-laminated materials. These are selected by the manufacturers according to the finished garment requirements in casual, athletics, ski or outdoor apparel.

23.7.3 Densely woven water breathable fabrics The densely woven waterproof breathable fabrics consist of cotton or synthetic micro-filament yarns with compacted weave structure. One of the famous waterproof breathable fabrics known as Ventile was manufactured by using long staple cotton with minimal space between the fibers. Usually combed yarns are woven parallel to each other with no pores for water to penetrate. Usually oxford weave is used. When the fabric surface is wetted by water the cotton fibers swell transversely reducing the size of pores in the fabric and require very high pressure to cause penetration. Therefore waterproof is provided without the application of any water repellent finishing treatment. Densely woven fabrics can also be produced from microdenier synthetic filament yarns. The individual filaments in these yarns are of less than 10 mm in diameter, so that fabrics with very small pores can be engineered [24].

432

Woven textile structure

23.7.4 Laminated waterproof breathable fabrics Laminated waterproof breathable fabrics are made by application of membranes into the textile product. These are thin membrane made from polymeric materials. They offer high resistance to water penetration but allow water vapor at the same time. The maximum thickness of the membrane is 10 mm. They are microporous and hydrophilic membranes. Microporous membranes have tiny holes on their surface, smaller than a raindrop but larger than water vapour molecule. Some of the membranes are made from polytetrafluoroethylene (PTFE) polymer, polyvinylidene fluoride (PVDF) [3,4]. The hydrophilic membranes are thin films of chemically modified polyester or polyurethane. These polymers are modified by the incorporation of polyethylene oxide [6], which constitutes the hydrophilic part of the membrane by forming amorphous regions in the main polymer system. This amorphous region acts as intermolecular pores allowing water vapour molecules to pass through but preventing the penetration of liquid water due to the solid nature of the membrane [24].

23.7.5 Coated waterproof breathable fabrics Coated fabrics with waterproof breathable fabrics consist of polymeric material applied to one surface of fabric [6,7]. Polyurethane is used as the coating material. The coatings are microporous and hydrophilic membranes. In microporous membrane the coating contains very fine interconnected channels much smaller than the finest raindrop but larger than water vapor molecules. Hydrophilic coatings are similar to hydrophilic membranes; the microporous material allows water vapour through the permanent airpermeable structure whereas the hydrophilic material transmits vapour through adsorption-diffusion and de-sorption mechanism. The desirable attributes of functional sportswear and leisurewear are: ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑

optimum heat and moisture regulation; good air and water vapour permeability; rapid moisture absorption and conveyance capacity; absence of dampness; rapid drying to prevent catching cold; low water absorption of the layer of clothing just positioned to the skin; dimensionally stable even when wet; durable; easy care; lightweight; soft and pleasant touch.

Application of woven fabrics

433

It is not possible to achieve all of these properties in a simple structure of any single fiber or their blend. The two layer structure has a layer close to skin of the wicking type from synthetic fibers, e.g. microdenier polyester, and the outer layer is usually cotton or rayon that absorbs and evaporates. Microdenier polyester is ideal for wicking perspiration away from the skin. The use of superfine or microfiber yarn enables production of dense fabrics leading to capillary action that gives the best wicking properties. No single fiber or blend of different fibers can give ideal sportswear. The right type of fiber should be in the right place. Blending of fibers does not give the same effect as that of multi-layer fabric. The wicking behavior of the fabric is mainly dependent on its base fiber’s moisture properties [24].

23.7.6 Moisture transport mechanism The mechanism by which moisture is transported in textiles is similar to the wicking of a liquid in capillaries. Capillary action is determined by diameter and surface energy of its inside face. The smaller diameter or greater surface energy gives greater tendency of a liquid to move up the capillary. In textile structures, the spaces between the fibers effectively form capillaries. Hence, narrow spaces between the fibers enable the textile to wick moisture. Fabric constructions, forming narrow capillaries pick up moisture easily. Such constructions include fabrics made from microfibers, which are packed closely together. However, capillary action ceases when all parts of a garment are equally wet. The surface energy in a textile structure is determined largely by the chemical structure of the exposed surface of the fiber. ∑ ∑

Hydrophilic fibers have a high surface energy. Consequently, they pick up moisture more readily than hydrophobic fibers. Hydrophobic fibers, by contrast, have low surface energy and repel moisture.

Special finishing processes can be used to increase the difference in surface energy between the face of a fabric and the back of the fabric to enhance its ability to wick [24].

23.7.7 Factors affecting moisture transport There are several factors which affect moisture transport in a fabric. The most important are: fiber type, cloth construction or weave, weight or thickness of the material and presence of chemical treatments. Synthetic fibers can have hydrophilic (wetting) or hydrophobic (nonwetting) surfaces. They also have a range of bulk absorbencies, usually reported by suppliers and testing

434

Woven textile structure

organizations as the percentage moisture regain [1] by weight. Synthetic fabrics are generally considered to be the best choice for garments worn as a base layer. This is due to the ability to provide a good combination of moisture management, softness and insulation. While most fabrics, both natural and synthetic, have the ability to wick moisture away from the skin, not all of these are fast-drying and air permeable; two factors which have a direct influence on cooling and perceived comfort. High-tech synthetic fabrics are lightweight, are capable of transporting moisture efficiently, and dry relatively quickly. It is generally agreed that fabrics with moisture wicking properties can regulate body temperature, improve muscle performance and delay exhaustion. While natural fibers such as cotton may be suitable for clothing worn for low levels of activity, synthetic fabrics made of nylon or polyester are better suited for high levels of activity. They absorb much less water than cotton, but can still wick moisture rapidly through the fabric. The main parameters for comfort and functionality are: ∑ ∑ ∑ ∑ ∑

water- and windproof, breathability and comfort; moisture and sweat management; warmth and temperature control; easy-care performance; smart and functional design [24].

23.7.8 Characteristics of sports clothing Sports clothing should have following characteristics: ∑ ∑

∑

Protective properties against variable atmospheric conditions existing dur­ing the clothes use as well as protec­tion against physical damage. A high resistance to external influences, including tear strength, resistance to abrasion, shape stability, colour fast­ness, making-up quality, constancy of protective functions, and other fea­tures contributing to the service life of such materials. Comfort-providing properties, generally described as wellness, including first of all physiological comfort. This in­cludes protection against overwarm­ing or cooling, owing to high water vapour permeability, i.e. carrying off perspiration, good warmth retention and adequate air permeability. Moreo­ver, the person wearing the garment will be positively af­fected by soft handle and good shape assumption by the fabric and cloth cut that does not limit their ease of movement, as well as the cloth’s aes­thetic appeal and practical constancy of protective and aesthetic functions throughout the period of use.

Application of woven fabrics

23.8

435

References

1. Demboski G and Bogeva-Gaceva G (2005), ‘Textile Structures for Technical Textiles Part II: Types and Features of Textile Assemblies,’ Bulletin of the Chemists and Technologists of Macedonia, 24, 1, 77–86. 2. Textiles Intelligence Limited (2007), ‘Developments In Medical Textiles,’ Technical Textiles Market, Issue 70. 3. www.scienceservingsociety.com 4. www.howstuffworks.com/airbag 5. Siejak V (1997), ‘New yarn for light weight airbag fabrics’, Technical Textiles, 40, E54–E56. 6. Sato H (1997), ‘The other fabric for air bag,’ Technical Usage Textiles, Trimestre, 49–50 7. Siejak V (1997), ‘Now yarns for the light-weight air bag fabrics’, Technical Textile, 40, E54–E56 8. Bandyopadhayay B N (2000), ‘Flame retardant automotive Textile’, Manmade Textile in India, 113–118 9. Menzol (1992), ‘Coated fabric structure for air bag applications’, US Patent No. 5,110,666. 10. US Patent No. 5,110,666, May 1992, ‘Coated fabric structure for air bag applications’. 11. jit.sagepub.com/cgi/reprint/37/1/5/fabric 12. www.sefar.us/cms/medien.nsf/img 13. www.usfabricsinc.com 14. Amit S (2007), ‘Design and development of a textile patch antenna using slow wave propagation technique’, M.Tech. Thesis, IIT, Delhi. 15. Marculescu D et al. (December 2003), ‘Electronic textile: a platform for pervasive computing’, Proceeding for the IEEE, 91, 12. 16. Stone R (2003), ‘Electronic textile charge ahead’, Science 301, 15 August. 17. Edmison J, Jones M, Martin T and Nakad J (2002) ‘Using pizzoelectric materials for wearable electronic textiles’, Proceedings of the sixth international symposium on wearable computers, Oct 2002. 18. Laxminarayana K, Ramaratnam A, Rajoria H, Cherian V (2003), Electrical and Computer Eng.: Lonkar, K. and Zhang, X., Nader Jalili, ‘Functional Fabric with Embedded Nanotube Actuators/Sensors,’ National Textile Center Annual Report. 19. Bar-Cohen Y (2001), ‘Electroactive polymers as artificial muscles – reality and challenges’, AIAA Review, (JPL), California Institute of Technology. 20. De Paoli M A and Gazoti W A (2002), ‘Electrochemistry, polymers and optoelectronic devices: a combination with a future’, J. Braz. Chem. Soc., 13(4), 410–424. 21. Rossi D de (2007), ‘Electronic textiles: A logical step’, Nature Materials, 6, 328–329. 22. Mattila H R (2006), Intelligent Textiles and Clothing, Woodhead Publishing, 399–419. 23. Graham-Rowe D (2007), New Scientist, of 07 April 2007, Magazine issue 2598. 24. Chaudhari S S, Chitnis R S and Ramkrishnan R, Waterproof Breathable Active Sports Wear Fabrics, The Synthetic and Art Silk Mills Research Association, Mumbai.

Index

ABAQUS FEM package, 264 ABAQUS software, 359, 362 Abbott model, 184–7 fabric bent by a couple M › M0, 186 point contact, 185 rigid and flexible section of yarn, 186 abrasion, 230, 232 classification, 232 factors affecting abrasion resistance, 236–41 fabric finishes, 240–1 fibre properties, 236–7 yarn and fabric structure, 237–40 fundamentals, 231–2 resistance, 232, 239 abrasive wear, 230 acrylic, 241 air permeability, 339 airjet spinning system, 324 alpha, 355 American Association of Textile Chemists and Colorists, 241 amino-silicon softeners, 326 Anderson–Darling normality test, 357 anisotropy, 297 ANN see artificial neural network areal density, 19, 22, 23, 24, 25, 63, 64, 104, 368 artificial intelligence, 252 artificial neural network model, 267, 276, 365–7 building predictive model, 278–81 development process, 280 evaluation, 285–8 fully connected feed-forward network with one hidden layer and one output layer, 279 predicting drape, 365–7 drape parameters network outputs, 367 statistical model vs neural network model, 368 range and prediction errors, 289 RBF network design parameters for optimised network, 288

436



error goal on prediction performance, 287 fabric bending moduli predictability, 289 hidden layer neurons effect on prediction performance, 286 predictability of initial fabric tensile moduli, 288 schematic diagram, 285 spread constant on prediction performance, 287 automotive textiles, 417–21 3-D woven fabrics, 418 airbags, 418–21 airbag working, 418–19 coated base fabric, 421 inflation, 419 laminated material, 421 manufacture, 419–20 nylon 6.6 vs polyester properties, 420–1 physical properties of nylon 6,6 and polyester, 420 axial deformation fundamentals, 138–41 Hooke’s law and modulus, 140–1 Poisson ratio, 141 strain, 139 stress, 138–9 tensile strength, 138 stress-strain diagram, 141 for brittle material, 141 back-propagation network, 268, 365 basis functions, 285 basket weave, 240 beam-forming array, 425–6 bending deformation, 224 bending equations beam is cantilevered with load applied at end, 175–6 beam is supported on both ends with single load on centre, 175 effect of time, 191–2 fundamentals, 174–6

Index homogeneous beam bending, 177 bending elasticity, 203 bending energy, 147, 148 bending hysteresis, 187–90, 263, 353 force distribution on an element during bending, 187 frictional restrain during recovery, 189 initial inclination of plate during bending, 188 bending law, 189–90 bending modulus, 282, 344 bending moment, 187–8, 193, 214–15, 345 due to friction, 214 due to Sp1, 215 bending recovery, 191, 200 at different curvatures, 200 bending rigidity, 116–17, 132, 133, 136, 173–4, 194, 200, 212–13, 224, 225, 284, 314, 345, 346, 351, 352, 353, 368 bending stress, 174–5 Bernoulli-Euler law, 344 bi-directional reflectance distribution function, 298 bi-quadric form, 286 Bkzier surface, 297 blended fibre density, 66, 67 blended yarn density, 67 block-regression method, 319 3-D braided composites, 408 braiding, 3 BRDF see bi-directional reflectance distribution function BRDF generator, 298, 299 breathable fabrics, 431 coated waterproof, 432–3 laminated waterproof, 432 buckling, 164, 381 behaviour of cloth under large deformation, 166–71 experimental set-up and loadcompression behaviour, 169 load and compression theoretical relation, 168 model, 167 for fabric, 170 recovery from deformation, 171 theoretical curves, 170 woven fabric, 164–72 deformation, 165–6 hysteresis in fabric deformation, 172 practical applications, 172 buckling load, 164 buckling phenomena, 165 bulk modulus, 218 cantilever method, 343–4 Castigliano’s theorem, 149–52, 155 applications, 150–2

437

cantilever, 151 inclination of a cantilever, 152 bending strain energy, 149–50 elastic body deformation, 149 Cauchy distribution, 266 chaos theory, 262 chemical setting process, 325 Chu’s drape coefficient, 347 classical beam theory, 344 cloth cover factor, 66, 67 clothing, 332 performance classification, 309 primary objective, 309 system, 334 thermal resistance, 333 Clothing Microclimate Testing Meter, 341 coefficient of friction, 230, 316 coefficient of kinetic friction, 231 coefficient of multiple determination, 262–3, 284 coefficient of static friction, 231 coefficient of surface friction, 235 coercive couple, 179, 181, 187, 191, 314 colour expert system, 254 comfort zone, 331 competitive learning, 279 complex interaction phenomena, 263 compressibility, 219, 381 compression, 218 compressible fabrics exponential behaviour, 222–3 definition, 217 fabric performance, 222 fundamentals, 218 low stress pressure–thickness curve, 223 modulus, 218 parameters compressive modulus, 218 compressive strength, 218 practical applications, 229 pressure–thickness relationship, 223 textile structures behaviour, 218–22 typical compression curves, 219 woven fabric behaviour, 217–29 compression resilience, 228 compressional energy, 315, 326 correlation graph, 228 compressional resistance, 264 compressive stress, 139 computational neuroscience, 266 computer-assisted manufacture, 251 computer integrated manufacturing, 251 Computers in the World of Textiles, 302 conceptual world, 261 three stages modelling, 261 observation, 261 prediction, 261

438

Index

conduction, 333 connectionism, 266 convection, 333 corduroy, 239 core-wrap composite yarn, 324 cosine rule, 161 cotton, 241, 269, 388 cloth, racetrack cross-section maximum picks per cm, 62–3 fabrics, 390 fibre density, 24 sewing threads, 389, 390 cotton–polyester core yarn fabrics, 324 cover factor, 18, 20, 26, 216, 323, 324, 391 creasing, 197–204 bending recovery at different curvatures, 200 deformation and recovery behaviour, 199–201 factors affecting fabric recovery, 203–4 mechanisms, 197–9 monofilament and multifilament materials bending, 198 relative contribution of non-recovery from creasing, 203 time on deformation and recovery, 202–3 yarn and fabrics bending behaviour, 200 crimp, 25, 59–60, 83, 88, 89–91, 97, 201, 339 crimp accentuation, 111 crimp amplitude, 125 crimp balance, 112–13, 121–2 crimp balance equation, 113, 121–2, 128–31, 133, 136, 282 flowchart for solution, 129 interaction with crimp interchange, 130–1 crimp change, 110 crimp correction factor, 180 crimp height, 131 crimp interchange, 128–31, 148 equation, 74, 76, 83, 84, 85, 87, 88, 89, 90, 92, 93, 96, 98, 100, 101, 102, 105 algorithm flowchart, 77 flowchart for solving in terms of thread diameters as variables, 80 interaction with crimp balance equation, 130–1, 136 phenomena, 73–5 fabric crimp amplitude changed, 75 fabric crimps changed, 75 fabric dimensions changed, 74 crimp percent, 24 crimp ratio, 135 crimp theory, 297 crisp set, 264 crisp values, 265 critical fibre length, 407 critical load, 164, 165, 381 Cusick’s drapemeter, 347, 348

Cygwin, 296 DARPA, 423 decatising, 325 decision variables, 277 dectronics textiles, 423–30 beam forming array, 425–6 mapper garment, 424–5 nanotube based e-textile, 426–7 organic field effect transistors, 427–30 design engineering, 251 designing, 275 definition, 245 deterministic models empirical modelling, 262–3 finite element modelling, 263–4 differential total material design, 255 digital drape meter, 348 digital image processing, 364–5 correlation of DC % by different modelling methods, 366 predicted drape image of fabrics using polar coordinate, 365 technique, 348 3-D dome structures, 395 drape, 353 coefficient, 347, 349, 350, 351, 352 distance ratio, 349, 350 drapeability, 347 Draper, 423 dry cleaning, 325 dry relaxation, 109 dynamic drape coefficient, 368 dynamic system, 292 e-textile, 423–6 technology beam forming array, 425–6 mapper garment, 424–5 nanotube based, 426–7 organic field transistors, 427–30 eco-testing, 373 edge abrasion, 232 edge-wear test, 238 elastic flexural rigidity, 191 elastic theory, 353 electronic jacquard, 250 empirical model, 262–3 limitations, 263 textile product design, 276 building predictive model, 276–7 evaluation, 284 range and prediction errors, 276–7 energy coefficient, 236 engineering, 245 error, 272 types, 272–3 random, 273

Index systematic, 272–3 error-correction learning, 279 Euclidean norm, 285 Euler’s formula, 164–5, 277–8, 381 exogeneous variables, 277 expert systems, 252–6 application in textile field, 254–6 basic structure, 253–4 frame of total material design system for textiles, 256 various components, 253 external bending couple, 194 FABCAD analytical phase, 255 design phase, 255 heuristic design, 255 revision stage, 255 synthesis stage, 255 fabric, 334 abrasion resistance, 230 areal density, 19 bending behaviour, 200 see also fabric bending buckling and tailorability of garments, 381–2 circular cross-section equation for jammed structure in terms of weave factor, 46–9 jammed structure for 1/3 weave, 47 relation between average thread spacing in warp and weft, 49 warp and weft cover factor relation, 49 comfort, 331 compressibility test, 315 compression and performance, 222 deformation of plain and twill fabrics, 297 deformed by shear stress, 209 extension in bias direction, 157–62 equilibrium of forces, 159 force application, 157 modulus at various angles, 162 resolution of forces along fabric edges, 158 strain after deformation, 160 strain before deformation, 160 finishes, 240–1 jamming condition, 57 low deformation bending behaviour, 314 shear behaviour, 313 surface behaviour, 317 tensile behaviour, 312 mechanical and surface parameters, 319 modelling maximum cover, 19–21 modulus, 147, 156 numerical examples of modelling properties, 21–9



439

properties and apparel performance, 373–4 properties and garment making-up process, 374–6 laying-up cutting, 375–6 pattern grading, 374–5 pressing, 376 seaming, 376 quality, 322 racetrack cross-section average thread spacing in warp and weft, 52 equation for jammed structure in terms of weave factor, 50–1 fabric parameters, 52–3 jammed structure for 1/3 weave, 50 warp and weft cover factor, 53 roughness, 234 shear hysteresis, 313 shrinkage, 380 simulations from fancy yarn, 296 smoothness, 230 stiffness, 324, 352 structure, 324–5 structure effect on abrasion resistance, 237–40 fabric thickness, 239 thread density, 239 weave type, 240 surface frictional coefficient, 234–5 friction coefficient output from KES instrument, 235 MMD principle, 236 tension, 390 thickness, 220, 239, 389 THV, 269 volume, 226 weave square cotton, 21–2 plain weave value, 22 twill weave value, 21 weight, 282 yarn configurations in creased fabrics, 202 and yarn structure, 237–40 fabric thickness, 239 2-D fabric, 393 representation, 394 weave and weave matrix, 403 weave equations, 402 2.5-D fabric, 393 3-D fabric advantages over 2-D fabric in composite formation, 407–8 angle interlock cross-sectional view, 399 classification, 394–402 complex preform manufacture via stitching, 402 dual direction shedding operation, 400 geometrical structure, 395–6 3-D dome, 395

440

Index

3-D hollow, 395 3-D nodal, 396 3-D solid, 395 manufacturing method, 396–402 angle interlock principle, 398–9 dual direction shedding method, 399–400 multilayer principle, 396–7 orthogonal principle, 397–8 stitching operation, 401–2 multilayer fabric, 397 orthogonal, manufacturing method, 398 representation, 394 stitch pattern through a composite laminate, 401 weave equations, 404–5 see also specific fabric fabric area, 226 fabric bending bent fabric cylinder analysis, 194 bias direction, 192–6 fabric bent by a couple M › M0, 186 into a cylinder, 193 idealised bending curve, 179 rigidity, 225, 353 rigidity prediction, 181–4 contributing factors to cloth stiffness, 181 fabric bent configuration, 182 force equilibrium in bent fabric, 183 yarn configuration in fabric, 182 sawtooth model for bent yarn analysis, 195 for twisted yarn analysis, 195 typical bending curve, 178 fabric cover factor, 18, 22, 24, 25, 26, 58, 68, 76, 282 after flattening, 70 maximum for square fabric, 60–1 for racetrack cross-section, 69–70 when warp is jammed, 69 fabric crimp, 76 amplitude changed, 75 changed, 75 fabric defects analysis system, 254 fabric deformation hysteresis, 172 fabric drape 2-D and 3-D drape, 343–7 2-D drape, 343–6 cantilever beam with concentrated load, 345 cantilever beam with uniformly distributed load, 346 fabric cantilever with concentrated weight, 345 fabric cantilever with distributed weight, 345–6





theories of fabric cantilever with different weight distributions, 344–5 3-D drape, 346–7 comparison of drape prediction methods, 364–5 data from standardised residuals analysis, 351 drape parameters of fabrics, 360 drape prediction ANN modelling, 365–7 FEA, 357–62 polar co-ordinated technique, 363–4 statistical method, 355–7 drape profile schematic diagram, 350 dynamic drape modelling, 367–9 low stress mechanical properties of woven fabrics and drapeability, 353–4 matrix plot for fabric low stress and mechanical properties, 356 measurement by digital image processing, 348–52 digital drape meter, 348 draped fabric image, 349 mechanical properties of woven fabrics, 352–3 modelling, 343–69 parameters, 349–52 amplitude, 351 drape coefficient, 350 drape distance ratio, 350 fold depth index, 351 network outputs, 367 number of nodes, 351–2 standardised residuals probability plot amplitude, 359 drape coefficient, 357 drape distance ratio, 358 fold depth index, 358 number of nodes, 359 subjective and objective measurement, 347–8 fabric gsm see areal density fabric handle affecting factors, 321–6 fabric structure, 324–5 fibre structure and properties, 322 finishing treatment, 325–6 yarn structure and spinning system, 322–4 assessing woven fabric comfort, 309–26 comfort objective measurement, 310–11 measurement, 311–16 bending, 313–15 compression, 315–16 shear properties, 313 surface properties, 316 tensile properties, 311–12 modelling requirements, 309

Index primary and total fabric handle, 317–21 primary handle values, 317–20 total handle values, 320–1 fabric mass, 23, 24, 25, 27, 68, 76 fabric mass per unit area see areal density fabric packing factor, 25, 68 fabric shrinkage, 109–17 application of models, 115–17 definition, 109 mechanisms, 110–12 prediction, 113–15 flowchart, 114 relationship between cloth and yarn shrinkage, 112–13 woven fabric, 111 fabric specific volume, 19, 22, 23, 24, 25, 27, 63, 64, 68, 76, 104 fabric thickness, 17–18, 23, 24, 25, 27, 58–9, 62, 63, 64, 68, 76, 83, 89–91, 94, 104, 132 Fashion Studio, 293 FAST 2, 382 FAST 3, 382 FAST system, 311, 321 FEA see finite element analysis feed-forward back-propagation neural nets, 273 fibre, 322 assembly structures directive for required functions, 415–16 function system, 415 pore size and distribution, 415 structural system, 414–15 bending rigidity, 227 configurational functions, 414 crimp, 224, 227, 322 density, 89–91, 225–6, 227 fineness, 339 inter-fibre friction, 200 maximum volume fraction, 415 moment of inertia, 225 properties, 236–7 single density, 225 radius, 225 structure and properties, 322 type, 224 wad density, 225 wad mass, 225 Ficks Law, 336 filter fabrics, 223, 421–3 wetting or non-wetting of solid by liquid phenomenon, 422 finite element analysis, 262, 263–4, 355, 357–62 constitutive equations, 360–2 domain discresitisation, 360 input parameters used, 362 measured drape parameters, 363

441



typical grid-point ‘O’ and its four neighbourhoods in fabric, 361 virtual drape images of fabric sample, 363 finite elements, 263 firmness, 70 flat abrasion, 232 resistance, 239 flex abrasion, 232, 238 flex abrasion test, 238 flexural rigidity, 182, 183, 192, 195, 344 flow equation, 340 fold depth index, 351 formability, 321, 373, 381, 382 fourth-order elasticity tensor, 360 friction fundamentals, 231–2 coefficient of friction, 231–2 free-body diagram of block resting on rough-inclined plane, 231 types kinetic friction, 232 rolling friction, 232 sliding friction, 232 static friction, 232 friction coefficient deviation, 235, 236 frictional coefficient, 224 frictional energy dissipation, 187 FRL drape meter, 346–7 Fukurami, 317, 318, 325 fuzzy logic, 264–6 modelling categories objective, 265 subjective, 265 fuzzy relation, 265 fuzzy set, 264 fuzzy set theory, 264 garment design, 334 making-up see garment making-up tailorability and fabric buckling, 381–2 garment making-up fabric suitability measurement, 379–81 manufacturing process, 374 modelling woven fabric behaviour, 372–92 process and fabric properties, 374–6 laying-up cutting, 375–6 pattern grading, 374–5 pressing, 376 seaming, 376 process and low stress fabric mechanical properties, 376–9 bending property, 377, 379 low stress mechanical properties of fabric, 378 shear property, 377 tensile property, 377

442

Index

Gaussian function, 285 genetic algorithms, 269–71 issues affecting the performance, 269–70 significant differences, 269 geometric model equation for jammed structure in terms of weave factor circular cross-section, 46–9 racetrack cross-section, 50–1 predicting cover in different woven structures, 53–7 similar cloth, 54–7 square cloth, 53–4 predicting weavability limit, 41–53 relationship between parameters in racetrack cross-section, 52–3 yarn diameter, 41 predicting woven fabric parameters, 31–41 flowchart for solving Peirce’s seven equations, 33 jammed structures, 32–9 module connector at A, 35 module connector at F, 36 module connector C, 34 non-jammed structure, 39–40 straight cross-threads, 40–1 predicting woven fabric properties, 30–72 numerical examples, 57–70 predicting tightness values, 70–2 prediction of fabric thickness, cover, mass and specific volume, 17–19 fabric cover, 18 fabric mass per unit area, 19 fabric specific volume, 19 fabric thickness, 17–18 warp and weft cover factor relation for jammed fabrics beta (d2/d1) variation on, 46, 47 fibre density variation, 42, 43–4 yarn packing factor variation, 42 woven fabric structure, 9–17 cross-threads pulled straight, 14 elliptical cross-section, 15–16 functional relationship between thread spacing, crimp height and crimp, 12–13 jammed structures, 13 non-circular cross-section, 14–15 Peirce model of plain weave, 10 racetrack cross-section, 16–17 relation between thread spacing, crimp height, weave angle and thread diameter, 11–12 geometrical roughness, 230, 234 global coordinate system, 360 Gore-tex, 337 Hand Evaluation and Standardisation

Committee, 311, 317 hardening phase, 410–11 Hari, 317, 318 heat flux density, 334 heat retention, 334 Hebbian learning, 279 Hercoset-treated wool fabric, 326 3-D hollow structures, 395 Hooke’s law, 140–1 horizon map generator, 298, 300 hybrid modelling, 271–2 using soft computing tools, 271 hysteresis, 172, 179 ideal fabric simulation system, 292–3 image processing technique, 349, 362, 369 insulation, 334 integrated product development, 273 inter-fibre friction, 200, 203 inter-yarn force, 118–21 inter-yarn friction, 199–200, 203 internal structure, 251 inverse multiquadric function, 285 irregular weave, 6, 7 ISO 7730, 331 jacquard loom, 250 jacquard system, 396–7 jammed structures, 13, 32–9, 65–7 1/3 weave circular cross-section along warp, 47 racetrack cross-section along warp, 50 fabric cover factor and fabric mass relation, 40 fabric parameters flowchart, 37 relation between average thread spacing in warp and weft circular cross-section, 49 racetrack cross section, 52 relation between warp and weft cover factor b effect on cotton, 46 b effect on polypropylene, 47 beta (d2/d1) variation effect, 46 circular cross-section, 49 fibre density (b = 0.5), 43 fibre density (b = 1), 43 fibre density (b = 2), 44 racetrack cross-section, 53 yarn packing factor (b = 0.5), 44 yarn packing factor (b = 1), 45 yarn packing factor (b = 2), 45 thread spacing and crimp height, 32 warp and weft cover factor for different b, 39 crimp relation, 38, 39 thread spacing relation, 38 weave effect, 48 weave factor equation

Index circular cross-section, 46–9 racetrack cross-section, 50–1 jamming, 96 Kawabata Evaluation System, 221, 321, 352 compression tester, 228 instrument measured surface roughness chart, 234 output of friction coefficient, 235 theory, 227 KES see Kawabata Evaluation System KES-F instruments, 215, 311 KES-FB, 311 KES-FB3, 221, 222, 228 Kevlar, 410 kinetic friction, 232 3-D knitted composites, 408 knitting, 3 technology, 271 knowledge-based garment manufacturing system, 254 Koshi, 317, 318, 325 Kozeny’s equation, 339 Laplace equation, 336 laser triangulation technique, 233 lateral strain, 141 learning algorithm, 278, 279 learning machine, 279 linear multiple regression technique, 262, 284 linear regression, 277 relationship, 223 linear strain see normal strain linen, 269 Linux, 296 LISP, 253 lubricants, 240 machine intelligence quotient, 273 mapper garment, 424–5 material design, 249 mathematical model textile product design, 276 building predictive model, 277–8 evaluation, 281–3 limitations, 262 principles, 260–1 range and prediction errors, 289 Matlab 7.6, 368 maximum threads, 71, 72 mean fabric curvature, 199 mean friction coefficient, 234 mean square errors, 267, 367 measured geometrical roughness, 234, 235 medical textiles, 416–17 metal spacers, 199 micro-deformation model, 297

443

micro-geometry shader, 298 minimum energy method, 301 Minitab 15 software, 355 modelling, for woven fabric design, 292–304 algorithm outline, 299 application, 294–300 weave pattern colour scheme, 299–300 woven construction simulation, 294–6 woven fabrics determination, 296–7 woven textiles visualisation, 298 boundary value problem computation, 304 limitations, 303–4 sample colour scheme for weave pattern, 299 structure–property relationships, 300–2 bending, 302 colour texture generated for sample colour scheme, 301 elongation, 301 thread shading textures, 300 types of computer modelling in design and manufacture, 292–4 woven texture, 302–3 modified plain weaves, 240 modulus cloth, 148 elasticity, 175, 176, 218 moisture vapour transmission rate, 337 moment of inertia, 353 moulding techniques, 375 multi-warp yarn system, 398 multilayer feed-forward network, 268, 280 multilayer perceptron, 267 multilinear regression techniques, 284 multiquadric function, 285 nanotube-based e-textile, 426–7 woven textile super-capacitor, 427 Nedgraphics, 293 neural computing, 266 neural networks, 262, 266–9, 272 model, 366–7 network outputs of drape parameters, 367 vs statistical model, 368 multilayer feed-forward network, 268 type supervised learning, 266 unsupervised learning, 266 neurons, 266 Newton–Raphsons method, 362 3-D nodal structures, 396 non-control zone, 379 nonlinear finite elements, 263 nonlinear regression models, 277 noobing, 393 normal strain, 140

444

Index

Numeri, 317, 318, 325 nylon 6,6, 420–1 OECTs see organic electrochemical transistors OFETs see organic field effect transistors Olofsson’s approach, 127, 190 open-cell arrangements, 335 operators, 270 organic electrochemical transistors, 427, 428, 429 organic field effect transistors, 427–30 working principles, 428 oxford weave, 240 packing coefficient, 24, 104 packing density, 224 packing factor, 23 parallel distributed processing, 266 partial design, 249–50 Peirce’s cantilever formula, 346 Peirce’s cantilever test, 343–4 Peirce’s equation, 219 Peirce’s geometrical model, 213 Peirce’s geometry, 295 Peirce’s rigid thread model, 152, 181, 183 perchloroethylene, 325 plain weave, 5, 240 Peirce model, 10 plain-woven fabric, 239 vs twill fabric, 324–5 plate buckling, 166 Pointcarré, 293 Poisson ratio, 83, 85, 88, 89, 91, 92, 93, 94, 97, 99, 102, 103, 105, 141, 142, 145, 160, 264, 360, 362 polar coordinate technique, 363–4 measured drape parameters, 364 polyester, 241, 390 double-knit fabrics, 241 fibre, 388 properties, 420–1 sewing threads, 389, 390 polyethylene compounds, 240 1/3 power law, 220 prediction error, 283 primary handle values, 317–20, 325 definition men’s summer suit fabric, 318 men’s winter suit fabric, 318 probabilistic selection, 270 processing elements, 266, 278 product design methods, 245–56 product synthesis, 246 PROLOG, 253 pucker formation, 389 puckering, 383 see also seam puckering pull-out phase, 412

pure shear, 207, 208 radial basis function, 285 neural network, 268, 367 design parameters for optimised RBF network, 288 effect of hidden layer neurons on prediction performance, 286 error goal on prediction performance, 287 fabric bending moduli predictability, 289 predictability of initial fabric tensile moduli, 288 schematic diagram, 285 spread constant on prediction performance, 287 radiation, 333 radii of curvature, 131, 134 recurrent neural networks, 280–1 regression equation, 319, 352 regression models, 262 regular weave, 5, 6, 403–4 relaxation rate, 192 relaxation shrinkage, 109 residual curvature, 179 resilience, 218 resilient back-propagation neural network, 269 resistance to air flow, 340 resistance to seam slippage per thread value, 392 reverse engineering, 252, 269 rolling friction, 232 rule-based expert system, 254 sateen, 238, 240 sawtooth model, 152–7, 194, 282 force analysis on half repeat of plain weave, 154 plain weave, 153 seam efficiency, 383 seam puckering correlation coefficients, 389–90 fabrics compressional behaviour and pucker, 388–9 lateral compression, 388 longitudinal compression, 388–9 force distribution on threads in a stitch, 385 pucker formation, 385–7 initial pucker, 385–6 subsequent pucker, 386–7 seam pucker model, 384 sewing thread properties and pucker, 387–8 diameter, 387 fibre density, 388 initial tensile modulus, 387 yarn diameter compressibility, 388 seam slippage, 390–2 process, 391–2

Index understanding the mechanism, 390–1 seam strength, 382–3 sewability, 381 definition, 382 measurement, 382–92 seam puckering, 383–90 correlation coefficients, 389–90 fabrics compressional behaviour and pucker, 388–9 pucker formation, 385–7 sewing thread properties and pucker, 387–8 seam slippage, 390–2 process, 391–2 understanding the mechanism, 390–1 seam strength, 382–3 Shari, 317, 318 shear, 354 classical definition, 207 normal shear, 208 pure shear, 208 simple shear and deformed simple shear, 208 concept, 209 practical applications, 216 properties in various directions, 215 stress–strain curve, 216 test, 210 shear angle, 205, 352 shear deformation, 216, 354 fundamentals, 206–7 shear classical definition, 207 shear modulus, 206 shear stress and shear strain definition, 206 representation, 207 stress–strain relationship and modulus, 211–15 estimation of frictional resistance in contact region, 215 fabric shear behaviour, 212 force distribution in contact region, 214 initial behaviour prediction, 211–15 shear deformation on a unit cell, 213 shear forces on fabric, 212 theory, 211 woven fabrics, 207–15 concept of shear, 209 deformation at crossover points in fabric, 210 fabric deformed by shear stress, 209 shear force calculation, 210–11 shear test, 210 stress–strain relationship and modulus, 211–15 shear force calculation, 210–11 on fabric, 212

445

shear hysteresis, 215, 216, 353 shear modulus, 206, 282, 360, 362 shear rigidity, 215, 216, 313, 354, 368 shear stiffness, 353 shear strain, 140, 161, 206, 207, 212 shear stress, 139, 206, 207 Shinayakasa, 322 Shirley bending hysteresis tester, 199 Shirley stiffness tester, 344 shrinkage, 109–10 fabric, 109–17 relaxation, 109 swelling, 110 yarn, 110 sigmoid function, 279 silicones, 240 silk, 269 simple bending theory, 174 simple shear, 208 simple strain, 207 simple trellis model, 297 simulation, 292 advantages in woven construction, 293 fabric simulations from fancy yarn, 296 ideal fabric simulation system, 292–3 fabric 3-D computer simulation, 293 fabric behaviour under real wear conditions simulation, 293 fabric mechanical and physical properties presentation, 293 yarn surface real simulation, 293 steps for two different yarn intersections, 296 woven construction, 294–6 single-layer feed-forward network, 280 sliding friction, 232 SMD see measured geometrical roughness soft computing, 353 methods, 264 structural design of woven fabrics, 76–82 module connector A, 78 module connector at B, 79 warp and weft crimp with decrease and constant thread diameters, 82 effect of varying thread diameters, 79–82 equal decrease in thread diameters, 81 varying thread diameters, 81 soft logic, 262 3-D solid modelling, 293, 304 3-D solid structures, 395 cross-sectional view, 396 solidus roughness, 230 solvent scouring, 325 spectograms, 271 spinning technology, 224 sports clothing, 434

446

Index

sports textiles, 430–4 coated waterproof breathable fabrics, 432–3 densely woven water breathable fabrics, 431 factors affecting moisture transport, 433–4 functional considerations, 430–1 laminated waterproof breathable fabrics, 432 moisture-transferring fabric, 431 moisture transport mechanism, 433 sports clothing characteristics, 434 standard functional approximation techniques, 278 starched cotton gingham, 352 start-up phase, 222 static friction, 232 static system, 292 statistical method, 355–7 neural network model, 368 steam pressing, 325, 375 process, 380 stitch density, 390 stitch geometry, 390 stitching, 408–9 stochastic learning, 279 strain, 138, 139–40, 156 lateral, 141 normal, 140 shear, 140 volumetric, 140 strain energy, 183, 192–3 stress, 138–9 compressive, 139 shear, 139 tensile, 139 types of applied stress, 139 stress relaxation, 190, 191 STRETCH, 423 3-D structures, 393 sum of squares due to error, 368 supervised learning, 266, 279 surface tension, 339 Swedish Institute for Textile Research, 310 swelling, 304 swelling shrinkage, 110 Sympatex, 337 synaptic weights, 278 system, 292 tailorability, 381–2 tailoring process, 373, 381 control chart, 379 rejection range, 380 Takagi-Sugeno-Kang fuzzy modelling, 265 TEFO see Swedish Institute for Textile Research tensile energy, 354 tensile modulus, 146–8, 282, 284 tensile resiliency, 326 tensile strength, 137, 138 tensile stress, 138, 139

tensile work, 326 tension, 218 textile function in enhancing thermal comfort, 332–3 product design see textile product design reinforced composites see textile reinforced composites sports see sports textiles textile composite properties density, 407 modulus of elasticity, 407 use of 2-D and 3-D textiles, 405–9 3-D fabric advantages over 2-D fabric in composite formation, 407–8 3-D woven composites advantages over 3-D braided and 3-D knitted composites, 408–9 3-D textile composites load-elongation curve of 2-D and 3-D composites, 412 orthogonal, load-displacement curve from tensile test, 411 tensile properties, 409–12 tensile stress-strain curve for 2-D and 3-D woven composites, 410 3-D woven carbon/epoxy composite, 411 Textile Machinery Society of Japan, 311 textile product design building predictive models, 275–89 ANN model, 278–81 empirical model, 276–7 mathematical model, 277–8 deterministic models, 262–4 empirical modelling, 262–3 finite element modelling, 263–4 evaluating predictive models, 281–8 ANN modelling, 285–8 empirical models, 284 experimental data for fabrics tensile moduli, 281 mathematical models, 281–3 expert systems, 252–6 application in textile field, 254–6 basic structure, 253–4 frame of total material design system for textiles, 256 five phases of general problem solving, 246 frame of total material design system, 256 integrated product development, 247 key issues, 248–50 aesthetic design vs engineering design in CAD, 249 creative design vs modification design, 250 partial and total material design, 249–50

Index

key principles of mathematical modelling, 261 manual design procedure for industrial fabrics, 248 mechanics of textile structure, 248 methods, 245–56 CAD of woven fabrics, 250–1 design engineering using modelling, 251 design process for textiles, 246 reverse engineering, 252 traditional design methods, 247 modelling, 260–73 mathematical modelling principles, 260–1 methodologies, 262 validation and models testing, 272–3 nondeterministic models, 264–72 fuzzy logic, 264–6 general algorithms, 269–71 hybrid modelling, 271–2 neural networks, 266–9 product synthesis, 246 traditional fabric design cycle, 248 textile reinforced composites, 406–9 properties rule of mixture, 406 tensile strength, 406–7 thermal comfort, 332–3 heat transfer through woven fabrics, 333–5 in humans, 331–2 measurement, 340–1 moisture vapour transfer through woven fabrics, 335–40 air transmission, 339–40 mechanism, 337–8 moisture loss from the body, 338–9 thermal resistance model, 334 woven fabric comfort assessment, 330–41 thermal resistance, 333–4 thermal-wet comfort, 340–1 thermo-physiological comfort, 335 thin-plate spline function, 285 thread density, 239 effect of change in fabric mass, 55 effect of change on yarn count, 55 thread spacing, 89–91, 136 thread tension, 387 tightness factor, 70 torsional rigidity, 192 total elastic strain, 360 total handle value (THV), 269, 317, 320–1 total material design, 249–50, 256 total stress, 360 total thread spacing, 71 total warp crimp, 51 training data, 277 TS-TS-NN-FL model, 272 twill, 240

447

twill fabric, 324–5 twill-weave fabrics, 238 twist correction factors, 201 twisting, 195 3-D unit cell, 264 unsupervised learning, 266, 279 usable lifetime, 222, 223 Van Wyk’s formula, 221, 226 Van Wyk’s law, 220 vapour pressure, 338 velvet, 239 velveteen, 239 Ventile, 431 verification data, 277 viscose, 390 volumetric strain, 140, 206 warp, 5 warp contraction, 85, 87, 97, 99, 100, 105 warp count, 89–91, 93 warp cover factor, 25, 58, 64, 65, 66, 68, 104 warp crimp, 25, 62, 85–6, 89–91, 93, 94, 95, 97, 99, 133 warp extension, 88, 92, 96, 101, 103 warp-faced twills, 238 warp jamming, 95, 97, 105 warp modular length, 124 warp shrinkage, 90 warp spacing, 95 warp tex, 133, 135 warp yarn density, 66 diameter, 66 weave, 5 irregular, 6, 7 plain, 5 regular, 5 value for 1/1 plain weave, 61 1/4 sateen weave, 61 2/4 twill weave, 61 weave angle, 72, 89–91, 131 weave factor, 6–7 calculation, 7 10-end huckaback weave, 8 regular weave, 7 warp and weft factors for typical weaves, 8 weaving, 3 2-D weaving, 394 process representation, 395 3-D weaving, 394 process representation, 395 weaving information file, 298 WECT see wire electrochemical transistor weft, 5

448

Index

weft contraction, 87, 92, 93, 100, 101, 103 weft count, 89–91, 93 weft cover factor, 58, 63, 66, 104 weft crimp, 25, 62, 85–6, 89–91, 93, 94, 95, 97, 99, 133 weft extension, 85, 87, 98, 100, 105 weft jamming, 83, 96 weft spacing, 90, 95 weft tex, 133, 135 wet setting process, 325–6 wetting, 336 wicking, 339 wind chill effect, 333 wire electrochemical transistor, 428, 429 logic circuits, 429 working principles, 428 WOFAX see worsted fabric expert system Wonder Weaves Systems, 293 wool, 203, 268, 269, 322, 323, 325 wool–polyester blended fabrics, 268, 323 World Reviews of Textile Design, 302 worsted fabric expert system, 255 2-D woven composites load displacement curve from a tensile test, 411 tensile stress-strain curve, 410 3-D woven composites, 409 advantages over 3-D braided and 3-D knitted composites, 408–9 load-displacement curve from a tensile test, 411 tensile stress-strain curve, 410 tensile stress-strain curve for carbon/epoxy composite, 411 woven fabrics, 134, 135 bending behaviour, 173–96 bending hysteresis, 187–90 bending in bias direction, 192–6 bending recovery, 191 deformation fundamentals, 174–6 effect of setting, 190 at higher curvatures, 191 modelling, 176–8 practical applications, 196 time effect in bending deformation, 191–2 buckling behaviour, 164–72 buckling deformation, 165–6 cloth buckling behaviour under large deformation, 166–71 hysteresis in fabric deformation, 172 practical applications, 172 CAD, 250–1 compression behaviour, 217–29 compression fundamentals, 218 exponential behaviour of compressible fabrics, 222–3 low stress pressure–thickness curve, 223

practical applications, 229 predicting compression, 223–9 textile structures, 218–22 contributing factors to cloth stiffness, 181 creasing, 197–204 deformation and recovery behaviour, 199–201 effect of time on deformation and recovery, 202–3 factors affecting fabric recovery, 203–4 mechanisms, 197–9 crimp interchange and crimp balance equations interaction (l1/D = l2/D), 130 interaction (l1/D < l2/D), 131 interaction (l1/D > l2/D), 130 design modelling, 292–304 application, 294–300 modelling limitations, 303–4 structure–property relationships, 300–2 types of computer modelling in design and manufacture, 292–4 woven texture, 302–3 drape modelling, 343–69 drape and mechanical properties of woven fabrics, 352–3 drape measurement by digital image processing, 348–52 low stress mechanical properties of woven fabrics and drapeability, 353–4 modelling dynamic drape, 367–9 predicting drape using ANN modelling, 365–7 subjective and objective drape measurement, 347–8 two-dimensional and three-dimensional drape, 343–7 fabric elongation computer animation, 297 fabric handle assessment, 309–26 comfort objective measurement, 310–11 factors affecting fabric handle, 321–6 measuring fabric handle, 311–16 primary and total fabric handle, 317–21 friction and other aspects of surface behaviour, 230–41 factors affecting abrasion resistance, 236–41 friction and abrasion fundamentals, 231–2 geometric model to predict properties, 30–72 idealised bending curve, 179 measuring roughness and other surface properties, 232–5 fabric surface frictional coefficient, 234–5

Index



fabric surface geometrical roughness, 233–4 friction coefficient output from KES instrument, 235 geometrical roughness, 235 measurement techniques, 232–3 principle of MMD, 236 surface friction, 233 surface roughness, 233 surface roughness chart measured by KES instrument, 234 measuring sewability seam puckering, 383–90 seam slippage, 390–2 seam strength, 382–3 modelling 3-D structures, 393–412 2-D and 3-D weaving, 394 3-D fabrics, 393–4 classifying 3-D woven fabrics, 394–402 modelling equations for weaving 2-D and 3-D fabrics, 402–5 tensile properties of 3-D textile composites, 409–12 use of 2-D and 3-D textiles in composites, 405–9 modelling and applications, 413–34 automotive textiles, 417–21 filter fabrics, 421–3 medical textiles, 416–17 sports textiles, 430–4 textile structure and function fundamental aspects, 414–16 textiles for dectronics, 423–30 modelling of behaviour during making-up of garments, 372–92 fabric buckling and tailorability of garments, 381–2 fabric properties and apparel performance, 373–4 garment making-up process and fabric properties, 374–6 low stress fabric mechanical properties and garment making-up process, 376–9 measuring fabric suitability for garment making-up process, 379–81 other structural changes fabric cover factor, 76 fabric mass, 76 fabric specific volume, 76 fabric thickness, 76 properties after structural modifications, 73–105 crimp interchange phenomena, 73–5 maximum fabric extension, 75–6 predicting fabric properties: numerical examples, 82–105



449

structural design using soft computing, 76–82 shear behaviour, 205–16 deformation, 207–15 fundamentals of deformation, 206–7 practical applications, 215 shear properties in various directions, 215 shrinkage, 109–17 application of models, 115–17 mechanisms, 110–12 predicting fabric shrinkage, 113–15 relationship between cloth and yarn shrinkage, 112–13 structure basics, 3–8 elements, 5 fabric structures produced by fabric formation methods, 4 formation, 3–4 modelling different weaves, 6–8 regular and irregular weaves, 5–6 structure geometrical modelling, 9–29 fabric properties numerical examples, 21–9 modelling maximum fabric cover, 19–21 prediction of fabric thickness, cover, mass and specific volume, 17–19 simple geometric model, 9–17 woven structure, 9 tensile behaviour, 137–62 axial deformation fundamentals, 138–41 Castigliano’s theorem, 149–52 fabric extension in the bias direction, 157–62 factors affecting tensile properties, 162 the sawtooth model, 152–7 tensile properties, 142–8 biaxial loading under large forces, 143–6 fabric with n1 ends and n2 picks, 144 geometrical changes during extension, 142–3 load-elongation behaviour, 142, 143 tensile modulus, 146–8 thermal properties assessment, 330–41 heat transfer through woven fabrics, 333–5 humans thermal comfort, 331–2 measuring thermal comfort, 340–1 moisture vapour transfer through woven fabrics, 335–40 textiles function in enhancing thermal comfort, 332–3 typical bending curve, 178 using geometric model to predict properties numerical examples, 57–70 predicting cover, 53–7 predicting parameters, 31–41 predicting tightness values, 70–2

450

Index

yarn behaviour, 118–36 crimp balance equation, 121–2 crimp interchange and crimp balance equations, 128–31 effect of settings, 127 practical applications, 136 predicting fabric properties: numerical examples, 131–6 predicting yarn path, 122–7 yarn path and inter-yarn forces, 118–21 woven textile fundamental aspects of structure and function, 414–16 directive fibre assembly structures, 415–16 fibre assembly structures functional system, 415 fibre configurational functions, 414 maximum fibre volume fraction, 415 pore size and distribution within fibre assembly structures, 415 structural system of fibre assembly, 414–15 wrinkling, 197 yarn, 3, 334 behaviour, 295 behaviour in woven fabrics, 118–36 crimp balance equation, 121–2 crimp interchange and crimp balance equations, 128–31 effect of settings, 127 practical applications, 136 predicting fabric properties: numerical examples, 131–6 predicting yarn path, 122–7 yarn path and inter-yarn forces, 118–21 bending behaviour, 200 bending deformation, 224 bending rigidity, 225 configuration in fabric, 182 configurations in creased fabrics, 202 count see yarn count crimp, 224 crimp interchange and crimp balance equations interaction (l1/D = l2/D), 130 interaction (l1/D < l2/D), 131 interaction (l1/D > l2/D), 130 cross-section elliptical, 15–16 non-circular, 14–15

racetrack, 16–17 diameter, 41, 136 elastic modulus, 147 elongation, 147 fancy, fabric simulations, 296 fibre density, 42 forces acting on elastica, 120 inter-yarn friction, 199–200 mobility, 386 packing factor, 42 effect of variation on warp and weft cover factor relation for jammed fabrics, 42–5 path see yarn path Peirce’s elliptical cross-section, 15 possible movements in fabric deformations, 386–7 yarn bending, 387 yarn rotation, 386–7 yarn sliding, 386 racetrack cross-section model, 16–17 rigid and flexible section, 186 rigidity, 136 sawtooth model bent yarn analysis, 195 twisted yarn analysis, 195 shape in fabrics, 120 shrinkage, 110 structure and spinning system, 322–4 structure effect on abrasion resistance, 237–40 crimp, 239 diameter, 238 ply, 238 twist, 237–8 tex see yarn tex twist, 224 warp and weft diameter, 133 yarn count fabric mass, 55 thread density, 55 weave, 55 yarn path and inter-yarn forces, 118–21 prediction in woven fabrics, 122–7 different values of weave angle, 126 limiting weave angle of 49.07∞, 125 produced by inter-yarn force, 119 yarn tex, 26, 27–9, 60–1, 62, 64, 94, 136 Young-Dupre’s equation, 336 Young’s modulus, 141, 174, 225, 315, 352, 353, 360, 362, 381, 410