Theory of Structure and Mechanics of Yarns

Theory of Structure and Mechanics of Yarns......Page 1
Copyright......Page 4
Contents......Page 5
Preface......Page 10
Introduction......Page 13
 1.1 Fiber characteristics: definitions and relations......Page 16
 1.2 Characteristics of general fibrous assemblies......Page 24
 1.3 Yarn characteristics: definitions and relations......Page 29
 1.4 Yarn fineness, twist and diameter in accordance with Koechlin’s concept......Page 39
 1.5 Empirical corrections to Koechlin’s concept......Page 43
 1.6 References......Page 46
 2.1 General structure of technological process......Page 48
 2.2 Outline of principles of fiber twisting in yarn......Page 53
 2.3 Notes to methodology of studying yarns......Page 55
 2.4 References......Page 57
 3.1 Description of fiber paths and fiber elementary vectors......Page 58
 3.2 A structural characteristic with respect to axial arrangement of fiber paths......Page 77
 3.3 A structural characteristic with respect to radial arrangement of fiber paths......Page 93
 3.4 A structural characteristic with respect totwisted fiber paths......Page 104
 3.5 Idea of regular yarn......Page 109
 3.6 Classification of structural models......Page 120
 3.7 References......Page 124
 4.1 Introduction to helical model......Page 126
 4.2 An alternative introduction to helical model......Page 133
 4.3 Retraction and limit of twisting – hypothesis of neutral radius......Page 137
 4.4 Retraction and limit of twisting – hypothesis of constant fiber volume......Page 144
 4.5 Retraction and limit of twisting – hypothesis of zero axial force......Page 149
 4.6 Yarn retraction in ideal helical model – comparison of hypotheses......Page 155
 4.7 Notes to retraction of staple yarns......Page 160
 4.8 References......Page 171
 5.1 Fundamental equation of radial fiber migration......Page 172
 5.2 An alternative way to determine the fundamental equation of radial migration......Page 178
 5.3 Treloar’s ideal radial fiber migration model......Page 179
 5.4 Treloar’s approximation......Page 193
 5.5 Equidistant radial fiber migration model......Page 206
 5.6 Approximation of equidistant radial migrationmodel......Page 215
 5.7 Characteristics of migration proposed by Hearle and coworkers......Page 221
 5.8 Radial migration in case of non-constant packing density......Page 235
 5.9 Two examples of experimental results......Page 245
 5.10 Creation of radial migration......Page 248
 5.11 Closing notes to fiber migration in yarns......Page 251
 5.12 References......Page 253
 6.1 General ideas of irregularity......Page 254
 6.2 Martindale’s model of sliver irregularity......Page 255
 6.3 Influences of fiber direction and fiber length on sliver irregularity......Page 260
 6.4 Some alternative ideas of yarn irregularity......Page 276
 6.5 Mass irregularity of structural units following binomial and Poisson distributions......Page 282
 6.6 References......Page 296
 7.1 Introductory images and experience......Page 298
 7.2 Probabilistic model of yarn hairiness – general equations......Page 300
 7.3 Exponential model of yarn hairiness......Page 308
 7.4 Double-exponential model of yarn hairiness......Page 318
 7.5 Experimental blackening function – evaluation of hairiness......Page 321
 7.6 Experience and observed trends......Page 332
 7.7 References......Page 341
 8.1 Differential equation of radial equilibrium......Page 343
 8.2 Deformations and packing density......Page 354
 8.3 Solution of differential equation of radial equilibrium......Page 359
 8.4 Some possibilities of solution of deformation law......Page 366
 8.5 A semi-empirical equation for yarn diameter......Page 383
 8.6 Suitable yarn twist......Page 393
 8.7 References......Page 406
 9.1 Stress–strain relation......Page 408
 9.2 Notes to parallel fiber bundles – fiber blends......Page 412
 9.3 Notes to parallel fiber bundles – variable fiber properties......Page 417
 9.4 Tensile behaviour of twisted yarns – general solution......Page 426
 9.5 Tensile behaviour of twisted yarns – simplified solution......Page 434
 9.6 Tensile behaviour of generalized helical model – simplified solution......Page 441
 9.7 Experimental results......Page 451
 9.8 References......Page 460
 10.1 Introduction......Page 462
 10.2 Yarn strength in relation to gauge length – Peirce’s theory [2]......Page 463
 10.3 Yarn strength in relation to gauge length – the alternative Weibull distribution......Page 476
 10.4 Yarn strengths as SEM stochastic process......Page 484
 10.5 Yarn strengths as SEMG stochastic process......Page 504
 10.6 References......Page 529
 11.1 Introductory remarks......Page 531
 11.2 Static equilibrium of fiber elements......Page 532
 11.3 Slippages of fiber ends......Page 540
 11.4 Slippages on the ‘middle’ part of fiber......Page 547
 11.5 Double-sided slippage at ‘middle’ parts of fiber......Page 562
 11.6 Simplest theoretical examples of slippage at ‘middle’ parts of fiber......Page 572
 11.7 Closing remarks on fiber-to-fiber slippage in yarns......Page 585
 11.8 Reference......Page 590
 12.2 Optimum twisting......Page 591
 12.3 Yarn strength according to Solovev......Page 600
 12.4 References......Page 609
Appendix 1......Page 611
Appendix 2......Page 613
Appendix 3......Page 618
Appendix 4......Page 625
Appendix 5......Page 632
Appendix 6......Page 639
Appendix 7......Page 646
Appendix 8......Page 650
Appendix 9......Page 658
Appendix 10......Page 660
Appendix 11......Page 667
Appendix 12......Page 675
Appendix 13......Page 681
Appendix 14......Page 696
Index......Page 711