Creep and Fatigue in Polymer Matrix Composites

Front Cover......Page 1
Creep and Fatigue in Polymer Matrix Composites......Page 4
Copyright......Page 5
Contents......Page 6
Contributors......Page 12
Preface......Page 14
Part One: Viscoelastic and viscoplastic modeling......Page 16
  1.1. Introduction......Page 18
   1.2.1. Thermoplastics......Page 19
   1.2.3. Polymer-matrix composites......Page 20
  1.3. Viscoelastic behavior......Page 21
   1.3.3. Effect of type of plastic......Page 22
   1.3.4. Creep and creep recovery......Page 23
   1.3.7. Fatigue......Page 24
   1.4.2. Weathering......Page 25
   1.4.5. Resistance to wear and friction......Page 26
   1.5.1. Thermal properties......Page 27
   1.5.2. Electrical properties......Page 28
  1.6. Viscoelastic behavior of polymers......Page 29
  1.7. Short-term behavior......Page 30
  1.8. Long-term behavior......Page 31
  1.9. Isochronous and isometric diagrams......Page 32
   1.10.1. Creep......Page 34
   1.10.3. Relaxation......Page 36
  1.11. Linearity......Page 37
  1.12. The time-temperature superposition principle......Page 40
  1.13. The time stress superposition principle......Page 41
  1.14. The time-temperature-stress superposition principle......Page 42
   1.15.1. The linear spring......Page 43
   1.15.2. The linear viscous dashpot......Page 44
   1.15.3. The Maxwell model......Page 45
    1.15.3.1. Creep......Page 46
    1.15.3.3. Relaxation......Page 47
    1.15.4.1. Creep......Page 48
    1.15.4.2. Recovery......Page 49
    1.15.4.3. Relaxation......Page 50
   1.15.5. The three-element solid......Page 52
   1.15.6. The four-element model......Page 53
   1.15.7. The generalized Maxwell model......Page 55
   1.15.8. The generalized Voigt or kelvin model......Page 56
   1.16.1. The limits of linearity......Page 58
    1.16.2.1. Green, Rivlin and Spencer model......Page 60
    1.16.2.2. Pipkin and Rogers model (Nonlinear superposition theory)......Page 62
    1.16.3.3. Brueller´s model......Page 63
    1.16.3.4. Schapery´s constitutive equation......Page 64
    1.16.3.5. Determination of the nonlinear parameters......Page 65
  1.17. Applications to different materials......Page 66
  References......Page 72
  Further reading......Page 74
  2.1. Correlation of short-term data......Page 76
  2.2. Time-temperature superposition......Page 78
  2.3. Time-age superposition......Page 86
  2.4. Effective time theory......Page 92
  2.5. Summary......Page 94
  2.7. Conclusions......Page 95
  References......Page 96
   3.2.1. Moisture sorption in stationary humid conditions......Page 98
   3.2.3. Moisture sorption in nonstationary humidity......Page 103
  3.3. Moisture absorption in fiber reinforced composites......Page 104
   3.3.1. Microstructural approach......Page 105
   3.3.2. Diffusion in anisotropic composite lamina......Page 106
   3.3.3. Diffusion in anisotropic composite laminate......Page 108
   3.3.5. Express procedure for evaluation of durability of complex shape pultruded composite profiles......Page 109
   3.3.6. Multiphase multilayer system......Page 110
  3.4. Swelling......Page 111
  3.5. Effect of moisture on elastic properties and strength of polymers and composites......Page 112
   3.6.1. Creep of linear viscoelastic materials......Page 117
   3.6.2. Superposition principles......Page 118
   3.6.3. Time-moisture superposition principle: creep of moisture-saturated polymers......Page 119
   3.6.4. Creep of polymers under moisture absorption......Page 121
   3.6.5. Viscoelastic stress-strain analysis during moisture uptake under tensile creep......Page 124
   3.7.1. Moisture sorption by polymer nanocomposites......Page 127
   3.7.2. Moisture effect on elastic properties of polymer NC and nanomodified FRP......Page 128
   3.7.3. Moisture effect on viscoelastic properties of polymer NC and nanomodified FRP......Page 130
  3.8. Conclusions......Page 132
  References......Page 133
  4.1. Introduction......Page 136
   4.2.1. Polarization switching model......Page 140
   4.2.2. Linear viscoelastic model......Page 143
   4.2.3. Linearized forms for the constitutive models......Page 144
  4.3. Fiber- and particle-unit-cell models......Page 146
   4.3.1. Formulation of the unit-cell models......Page 147
   4.3.2. Experimental validation......Page 148
   4.3.3. Parametric studies......Page 153
  4.4. Hybrid piezocomposite model......Page 157
   4.4.1. Formulation of the unit-cell model......Page 158
   4.4.2. Numerical implementation......Page 161
  4.5. Conclusions......Page 166
  References......Page 167
  Further reading......Page 170
  5.2. Specific features of constituents......Page 172
  5.3. Distinctive characteristics of behavior of heterogeneous materials with polymeric matrix......Page 177
  5.4. Viscoelasticity of matrix......Page 180
   5.5.1. Mathematical Methods of Viscoelasticity......Page 182
  5.6. Poisson ratio change during creep......Page 191
  5.7. Viscoelasticity of particulate composites: spherical inclusions......Page 194
  5.8. Viscoelasticity of particulate composites: elongated inclusions......Page 210
  5.9. Viscoelasticity of particulate composites: oblate and platelet inclusions......Page 211
  5.10. Viscoelasticity of fibrous composites......Page 216
  5.12. Hollow fibers and nanotubes......Page 218
  5.13. Viscoelasticity of foams and nanoporous materials......Page 220
  5.14. More complicated cases......Page 224
  5.15. Concluding remarks......Page 225
  References......Page 226
  Further Reading......Page 229
  6.1. Introduction......Page 230
  6.2. Viscoplastic creep modeling for polymer composites......Page 233
   6.2.1. Small strain-framework constitutive analysis......Page 234
   6.2.2. Creep-failure time prediction of polymer composites......Page 240
   6.2.3. Finite strain viscoplasticity......Page 246
  6.3. Concluding remarks......Page 257
  6.4. Future trends......Page 258
  References......Page 259
  Further reading......Page 263
 Chapter 7: Polymer matrix composites: Update......Page 264
  References......Page 265
Part Two: Creep rupture......Page 266
  8.2. Failure morphology......Page 268
  8.3. Simple FEA and critical-point stress......Page 269
  8.4. Time and temperature dependence on interface strength......Page 271
  8.5. RVE modeling......Page 273
  8.6. Periodic boundary condition......Page 274
  8.7. Matrix modeling......Page 276
  8.8. Interface modeling......Page 277
  8.9. Numerical results and discussion......Page 279
  References......Page 281
  9.1. Introduction......Page 284
   9.2.1. Kinetic rate theory for time-dependent failure......Page 285
   9.2.2. Energy-based failure criteria......Page 286
   9.2.3. A new approach to the Crochet time-dependent yielding model......Page 288
   9.2.4. Fracture mechanics extended to viscoelastic materials......Page 290
   9.2.5. Continuum damage mechanics......Page 291
   9.3.1. Orthotropic static failure theories extended to account for time-dependent creep rupture......Page 293
   9.3.2. Energy-based failure criterion extended to multidirectional polymer matrix composites......Page 294
  9.4. Long-term failure: accelerated experimental methodologies......Page 297
   9.4.2. Relationship between creep rupture and constant strain/stress rate rupture curves......Page 298
   9.4.4. Semiempirical extrapolation......Page 301
  9.5. Cumulative damage models: multiple step creep loading......Page 302
  9.6. Micromechanical model......Page 307
   9.6.1. Creep stress loading condition......Page 308
   9.6.3. Relationship between CSR and creep lifetime curves......Page 309
   9.6.4. Two-step creep loading......Page 311
  References......Page 312
  10.1. Introduction......Page 318
  10.2. Damage modes in composites......Page 319
  10.3. Damage characterization methods......Page 321
   10.4.1. Intrinsic damage modes......Page 322
   10.4.2. Extrinsic damage modes......Page 325
   10.5.1. Intrinsic damage modes......Page 328
   10.5.2. Extrinsic damage modes......Page 331
  References......Page 332
Part Three: Fatigue modeling, characterization, and monitoring......Page 338
  11.1. Introduction......Page 340
   11.2.1. Procedure of ATM......Page 341
   11.2.2. Master curve of CSR strength......Page 342
   11.2.3. Master curve of creep strength......Page 343
   11.2.4. Master curve of fatigue strength for zero stress ratio......Page 344
   11.3.1. Specimen and testing method......Page 346
   11.3.3. Flexural creep strength......Page 348
   11.3.4. Flexural fatigue strength for zero stress ratio......Page 350
  11.4. Applicability of ATM......Page 351
  11.5. Theoretical verification of ATM......Page 354
   11.6.2. Experiments......Page 356
   11.6.3. Creep compliance of matrix resin......Page 357
   11.6.5. Creep failure tests of CFRP strand......Page 358
  11.7. Future trends and research......Page 359
  References......Page 361
   12.1.1. Fatigue of FRP composites......Page 364
   12.1.2. Creep strain and rupture of FRP composites......Page 366
   12.2.3. Fatigue failure of polymers based on kinetic theory of fracture......Page 367
   12.2.4. Creep rupture of polymers based on kinetic theory of fracture......Page 375
   12.2.5. Creep strain calculation......Page 376
   12.2.6. Shape parameter λ......Page 378
   12.2.7. Application of KTF to composite laminae......Page 379
   12.3.2. Introduction......Page 381
    12.3.3.1. Calibration of elastic properties......Page 382
    12.3.3.2. Calibration of U and γ for in-situ matrix......Page 383
    12.3.3.3. Calibration of U and γ for delamination layer matrix......Page 384
    12.3.4.2. In-plane mesh convergence......Page 388
    12.3.4.3. Through-thickness mesh convergence......Page 390
   12.3.5. Progressive fatigue implementation in FE code Abaqus......Page 391
   12.3.6. Fatigue prediction results......Page 393
    12.3.6.1. Layup [0/45/90/-45]2S......Page 394
    12.3.6.2. Layup [60/0/-60]3S......Page 395
    12.3.6.3. Layup [30/60/90/-60/-30]2S......Page 398
   12.4.1. Introduction......Page 400
    12.4.2.2. Constituent property extraction......Page 401
   12.4.3. Progressive creep strain and rupture implementation in FE code Abaqus......Page 403
    12.4.4.2. FE combined creep strain and rupture predictions......Page 405
  12.5. Review of literature on KTF-based durability modeling of FRP composites......Page 409
  12.6. Conclusions......Page 412
  References......Page 413
  13.2. Fatigue testing methods......Page 418
   13.2.1. Tension-tension fatigue......Page 422
   13.2.2. Tension-compression and compression-compression fatigue......Page 426
   13.2.3. Bending fatigue......Page 427
   13.2.4. Shear dominated fatigue......Page 428
   13.2.5. Multiaxial fatigue......Page 429
   13.3.1. Stress state near tabbed regions in uniaxial fatigue loading......Page 430
   13.3.2. Topology optimization in biaxially loaded specimens......Page 432
   13.4.1. Typical fatigue damage in structural composites......Page 433
   13.4.2. Inspection techniques for visualization of fatigue damage......Page 437
  13.5. Future trends and challenges......Page 442
  13.6. Sources of further information and advice......Page 443
  References......Page 444
  Further reading......Page 452
  14.1. Introduction......Page 454
  14.2. Fatigue damage......Page 456
   14.3.1. Fatigue data characterization......Page 457
  14.4. The S-N curve model proposed by Kim and Zhang......Page 460
   14.5.2. Boundary conditions and damage in domain 2......Page 465
   14.5.3. Compatibility conditions between N and σmax in domain 3......Page 466
  14.7. Isodamage point b......Page 469
  14.8. Numerical determination of n value......Page 470
  14.9. Examples for predicting the remaining fatigue life......Page 471
   14.9.1. Determination of n value......Page 472
  14.10. Concluding remarks......Page 475
  References......Page 476
  15.1. Introduction......Page 480
  15.2. Modeling the viscoelastic behavior of SMP and SMPC......Page 482
  15.3. Finite element simulation procedure for modeling of viscoelastic properties of SMPC......Page 487
  15.4. Finite element simulation results......Page 488
   15.5.2. Experimentation......Page 492
   15.5.4. Bending angle recovery......Page 496
   15.6.1. Space environment......Page 497
   15.6.2. Durability of SPMCs......Page 498
   15.6.3. SMPC space engineering applications......Page 504
  15.7. Conclusion......Page 507
  References......Page 508
  16.1. Introduction......Page 512
  16.2. Material model......Page 513
   16.3.2. Stiffness reduction measurements......Page 516
   16.3.3. Microdamage and stiffness degradation in fiber composites......Page 517
   16.4.1. Viscoplasticity modeling in creep test......Page 523
   16.4.2. Experimental procedure......Page 527
   16.4.3. Experimental results for fiber composites......Page 528
   16.5.1. Viscoelasticity in creep and strain recovery test......Page 533
   16.5.2. Examples of nonlinear viscoelastic behavior......Page 536
  Appendix. Time dependence of VP-strain in one creep test......Page 541
  References......Page 543
  Further reading......Page 545
  17.1. Introduction......Page 546
  17.2. FRP structures in bridge industry......Page 547
  17.3. Structural health monitoring......Page 552
  17.4. FRP structures and SHM......Page 553
  17.5. Case studies......Page 554
    17.5.1.3. Repairs......Page 555
    17.5.1.5. Testing and analysis......Page 557
    17.5.1.6. Conclusions......Page 559
   17.5.2. Bridge wrapping (nonbond-critical)......Page 560
    17.5.2.2. Structure......Page 561
    17.5.2.4. SHM instrumentation......Page 562
   17.5.3. External reinforcement (bond-critical)......Page 564
    17.5.3.3. Repairs......Page 565
    17.5.3.4. SHM instrumentation......Page 566
    17.5.3.6. Conclusions......Page 567
  17.6. Summary......Page 568
  References......Page 570
Index......Page 574
Back Cover......Page 590