Fatigue life prediction of composites and composite structures

Front Cover......Page 1
Fatigue Life Prediction of Composites and Composite Structures......Page 4
Copyright......Page 5
Contents......Page 6
Contributors......Page 12
Preface......Page 14
 1.1. Introduction......Page 16
  1.2.1. Overview......Page 20
  1.2.2. Fatigue test parameters......Page 22
  1.2.3. Fatigue nomenclature......Page 23
  1.3.1. Overview......Page 24
  1.3.2. Fatigue life prediction theories......Page 26
   1.3.2.1. Macroscopic failure theories-Also designated empirical theories......Page 27
   1.3.2.2. Strength and stiffness degradation fatigue theories......Page 31
   1.3.2.3. Multiscale modeling......Page 34
   1.3.2.4. Diverse fatigue considerations......Page 36
  1.3.3. Fatigue life prediction under complex irregular loading......Page 38
 1.4. Conclusions-Future prospects......Page 47
 References......Page 51
Part One: Fatigue life behavior and modeling......Page 60
  2.1. Introduction......Page 62
  2.2. Fatigue experiments......Page 63
   2.2.2. Grips......Page 64
  2.3. Measurements and sensors......Page 65
   2.4.2. Frictional heating......Page 67
  2.5. Specimens......Page 68
   2.5.3. Tabs......Page 69
   2.5.4. Planform......Page 70
   2.5.6. Thickness......Page 71
  2.6. S-N diagrams......Page 72
   2.6.1. Statistical description of fatigue data......Page 73
   2.6.2. Censoring and run-outs......Page 74
  2.7. S-N formulations......Page 75
   2.7.1. Two-parameter S-N curve......Page 76
   2.7.3. Strength-based S-N curve......Page 78
   2.7.4. Statistical formulations......Page 79
   2.7.5. S-N curves that take into account the R-value......Page 80
   2.7.7. Final notes on S-N curves and the CLD......Page 86
  References......Page 88
  Further reading......Page 90
  3.1. Introduction......Page 92
  3.2. Major residual strength models from the literature......Page 93
   3.2.1. Broutman and Sahu......Page 94
   3.2.2. Reifsnider and Stinchcomb......Page 97
   3.2.3. Schaff and Davidson......Page 98
   3.2.5. Other residual strength models......Page 99
  3.3. Fitting of experimental data......Page 100
  3.4. Prediction results......Page 108
  3.5. Conclusions and future trends......Page 109
  References......Page 111
  4.1. Introduction......Page 114
   4.2.1. Material and specimens......Page 118
    4.2.2.1. Dynamic mechanical analysis......Page 119
    4.2.2.3. Pure creep experiment......Page 120
    4.2.2.4. Fatigue experiments......Page 121
    4.2.2.5. Instrumentation......Page 122
   4.3.2. Quasistatic behavior......Page 123
   4.3.3. Pure creep behavior......Page 124
    4.3.4.1. Fatigue life......Page 127
    4.3.4.2. Hysteresis loops-stiffness degradation-energy dissipation......Page 131
    4.3.4.3. Self-generated temperature-Damage evolution......Page 137
   4.3.5. Failure analysis......Page 142
  4.4. Conclusions and outlook......Page 144
  References......Page 145
  5.1. Introduction......Page 150
   5.2.2. Normalized stiffness degradation approach......Page 151
   5.2.3. Normalized fatigue life model......Page 154
   5.2.4. Modeling strategy for the filled fibrous composites with nanoparticles......Page 157
    5.2.5.1. The Halpin-Tsai micromechanics model......Page 158
    5.2.5.2. Nielsen micromechanics model......Page 159
    5.2.6.1. The Nano-NSDM based on the Halpin-Tsai model......Page 160
    5.2.7.1. Fatigue life prediction for epoxy resin modified by silica nanoparticles......Page 161
    5.2.7.2. Fatigue life prediction for GFRP with nanoparticles......Page 162
    5.2.7.3. Fatigue modeling of CSM/epoxy composites......Page 166
     Fatigue damage accumulation model......Page 167
     Tests results-Model evaluation......Page 168
    5.2.7.4. Fatigue life of thermoplastic nanocomposites......Page 170
     Experimental procedure......Page 175
  5.3. Fatigue life prediction based on the micromechanical-energy method......Page 183
   5.3.1. The energy method......Page 184
   5.3.2. Modeling strategy (Nano-EFAT model)......Page 185
   5.3.3. Tests results......Page 186
   5.3.4. Evaluation of the Nano-EFAT model......Page 187
  5.4. Displacement-controlled flexural fatigue behavior of composites with nanoparticles......Page 188
   5.4.2. Specimen preparation......Page 190
   5.4.3. Calculation of the bending stress......Page 192
    5.4.5.1. Static bending strength......Page 195
    5.4.5.2. Cyclic flexural bending fatigue life......Page 198
    5.4.5.3. Dispersion and morphology analysis......Page 199
  5.5. Conclusions and outlook......Page 202
  References......Page 203
  Further reading......Page 208
  6.1. Introduction......Page 210
   6.2.1. Influence of matrix nature on fatigue behavior: TP vs TS composites......Page 211
   6.2.2. Influence of reinforcement architecture......Page 212
   6.2.3. Autogenous heating in polymer matrix composites under fatigue loading......Page 214
   6.2.4. Influence of viscous effects on fatigue accumulated damage......Page 215
   6.2.5. Creep-fatigue interaction in TP composites......Page 216
   6.2.6. Influence of stress concentration on the fatigue behavior of TP laminates......Page 217
   6.3.1. Materials and specimens description......Page 218
   6.3.2. Experimental set-up......Page 219
   6.4.1. Matrix-dominated fatigue behavior [12, 14, 81, 82]......Page 220
   6.4.2. Fiber-dominated fatigue behavior [13]......Page 227
   6.4.3. Autogenous heating under fatigue loading......Page 233
   6.4.4. Creep-fatigue interaction in TP-based composites [14]......Page 234
   6.4.5. Influence of matrix nature on the strain energy release rate in notched laminates [15, 16]......Page 240
  6.5. Conclusions and outlook......Page 243
  References......Page 245
  7.1. Introduction......Page 254
  7.2. Assessment of existing approaches for fatigue of composites......Page 255
  7.3. Aspects of fatigue behavior of thick laminates......Page 260
  7.4. Composite material characterization for failure parameters......Page 264
   7.4.1. Fatigue failure criteria......Page 265
   7.4.2. Determination of fatigue strengths of the composite material......Page 266
  7.5. Failure criteria and failure modes in progressive damage......Page 268
  7.6. Material degradation due to fatigue damage......Page 270
  7.7. Progressive damage development and progression......Page 272
  7.8. Application to a thick composite laminate......Page 275
  7.9. Conclusions......Page 280
  References......Page 281
  8.1. Introduction......Page 284
   8.2.1. Stress analysis......Page 285
   8.2.2. Matrix multi-cracking......Page 287
   8.2.3. Interface debonding......Page 288
   8.2.4. Fibers failure......Page 290
   8.2.5. Hysteresis theory......Page 291
    8.2.5.1. Interface partial debonding......Page 292
    8.2.5.2. Interface complete debonding......Page 294
    8.2.5.3. Hysteresis loops......Page 295
   8.2.6. Life prediction method......Page 296
   8.3.1. Effects of fatigue peak stress......Page 298
   8.3.2. Effects of fatigue stress ratio......Page 301
   8.3.3. Effects of matrix crack spacing......Page 303
   8.3.4. Effects of fiber volume fraction......Page 313
   8.4.1. Unidirectional CMCs......Page 320
    8.4.2.2. Cross-ply SiC/MAS at 1093C in air atmosphere......Page 325
    8.4.3.2. 2D SiC/Si-N-C at 1000C......Page 330
    8.4.3.3. 2D SiC/[Si-B4C] at 1200C in air and in steam atmospheres......Page 333
    8.4.5.1. 3D C/SiC at elevated temperature......Page 336
    8.4.5.2. 3D SiC/SiC at elevated temperature......Page 342
  References......Page 345
  Further reading......Page 348
  9.1. Introduction......Page 350
   9.2.1. 3D printing equipment......Page 351
   9.2.2. Specimen preparation......Page 353
   9.2.3. Experimental setup......Page 354
  9.3. Experimental analysis......Page 355
  9.4. Statistical analysis......Page 357
  9.5. Discussion......Page 360
  References......Page 362
  10.1. Introduction......Page 364
  10.2. Theoretical background......Page 367
   10.2.1. Artificial neural networks......Page 368
   10.2.2. Adaptive neuro-fuzzy inference system......Page 370
   10.2.3. Genetic programming......Page 373
   10.2.4. The gene expression programming algorithm......Page 376
  10.3. Modeling examples......Page 378
    10.3.1.1. Material #1, GFRP multidirectional laminate with stacking sequence [0/(±45)2/0]T......Page 380
    10.3.1.3. Material #3, multidirectional glass/epoxy laminate with a stacking sequence [(±45/0)4/±45]T......Page 381
   10.3.2. Application of the methods......Page 383
    10.3.2.1. Artificial neural networks......Page 384
    10.3.2.2. Adaptive neuro-fuzzy inference system......Page 386
    10.3.2.3. Genetic programming......Page 388
    10.3.2.4. Gene expression programming......Page 389
  10.4. Comparison to conventional methods of fatigue life modeling......Page 391
  10.5. Conclusions and future prospects......Page 394
  References......Page 395
Part Two: Fatigue life prediction and monitoring......Page 400
  11.1. Introduction......Page 402
   11.2.1. Classic fatigue life prediction methodology......Page 403
    11.2.1.1. Cycle counting......Page 404
    11.2.1.2. Representation of CA fatigue data......Page 405
    11.2.1.3. Assessment of the mean stress effect......Page 406
    11.2.1.4. Fatigue failure criterion......Page 408
    11.2.1.5. Damage summation......Page 409
    11.2.2.2. Acquiring strength degradation data......Page 410
    11.2.2.4. Modeling strength degradation......Page 412
    11.2.2.5. Load sequence effects......Page 414
    11.2.2.7. Advantages and disadvantages of strength degradation compared to classic methodology......Page 416
   11.3.1. Multidirectional glass/epoxy laminate with stacking sequence [(±45/0)4/±45]T......Page 418
   11.3.2. Multidirectional glass/polyester laminate with stacking sequence [0/(±45)2/0]T......Page 423
   11.4.1. Cycle counting......Page 424
   11.4.2. Interpretation of fatigue data-S-N curves......Page 425
   11.4.3. Constant life diagrams......Page 427
   11.4.4. Lifetime predictions......Page 429
  11.5. Concluding remarks and future prospects......Page 432
  References......Page 435
  12.1. Introduction......Page 440
  12.2. Constant fatigue life (CFL) diagram approach......Page 443
   12.3.1. Symmetric and asymmetric Goodman diagrams......Page 444
   12.3.2. Shifted Goodman diagram......Page 446
   12.3.3. Inclined Goodman diagram......Page 447
   12.4.1. Piecewise linear CFL diagram......Page 449
   12.4.2. Symmetric and asymmetric Gerber diagrams......Page 450
   12.4.3. Shifted asymmetric and symmetric Gerber diagrams......Page 452
   12.4.4. Inclined Gerber diagram......Page 453
   12.4.5. Bell-shaped CFL diagram......Page 454
    12.4.6.1. Formulation......Page 456
    12.4.6.3. Procedure for predicting the S-N curves for any stress ratios with the help of the anisomorphic CFL diagram......Page 458
  12.5. Prediction of constant fatigue life (CFL) diagrams and S-N curves......Page 459
   12.5.1. Application to the fiber-dominated fatigue behavior of composite laminates......Page 460
   12.5.2. Application to the matrix-dominated fatigue behavior of composite laminates......Page 463
  12.6. Extended anisomorphic constant fatigue life (CFL) diagram......Page 466
  12.7. Conclusions......Page 470
  12.8. Future trends......Page 471
  References......Page 474
  13.2. Definition of crack initiation......Page 480
   13.3.1. Fatigue crack initiation literature......Page 481
   13.3.2. Multiscale fatigue crack initiation criterion......Page 483
   13.3.3. Validation of crack initiation model......Page 488
    13.3.3.1. Calculation of local stress in the matrix around the fibers......Page 489
    13.3.3.2. Application to C_TS_1......Page 492
    13.3.3.3. Application to G_TS_1......Page 493
    13.3.3.4. Application to C_TS_2......Page 497
    13.3.3.5. Application to C_TP_1......Page 499
  13.4. Discussion of validation results......Page 503
  13.5. Conclusion and future challenges......Page 505
  References......Page 506
  14.1. Introduction......Page 510
   14.2.1. Ply response under quasi-static monotonic loading......Page 513
   14.2.2. Loading-unloading-reloading (L-U-R)......Page 514
   14.2.3. Stiffness degradation......Page 518
    14.2.3.1. Pre-failure material models......Page 519
    14.2.3.2. Post-failure material models......Page 521
  14.3. Failure onset conditions......Page 522
  14.4. Strength degradation due to cyclic loading......Page 524
  14.5. Constant life diagrams and S-N curves......Page 532
  14.6. FAtigue DAmage Simulator (FADAS)......Page 534
   14.6.1. Calculations under VA cyclic stresses......Page 538
   14.6.2. Computational procedure......Page 540
   14.6.3. Validation of numerical predictions: Experimental data......Page 541
    14.6.4.1. Constant amplitude fatigue of MD laminate loaded on-and off-axis......Page 543
    14.6.4.2. Life prediction of [±45]S specimens under CA and spectrum loading......Page 546
    14.6.4.3. Residual strength of [±45]S coupons......Page 548
  14.7. Conclusions......Page 549
  References......Page 550
  15.1. Introduction......Page 554
  15.2. Theoretical background: Classical laminate theory for fatigue-life prediction......Page 555
   15.2.1. Stiffness measurement under quasi-static and fatigue loads......Page 558
   15.2.3. Poisson´s ratios measured in quasi-static and fatigue tests......Page 561
  15.3. Fatigue experiments......Page 562
  15.4. Damage mechanisms and stiffness progresses depending on fiber volume content and mean stress......Page 564
   15.4.1. UD 90 degree with 30% and 55% fiber volume content......Page 565
   15.4.3. UD 0 degree with 30% and 55% fiber volume content......Page 567
  15.5. Application of the predictive method......Page 570
   15.5.1. Quasi-static input parameters for CLT......Page 571
   15.5.2. Cycle-dependent moduli and Poisson´s ratios as input for CLT......Page 572
   15.5.3. Calculated stiffness degradation of multidirectional lay-up by CLT vs experiment......Page 574
   15.6.1. Damage mechanisms......Page 577
   15.6.2. Specimen geometry and embedded layers......Page 578
  15.7. Conclusions and future perspectives......Page 579
  References......Page 582
  16.1. Introduction......Page 584
   16.2.1. Loads on the wind turbine rotor......Page 585
   16.2.2. Load distribution on the wind turbine blade......Page 586
   16.2.3. Stresses in the blade material......Page 587
   16.2.4. Fatigue loading......Page 588
   16.2.5. Deflection of the wind turbine blade......Page 590
  16.3. DTU 10MW reference turbine......Page 591
   16.3.2. Blade tip deflection......Page 593
  16.4. The load-carrying composite in a wind turbine blade......Page 594
   16.4.1. Fatigue testing......Page 595
   16.4.2. Fatigue measurement on a quasi-unidirectional glass fiber composite......Page 597
  16.5. Nondestructive fatigue damage characterization methods......Page 601
   16.5.1. Transilluminated white light imagining (TWLI) in situ characterization method......Page 602
   16.5.2. 3D micro-X-ray computer tomography technique (XCT) ex situ characterization method......Page 603
  16.6. Fatigue damage evolution during tension/tension fatigue......Page 606
   16.6.1. Stage I: Initial stiffness drop studied using the in situ TWLI test-setup......Page 607
   16.6.2. Stage II: Gradual stiffness degradation......Page 609
   16.6.3. Stage III: Final damage localization......Page 612
  16.8. Stiffness degradation during tension/compression fatigue......Page 615
  References......Page 617
Part Three: Applications......Page 620
  17.1. Introduction......Page 622
   17.2.1. Existing models......Page 624
   17.2.2. Fatigue damage accumulation under stationary loading......Page 626
   17.2.3. Fatigue damage accumulation under non-stationary loading......Page 628
   17.3.1. Uncertainty modeling of external loading......Page 629
   17.3.2. Uncertainty modeling of material properties......Page 630
   17.4.1. Fatigue reliability under stationary loading......Page 633
   17.4.2. Method I: Moments matching approach......Page 635
   17.4.3. Method II: FORM approach......Page 636
   17.4.4. Fatigue reliability under non-stationary loading......Page 637
   17.5.1. Numerical example 1......Page 639
   17.5.2. Numerical example 2......Page 640
   17.5.3. Experimental validation......Page 643
  Conclusion......Page 646
  References......Page 647
  18.1. Introduction......Page 650
  18.2. Engineering software for fatigue life modeling/prediction......Page 653
   18.3.1. Fatigue life prediction method for laminates......Page 655
   18.3.2. Experimental work......Page 658
    18.3.3.1. Test results for quasi-static loading......Page 659
   18.3.4. Results of fatigue tests......Page 660
    18.3.5.1. FE analysis......Page 662
    18.3.5.2. Fatigue life prediction......Page 663
   18.3.6. Example: Multifunctional truck cross member......Page 668
   18.3.8. Nomenclature......Page 670
   18.4.1. Datasets description......Page 671
   18.4.2. Multidirectional laminate [0/(±45)2/0]T......Page 672
   18.4.3. CCfatigue software application......Page 675
   18.4.4. Variable loading fatigue lifetime prediction......Page 680
   18.4.5. Multiaxial fatigue lifetime prediction......Page 686
   18.4.6. Summary......Page 690
  References......Page 691
  19.1. Introduction......Page 696
  19.2. Framework of developed modeling technique......Page 699
  19.3. Loading......Page 701
   19.3.1. External conditions......Page 702
  19.4. Static analysis......Page 703
   19.5.1. Stress analysis......Page 707
   19.5.2. Failure analysis......Page 708
   19.5.4. Sudden degradation rules......Page 709
   19.5.5. Evaluation of accumulated fatigue damage modeling......Page 710
  19.6. Stochastic characterization of the wind flow......Page 713
  19.7. Stochastic implementation on fatigue modeling......Page 715
   19.7.1. Sources of cyclic loadings......Page 717
   19.7.2. Stochastic analysis......Page 718
   19.7.3. Results and discussion......Page 719
  19.8. Summary and conclusion......Page 721
   19.8.1. Main contributions......Page 722
  References......Page 723
  Further reading......Page 725
  20.1. Introduction......Page 726
  20.2. Structural health monitoring......Page 729
  20.3. Non homogeneous hidden semi-Markov model......Page 730
   20.4.1. Data processing and feature extraction......Page 733
   20.4.2. Data fusion process......Page 735
   20.5.1. Strain data feature extraction......Page 736
   20.5.2. AE feature extraction......Page 739
   20.5.4. RUL estimations......Page 742
   20.5.5. Performance metrics......Page 745
  20.6. Conclusions......Page 750
  References......Page 751
Index......Page 756
Back Cover......Page 766