Mechanical Vibration and Shock Analysis Volume 4: Fatigue Damage

pdfresizer.com-pdf-resize......Page 1
9781118931189.fmatter......Page 2
Title Page......Page 3
Copyright......Page 4
Table of Contents......Page 5
Foreword to Series......Page 12
Introduction......Page 16
List of Symbols......Page 18
1.1.1.1. Hooke’s law......Page 21
1.1.1.2. Stress–strain curve......Page 22
1.1.2. Fatigue......Page 29
1.2.1. Cyclic stress......Page 30
1.2.2. Alternating stress......Page 32
1.2.4. Combined steady and cyclic stress......Page 33
1.2.6. Random and transitory stresses......Page 34
1.3. Damage arising from fatigue......Page 35
1.4.1. S-N curve......Page 38
1.4.2. Influence of the average stress on the S-N curve......Page 41
1.4.3. Statistical aspect......Page 42
1.4.4. Distribution laws of endurance......Page 43
1.4.5. Distribution laws of fatigue strength......Page 46
1.4.6. Relation between fatigue limit and static properties of materials......Page 48
1.4.7.2. Basquin relation......Page 51
1.4.7.3. Some other laws......Page 59
1.5.1. General......Page 61
1.5.2. Scale......Page 62
1.5.3. Overloads......Page 63
1.5.4. Frequency of stresses......Page 64
1.5.6. Non-zero mean stress......Page 65
1.6.1. Haigh diagram......Page 68
1.7. Prediction of fatigue life of complex structures......Page 78
1.8. Fatigue in composite materials......Page 79
2.1. Evolution of fatigue damage......Page 81
2.2. Classification of various laws of accumulation......Page 82
2.3.1. Miner’s rule......Page 83
2.3.2. Scatter of damage to failure as evaluated by Miner......Page 87
2.3.3. Validity of Miner’s law of accumulation of damage in case of random stress......Page 91
2.4.1. Principle......Page 93
2.4.2.1. Method of equivalent cycles......Page 94
2.4.2.2. Method of equivalent stresses......Page 96
2.5. Henry’s method......Page 97
2.7. Corten and Dolan’s method......Page 99
2.8. Other theories......Page 102
3.1. General......Page 104
3.2.1. Presentation of method......Page 108
3.2.2. Derived methods......Page 111
3.2.4. Level-restricted peak count method......Page 112
3.3.1. Presentation of method......Page 114
3.3.2. Elimination of small variations......Page 116
3.4.1. Presentation of method......Page 117
3.4.2. Elimination of small variations......Page 119
3.5.1. Presentation of method......Page 120
3.5.2. Elimination of small variations......Page 123
3.6. Range-pair count method......Page 125
3.7. Hayes’ counting method......Page 129
3.8. Ordered overall range counting method......Page 131
3.9. Level-crossing count method......Page 133
3.10. Peak valley peak counting method......Page 137
3.11. Fatigue-meter counting method......Page 142
3.12. Rainflow counting method......Page 144
3.12.1. Principle of method......Page 145
3.12.2. Subroutine for rainflow counting......Page 150
3.13. NRL (National Luchtvaart Laboratorium) counting method......Page 153
3.14. Evaluation of time spent at a given level......Page 156
3.16. Test acceleration......Page 157
3.17. Presentation of fatigue curves determined by random vibration tests......Page 160
4.1. Introduction......Page 162
4.2. Calculation of fatigue damage due to signal versus time......Page 163
4.3.1. General case......Page 165
4.3.2. Particular case of a wideband response, e.g. at the limit r = 0......Page 170
4.3.3.1. Expression for mean damage......Page 171
4.3.3.2. Notes......Page 176
4.3.3.3. Calculation of gamma function......Page 181
4.3.5. Steinberg approach......Page 184
4.4. Equivalent narrowband noise......Page 185
4.4.1. Use of relation established for narrowband response......Page 186
4.4.2. Alternative: use of mean number of maxima per second......Page 188
4.5.1. Approximation to real maxima distribution using a modified Rayleigh distribution......Page 190
4.5.2. Wirsching and Light’s approach......Page 194
4.5.3. Chaudhury and Dover’s approach......Page 195
4.5.4. Approximate expression of the probability density of peaks......Page 199
4.6. Other approaches......Page 201
4.7.1. Wirsching’s approach......Page 204
4.7.2. Tunna’s approach......Page 208
4.7.4. Hancock’s approach......Page 210
4.7.6. Kam and Dover’s approach......Page 211
4.7.7. Larsen and Lutes (“single moment”) method......Page 212
4.7.8. Jiao-Moan’s method......Page 213
4.7.9. Dirlik’s probability density......Page 214
4.7.9.1. Probability density of ordinary half-ranges......Page 215
4.7.9.2. Probability density of rainflow half-ranges......Page 219
4.7.9.4. Differences between the probability of peaks and of ranges......Page 221
4.7.9.5. Expression of the fatigue damage from the Dirlik probability density......Page 224
4.7.11. Zhao and Baker model......Page 226
4.7.12. Tovo and Benasciutti method......Page 227
4.8. Comparison of S-N curves established under sinusoidal and random loads......Page 230
4.9. Comparison of theory and experiment......Page 235
4.11. Effects of peak truncation......Page 240
4.12. Truncation of stress peaks......Page 241
4.12.1. Particular case of a narrowband noise......Page 242
4.12.2. Layout of the S-N curve for a truncated distribution......Page 251
5.1. Calculation of standard deviation of damage: Bendat’s method......Page 255
5.2. Calculation of standard deviation of damage: Mark’s method......Page 260
5.3. Comparison of Mark and Bendat’s results......Page 265
5.4.1. Narrowband vibration......Page 271
5.4.2. Wideband vibration......Page 274
5.5.1. Definition of statistical curves......Page 275
5.5.2. Bendat’s formulation......Page 276
5.5.3. Mark’s formulation......Page 279
6.1. S-N curve represented by two segments of a straight line on logarithmic scales (taking into account fatigue limit)......Page 284
6.2. S-N curve defined by two segments of straight line on log-lin scales......Page 287
6.3.1. Corten-Dolan’s accumulation law......Page 290
6.3.2. Morrow’s accumulation model......Page 292
6.4. Random vibration with non-zero mean: use of modified Goodman diagram......Page 294
6.5.1. Influence of distribution law of instantaneous values......Page 297
6.5.3. Calculation of damage using Weibull distribution......Page 298
6.5.4. Comparison of Rayleigh assumption/peak counting......Page 301
6.6. Non-linear mechanical system......Page 303
7.1. Overview......Page 305
7.2.1. Baushinger effect......Page 306
7.2.4. Stress–strain curve......Page 307
7.2.6. Significant factors influencing hysteresis and fracture by fatigue......Page 311
7.2.7. Cyclic stress–strain curve (or cyclic consolidation curve)......Page 312
7.3.2. Cyclic strain hardening......Page 313
7.3.3. Cyclic strain softening......Page 315
7.3.4. Cyclically stable metals......Page 316
7.4. Influence of the level application sequence......Page 317
7.5. Development of the cyclic stress–strain curve......Page 319
7.6. Total strain......Page 320
7.7. Fatigue strength curveIn......Page 321
7.8.1. Orowan relation......Page 322
7.8.3.1. Coffin law......Page 323
7.8.3.2. Useful lifetime in fatigue in terms of energy dissipation......Page 329
7.8.3.3. Total energy required for fracture by fatigue......Page 330
7.8.4. Shanley relation......Page 333
7.8.7. Martin relation......Page 334
7.8.9. Manson relation......Page 335
7.9.1. Overview......Page 337
7.9.3. Influence of temperature and frequency......Page 338
7.9.4. Effect of frequency on plastic strain range......Page 340
7.9.5. Equation of generalized fatigue......Page 341
7.10.1. Miner rule......Page 342
7.10.2. Yao and Munse relation......Page 343
7.11. Influence of an average strain or stress......Page 345
7.12. Low-cycle fatigue of composite material......Page 348
8.1. Overview......Page 350
8.2.1. Major phases......Page 353
8.2.2. Initiation of cracks......Page 354
8.3. Critical size: strength to fracture......Page 356
8.4. Modes of stress application......Page 358
8.5.1. Stress in crack root......Page 359
8.5.2. Mode I......Page 361
8.5.3. Mode II......Page 364
8.5.5. Field of equation use......Page 365
8.5.6. Plastic zone......Page 367
8.5.7. Other form of stress expressions......Page 369
8.5.8. General form......Page 371
8.5.9. Widening of crack opening......Page 372
8.6. Fracture toughness: critical K value......Page 373
8.7. Calculation of the stress intensity factor......Page 377
8.8. Stress ratio......Page 380
8.9. Expansion of cracks: Griffith criterion......Page 382
8.11. Factors affecting the propagation of cracks......Page 384
8.11.1.1. Other results......Page 385
8.11.2. Geometric factors......Page 387
8.11.4. Factors linked to the environment......Page 388
8.12. Speed of propagation of cracks......Page 389
8.14. Laws of crack propagation......Page 394
8.14.1. Head law......Page 395
8.14.3. Frost and Dugsdale [FRO 58]......Page 396
8.14.4. McEvily and Illg......Page 397
8.14.5. Paris and Erdogan......Page 398
8.15. Stress intensity factor......Page 411
8.16. Dispersion of results......Page 412
8.18. Determination of the propagation threshold KS......Page 413
8.19. Propagation of cracks in the domain of lowcycle fatigue......Page 415
8.20. Integral J......Page 416
8.21. Overload effect: fatigue crack retardation......Page 418
8.22. Fatigue crack closure......Page 420
8.24. Calculation of a useful lifetime......Page 422
8.25. Propagation of cracks under random load......Page 425
8.25.1. Rms approach......Page 426
8.25.1.2. Roberts and Erdogan......Page 428
8.25.2. Narrowband random loads......Page 431
8.25.3. Calculation from a load collective......Page 437
A1.2. Properties......Page 441
A1.3. Approximations for arbitrary x......Page 444
A2.1. Definition......Page 445
A3.1.......Page 447
A3.2.......Page 449
A3.3.......Page 450
A3.4.......Page 451
A3.5.......Page 452
A3.6.......Page 453
Bibliography......Page 455
Index......Page 500
Summary of Other Volumes in the Series......Page 504
Summary of Volume 1 Sinusoidal Vibration......Page 505
Summary of Volume 2 Mechanical Shock......Page 511
Summary of Volume 3 Random Vibration......Page 517
Summary of Volume 5 Specification Development......Page 525