Mechanical Vibration and Shock Analysis, Fatigue Damage

Christian Lalanne is a Consultant Engineer who previously worked as an expert at the French Atomic Energy Authority and who has specialized in the study of vibration and shock for more than 40 years. He has been associated with the new methods of drafting testing specifications and associated informatic tools.

• Foreword to Series xiiiIntroduction   xviiList of Symbols   xixChapter 1. Concepts of Material Fatigue 11.1. Introduction 11.1.1. Reminders on the strength of materials 11.1.2. Fatigue  91.2. Types of dynamic loads (or stresses)  101.2.1. Cyclic stress 101.2.2. Alternating stress 121.2.3. Repeated stress 131.2.4. Combined steady and cyclic stress 131.2.5. Skewed alternating stress  141.2.6. Random and transitory stresses 141.3. Damage arising from fatigue   151.4. Characterization of endurance of materials 181.4.1. S-N curve 181.4.2. Influence of the average stress on the S-N curve 211.4.3. Statistical aspect 221.4.4. Distribution laws of endurance  231.4.5. Distribution laws of fatigue strength 261.4.6. Relation between fatigue limit and static properties of materials 281.4.7. Analytical representations of S-N curve    311.5. Factors of influence 411.5.1. General  411.5.2. Scale 421.5.3. Overloads 431.5.4. Frequency of stresses    441.5.5. Types of stresses 451.5.6. Non-zero mean stress   451.6. Other representations of S-N curves 481.6.1. Haigh diagram 481.6.2. Statistical representation of Haigh diagram   581.7. Prediction of fatigue life of complex structures 581.8. Fatigue in composite materials   59Chapter 2. Accumulation of Fatigue Damage 612.1. Evolution of fatigue damage    612.2. Classification of various laws of accumulation 622.3. Miner’s method 632.3.1. Miner’s rule 632.3.2. Scatter of damage to failure as evaluated by Miner 672.3.3. Validity of Miner’s law of accumulation of damage in case of random stress 712.4. Modified Miner’s theory 732.4.1. Principle 732.4.2. Accumulation of damage using modified Miner’s rule    742.5. Henry’s method 772.6. Modified Henry’s method   792.7. Corten and Dolan’s method    792.8. Other theories 82Chapter 3. Counting Methods for Analyzing Random Time History   853.1. General   853.2. Peak count method893.2.1. Presentation of method  893.2.2. Derived methods 923.2.3. Range-restricted peak count method 933.2.4. Level-restricted peak count method 933.3. Peak between mean-crossing count method 953.3.1. Presentation of method  953.3.2. Elimination of small variations  973.4. Range count method 983.4.1. Presentation of method  983.4.2. Elimination of small variations  1003.5. Range-mean count method  1013.5.1. Presentation of method  1013.5.2. Elimination of small variations  1043.6. Range-pair count method    1063.7. Hayes’ counting method1103.8. Ordered overall range counting method 1123.9. Level-crossing count method  1143.10. Peak valley peak counting method 1183.11. Fatigue-meter counting method 1233.12. Rainflow counting method    1253.12.1. Principle of method 1263.12.2. Subroutine for rainflow counting 1313.13. NRL (National Luchtvaart Laboratorium) counting method    1343.14. Evaluation of time spent at a given level 1373.15. Influence of levels of load below fatigue limit on fatigue life  1383.16. Test acceleration 1383.17. Presentation of fatigue curves determined by random vibration tests 141Chapter 4. Fatigue Damage by One-degree-of-freedom Mechanical System 1434.1. Introduction 1434.2. Calculation of fatigue damage due to signal versus time 1444.3. Calculation of fatigue damage due to acceleration spectral density 1464.3.1. General case 1464.3.2. Particular case of a wideband response, e.g. at the limit r ?­ 0 1514.3.3. Particular case of narrowband response 1524.3.4. Rms response to narrowband noise G0 of width ?´f when G0 ?´ f ?­ constant 1644.3.5. Steinberg approach 1654.4. Equivalent narrowband noise  1664.4.1. Use of relation established for narrowband response 1674.4.2. Alternative: use of mean number of maxima per second  1694.5. Calculation of damage from the modified Rice distribution of peaks 1714.5.1. Approximation to real maxima distribution using a modified Rayleigh distribution 1714.5.2. Wirsching and Light’s approach 1754.5.3. Chaudhury and Dover’s approach 1764.5.4. Approximate expression of the probability density of peaks   1804.6. Other approaches 1824.7. Calculation of fatigue damage from rainflow domains 1854.7.1. Wirsching’s approach   1854.7.2. Tunna’s approach 1894.7.3. Ortiz-Chen’s method 1914.7.4. Hancock’s approach 1914.7.5. Abdo and Rackwitz’s approach 1924.7.6. Kam and Dover’s approach   1924.7.7. Larsen and Lutes (“single moment”) method 1934.7.8. Jiao-Moan’s method 1944.7.9. Dirlik’s probability density   1954.7.10. Madsen’s approach 2074.7.11. Zhao and Baker model    2074.7.12. Tovo and Benasciutti method  2084.8. Comparison of S-N curves established under sinusoidal and random loads  2114.9. Comparison of theory and experiment 2164.10. Influence of shape of power spectral density and value of irregularity factor 2214.11. Effects of peak truncation  2214.12. Truncation of stress peaks    2224.12.1. Particular case of a narrowband noise 2234.12.2. Layout of the S-N curve for a truncated distribution 232Chapter 5. Standard Deviation of Fatigue Damage 2375.1. Calculation of standard deviation of damage: Bendat’s method  2375.2. Calculation of standard deviation of damage: Mark’s method    2425.3. Comparison of Mark and Bendat’s results    2475.4. Standard deviation of the fatigue life 2535.4.1. Narrowband vibration   2535.4.2. Wideband vibration   2565.5. Statistical S-N curves 2575.5.1. Definition of statistical curves  2575.5.2. Bendat’s formulation    2585.5.3. Mark’s formulation. 261Chapter 6. Fatigue Damage using Other Calculation Assumptions  2676.1. S-N curve represented by two segments of a straight line on logarithmic scales (taking into account fatigue limit)   2676.2. S-N curve defined by two segments of straight line on log-lin scales 2706.3. Hypothesis of non-linear accumulation of damage 2736.3.1. Corten-Dolan’s accumulation law 2736.3.2. Morrow’s accumulation model  2756.4. Random vibration with non-zero mean: use of modified Goodman diagram 2776.5. Non-Gaussian distribution of instantaneous values of signal  2806.5.1. Influence of distribution law of instantaneous values   2806.5.2. Influence of peak distribution 2816.5.3. Calculation of damage using Weibull distribution 2816.5.4. Comparison of Rayleigh assumption/peak counting 2846.6. Non-linear mechanical system 286Chapter 7. Low-cycle Fatigue 2897.1. Overview 2897.2. Definitions  2907.2.1. Baushinger effect 2907.2.2. Cyclic strain hardening    2917.2.3. Properties of cyclic stress–strain curves    2917.2.4. Stress–strain curve 2917.2.5. Hysteresis and fracture by fatigue 2957.2.6. Significant factors influencing hysteresis and fracture by fatigue   2957.2.7. Cyclic stress–strain curve (or cyclic consolidation curve)    2967.3. Behavior of materials experiencing strains in the oligocyclic domain 2977.3.1. Types of behaviors 2977.3.2. Cyclic strain hardening    2977.3.3. Cyclic strain softening   2997.3.4. Cyclically stable metals    3007.3.5. Mixed behavior 3017.4. Influence of the level application sequence 3017.5. Development of the cyclic stress–strain curve 3037.6. Total strain  3047.7. Fatigue strength curve 3057.8. Relation between plastic strain and number of cycles to fracture   3067.8.1. Orowan relation 3067.8.2. Manson relation 3077.8.3. Coffin relation 3077.8.4. Shanley relation 3177.8.5. Gerberich relation 3187.8.6. Sachs, Gerberich, Weiss and Latorre relation 3187.8.7. Martin relation 3187.8.8. Tavernelli and Coffin relation  3197.8.9. Manson relation 3197.8.10. Ohji et al. relation 3217.8.11. Bui-Quoc et al. relation  3217.9. Influence of the frequency and temperature in the plastic field  3217.9.1. Overview 3217.9.2. Influence of frequency   3227.9.3. Influence of temperature and frequency 3227.9.4. Effect of frequency on plastic strain range 3247.9.5. Equation of generalized fatigue 3257.10. Laws of damage accumulation  3267.10.1. Miner rule 3267.10.2. Yao and Munse relation  3277.10.3. Use of the Manson–Coffin relation 3297.11. Influence of an average strain or stress 3297.12. Low-cycle fatigue of composite material 332Chapter 8. Fracture Mechanics    3358.1. Overview 3358.2. Fracture mechanism 3388.2.1. Major phases 3388.2.2. Initiation of cracks 3398.2.3. Slow propagation of cracks   3418.3. Critical size: strength to fracture 3418.4. Modes of stress application    3438.5. Stress intensity factor 3448.5.1. Stress in crack root 3448.5.2. Mode I  3468.5.3. Mode II  3498.5.4. Mode III 3508.5.5. Field of equation use 3508.5.6. Plastic zone 3528.5.7. Other form of stress expressions 3548.5.8. General form 3568.5.9. Widening of crack opening   3578.6. Fracture toughness: critical K value 3588.7. Calculation of the stress intensity factor 3628.8. Stress ratio  3658.9. Expansion of cracks: Griffith criterion 3678.10. Factors affecting the initiation of cracks 3698.11. Factors affecting the propagation of cracks    3698.11.1. Mechanical factors 3708.11.2. Geometric factors 3728.11.3. Metallurgical factors   3738.11.4. Factors linked to the environment 3738.12. Speed of propagation of cracks 3748.13. Effect of a non-zero mean stress 3798.14. Laws of crack propagation    3798.14.1. Head law 3808.14.2. Modified Head law 3818.14.3. Frost and Dugsdale 3818.14.4. McEvily and Illg 3828.14.5. Paris and Erdogan 3838.15. Stress intensity factor 3968.16. Dispersion of results 3978.17. Sample tests: extrapolation to a structure 3988.18. Determination of the propagation threshold KS 3988.19. Propagation of cracks in the domain of low-cycle fatigue    4008.20. Integral J 4018.21. Overload effect: fatigue crack retardation 4038.22. Fatigue crack closure 4058.23. Rules of similarity 4078.24. Calculation of a useful lifetime 4078.25. Propagation of cracks under random load 4108.25.1. Rms approach 4118.25.2. Narrowband random loads  4168.25.3. Calculation from a load collective 422Appendix    427Bibliography  441Index 487Summary of Other Volumes in the Series 491