Mechanical Vibration and Shock Analysis, Fatigue Damage.

By: Lalanne, ChristianMaterial type: TextTextSeries: ISTEPublisher: Somerset : John Wiley & Sons, Incorporated, 2014Copyright date: ©2014Edition: 3rd edDescription: 1 online resource (543 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9781118931196Subject(s): Materials -- Fatigue | Mechanical engineering -- SpecificationsGenre/Form: Electronic books.Additional physical formats: Print version:: Mechanical Vibration and Shock Analysis, Fatigue DamageDDC classification: 620.1126 LOC classification: TA418.38.L35 2014ebOnline resources: Click to View
Contents:
Cover -- Title Page -- Contents -- Foreword to Series -- Introduction -- List of Symbols -- Chapter 1. Concepts of Material Fatigue -- 1.1. Introduction -- 1.1.1. Reminders on the strength of materials -- 1.1.2. Fatigue -- 1.2. Types of dynamic loads (or stresses) -- 1.2.1. Cyclic stress -- 1.2.2. Alternating stress -- 1.2.3. Repeated stress -- 1.2.4. Combined steady and cyclic stress -- 1.2.5. Skewed alternating stress -- 1.2.6. Random and transitory stresses -- 1.3. Damage arising from fatigue -- 1.4. Characterization of endurance of materials -- 1.4.1. S-N curve -- 1.4.2. Influence of the average stress on the S-N curve -- 1.4.3. Statistical aspect -- 1.4.4. Distribution laws of endurance -- 1.4.5. Distribution laws of fatigue strength -- 1.4.6. Relation between fatigue limit and static properties of materials -- 1.4.7. Analytical representations of S-N curve -- 1.5. Factors of influence -- 1.5.1. General -- 1.5.2. Scale -- 1.5.3. Overloads -- 1.5.4. Frequency of stresses -- 1.5.5. Types of stresses -- 1.5.6. Non-zero mean stress -- 1.6. Other representations of S-N curves -- 1.6.1. Haigh diagram -- 1.6.2. Statistical representation of Haigh diagram -- 1.7. Prediction of fatigue life of complex structures -- 1.8. Fatigue in composite materials -- Chapter 2. Accumulation of Fatigue Damage -- 2.1. Evolution of fatigue damage -- 2.2. Classification of various laws of accumulation -- 2.3. Miner's method -- 2.3.1. Miner's rule -- 2.3.2. Scatter of damage to failure as evaluated by Miner -- 2.3.3. Validity of Miner's law of accumulation of damage in case of random stress -- 2.4. Modified Miner's theory -- 2.4.1. Principle -- 2.4.2. Accumulation of damage using modified Miner's rule -- 2.5. Henry's method -- 2.6. Modified Henry's method -- 2.7. Corten and Dolan's method -- 2.8. Other theories.
Chapter 3. Counting Methods for Analyzing Random Time History -- 3.1. General -- 3.2. Peak count method -- 3.2.1. Presentation of method -- 3.2.2. Derived methods -- 3.2.3. Range-restricted peak count method -- 3.2.4. Level-restricted peak count method -- 3.3. Peak between mean-crossing count method -- 3.3.1. Presentation of method -- 3.3.2. Elimination of small variations -- 3.4. Range count method -- 3.4.1. Presentation of method -- 3.4.2. Elimination of small variations -- 3.5. Range-mean count method -- 3.5.1. Presentation of method -- 3.5.2. Elimination of small variations -- 3.6. Range-pair count method -- 3.7. Hayes' counting method -- 3.8. Ordered overall range counting method -- 3.9. Level-crossing count method -- 3.10. Peak valley peak counting method -- 3.11. Fatigue-meter counting method -- 3.12. Rainflow counting method -- 3.12.1. Principle of method -- 3.12.2. Subroutine for rainflow counting -- 3.13. NRL (National Luchtvaart Laboratorium) counting method -- 3.14. Evaluation of time spent at a given level -- 3.15. Influence of levels of load below fatigue limit on fatigue life -- 3.16. Test acceleration -- 3.17. Presentation of fatigue curves determined by random vibration tests -- Chapter 4. Fatigue Damage by One-degree-of-freedom Mechanical System -- 4.1. Introduction -- 4.2. Calculation of fatigue damage due to signal versus time -- 4.3. Calculation of fatigue damage due to acceleration spectral density -- 4.3.1. General case -- 4.3.2. Particular case of a wideband response, e.g. at the limit r = 0 -- 4.3.3. Particular case of narrowband response -- 4.3.4. Rms response to narrowband noise G0 of width Δf when G0 Δf = constant -- 4.3.5. Steinberg approach -- 4.4. Equivalent narrowband noise -- 4.4.1. Use of relation established for narrowband response -- 4.4.2. Alternative: use of mean number of maxima per second.
4.5. Calculation of damage from the modified Rice distribution of peaks -- 4.5.1. Approximation to real maxima distribution using a modified Rayleigh distribution -- 4.5.2. Wirsching and Light's approach -- 4.5.3. Chaudhury and Dover's approach -- 4.5.4. Approximate expression of the probability density of peaks -- 4.6. Other approaches -- 4.7. Calculation of fatigue damage from rainflow domains -- 4.7.1. Wirsching's approach -- 4.7.2. Tunna's approach -- 4.7.3. Ortiz-Chen's method -- 4.7.4. Hancock's approach -- 4.7.5. Abdo and Rackwitz's approach -- 4.7.6. Kam and Dover's approach -- 4.7.7. Larsen and Lutes ("single moment") method -- 4.7.8. Jiao-Moan's method -- 4.7.9. Dirlik's probability density -- 4.7.10. Madsen's approach -- 4.7.11. Zhao and Baker model -- 4.7.12. Tovo and Benasciutti method -- 4.8. Comparison of S-N curves established under sinusoidal and random loads -- 4.9. Comparison of theory and experiment -- 4.10. Influence of shape of power spectral density and value of irregularity factor -- 4.11. Effects of peak truncation -- 4.12. Truncation of stress peaks -- 4.12.1. Particular case of a narrowband noise -- 4.12.2. Layout of the S-N curve for a truncated distribution -- Chapter 5. Standard Deviation of Fatigue Damage -- 5.1. Calculation of standard deviation of damage: Bendat's method -- 5.2. Calculation of standard deviation of damage: Mark's method -- 5.3. Comparison of Mark and Bendat's results -- 5.4. Standard deviation of the fatigue life -- 5.4.1. Narrowband vibration -- 5.4.2. Wideband vibration -- 5.5. Statistical S-N curves -- 5.5.1. Definition of statistical curves -- 5.5.2. Bendat's formulation -- 5.5.3. Mark's formulation -- Chapter 6. Fatigue Damage using Other Calculation Assumptions -- 6.1. S-N curve represented by two segments of a straight line on logarithmic scales (taking into account fatigue limit).
6.2. S-N curve defined by two segments of straight line on log-lin scales -- 6.3. Hypothesis of non-linear accumulation of damage -- 6.3.1. Corten-Dolan's accumulation law -- 6.3.2. Morrow's accumulation model -- 6.4. Random vibration with non-zero mean: use of modified Goodman diagram -- 6.5. Non-Gaussian distribution of instantaneous values of signal -- 6.5.1. Influence of distribution law of instantaneous values -- 6.5.2. Influence of peak distribution -- 6.5.3. Calculation of damage using Weibull distribution -- 6.5.4. Comparison of Rayleigh assumption/peak counting -- 6.6. Non-linear mechanical system -- Chapter 7. Low-cycle Fatigue -- 7.1. Overview -- 7.2. Definitions -- 7.2.1. Baushinger effect -- 7.2.2. Cyclic strain hardening -- 7.2.3. Properties of cyclic stress-strain curves -- 7.2.4. Stress-strain curve -- 7.2.5. Hysteresis and fracture by fatigue -- 7.2.6. Significant factors influencing hysteresis and fracture by fatigue -- 7.2.7. Cyclic stress-strain curve (or cyclic consolidation curve) -- 7.3. Behavior of materials experiencing strains in the oligocyclic domain -- 7.3.1. Types of behaviors -- 7.3.2. Cyclic strain hardening -- 7.3.3. Cyclic strain softening -- 7.3.4. Cyclically stable metals -- 7.3.5. Mixed behavior -- 7.4. Influence of the level application sequence -- 7.5. Development of the cyclic stress-strain curve -- 7.6. Total strain -- 7.7. Fatigue strength curve -- 7.8. Relation between plastic strain and number of cycles to fracture -- 7.8.1. Orowan relation -- 7.8.2. Manson relation -- 7.8.3. Coffin relation -- 7.8.4. Shanley relation -- 7.8.5. Gerberich relation -- 7.8.6. Sachs, Gerberich, Weiss and Latorre relation -- 7.8.7. Martin relation -- 7.8.8. Tavernelli and Coffin relation -- 7.8.9. Manson relation -- 7.8.10. Ohji et al. relation -- 7.8.11. Bui-Quoc et al. relation.
7.9. Influence of the frequency and temperature in the plastic field -- 7.9.1. Overview -- 7.9.2. Influence of frequency -- 7.9.3. Influence of temperature and frequency -- 7.9.4. Effect of frequency on plastic strain range -- 7.9.5. Equation of generalized fatigue -- 7.10. Laws of damage accumulation -- 7.10.1. Miner rule -- 7.10.2. Yao and Munse relation -- 7.10.3. Use of the Manson-Coffin relation -- 7.11. Influence of an average strain or stress -- 7.12. Low-cycle fatigue of composite material -- Chapter 8. Fracture Mechanics -- 8.1. Overview -- 8.2. Fracture mechanism -- 8.2.1. Major phases -- 8.2.2. Initiation of cracks -- 8.2.3. Slow propagation of cracks -- 8.3. Critical size: strength to fracture -- 8.4. Modes of stress application -- 8.5. Stress intensity factor -- 8.5.1. Stress in crack root -- 8.5.2. Mode I -- 8.5.3. Mode II -- 8.5.4. Mode III -- 8.5.5. Field of equation use -- 8.5.6. Plastic zone -- 8.5.7. Other form of stress expressions -- 8.5.8. General form -- 8.5.9. Widening of crack opening -- 8.6. Fracture toughness: critical K value -- 8.7. Calculation of the stress intensity factor -- 8.8. Stress ratio -- 8.9. Expansion of cracks: Griffith criterion -- 8.10. Factors affecting the initiation of cracks -- 8.11. Factors affecting the propagation of cracks -- 8.11.1. Mechanical factors -- 8.11.2. Geometric factors -- 8.11.3. Metallurgical factors -- 8.11.4. Factors linked to the environment -- 8.12. Speed of propagation of cracks -- 8.13. Effect of a non-zero mean stress -- 8.14. Laws of crack propagation -- 8.14.1. Head law -- 8.14.2. Modified Head law -- 8.14.3. Frost and Dugsdale -- 8.14.4. McEvily and Illg -- 8.14.5. Paris and Erdogan -- 8.15. Stress intensity factor -- 8.16. Dispersion of results -- 8.17. Sample tests: extrapolation to a structure -- 8.18. Determination of the propagation threshold KS.
8.19. Propagation of cracks in the domain of low-cycle fatigue.
Summary: Fatigue damage in a system with one degree of freedom is one of the two criteria applied when comparing the severity of vibratory environments. The same criterion is also used for a specification representing the effects produced by the set of vibrations imposed in a real environment. In this volume, which is devoted to the calculation of fatigue damage, Christian Lalanne explores the hypotheses adopted to describe the behavior of material affected by fatigue and the laws of fatigue accumulation. The author also considers the methods for counting response peaks, which are used to establish the histogram when it is not possible to use the probability density of the peaks obtained with a Gaussian signal. The expressions for mean damage and its standard deviation are established and other hypotheses are tested.
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Cover -- Title Page -- Contents -- Foreword to Series -- Introduction -- List of Symbols -- Chapter 1. Concepts of Material Fatigue -- 1.1. Introduction -- 1.1.1. Reminders on the strength of materials -- 1.1.2. Fatigue -- 1.2. Types of dynamic loads (or stresses) -- 1.2.1. Cyclic stress -- 1.2.2. Alternating stress -- 1.2.3. Repeated stress -- 1.2.4. Combined steady and cyclic stress -- 1.2.5. Skewed alternating stress -- 1.2.6. Random and transitory stresses -- 1.3. Damage arising from fatigue -- 1.4. Characterization of endurance of materials -- 1.4.1. S-N curve -- 1.4.2. Influence of the average stress on the S-N curve -- 1.4.3. Statistical aspect -- 1.4.4. Distribution laws of endurance -- 1.4.5. Distribution laws of fatigue strength -- 1.4.6. Relation between fatigue limit and static properties of materials -- 1.4.7. Analytical representations of S-N curve -- 1.5. Factors of influence -- 1.5.1. General -- 1.5.2. Scale -- 1.5.3. Overloads -- 1.5.4. Frequency of stresses -- 1.5.5. Types of stresses -- 1.5.6. Non-zero mean stress -- 1.6. Other representations of S-N curves -- 1.6.1. Haigh diagram -- 1.6.2. Statistical representation of Haigh diagram -- 1.7. Prediction of fatigue life of complex structures -- 1.8. Fatigue in composite materials -- Chapter 2. Accumulation of Fatigue Damage -- 2.1. Evolution of fatigue damage -- 2.2. Classification of various laws of accumulation -- 2.3. Miner's method -- 2.3.1. Miner's rule -- 2.3.2. Scatter of damage to failure as evaluated by Miner -- 2.3.3. Validity of Miner's law of accumulation of damage in case of random stress -- 2.4. Modified Miner's theory -- 2.4.1. Principle -- 2.4.2. Accumulation of damage using modified Miner's rule -- 2.5. Henry's method -- 2.6. Modified Henry's method -- 2.7. Corten and Dolan's method -- 2.8. Other theories.

Chapter 3. Counting Methods for Analyzing Random Time History -- 3.1. General -- 3.2. Peak count method -- 3.2.1. Presentation of method -- 3.2.2. Derived methods -- 3.2.3. Range-restricted peak count method -- 3.2.4. Level-restricted peak count method -- 3.3. Peak between mean-crossing count method -- 3.3.1. Presentation of method -- 3.3.2. Elimination of small variations -- 3.4. Range count method -- 3.4.1. Presentation of method -- 3.4.2. Elimination of small variations -- 3.5. Range-mean count method -- 3.5.1. Presentation of method -- 3.5.2. Elimination of small variations -- 3.6. Range-pair count method -- 3.7. Hayes' counting method -- 3.8. Ordered overall range counting method -- 3.9. Level-crossing count method -- 3.10. Peak valley peak counting method -- 3.11. Fatigue-meter counting method -- 3.12. Rainflow counting method -- 3.12.1. Principle of method -- 3.12.2. Subroutine for rainflow counting -- 3.13. NRL (National Luchtvaart Laboratorium) counting method -- 3.14. Evaluation of time spent at a given level -- 3.15. Influence of levels of load below fatigue limit on fatigue life -- 3.16. Test acceleration -- 3.17. Presentation of fatigue curves determined by random vibration tests -- Chapter 4. Fatigue Damage by One-degree-of-freedom Mechanical System -- 4.1. Introduction -- 4.2. Calculation of fatigue damage due to signal versus time -- 4.3. Calculation of fatigue damage due to acceleration spectral density -- 4.3.1. General case -- 4.3.2. Particular case of a wideband response, e.g. at the limit r = 0 -- 4.3.3. Particular case of narrowband response -- 4.3.4. Rms response to narrowband noise G0 of width Δf when G0 Δf = constant -- 4.3.5. Steinberg approach -- 4.4. Equivalent narrowband noise -- 4.4.1. Use of relation established for narrowband response -- 4.4.2. Alternative: use of mean number of maxima per second.

4.5. Calculation of damage from the modified Rice distribution of peaks -- 4.5.1. Approximation to real maxima distribution using a modified Rayleigh distribution -- 4.5.2. Wirsching and Light's approach -- 4.5.3. Chaudhury and Dover's approach -- 4.5.4. Approximate expression of the probability density of peaks -- 4.6. Other approaches -- 4.7. Calculation of fatigue damage from rainflow domains -- 4.7.1. Wirsching's approach -- 4.7.2. Tunna's approach -- 4.7.3. Ortiz-Chen's method -- 4.7.4. Hancock's approach -- 4.7.5. Abdo and Rackwitz's approach -- 4.7.6. Kam and Dover's approach -- 4.7.7. Larsen and Lutes ("single moment") method -- 4.7.8. Jiao-Moan's method -- 4.7.9. Dirlik's probability density -- 4.7.10. Madsen's approach -- 4.7.11. Zhao and Baker model -- 4.7.12. Tovo and Benasciutti method -- 4.8. Comparison of S-N curves established under sinusoidal and random loads -- 4.9. Comparison of theory and experiment -- 4.10. Influence of shape of power spectral density and value of irregularity factor -- 4.11. Effects of peak truncation -- 4.12. Truncation of stress peaks -- 4.12.1. Particular case of a narrowband noise -- 4.12.2. Layout of the S-N curve for a truncated distribution -- Chapter 5. Standard Deviation of Fatigue Damage -- 5.1. Calculation of standard deviation of damage: Bendat's method -- 5.2. Calculation of standard deviation of damage: Mark's method -- 5.3. Comparison of Mark and Bendat's results -- 5.4. Standard deviation of the fatigue life -- 5.4.1. Narrowband vibration -- 5.4.2. Wideband vibration -- 5.5. Statistical S-N curves -- 5.5.1. Definition of statistical curves -- 5.5.2. Bendat's formulation -- 5.5.3. Mark's formulation -- Chapter 6. Fatigue Damage using Other Calculation Assumptions -- 6.1. S-N curve represented by two segments of a straight line on logarithmic scales (taking into account fatigue limit).

6.2. S-N curve defined by two segments of straight line on log-lin scales -- 6.3. Hypothesis of non-linear accumulation of damage -- 6.3.1. Corten-Dolan's accumulation law -- 6.3.2. Morrow's accumulation model -- 6.4. Random vibration with non-zero mean: use of modified Goodman diagram -- 6.5. Non-Gaussian distribution of instantaneous values of signal -- 6.5.1. Influence of distribution law of instantaneous values -- 6.5.2. Influence of peak distribution -- 6.5.3. Calculation of damage using Weibull distribution -- 6.5.4. Comparison of Rayleigh assumption/peak counting -- 6.6. Non-linear mechanical system -- Chapter 7. Low-cycle Fatigue -- 7.1. Overview -- 7.2. Definitions -- 7.2.1. Baushinger effect -- 7.2.2. Cyclic strain hardening -- 7.2.3. Properties of cyclic stress-strain curves -- 7.2.4. Stress-strain curve -- 7.2.5. Hysteresis and fracture by fatigue -- 7.2.6. Significant factors influencing hysteresis and fracture by fatigue -- 7.2.7. Cyclic stress-strain curve (or cyclic consolidation curve) -- 7.3. Behavior of materials experiencing strains in the oligocyclic domain -- 7.3.1. Types of behaviors -- 7.3.2. Cyclic strain hardening -- 7.3.3. Cyclic strain softening -- 7.3.4. Cyclically stable metals -- 7.3.5. Mixed behavior -- 7.4. Influence of the level application sequence -- 7.5. Development of the cyclic stress-strain curve -- 7.6. Total strain -- 7.7. Fatigue strength curve -- 7.8. Relation between plastic strain and number of cycles to fracture -- 7.8.1. Orowan relation -- 7.8.2. Manson relation -- 7.8.3. Coffin relation -- 7.8.4. Shanley relation -- 7.8.5. Gerberich relation -- 7.8.6. Sachs, Gerberich, Weiss and Latorre relation -- 7.8.7. Martin relation -- 7.8.8. Tavernelli and Coffin relation -- 7.8.9. Manson relation -- 7.8.10. Ohji et al. relation -- 7.8.11. Bui-Quoc et al. relation.

7.9. Influence of the frequency and temperature in the plastic field -- 7.9.1. Overview -- 7.9.2. Influence of frequency -- 7.9.3. Influence of temperature and frequency -- 7.9.4. Effect of frequency on plastic strain range -- 7.9.5. Equation of generalized fatigue -- 7.10. Laws of damage accumulation -- 7.10.1. Miner rule -- 7.10.2. Yao and Munse relation -- 7.10.3. Use of the Manson-Coffin relation -- 7.11. Influence of an average strain or stress -- 7.12. Low-cycle fatigue of composite material -- Chapter 8. Fracture Mechanics -- 8.1. Overview -- 8.2. Fracture mechanism -- 8.2.1. Major phases -- 8.2.2. Initiation of cracks -- 8.2.3. Slow propagation of cracks -- 8.3. Critical size: strength to fracture -- 8.4. Modes of stress application -- 8.5. Stress intensity factor -- 8.5.1. Stress in crack root -- 8.5.2. Mode I -- 8.5.3. Mode II -- 8.5.4. Mode III -- 8.5.5. Field of equation use -- 8.5.6. Plastic zone -- 8.5.7. Other form of stress expressions -- 8.5.8. General form -- 8.5.9. Widening of crack opening -- 8.6. Fracture toughness: critical K value -- 8.7. Calculation of the stress intensity factor -- 8.8. Stress ratio -- 8.9. Expansion of cracks: Griffith criterion -- 8.10. Factors affecting the initiation of cracks -- 8.11. Factors affecting the propagation of cracks -- 8.11.1. Mechanical factors -- 8.11.2. Geometric factors -- 8.11.3. Metallurgical factors -- 8.11.4. Factors linked to the environment -- 8.12. Speed of propagation of cracks -- 8.13. Effect of a non-zero mean stress -- 8.14. Laws of crack propagation -- 8.14.1. Head law -- 8.14.2. Modified Head law -- 8.14.3. Frost and Dugsdale -- 8.14.4. McEvily and Illg -- 8.14.5. Paris and Erdogan -- 8.15. Stress intensity factor -- 8.16. Dispersion of results -- 8.17. Sample tests: extrapolation to a structure -- 8.18. Determination of the propagation threshold KS.

8.19. Propagation of cracks in the domain of low-cycle fatigue.

Fatigue damage in a system with one degree of freedom is one of the two criteria applied when comparing the severity of vibratory environments. The same criterion is also used for a specification representing the effects produced by the set of vibrations imposed in a real environment. In this volume, which is devoted to the calculation of fatigue damage, Christian Lalanne explores the hypotheses adopted to describe the behavior of material affected by fatigue and the laws of fatigue accumulation. The author also considers the methods for counting response peaks, which are used to establish the histogram when it is not possible to use the probability density of the peaks obtained with a Gaussian signal. The expressions for mean damage and its standard deviation are established and other hypotheses are tested.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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