Fracture Mechanics 2

Name: Fracture Mechanics 2 | Applied Reliability
Brand: Wiley-ISTE
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Applied Reliability

Ammar Grous(Autor*in)

Wiley-ISTE (Verlag)

Erschienen am 5. Februar 2013

368 Seiten

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978-1-118-58006-6 (ISBN)

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Inhalt

Intro
Title Page
Contents
Preface
Glossary
Chapter 1. Fracture Mechanisms by Fatigue
1.1. Introduction
1.2. Principal physical mechanisms of cracking by fatigue
1.2.1. Fracture mechanics
1.2.2. Criteria of fracture (plasticity) in mechanics
1.3. Modes of fracture
1.3.1. Directed works
1.4. Fatigue of metals: analytical expressions used in reliability
1.4.1. Wöhler's law
1.4.2. Basquin's law (1910)
1.4.3. Stromayer's law (1914)
1.4.4. Palmgren's law
1.4.5. Corson's law (1949)
1.4.6. Bastenaire's law
1.4.7. Weibull's law
1.4.8. Henry's law
1.4.9. Corten and Dolen's law
1.4.10. Manson-Coffin's law
1.5. Reliability models commonly used in fracture mechanics by fatigue
1.5.1. Coffin-Manson's model for the analysis of crack propagation
1.5.2. Neuber's relation (1958)
1.5.3. Arrhenius' model
1.5.4. Miner's law (1954)
1.6. Main common laws retained by fracture mechanics
1.6.1. Fost and Dugdale's law
1.6.2. McEvily's law (1979)
1.6.3. Paris's law
1.6.4. G.R. Sih's law
1.7. Stress intensity factors in fracture mechanics
1.7.1. Maddox's model
1.7.2. Gross and Srawley's model
1.7.3. Lawrence's model
1.7.4. Martin and Bousseau's model
1.7.5. Gurney's model
1.7.6. Engesvik's model
1.7.7. Yamada and Albrecht's model
1.7.8. Tomkins and Scott's model
1.7.9. Harrison's model
1.8. Intrinsic parameters of the material (C and m)
1.9. Fracture mechanics elements used in reliability
1.10. Crack rate (life expectancy) and s.i.f. (Ks)
1.10.1. Simplified version of Taylor's law for machining
1.11. Elements of stress (S) and resistance theory (R)
1.11.1. Case study, part 2 - suspension bridge (Cirta)
1.11.2. Case study: failure surface of geotechnical materials
1.12. Conclusion
1.13. Bibliography
Chapter 2. Analysis Elements for Determining the Probability of Rupture by Simple Bounds
2.1. Introduction
2.1.1. First-order bounds or simple bounds: systems in series
2.1.2. First-order bounds or simple bounds: systems in parallel
2.2. Second-order bounds or Ditlevsen's bounds
2.2.1. Evaluating the probability of the intersection of two events
2.2.2. Estimating multinomial distribution-normal distribution
2.2.3. Binomial distribution
2.2.4. Approximation of ?2 (for m = 3)
2.3. Hohenbichler's method
2.4. Hypothesis test, through the example of a normal average with unknown variance
2.4.1. Development and calculations
2.5. Confidence interval for estimating a normal mean: unknown variance
2.6. Conclusion
2.7. Bibliography
Chapter 3. Analysis of the Reliability of Materials and Structures by the Bayesian Approach
3.1. Introduction to the Bayesian method used to evaluate reliability
3.2. Posterior distribution and conjugate models
3.2.1. Independent events
3.2.2. Counting diagram
3.3. Conditional probability or Bayes' law
3.4. Anterior and posterior distributions
3.5. Reliability analysis by moments methods, FORM/SORM
3.6. Control margins from the results of fracture mechanics
3.7. Bayesian model by exponential gamma distribution
3.8. Homogeneous Poisson process and rate of occurrence of failure
3.9. Estimating the maximum likelihood
3.9.1. Type I censored exponential model
3.9.2. Estimating the MTBF (or rate of repair/rate of failure)
3.9.3. MTBF and confidence interval
3.10. Repair rate or ROCOF
3.10.1. Power law: non-homogeneous Poisson process
3.10.2. Distribution law - gamma (reminder)
3.10.3. Bayesian model of a priori gamma distribution
3.10.4. Distribution tests for exponential life (or HPP model)
3.10.5. Bayesian procedure for the exponential system model
3.11. Bayesian case study applied in fracture mechanics General argument:
3.12. Conclusion
3.13. Bibliography
Chapter 4. Elements of Analysis for the Reliability of Components by Markov Chains
4.1. Introduction
4.2. Applying Markov chains to a fatigue model
4.3. Case study with the help of Markov chains for a fatigue model
4.3.1. Position of the problem
4.3.2. Discussion
4.3.3. Explanatory information
4.3.4. Directed Works
4.3.5. Approach for solving the problem
4.3.6. Which solution should we choose?
4.4. Conclusion
4.5. Bibliography
Chapter 5. Reliability Indices
5.1. Introduction
5.2. Design of material and structure reliability
5.2.1. Reliability of materials and structures
5.3. First-order reliability method
5.4. Second-order reliability method
5.5. Cornell's reliability index
5.6. Hasofer-Lind's reliability index
5.7. Reliability of material and structure components
5.8. Reliability of systems in parallels and series
5.8.1. Parallel system
5.8.2. Parallel system (m/n)
5.8.3. Serial assembly system
5.9. Conclusion
5.10. Bibliography
Chapter 6. Fracture Criteria Reliability Methods through an Integral Damage Indicator
6.1. Introduction
6.2. Literature review of the integral damage indicator method
6.2.1. Brief recap of the FORM/SORM method
6.2.2. Recap of the Hasofer-Lind index method
6.3. Literature review of the probabilistic approach of cracking law parameters in region II of the Paris law
6.4. Crack spreading by a classical fatigue model
6.5. Reliability calculations using the integral damage indicator method
6.6. Conclusion
6.7. Bibliography
Chapter 7. Monte Carlo Simulation
7.1. Introduction
7.1.1. From the origin of the Monte Carlo method!
7.1.2. The terminology
7.2. Simulation of a singular variable of a Gaussian
7.2.1. Simulation of non-Gaussian variable
7.2.2. Simulation of correlated variables
7.2.3. Simulation of correlated Gaussian variables
7.2.4. Simulation of correlated non-Gaussian variables
7.3. Determining safety indices using Monte Carlo simulation
7.3.1. General tools and problem outline
7.3.2. Presentation and discussion of our experimental results
7.3.3. Use of the randomly selected numbers table
7.4. Applied mathematical techniques to generate random numbers by MC simulation on four principle statistical laws
7.4.1. Uniform law
7.4.2. Laplace-Gauss (normal) law
7.4.3. Exponential law
7.4.4. Initial value control
7.5. Conclusion
7.6. Bibliography
Chapter 8. Case Studies
8.1. Introduction
8.2. Reliability indicators (?) and MTBF
8.2.1. Model of parallel assembly
8.2.2. Model of serial assembly
8.3. Parallel or redundant model
8.4. Reliability and structural redundancy: systems without distribution
8.4.1. Serial model
8.5. Rate of constant failure
8.5.1. Reliability of systems without repairing: parallel model
8.6. Reliability applications in cases of redundant systems
8.6.1. Total active redundancy
8.6.2. Partial active redundancy
8.7. Reliability and availability of repairable systems
8.8. Quality assurance in reliability
8.8.1. Projected analysis of reliability
8.9. Birnbaum-Saunders distribution in crack spreading Justification:
8.9.1. Probability density and distribution function (Birnbaum-Saunders cumulative distribution through cracking)
8.9.2. Graph plots for the four probability density functions and distribution functions
8.10. Reliability calculation for ages (t) in hours of service, Ri(t) = ?
8.11. Simulation methods in mechanical reliability of structures and materials: the Monte Carlo simulation method
8.11.1. Weibull law
8.11.2. Log-normal Law (of Galton)
8.11.3. Exponential law
8.11.4. Generation of random numbers
8.12. Elements of safety via the couple: resistance and stress (R, S)
8.13. Reliability trials
8.13.1. Controlling risks and efficiency in mechanical reliability
8.13.2. Truncated trials
8.13.3. Censored trials
8.13.4. Trial plan
8.13.5. Coefficients for the trial's acceptance plan
8.13.6. Trial's rejection plan (in the same conditions)
8.13.7. Trial plan in reliability and K Pearson test ?2
8.14. Reliability application on speed reducers (gears)
8.14.1. Applied example on hydraulic motors
8.15. Reliability case study in columns under stress of buckling Problem outline from an RDM and reliability perspective:
8.15.1. RDM solution a) According to AISC standards,
8.15.2. Problem outline and probabilistic solution (reliability and error)
8.16. Adjustment of least squared for nonlinear functions
8.16.1. Specific case study 1: a Weibull law with two parameters Parti
8.17. Conclusion
8.18. Bibliography
Appendix
Index

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