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Preface
Glossary
Chapter 1 Fracture Mechanisms by Fatigue
Introduction
Principal physical mechanisms of cracking by fatigue
Fracture mechanics
Criteria of fracture (plasticity) in mechanics
Modes of fracture
Directed works
Fatigue of metals: analytical expressions used in reliability
Wöhler’s law
Basquin’s law
Stromayer’s law
Palmgren’s law
Corson’s law
Bastenaire’s law
Weibull’s law
Henry’s law
Corten and Dolen’s law
Manson–Coffin’s law
Reliability models commonly used in fracture mechanics by fatigue
Coffin–Manson’s model for the analysis of crack propagation
Neuber’s relation
Arrhenius’ model
Miner’s law
Main common laws retained by fracture mechanics
Fost and Dugdale’s law
McEvily’s law
Paris’s law
GR Sih’s law
Stress intensity factors in fracture mechanics
Maddox’s model
Gross and Srawley’s model
Lawrence’s model
Martin and Bousseau’s model
Gurney’s model
Engesvik’s model
Yamada and Albrecht’s model
Tomkins and Scott’s model
Harrison’s model
Intrinsic parameters of the material (C and m)
Fracture mechanics elements used in reliability
Crack rate (life expectancy) and sif (Kσ)
Simplified version of Taylor’s law for machining
Elements of stress (S) and resistance theory (R)
Case study, part – suspension bridge (Cirta)
Case study: failure surface of geotechnical materials
Conclusion
Bibliography
Chapter 2 Analysis Elements for Determining the Probability of Rupture by Simple Bounds
Introduction
First-order bounds or simple bounds: systems in series
First-order bounds or simple bounds: systems in parallel
Second-order bounds or Ditlevsen’s bounds
Evaluating the probability of the intersection of two events
Estimating multinomial distribution–normal distribution
Binomial distribution
Hohenbichler’s method
Hypothesis test, through the example of a normal average with unknown variance
Development and calculations
Confidence interval for estimating a normal mean: unknown variance
Conclusion
Bibliography
Chapter 3 Analysis of the Reliability of Materials and Structures by the Bayesian Approach
Introduction to the Bayesian method used to evaluate reliability
Posterior distribution and conjugate models
Independent events
Counting diagram
Conditional probability or Bayes’ law
Anterior and posterior distributions
Reliability analysis by moments methods, FORM/SORM
Control margins from the results of fracture mechanics
Bayesian model by exponential gamma distribution
Homogeneous Poisson process and rate of occurrence of failure
Estimating the maximum likelihood
Type I censored exponential model
Estimating the MTBF (or rate of repair/rate of failure)
MTBF and confidence interval
Repair rate or ROCOF
Power law: non-homogeneous Poisson process
Distribution law – gamma (reminder)
Bayesian model of a priori gamma distribution
Distribution tests for exponential life (or HPP model)
Bayesian procedure for the exponential system model
Bayesian case study applied in fracture mechanics
Conclusion
Bibliography
Chapter 4 Elements of Analysis for the Reliability of Components by Markov Chains
Introduction
Applying Markov chains to a fatigue model
Case study with the help of Markov chains for a fatigue model
Position of the problem
Discussion
Explanatory information
Directed works
Approach for solving the problem
Which solution should we choose?
Conclusion
Bibliography
Chapter 5 Reliability Indices
Introduction
Design of material and structure reliability
Reliability of materials and structures
First-order reliability method
Second-order reliability method
Cornell’s reliability index
Hasofer–Lind’s reliability index
Reliability of material and structure components
Reliability of systems in parallels and series
Parallel system
Parallel system (m/n)
Serial assembly system
Conclusion
Bibliography
Chapter 6 Fracture Criteria Reliability Methods through an Integral Damage Indicator
Introduction
Literature review of the integral damage indicator method
Brief recap of the FORM/SORM method
Recap of the Hasofer–Lind index method
Literature review of the probabilistic approach of cracking law
parameters in region II of the Paris law
Crack spreading by a classical fatigue model
Reliability calculations using the integral damage indicator method
Conclusion
Bibliography
Chapter 7 Monte Carlo Simulation
Introduction
From the origin of the Monte Carlo method!
The terminology
Simulation of a singular variable of a Gaussian
Simulation of non-Gaussian variable
Simulation of correlated variables
Simulation of correlated Gaussian variables
Simulation of correlated non-Gaussian variables
Determining safety indices using Monte Carlo simulation
General tools and problem outline
Presentation and discussion of our experimental results
Use of the randomly selected numbers table
Applied mathematical techniques to generate random numbers
by MC simulation on four principle statistical laws
Uniform law
Laplace–Gauss (normal) law
Exponential law
Initial value control
Conclusion
Bibliography
Chapter 8 Case Studies
Introduction
Reliability indicators (λ) and MTBF
Model of parallel assembly
Model of serial assembly
Parallel or redundant model
Reliability and structural redundancy: systems without distribution
Serial model
Rate of constant failure
Reliability of systems without repairing: parallel model
Reliability applications in cases of redundant systems
Total active redundancy
Partial active redundancy
Reliability and availability of repairable systems
Quality assurance in reliability
Projected analysis of reliability
Birnbaum–Saunders distribution in crack spreading
Probability density and distribution function
(Birnbaum–Saunders cumulative distribution through cracking)
Graph plots for the four probability density functions and
distribution functions
Reliability calculation for ages (τ) in hours of service, Ri(τ) = ?
Simulation methods in mechanical reliability of structures and materials: the Monte Carlo simulation method
Weibull law
Log-normal Law (of Galton)
Exponential law
Generation of random numbers
Elements of safety via the couple: resistance and stress (R, S)
Reliability trials
x Fracture Mechanics
Controlling risks and efficiency in mechanical reliability
Truncated trials
Censored trials
Trial plan
Coefficients for the trial’s acceptance plan
Trial’s rejection plan (in the same conditions)
Trial plan in reliability and K Pearson test χ
Reliability application on speed reducers (gears)
Applied example on hydraulic motors
Reliability case study in columns under stress of buckling
RDM solution
Problem outline and probabilistic solution
(reliability and error)
Adjustment of least squared for nonlinear functions
Specific case study : a Weibull law with two parameters
Conclusion
Bibliography
Appendix
Index