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Applied Reliability: Fracture Mechanics, Volume 2 (Iste)

Applied Reliability: Fracture Mechanics, Volume 2 (Iste) Cover

 

Synopses & Reviews

Publisher Comments:

This second book of a 3-volume set on Fracture Mechanics completes the first volume through the analysis of adjustment tests suited to correctly validating the justified use of the laws conforming to the behavior of the materials and structures under study.
This volume focuses on the vast range of statistical distributions encountered in reliability. Its aim is to run statistical measurements, to present a report on enhanced measures in mechanical reliability and to evaluate the reliability of repairable or unrepairable systems. To achieve this, the author presents a theoretical and practice-based approach on the following themes: criteria of failures; Bayesian applied probability; Markov chains; Monte Carlo simulation as well as many other solved case studies.
This book distinguishes itself from other works in the field through its originality in presenting an educational approach which aims at helping practitioners both in academia and industry. It is intended for technicians, engineers, designers, students, and teachers working in the fields of engineering and vocational education. The main objective of the author is to provide an assessment of indicators of quality and reliability to aid in decision-making. To this end, an intuitive and practical approach, based on mathematical rigor, is recommended.

Synopsis:

The science of engineering is soiled by uncertainties. The experimental data cost. The design stumbles at random. The objective of the design is to maximize the chances of success of a dimensioning. The objective of this work is to allow the users to understand the main methods. This volume is centered on a vast range of statistical distributions met in reliability. The aim is to run statistical measures, to present a report of enhanced measures in mechanical reliability and to evaluate the reliability of the repairable or not repairable systems. To reach these purposes, we present an approach theory /practice based on these themes: Criteria of failures; Bayesian Applied Probability; Chains of Markov; Simulation of Monte Carlo and finally many solved cases of studies.

Table of Contents

Preface  xi

Glossary  xix

Chapter 1. Fracture Mechanisms by Fatigue  1

1.1. Introduction  1

1.2. Principal physical mechanisms of cracking by fatigue  2

1.2.1. Fracture mechanics   2

1.2.2. Criteria of fracture (plasticity) in mechanics   4

1.3. Modes of fracture    7

1.3.1. Directed works    11

1.4. Fatigue of metals: analytical expressions used in reliability   13

1.4.1. Wöhler’s law    14

1.4.2. Basquin’s law (1910)    15

1.4.3. Stromayer’s law (1914)    16

1.4.4. Palmgren’s law    16

1.4.5. Corson’s law (1949)  17

1.4.6. Bastenaire’s law   17

1.4.7. Weibull’s law    18

1.4.8. Henry’s law    18

1.4.9. Corten and Dolen’s law    19

1.4.10. Manson–Coffin’s law   20

1.5. Reliability models commonly used in fracture mechanics by fatigue   22

1.5.1. Coffin–Manson’s model for the analysis of crack propagation  24

1.5.2. Neuber’s relation (1958)   25

1.5.3. Arrhenius’ model 28

1.5.4. Miner’s law (1954)   29

1.6. Main common laws retained by fracture mechanics   31

1.6.1. Fost and Dugdale’s law    33

1.6.2. McEvily’s law (1979)    34

1.6.3. Paris’s law 35

1.6.4. G.R. Sih’s law   39

1.7. Stress intensity factors in fracture mechanics    40

1.7.1. Maddox’s model 40

1.7.2. Gross and Srawley’s model 41

1.7.3. Lawrence’s model   41

1.7.4. Martin and Bousseau’s model   42

1.7.5. Gurney’s model    43

1.7.6. Engesvik’s model 43

1.7.7. Yamada and Albrecht’s model   44

1.7.8. Tomkins and Scott’s model 45

1.7.9. Harrison’s model 46

1.8. Intrinsic parameters of the material (C and m)  46

1.9. Fracture mechanics elements used in reliability   48

1.10. Crack rate (life expectancy) and s.i.f. (Kσ)  51

1.10.1. Simplified version of Taylor’s law for machining  54

1.11. Elements of stress (S) and resistance theory (R)   55

1.11.1. Case study, part 2 – suspension bridge (Cirta)   55

1.11.2. Case study: failure surface of geotechnical materials   57

1.12. Conclusion     65

1.13. Bibliography  65

Chapter 2. Analysis Elements for Determining the Probability of Rupture by Simple Bounds  69

2.1. Introduction  69

2.1.1. First-order bounds or simple bounds: systems in series   70

2.1.2. First-order bounds or simple bounds: systems in parallel   70

2.2. Second-order bounds or Ditlevsen’s bounds    70

2.2.1. Evaluating the probability of the intersection of two events 71

2.2.2. Estimating multinomial distribution–normal distribution   74

2.2.3. Binomial distribution  74

2.2.4. Approximation of o2 (for m ≥ 3)   76

2.3. Hohenbichler’s method   78

2.4. Hypothesis test, through the example of a normal average with unknown variance    80

2.4.1. Development and calculations   82

2.5. Confidence interval for estimating a normal mean: unknown variance    84

2.6. Conclusion   85

2.7. Bibliography     85

Chapter 3. Analysis of the Reliability of Materials and Structures by the Bayesian Approach    87

3.1. Introduction to the Bayesian method used to evaluate reliability  87

3.2. Posterior distribution and conjugate models    88

3.2.1. Independent events   91

3.2.2. Counting diagram  95

3.3. Conditional probability or Bayes’ law99

3.4. Anterior and posterior distributions  103

3.5. Reliability analysis by moments methods, FORM/SORM   106

3.6. Control margins from the results of fracture mechanics 107

3.7. Bayesian model by exponential gamma distribution  110

3.8. Homogeneous Poisson process and rate of occurrence of failure  112

3.9. Estimating the maximum likelihood   113

3.9.1. Type I censored exponential model  113

3.9.2. Estimating the MTBF (or rate of repair/rate of failure)  113

3.9.3. MTBF and confidence interval   114

3.10. Repair rate or ROCOF 117

3.10.1. Power law: non-homogeneous Poisson process 118

3.10.2. Distribution law – gamma (reminder)  119

3.10.3. Bayesian model of a priori gamma distribution 122

3.10.4. Distribution tests for exponential life (or HPP model)   124

3.10.5. Bayesian procedure for the exponential system model   126

3.11. Bayesian case study applied in fracture mechanics  131

3.12. Conclusion     137

3.13. Bibliography 138

Chapter 4. Elements of Analysis for the Reliability of Components by Markov Chains   141

4.1. Introduction  141

4.2. Applying Markov chains to a fatigue model    142

4.3. Case study with the help of Markov chains for a fatigue model 145

4.3.1. Position of the problem    146

4.3.2. Discussion  149

4.3.3. Explanatory information   149

4.3.4. Directed works    154

4.3.5. Approach for solving the problem 155

4.3.6. Which solution should we choose?  156

4.4. Conclusion   157

4.5. Bibliography     157

Chapter 5. Reliability Indices   159

5.1. Introduction  159

5.2. Design of material and structure reliability  161

5.2.1. Reliability of materials and structures 162

5.3. First-order reliability method    165

5.4. Second-order reliability method 165

5.5. Cornell’s reliability index    166

5.6. Hasofer–Lind’s reliability index   168

5.7. Reliability of material and structure components  171

5.8. Reliability of systems in parallels and series    172

5.8.1. Parallel system    172

5.8.2. Parallel system (m/n) 173

5.8.3. Serial assembly system    173

5.9. Conclusion   179

5.10. Bibliography   179

Chapter 6. Fracture Criteria Reliability Methods through an Integral Damage Indicator 181

6.1. Introduction  181

6.2. Literature review of the integral damage indicator method   185

6.2.1. Brief recap of the FORM/SORM method   186

6.2.2. Recap of the Hasofer–Lind index method   187

6.3. Literature review of the probabilistic approach of cracking law parameters in region II of the Paris law   188

6.4. Crack spreading by a classical fatigue model    190

6.5. Reliability calculations using the integral damage indicator method     197

6.6. Conclusion   199

6.7. Bibliography     201

Chapter 7. Monte Carlo Simulation    205

7.1. Introduction  205

7.1.1. From the origin of the Monte Carlo method!  205

7.1.2. The terminology 206

7.2. Simulation of a singular variable of a Gaussian   209

7.2.1. Simulation of non-Gaussian variable 210

7.2.2. Simulation of correlated variables 210

7.2.3. Simulation of correlated Gaussian variables   210

7.2.4. Simulation of correlated non-Gaussian variables 210

7.3. Determining safety indices using Monte Carlo simulation   212

7.3.1. General tools and problem outline 212

7.3.2. Presentation and discussion of our experimental results   214

7.3.3. Use of the randomly selected numbers table   215

7.4. Applied mathematical techniques to generate random numbers by MC simulation on four principle statistical laws  220

7.4.1. Uniform law    220

7.4.2. Laplace–Gauss (normal) law   221

7.4.3. Exponential law    222

7.4.4. Initial value control  222

7.5. Conclusion   231

7.6. Bibliography     232

Chapter 8. Case Studies    235

8.1. Introduction  235

8.2. Reliability indicators (λ) and MTBF   235

8.2.1. Model of parallel assembly 235

8.2.2. Model of serial assembly    236

8.3. Parallel or redundant model    237

8.4. Reliability and structural redundancy: systems without distribution 239

8.4.1. Serial model    239

8.5. Rate of constant failure   240

8.5.1. Reliability of systems without repairing: parallel model   243

8.6. Reliability applications in cases of redundant systems  248

8.6.1. Total active redundancy    252

8.6.2. Partial active redundancy    253

8.7. Reliability and availability of repairable systems   258

8.8. Quality assurance in reliability 264

8.8.1. Projected analysis of reliability  264

8.9. Birnbaum–Saunders distribution in crack spreading  268

8.9.1. Probability density and distribution function (Birnbaum–Saunders cumulative distribution through cracking)   269

8.9.2. Graph plots for the four probability density functions and distribution functions    270

8.10. Reliability calculation for ages (τ) in hours of service, Ri(τ) = ?  270

8.11. Simulation methods in mechanical reliability of structures and materials: the Monte Carlo simulation method 275

8.11.1. Weibull law    277

8.11.2. Log-normal Law (of Galton)   278

8.11.3. Exponential law  278

8.11.4. Generation of random numbers   279

8.12. Elements of safety via the couple: resistance and stress (R, S) 284

8.13. Reliability trials    286

8.13.1. Controlling risks and efficiency in mechanical reliability 288

8.13.2. Truncated trials 291

8.13.3. Censored trials  292

8.13.4. Trial plan 293

8.13.5. Coefficients for the trial’s acceptance plan   296

8.13.6. Trial’s rejection plan (in the same conditions)   297

8.13.7. Trial plan in reliability and K Pearson test χ2  299

8.14. Reliability application on speed reducers (gears)   300

8.14.1. Applied example on hydraulic motors  303

8.15. Reliability case study in columns under stress of buckling   305

8.15.1. RDM solution    307

8.15.2. Problem outline and probabilistic solution (reliability and error)   309

8.16. Adjustment of least squared for nonlinear functions 311

8.16.1. Specific case study 1: a Weibull law with two parameters  311

8.17. Conclusion  314

8.18. Bibliography  314

Appendix 317

Index  333

Product Details

ISBN:
9781118580028
Subtitle:
Fracture Mechanics 2
Publisher:
Wiley-ISTE
Author:
Grous, Ammar
Subject:
Material Science
Subject:
Corrosion
Subject:
Materials Science-General
Subject:
Applied Reliability, Fracture Mechanics, Mechanisms of Fatigue-Crack, Analysis of the Control of the Probability of Failure, Analysis of the Reliability of Materials and Structures, Analysis of the Reliability of Components, Reliability Indices, Fiabilist
Subject:
Applied Reliability, Fracture Mechanics, Mechanisms of Fatigue-Crack, Analysis of the Control of the Probability of Failure, Analysis of the Reliability of Materials and Structures, Analysis of the Reliability of Components, Reliability Indices, Fiabilist
Copyright:
Edition Description:
WOL online Book (not BRO)
Series:
ISTE
Series Volume:
Fracture Mechanics,
Publication Date:
20130130
Binding:
Electronic book text in proprietary or open standard format
Language:
English

Related Subjects

Science and Mathematics » Materials Science » General

Applied Reliability: Fracture Mechanics, Volume 2 (Iste)
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Product details pages Wiley-Iste - English 9781118580028 Reviews:
"Synopsis" by , The science of engineering is soiled by uncertainties. The experimental data cost. The design stumbles at random. The objective of the design is to maximize the chances of success of a dimensioning. The objective of this work is to allow the users to understand the main methods. This volume is centered on a vast range of statistical distributions met in reliability. The aim is to run statistical measures, to present a report of enhanced measures in mechanical reliability and to evaluate the reliability of the repairable or not repairable systems. To reach these purposes, we present an approach theory /practice based on these themes: Criteria of failures; Bayesian Applied Probability; Chains of Markov; Simulation of Monte Carlo and finally many solved cases of studies.
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