## Random Fatigue: From Data to TheoryFor many years fatigue has been a significant and difficult problem for engineers, especially for those who design structures such as aircraft, bridges, pressure vessels, and cranes. Fatigue of engineering materials is commonly regarded as an important deterioration process and a principal mode of failure for various structural and mechanical systems. This book presents a unified approach to stochastic modeling of the fatigue phenomenon, particularly the fatigue crack growth process. The main approaches to construction of these stochastic models are presented to show their methodological consistency and potential usefulness in engineering practice. The analyses contained in this work should also inspire the development of new approaches for designing and performing fatigue experiments. |

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### Contents

1 | |

9 | |

Mathematical Prerequisites | 47 |

Statistical Characteristics | 87 |

Evolutionary Probabilistic Models | 109 |

Cumulative Jump Models | 125 |

Differential Equation Models | 167 |

Chapter VII Comparisons and Applications | 217 |

241 | |

Author Index | 259 |

263 | |

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### Common terms and phrases

amplitude analysis assumed basic boundary conditions characterized coefﬁcients constant constant-amplitude correlation crack growth equations crack growth process crack growth rate crack length crack size crack size distribution crack tip critical crack cumulative deﬁned deﬁnition denotes depends deterministic discrete random variable distribution function effects empirical Engineering Fracture Mechanics entropy estimation fatigue crack growth fatigue damage fatigue process ﬁnite ﬁrst ﬁxed Fracture Mechanics Gaussian process given by Eq inﬁnite initial crack inspection interval linear loading process Markov chain Markov process material modelling of fatigue narrow-band number of cycles obtained overload parameters plastic zone Poisson process predicted probabilistic probability density function probability distribution problem quantity random fatigue random loading random process random variable reliability retardation sample functions Section signiﬁcant Sobczyk solution speciﬁc specimen stationary process statistical stochastic differential equation stochastic model stochastic process stress intensity factor stress level structure sufﬁciently theory tion vector white noise Wiener process