## Abstract

This paper extends the theoretical framework presented in the preceding Part I to the lifetime distribution of quasibrittle structures failing at the fracture of one representative volume element under constant amplitude fatigue. The probability distribution of the critical stress amplitude is derived for a given number of cycles and a given minimum-to-maximum stress ratio. The physical mechanism underlying the Paris law for fatigue crack growth is explained under certain plausible assumptions about the damage accumulation in the cyclic fracture process zone at the tip of subcritical crack. This law is then used to relate the probability distribution of critical stress amplitude to the probability distribution of fatigue lifetime. The theory naturally yields a power-law relation for the stress-life curve (S-N curve), which agrees with Basquin's law. Furthermore, the theory indicates that, for quasibrittle structures, the S-N curve must be size dependent. Finally, physical explanation is provided to the experimentally observed systematic deviations of lifetime histograms of various ceramics and bones from the Weibull distribution, and their close fits by the present theory are demonstrated.

Original language | English (US) |
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Pages (from-to) | 1322-1337 |

Number of pages | 16 |

Journal | Journal of the Mechanics and Physics of Solids |

Volume | 59 |

Issue number | 7 |

DOIs | |

State | Published - Jul 2011 |

### Bibliographical note

Funding Information:The theoretical development was partially supported under Grant CMS-0556323 to Northwestern University (NU) from the U.S. National Science Foundation. The applications to concrete and to composites were partially supported by the U.S. Department of Transportation through the NU Infrastructure Technology Institute under Grant 27323, and also under Grant N007613 to NU from Boeing, Inc., respectively.

## Keywords

- Fracture
- Probabilistic mechanics
- Side effect
- Statistical modeling
- Structural safety