### Abstract

Rational determination of safety factors necessitates establishing the probability density function (pdf) of the structural strength. For perfectly ductile and perfectly brittle materials, the proper pdf's of the nominal strength of structure are known to be Gaussian andWeibullian, respectively, and are invariable with structure size and geometry. However, for quasibrittle materials, many of which came recently to the forefront of attention, the pdf has recently been shown to depend on structure size and geometry, varying gradually from Gaussian pdf with a remote Weibull tail at small sizes to a fully Weibull pdf at large sizes. The recent results are reviewed, and then mathematically extended in two ways: (1) to a mathematical description of structural lifetime as a function of applied (time-invariable) nominal stress, and (2) to a mathematical description of the statistical parameters of the pdf of structural strength as a function of structure size and shape. Finally, recent experimental data are analyzed and applicability of the present theory is verified.

Original language | English (US) |
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Title of host publication | IUTAM Symposium on Scaling in Solid Mechanics - Proceedings of the IUTAM Symposium |

Pages | 135-144 |

Number of pages | 10 |

DOIs | |

State | Published - Dec 1 2009 |

Event | IUTAM Symposium on Scaling in Solid Mechanics - Cardiff, United Kingdom Duration: Jun 25 2007 → Jun 29 2007 |

### Publication series

Name | Solid Mechanics and its Applications |
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Volume | 10 |

ISSN (Print) | 1875-3507 |

### Other

Other | IUTAM Symposium on Scaling in Solid Mechanics |
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Country | United Kingdom |

City | Cardiff |

Period | 6/25/07 → 6/29/07 |

### Keywords

- Cohesive fracture
- Extreme value statistics
- Probabilistic mechanics
- Scaling
- Size effect
- Structural strength

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## Cite this

*IUTAM Symposium on Scaling in Solid Mechanics - Proceedings of the IUTAM Symposium*(pp. 135-144). (Solid Mechanics and its Applications; Vol. 10). https://doi.org/10.1007/978-1-4020-9033-2-13