Statistical approach to fracture

The disparities in the nature, size, geometry, location and orientation of flaws between nominally identical test specimens explain the great variations in the stress frequently observed. 

Hypothesis the rupture of a chain with N undifferentiated Unks is set off by the rupture of the weakest link. Let be the survival probability of a link the survival probability of the chain can be written as PsN that is, by reasoning on the rupture probabilities 1 - = (1 - Pj) or also  

Weibrrll proposed the following expression (Weflnrll distribution) for ) (x)  

We generally consider that the raptnre starts in a region subjected to tension through stress a, which reduces the previous expression to  

For each rupture stress Oj, measured experimentally over a batch of N similar test specimens, a mpture probability P is assigned, the stresses being previously arranged as per increasing value. 

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Freudenihal, A.M. (1968) Statistical approach to fracture, in Fracture (ed. H. liebowitz). Academic Press,... 

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