Probabilistic aspects of material failure

The Weibull distribution currently plays a key role in the analysis of material failure data. This distribution was originally proposed by Weibull, who justified its use based on the weakest link principle of material failure and an empirical analysis of failure data on specimens of homogeneous composition. Further support for the appropriateness of this distribution came from Epstein, who may have been the first to recognize it as a member of the Fisher-Tippett-Gnedenko family of extremal distributions. The aim of this note is to point out that if one were to incorporate some elementary principles of fracture mechanics in the development of probability models for the strength of material, then the use of the Weibull is subject to question. The search for alternate models is therefore germane and some possibilities along these lines are outlined here.