Fracture Strength: Stress Concentration, Extreme Value Statistics, and the Fate of the Weibull Distribution

The Weibull distribution is often used to predict the fracture of brittle materials, based on a ``weakest link'' hypothesis, but it may not be an apt description. This is especially true for so-called quasibrittle materials such as ceramics, in which subcritical cracking during loading is significant. The authors use analytical and numerical arguments to explain the shortcomings of the traditional approach, and demonstrate that several orders of magnitude improvement in failure prediction can be achieved by using a simple nonlinear transform.