Characterization of material strength properties using probabilistic mixture models

Abstract

We consider the use of parametric mixture models for modelling the characteristics of brittle materials. Such mixture models are generalizations of well-known Weibull and related models often used in reliability studies. The properties of such mixture models are described. An attractive feature of such models is that they include standard models as a special case, but allow these standard models to be extended in a natural way. It is argued that they therefore offer a more flexible system for capturing the properties of brittle materials and moreover that the parameters characterizing such mixture models have useful interpretations in practice. The fitting of such models is described to experimental data involving a Carbon 10 data set. An important aspect of the use of such models is their validation against experiment. The use of a bootstrap method for doing this is described. The advantage of a bootstrap technique is that it allows confidence statements and significance levels to be computed without resort to elaborate statistical analysis or reliance on asymptotic theory. A numerical example is given illustrating its ease of use.