Universal Effective Toughness Distribution for Heterogeneous Brittle Materials Application to Indentation Crack Arrest

A brittle material whose microstructure is heterogeneous and random will display at large enough scales a deterministic brittle character. Prior to this limit, the effective macroscopic toughness of the material has a statistical distribution whose shape is discussed in the present paper. It is proposed that it has a universal shape characterized by only two parameters, namely, an asymptotic toughness, and a size-dependent width. Predictions of this theoretical result expressed in terms of crack size distribution are tested against experimental indentation data.