Energetical formulation of size effect law for quasi-brittle fracture

A criterion for quasi-brittle failure based on local quantities is proposed. The propagation of long cracks is controlled by the energy release rate, while the initiation of the crack is shown to be well described by the derivative of the energy release rate with respect to the crack length. An equation based on well-known models for the analysis of the size and boundary effects is then adapted to describe the competition between these two quantities in order to characterize the local failure. The predictions of rupture of pre-cracked specimens of different sizes and materials are compared to the experimental results given in the literature. The generality of the formulation for describing the crack propagation mechanisms for other defects, such as v-notches and holes, is finally discussed.