Asymptotic analysis of size dependent fracture strength using boundary effect concept

In this paper, the extensively-reported “size effect” phenomena in fracture mechanics tests are explained using the boundary effect concept. It is pointed out that the widely-observed size effect in fracture, including the dependence of the fracture energy on ligament, strength and fracture toughness on crack and/or ligament and the strength of geometrically similar specimens on characteristic size, is in fact, due to the boundary influence on the crack tip damage zone. Furthermore, the recently-developed asymptotic model is used to demonstrate that the dependence of strength on crack and ligament lengths as well as on the characteristic size of geometrically similar specimens is a result of the dominance of the distance of the crack tip to specimen boundaries on the specimen failure mode. To verify further the boundary effect concept, the asymptotic model is also applied to two sets of selected experimental data available in the literature, and the implications are discussed.