Coupled fracture modes under anti-plane loading

The linear elastic analysis of homogeneous, isotropic cracked bodies is a Twentieth Century development. It was recognised that the crack tip stress field is a singularity, but it was not until the introduction of the essentially two dimensional stress intensity factor concept in 1957 that widespread application to practical engineering problems became possible. The existence of three dimensional corner point effects in the vicinity of a corner point where a crack front intersects a free surface was investigated in the late 1970s: it was found that modes II and III cannot exist in isolation. The existence of one of these modes always induces the other. An approximate solution for corner point singularities by Bažant and Estenssoro explained some features of corner point effects but there were various paradoxes and inconsistencies. In an attempt to explain these a study was carried out on the coupled in-plane fracture mode induced by a nominal anti-plane (mode III) loading applied to plates and discs weakened by a straight crack. The results derived from a large bulk of finite element models showed clearly that Bažant and Estenssoro’s analysis is incomplete. Some of the results of the study are summarised, together with some recent results for a disc under in-plane shear loading. On the basis of these results, and a mathematical argument, the results suggest that the stress field in the vicinity of a corner point is the sum of two singularities: one due to stress intensity factors and the other due to an as yet undetermined corner point singularity.