Solution of the boundary value problem for a kinking crack in a bulk compression field

Abstract

The solution of the boundary value problem for a macroscopic crack with a small wing crack, in a linear elastic brittle material, due to a bulk compressive stress field is considered. The crack, initially subject to pure mode II loading, propagates by kinking at its end and extending along a new trajectory, in the classical opening mode. The innovations of this paper are, firstly, the introduction of a free surface into an infinite plane solution, so that the original crack is an edge crack in a half-plane, and, secondly, the ability to consider rapidly varying stress gradients on both segments of the kinked crack. Solutions are presented for (a) an inclined crack in a uniform compressive field and (b) cracks subject to contact loading from a rigid punch loading the half-plane via a linear elastic interlayer.