Brittle fracture due to an array of microcracks

Abstract

The method of distributed dislocations is used to analyse the response of an infinite elastic solid containing a single periodic array of inclined curved cracks. Uniform remote loading is applied to the body, and the cracks are of arbitrary but identical shapes. Expressions are derived for the stress intensity factors at each crack tip, the crack displacement profile and the extra compliance of the body due to the presence of the cracks. For an array of straight cracks, the stress intensity factors, and the extra compliance are found as a function of crack orientation and spacing. Using this framework, we examine brittle fracture by the development of a periodic array of cracks in a solid which suffers all combinations of remote proportional loading. The solution for remote shear is explored in detail. The various types of response are summarized in a fracture map, and are compared with experimental observations for polymers and rocks.