Multiple void-crack interaction

Abstract

This paper presents a method for fracture analysis of a general two-dimensional system containing multiple holes, or voids, and cracks. The superposition technique is used to break the problem into a number of single-hole and single-crack problems. Each hole problem is modeled using the method of pseudo-tractions, and each crack problem is modeled by a distribution of dislocations. An integral equation approach is developed, based on two types of fundamental solutions, one due to point loads in a solid with a hole and the other due to point dislocations in an infinite elastic body. The resulting integral equations present Cauchy-type singularities only on the crack part of the multiple hole-crack problem. The results in terms of stress intensity factors (SIFs) are presented for a variety of hole-and-crack arrangements, relative sizes of cracks and holes, spacings and crack orientations. The amplification and retardation effects on SIFs are investigated. It is found that the hole-crack arrangements have significant effects on the nature of the amplification or retardation. In the fractured porous elastic medium (modeled as a crack surrounded by holes), amplification or retardation can occur, depending on the relative size of the holes and cracks and the spacing between them. Very strong retardation exists as the spacing becomes small. Some optimal retardations (void toughening) are achieved by adjusting the geometry parameters. An array of periodical crack-hole structure is examined as a numerical example.