Dislocation model of the interaction between a tensile crack and a hole

Abstract

The representation of a crack by discrete dislocations and that of a hole by surface dislocations is used to study the interaction between a tensile crack and a hole. It is shown that for a given size and shape of a pre-existing hole in a homogeneous material, a crack of only one size can exist in equilibrium. This equilibrium size of the crack depends on the size and shape of the hole and also on the distance between the crack and the hole. All cracks whose size is greater than or lesser than the equilibrium size are unstable. The effect of the size and shape of the hole on the equilibrium size of the crack is illustrated. The asymmetry in the dislocation configuration of the crack and the hole is useful in understanding the stress concentration that exists around the crack tip and the corners of the hole and to further study the mechanism of the growth of the crack and the hole.