Analysis of interfacial cracks emanating from a hole in a bi-material plate

Abstract

In this paper the boundary collocation method has been used successfully to analyse the interfacial cracks emanating from a hole in a bi-material plate. The stress functions are assumed such that they can satisfy a series of governing conditions, such as the equilibrium equations in the domain, the boundary conditions on the crack surfaces, and the stress and displacement conditions on the crack surfaces and across the interface. Moreover, they can also represent the stress singularity at the crack tips. Thus, only the boundary conditions on the hole and the external boundary of the plate are necessarily to be considered, and they can be approximately satisfied by the collocation method and least square technique. Numerical investigations for two cases, two-equal-crack and one crack, are carried out. It is shown that the proposed method is effective and gives satisfactory results. In addition, the proposed approach shows many advantages compared to other methods and can be used for investigating more general cases of cracks emanating from a hole in a bi-material plate.