Boundary Element Analysis Of The Interactions OfCracks And Holes In Plane Elastic Bodies

Abstract

By applying the new boundary integral formulation for two-dimensional elastic bodies containing cracks and holes proposed recently by Chau and Wang (1996), an effective boundary element method for calculating the interaction between cracks and holes is presented in this paper. In the crack tips, singular interpolation functions of order /* are introduced to model crack tip singularity. The singular boundary integrals involved at the element level are integrated analytically. For each of the hole boundaries, an additional unknown constant is introduced such that displacement compatibility condition can be satisfied exactly by the complex boundary function H(t). Another nice feature of the present formulation is that the stress intensity factors (both KI and KU ) in crack tips are expressed in terms of the nodal unknown of Hft) exactly, and no extrapolation of data is required. To demonstrate the accuracy and efficiency of our boundary element method, an infinite elastic plane containing a circular hole and a kinked crack subject to far field uniaxial tension is considered; and their interaction is evaluated in terms of the change in stress intensity factors. When the hole is far from the crack or when the crack-hole interaction is negligible, our solutions agree well with the existing results for a kinked crack.