Antiplane Interaction of a Crack with a Circular Inclusion in an Elastic Half Plane

Abstract

The antiplane interaction problem for an elastic circular inclusion embedded in an elastic half plane with an arbitrarily located crack is considered in this paper. Based on the technique of analytical continuation and the structure of Moebius transformation, a rapidly convergent series solution pertaining to either the circular inclusion or half-plane matrix is derived in an explicit form. By introducing a distribution of screw dislocations for modeling an arbitrarily located crack, a system of singular integral equations with a logarithmic kernel is established, which can be solved numerically by applying the appropriate interpolation functions. Several numerical examples are given to illustrate the effects of geometrical parameters and material properties on the mode III stress intensity factors as well as the local stress along the interface.