Axial translation of a rigid disc inclusion embedded in a penny-shaped crack in a transversely isotropic solid

Abstract

In this paper, an analytical solution for the axisymmetric interaction of a rigid disc inclusion embedded in bonded contact with the surfaces of a penny-shaped crack and a transversely isotropic medium is investigated. By using a method of potential functions and treating dual and triple integral equations, the mixed boundary value problem is written in the form of two coupled integral equations, which are amenable to numerical treatments. The axial stiffness of the inclusion and the shearing stress intensity factor at the tip of the penny-shaped crack for different degrees of material anisotropy are illustrated graphically. Useful limiting cases such as a rigid disc inclusion in an uncracked medium and in a completely cracked solid are recovered.