Analysis of Internal Stress in an Elliptic Inclusion with Imperfect Interface in Plane Elasticity

Abstract

This paper reports a semianalytic solution for the internal stresses associated with an elliptic inclusion embedded within an infinite matrix in plane elasticity. The bonding at the inclusion-matrix interface is assumed to be homogeneously imperfect with corresponding interface conditions defined in terms of linear relations between interface tractions and displacement jumps. Complex variable techniques are used to obtain infinite series representations of the internal stresses (specifically, the mean stress and the von Mises equivalent stress) that, when evaluated numerically, demonstrate how the internal stresses vary with the aspect ratio of the inclusion and the parameter h describing the imperfection in the interface. These results can be used to evaluate the effects of the imperfect interface and the aspect ratio of the inclusion on internal failure caused by void formation and plastic yielding within the inclusion. Remarkably, the mean stress and von Mises equivalent stress are both found to be nonmonotonic functions of the imperfect interface parameter h. Consequently, in each case, we can identify a specific value (h*) of h that corresponds to the maximum peak stress (mean or von Mises) inside the inclusion. This special value h* of the interface parameter depends on the aspect ratio of the elliptic inclusion and the imperfect interface condition.