Analysis of internal stress in an elliptic inclusion with imperfect interface in plane elasticity

This paper reports a semianalytic solution for the internal stresses associ ated 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 jum ps. Complex variable techniques are used to obtain infinite series represen tations 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 p arameter h describing the imperfection in the interface. These results can be used to evaluate the effects of the imperfect interface and the aspect r atio of the inclusion on internal failure caused by void formation and plas tic yielding within the inclusion. Remarkably, the mean stress and von Mise s equivalent stress are both found to be nonmonotonic functions of the impe rfect interface parameter h. Consequently in each case, we can identify a s pecific value (h*) of h that corresponds to the maximum peak stress (mean o r von Mises) inside the inclusion. This special value h* of the interface p arameter depends on the aspect ratio of the elliptic inclusion and the impe rfect interface condition.