Stress analysis of an elliptic inclusion with imperfect interface in planeelasticity

In this paper, a semi-analytic solution of the problem associated with an e lliptic inclusion embedded within an infinite matrix is developed for plane strain deformations. The bonding at the inclusion-matrix interface is assu med to be homogeneously imperfect. The interface is modeled as a spring (in terphase) layer with vanishing thickness. The behavior of this interphase l ayer is based on the assumption that tractions are continuous but displacem ents are discontinuous across the interface. Complex variable techniques are used to obtain infinite series representati ons of the stresses which, when evaluated numerically, demonstrate how the peak stress along the inclusion-matrix interface and the average stress ins ide the inclusion vary with the aspect ratio of the inclusion and a represe ntative parameter h (related to the two interface parameters describing the imperfect interface in two-dimensional elasticity) characterizing the impe rfect interface. In addition, and perhaps most significantly, for different aspect ratios of the elliptic inclusion, we identify a specific value (h*) of the (representative) interface parameter h which corresponds to maximum peak stress along the inclusion-matrix interface. Similarly, for each aspe ct ratio, we identify a specific value of h (also referred to as h* in the paper) which corresponds to maximum peak strain energy density along the in terface, as defined by Achenbach and Zhu (1990). In each case, we plot the relationship between the new parameter h(*)and the aspect ratio of the elli pse. This gives significant and valuable information regarding the failure of the interface using two established failure criteria.