Debonding along the interface of an elliptic rigid inclusion

Abstract

The two-dimensional problem of a crack lying along the interface of an elliptic rigid inclusion embedded in an infinite elastic matrix is theoretically studied. Based on the complex variable method of Muskhelishvili, closed form solutions of the stresses and displacements around the crack are obtained when both general biaxial loads at infinity and uniform normal internal pressure are applied. These solutions are then combined with the virtual work argument of Griffith to give a criterion of the crack extension, namely the growth of the debonding of the interface. The critical applied loads are expressed explicitly by a function of four parameters; the size, the ratio of the length of the minor axis to that of the major axis of the inclusion, the angle subtended by the crack arc and the polar angle of the middle point of the crack arc. It is shown that when the applied load is only a simple tension or only an internal pressure the critical load is inversely proportional to the square-root of the size of the inclusion. The variations of the critical load with the angle subtended by the crack arc and with the ratio of the length of the semi-axes are graphically shown and discussed.