THE DISPLACEMENT FIELD DUE TO AN INTERFACE CRACK ALONG AN ELASTIC INCLUSION IN A DIFFERING ELASTIC MATRIX

A two dimensional mathematical model of an interface crack which lies along an elastic inclusion embedded in an elastic matrix with different elastic constants is considered. In contrast to a previous study by Toya, which determined only the displacemcent of the crack faces for a far-field biaxial load, a formula for the entire displacement throughout the matrix and inclusion is obtained for a far-field biaxial load. Herrmann [16], which considered a fixed rigid inclusion, and this paper are the first solutions for the entire displacement of an interface crack problem with in plane far-field loading. From this expression for the displacement, a natural decomposition of the problem is identified and the extent of the predicted interpenetration of the crack faces is discussed for each case. It is seen, analogous to a Griffith crack, that interpenetration regions always occur and are large for most mixed far-field loads. This confirms the statement in England [10] that ''it might be expected ... that a similar wrinkling and crossover phenomena will be observed near the ends of the crack.'' This elegant closed-form expression for the displacements throughout both the matrix and the inclusion is of interest either for use as a benchmark for numerical studies of interface problems or to determine a domain of influence for interface cracks in fiber-reinforced and particular composites.