The force on a singularity in a two-phase layer

Abstract

T he force acting on a centre of dilatation in the interior of one of two dissimilar layers of infinite extent but of different thicknesses is determined within the limits of the linear theory of elasticity. A remarkable feature of this force is that it is expressible in terms of the distances of the infinite series of images of the singularity from the interface and the plane boundaries. Owing to the dissimilarity in the elastic parameters and the presence of the plane boundaries, the influence of the force can be more drastic than that predicted by the case of a centre of dilatation in the interior of one of two bonded semi-infinite solids. The solution covers many interesting limiting cases, such as the effect of a thick elastic coating on an elastic half-space. As a pilot study on the effect of close boundaries on the force acting on singularities, a formula is first established for the force acting on an infinitesimal prismatic dislocation loop at an arbitrary site inside a free homogeneous layer.