A griffith crack at the interface of two bonded dissimilar elastic half planes in which body forces are acting

Abstract

The plane strain problem of determining the stress distribution in the neighbourhood of a Griffith crack situated at the interface of two bonded dissimilar isotropic half planes is investigated. Two types of loadings are considered. Firstly, the crack surfaces are subjected to arbitrary surface tractions, while the body forces are assumed to be zero everywhere in the composite plane. Secondly, there is arbitrary distribution of body forces in the upper as well as the lower half plane, while the crack surfaces are stress free. A special case of the first type of loading, namely, that in which the crack surfaces are subjected to a self equilibrating load system has been discussed separately in detail. This special case is well known in the literature and it has been used here to tackle the problem with second type of loading. Another problem whose solution has been obtained here and used to tackle the problem with the second type of loading is that in which the upper as well as the lower half plane is subjected to arbitrary distribution of body forces, but there is no crack at the interface. Particular distributions of concentrated loads in the nonhomogeneous infinite plane are discussed in detail. Analytical results are compared with the known ones in the literature and numerical results are presented grapically.