Stress singularities in a two-material wedge

Abstract

A method for the determination of stresses in a two-material wedge-shaped region is presented. The method is applicable for plane strain or plane stress problems and treats the general case where each region is a wedge of arbitrary angle. The results are obtained by the use of the Mellin transform and the theory of residues. The characteristic equation is investigated to determine the stress singularity resulting from certain combination of geometry and material properties. A formal solution is then presented for the case where the loading is in the form of a point dislocation along the interface. This solution is the Green's function for the more general mismatch problems and therefore has applications in solving other problems with compatible boundary conditions. The results obtained show that for small values of r the dominant effect is due to geometry and the secondary effect is caused by the choice of elastic constants of the materials.