Closed-form solutions for interfacial edge dislocations in anisotropic bicrystals by the image method

Abstract

Exact solutions for interfacial edge dislocations in an anisotropic bicrystal under plane strain are derived in elementary closed-form by the method of image dislocations. The stresses in the two adjoining crystals, which may have dissimilar elastic constants and/or dissimilar material axis orientations, are shown to be given by the sum of three rational functions of first to second order degree polynomials. Numerical results for an interfacial glide edge dislocation in several bicrystals of hexagonal ceramics show complex dependence on the material and orientational inhomogeneities. In particular, the interfacial stresses when plotted against the c-axis orientations of the two crystals are shown to possess extrema, saddle points, and a center of symmetry/antisymmetry.