Solutions for the stress and displacement fields due to an arbitrary dislocation segment within an isotropic bi-material medium consisting of joined three-dimensional half-spaces, were derived and expressed in terms of line integrals; the integrands of which were given in an exact analytical form that could also be integrated to yield analytical expressions for the stress-displacement field. The solution was constructed by using a general solution which had been derived by Walpole (1996), for treating any elastic singularity in joined isotropic half-spaces, and combining it with Mura's integral formula for the displacement gradient of an arbitrary dislocation segment in an homogeneous medium. The resultant new solution provided a framework for deriving analytical expressions for the stress and displacement fields of dislocation curves of arbitrary shape and orientation. The advantage of this method was that the new solution was naturally divisible into two components: an homogenous component representing the field of a dislocation in an infinitely homogenous medium, and an image component. This made it straightforward to modify existing dislocation dynamics codes that already included the homogenous part. In order to illustrate the accuracy of the method, the stress field expressions of an edge dislocation with its Burgers vector perpendicular to the bi-material interface were derived as a degenerate case of the general result. The present solution was identical to the literature solution for this case.

Line-Integral Solution for the Stress and Displacement Fields of an Arbitrary Dislocation Segment in Isotropic Bi-Materials in 3D Space. S.Akarapu, H.M.Zbib: Philosophical Magazine, 2009, 89[25], 2149-66