Green's function for an anisotropic film-substrate embedded with a screw dislocation

In this paper, the Green's function for an elastically anisotropic dissimilar film-substrate embedded with a screw dislocation is obtained analytically in series form by the method of continuously distributed image dislocations. The film-substrate interface conditions are satisfied exactly a priori, and it remains to satisfy only the free surface condition. This leads to a Fredholm integral equation of the second kind with the image dislocation density as the unknown. The solution is expressed in the form of a Neumann series, whose terms are certain integral transforms of rational functions. The series can be used as Green's function for a broad range of thin film problems, e.g., mode III crack, screw dislocation pileup, and edge stress concentration problems. Numerical studies of the Green's function focus on a screw dislocation in various semi-infinite film-substrate systems. The solutions satisfy the free surface condition very well using only three terms of the series. The importance of the free surface, elastic anisotropy and material inhomogeneity is emphasized in the numerical investigations.