Green's function methodology for fracture mechanics of SiC-SiC composite structures

A fundamental solution of plane elasticity in a finite domain is developed in this paper. A closed-form Green's function for the elastic field of an edge dislocation of arbitrary Burger's vector at an arbitrary point in an orthotropic finite elastic domain, that is free of traction, is presented. The method is based on the classical theory of potential fields, with an additional distribution of surface dislocations to satisfy the free traction boundary condition. A solution is first developed for a dislocation from the original dislocation, and a regular component associated with the surface distribution. The Schwarz-Christoffel transformation is then utilized to map the field quantities to a finite, polygonal domain. A closed form solution containing Jacobi elliptic functions is developed for rectangular domains, and applications of the method to problems of fracture and plasticity are emphasized