Thermoelastic fracture solutions using distributions of singular influence functions—I: Determining crack stress fields from dislocation distributions

Abstract

A numerical technique has been developed for the determination of stress fields assoicated with a variety of two-dimensional fracturing problems. The procedure allows the analysis of cracks intersecting the free surface of a half-space, of branched or blunted cracks, and of infinitely long arrays of periodically-spaced cracks. The technique employs an efficient surface integral method, using the well-known mathematical equivalence of cracks and distributions of edge dislocations. New conditions are developed for closing the set of equations governing cracks intersecting a free surface, based on a consideration of the stresses at the point of intersection.