Weight Function Theory for Three-Dimensional Elastic Crack Analysis

Abstract

Recent developments in elastic crack analysis are discussed based on extensions and applications of weight function theory in the three-dimensional regime. It is shown that the weight function, which gives the stress intensity factor distribution along the crack front for arbitrary distributions of applied force, has a complementary interpretation: It characterizes the variation in displacement field throughout the body associated, to first order, with a variation in crack-front position. These properties, together with the fact that weight functions have now been determined for certain three-dimensional crack geometries, have allowed some new types of investigation. They include study of the three-dimensional elastic interactions between cracks and nearby or emergent dislocation loops, as are important in some approaches to understanding brittle versus ductile response of crystals, and also the interactions between cracks and inclusions which are of interest for transformation toughening. The new developments further allow determination of stress-intensity factors and crack-face displacements for cracks whose fronts are slightly perturbed from some reference geometry (for example, from a straight or circular shape), and those solutions allow study of crack trapping in growth through a medium of locally nonuniform fracture toughness. Finally, the configurational stability of cracking processes can be addressed: For example, when will an initially circular crack, under axisymmetric loading, remain circular during growth?