Conserved integrals and energetic forces

Conserved integrals of the Eshelby type representing energetic forces on dislocations, inclusions, voids, cracks and the like are reviewed and related to in-variant transformations. Applications are discussed based on path independence for 2D integrals of J and M type and on the Maxwell reciprocity satisfied by energetic forces. Such concepts have had wide use in crack mechanics to aid analysis of near tip fields and provide elegant short-cut solutions of boundary value problems. Here new applications of path independence to dislocations show that the M inte-gral when centered on a dislocation line is equal to the prelogarithmic energy factor and, also, that simple expressions involving the factor result for the image force drawing a dislocation to a V-notch tip and to a bicrystal interface. A review of reci-procity for energetic forces reveals a wide range of applications to such topics as weight functions for elastic crack analysis, the structure of inelastic constitutive relations, and compliance methods in nonlinear fracture mechanics, and in a new application there is developed the full 2D interaction effects between a crack tip and a nearby dislocation in a crystal of general anisotropy. 1