Domain-independent values of the J-integral for cracks in three-dimensional residual stress bearing bodies

This paper describes an approach for computing domain-independent values of the J-integral in the finite element context for three-dimensional bodies containing residual stress. In the analysis of cracked bodies containing residual stress, the usual domain integral formulation results in domain-dependent values of J, and this paper discusses modifications that yield domain independence. Two correction terms are defined. The first of these relates to the spatial gradients of non-mechanical strains in the crack-driving direction, and the second accounts for plastic dissipation included in the material state, but unrelated to fracture. The paper further presents results for two examples recently discussed in the literature. Application of the corrections in these two cases demonstrates the ability of the approach to obtain path-independent domain integral results in residual stress bearing bodies.