Griffith-Formula and J-Integral for a Crack in a Power-Law Hardening Material

We consider an elastic body with pre-existing crack which is subjected to external loadings. It is assumed that the constitutive relation is of power-law type (Ramberg/Osgood model). Several fracture criteria are based on the energy release rate, which is the derivative of the potential deformation energy with respect to the crack length. The goal of this paper is to derive the Griffith-formula and the Eshelby–Cherepanov–Rice integral for the energy release rate of this nonlinear model taking into account the actual regularity of the corresponding displacement and stress fields.