Path Dependence of the J-Integral and the Role of J as a Parameter Characterizing the Near-Tip Field

Abstract

The J-integral has significant path dependence immediately adjacent to a blunted crack tip under small-scale yielding conditions in an elastic-plastic material subject to mode I loads and plane-strain conditions. Since the J-integral, evaluated on a contour remote from the crack tip, can be used as the one fracture-mechanics parameter required to represent the intensity of the load when small-scale yielding conditions exist, J retains its role as a parameter characterizing the crack-tip stress fields, at least for materials modelled by the von Mises flow theory. Some results obtained using both the finite-element method and the slip-line theory are suggestive of a situation in which an outer field parameterized by a path-independent value of J controls the deformation in an inner or crack-tip field in which J is path dependent. The outer field is basically the solution to the crack problem when large deformation effects involved in the blunting are ignored. Thus, the conventional small-strain approaches in which the crack-tip deformation is represented by a singularity have been successful in characterizing such features as the crack-tip opening displacement in terms of a value of the J-integral on a remote contour. An interesting deduction concerns a nonlinear elastic material with characteristics in monotonic stressing similar to an elastic-plastic material. Since J is path independent everywhere in such a material, the stress and strain fields near the crack tip in such a material must differ greatly from those arising in the elastic-plastic materials studied so far. This result is of significance because it is believed that such nonlinear elastic constitutive laws can represent the limited strain-path independence suggested by models for plastic flow of polycrystalline aggregates based on crystalline slip within grains.