Application of Rice's path-independent J integral and its extended formulations is now well established to correlate the crack growth initiation for materials under extensive plastic deformation. An elastic-plastic finite element analysis suitably formulated to admit linear work hardening of materials for a circumferentially notched axisymmetric implant specimen, commonly used to determine the fracture resistant parameters of welded joints, has been carried out under contained yielding and monotonically increasing tensile loads. The direct procedure for estimating J around the smoothly blunted notch of two different shapes has been followed to examine the role of J as a notch tip characterizing parameter and to establish a possible relationship between J and other specimen parameters. The numerical results include notch tip parameters and near-tip deformation fields. Also, the effects of the difference in weld and base metal properties on J have been investigated here. Even though the results do not predict a unique J value, they may still be employed confidently for engineering purposes in view of the justification demonstrated by the nearly path-independent J solutions obtained from a rather crude finite element formulation based on linear displacement distributions. In the present paper, an attempt has been made to predict the specimen response with the available J relations and to explore the numerical solution sensitivity to the changes in notch parameters. The problem has been decomposed into two models; one representing the circumferential notch having its faces inclined to the axis of notch symmetry while the other refers to a parallel sided flat notch in the implant specimen. An axisymmetric FE analysis that employs linear displacement distributions of the elements, suitably modelled to admit linear work hardening of the materials for incremental flow theory, has been carried out under axisymmetric tensile loads. The numerical results include notch tip parameters and near-tip deformation fields for both cases. Also, the effects of the difference in weld and base metal properties on various J relations have been investigated for a typical notch geometry. We first consider the inclined notch test specimen where both elastic and elastic-plastic analyses have been performed, yielding some approximate expressions between J and other relevant specimen parameters. In the same way, relationships between the various J formulations, the applied loads and the various geometric parameters have been studied for the flat notched specimen. The advantage in the use of such unique expressions is that only one specimen variable is sufficient to determine the J integral and therefore the elaborate numerical procedures are avoided.
