J-Integral Estimation Procedures

Abstract

This paper presents efficient procedures for estimating the J -integral, a parameter for characterizing stable crack growth under inelastic conditions. Two different formulations are shown. The basis of the first approximate J -integral formula is the familiar extension of the elastic strain energy release rate computation for elastic-plastic loads. This extension is particularly suited for contained plasticity. With continued yielding, when the global load-deflection curve exhibits nonlinear behavior (i.e., net section yielding commences), this first J -approximation formula deviates from the actual J -integral. A second approximate formula derived here can be used at this point which is based on the definition that J -integral can be interpreted as the potential energy difference between two identically loaded specimens having crack sizes that differ infinitesimally. This latter formula is exact for linear loading and rigid-plastic material response, and is shown to predict J accurately in the elastic-plastic range of loading. Several standard cracked geometries for which documented J -integral solutions exist were applied to test the estimation procedures. This technique is very general and can be applied to virtually any structure or continuum. And no special assumption of material hardening, such as Ramberg Osgood, is necessary. These estimation techniques are significantly easier and more economical to use than a conventional finite element procedure, which models details of a cracked geometry.