Three-dimensional fracture analysis of CT specimens with a ductile damage model based on endochronic plasticity theory

For many fracture problems of practical engineering importance, the three-dimensional effects are significant and a three-dimensional analysis for the problems is thus required. In this paper, an endochronic theory coupled with anisotropic damage is first established, which is actually an elasto-plastic damage theory coupled with isotropic-nonlinear kinematic hardening. The ductile damage evolution equation is derived from the orthogonality rule with a new intrinsic time scale introduced especially for damage evolution. Then, a three-dimensional finite element program incorporating the endochronic damage model is formulated and employed to analyze the widely used CT fracture specimen. Two failure criteria are proposed for the prediction of crack initiation direction and crack initiation load. From the analysis, significant three-dimensional effects are observed and the crack is estimated to initiate first at the middle of the crack front line. Experiments have been conducted to verify the proposed theory and the results are found to compare well with the theoretical values.