Effect of T-stress and loading rate on crack initiation in rate sensitive plastic materials

Abstract

The objectives of this paper are to examine the validity of a two-parameter (J–Q) characterization of quasi-static crack tip fields in rate sensitive plastic solids and, also to investigate the influence of strain rate sensitivity of the material on the variation of fracture toughness with loading rate. To this end, 2D plane strain finite element analyses of a boundary layer model loaded quasi-statically and a single edge notched (tensile) specimen under dynamic loading are performed. The material is assumed to obey a $J_2$ viscoplasticity model and a small strain formulation is employed. The results demonstrate that a valid J–Q field exists in low to moderately rate sensitive materials under quasi-static loading (i.e., when inertial effects are neglected). The opposing effects of strain rate sensitivity and material inertia are reflected in the stress field ahead of the tip in the dynamically loaded specimen. The variation of fracture toughness $K_d_c$ with loading rate $\.{K}$for cleavage cracking is predicted using a simple critical stress criterion. It is found that strain rate sensitivity index of the material has a profound effect on the $K_d_c - \.{K}$ variation.