Evaluation of the elastic T-stress in surface-cracked plates using the line-spring method

Abstract

The elastic T-stress has been found to be an important parameter in characterizing the very near tip elastic-plastic stress state under 2-D plane strain conditions (Larsson and Carlsson [1]; Bilby et al. [2]; Betegón and Hancock [3]; etc.). Several computational methods have been developed to evaluate the T-stress (Larsson and Carlsson [1]; Kfouri [4]; Sham [5]). However, none of these methods can be readily adapted to calculate the elastic T-stress in a surface-cracked plate (SCP), which is essentially 3-D in nature. In this paper, the line-spring method, which has proven effective in computing the stress intensity factor of SCPs, is used to evaluate the elastic T-stress along the crack front. SCPs with same length and width, but different crack geometries, from low aspect ratio (a/c=0.24) to high aspect ratio (a/c=0.70), under both remote tension and bending, are studied using the line-spring method. Detailed, three-dimensional continuum finite element (FE) solutions of some ‘extreme’ cases, in terms of both aspect ratio and crack depth, under either remote tension or bending, are compared with the line-spring solutions. The line-spring solutions are in excellent agreement with the 3-D elastic FE solutions, but use 2 to 3 orders of magnitude less computational time and considerably less preparation and post-processing efforts. A concluding example demonstrates the utility of the T-stress in more accurately describing the crack front elastic-plastic field in a SCP at load levels up to moderate scale yielding.