Evaluation of elastic T-stress by the stress difference method

Abstract

A simple method, called the stress difference method, is proposed to compute the elastic T-stress at a crack tip, incorporating the iterative single-domain dual-boundary-element method and a tip-node rule imposing zero displacement jump at the crack tip. In this method, the difference between σ 11 and σ 22 at a point ahead of the crack tip is demonstrated to be able to evaluate the elastic T-stress efficiently and accurately, in comparison to the I-integral method. Convergence of the T-stress computed by this method with mesh and spatial distribution of σ 11− σ 22 near a crack tip was examined to validate the numerical technique for the T-stress. When applying to a thermoelastic crack, the present stress difference method also shows good agreement with the corresponding I-integral method. On the other hand, the present inspection method for the T-stress is obviously more advantageous than the I-integral method because of its simplicity in expression and much less computational effort. It is also shown that the tip-node rule for the crack tip element with regular polynomial interpolation and node distribution offers good estimates of the stress intensity factor, in contrast to the quarter-point element method.