The determination of the elastic T-term using higher order weight functions

It has been shown in a recent work [1] that the elastic T-term at the tip of a mixed mode crack can be determined by the so-called second order weight functions through a work-conjugate integral that is akin to that of the Bueckner-Rice weight function method for evaluating stress intensity factors. In this paper, the development of the second order weight functions is reviewed. These second order weight functions are determined using a unified finite element method introduced in [2]. The finite element procedure handles both traction and displacement boundaries and it permits the Bueckner-Rice weight functions and the second order weight functions for the elastic T-term to be determined in one single finite element run. The accuracy of the computed weight functions is assessed by comparing the computed results with special closed form solutions. The numerical values of the elastic T-term for single edge notch specimens under tension, pure bending and three-point bend are given. The corresponding second order weight functions are tabulated.