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

Abstract

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.

Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization

“…(75) shows clearly that the second term or T-stress has an effect on the crack-tip field, and if an applied T-stress varies at a constant K, the plastic zone will vary in size and in shape. Different analytical and numerical methods including the higher-order weight function [246], the Green's function [247], the stress difference [248] and the FEA calculation [249,250] were developed to determine the T-stress for a variety of fracture specimens and geometries. In reference to the T-stress and K-factor, Leevers and Radon [251] introduced a biaxiality ratio parameter, B ¼ T ffiffiffiffiffiffi pa p =K I , that is widely used.…”

Linear elastic behaviour of flaws: Purely elastic treatment

“…• method denoted as the "pure boundary layer method" (22), • method denoted by identification of the coefficients of the Williams series expansion by a variational approach (21), • method denoted as the J -integral, or Eshelby's method, by stress analysis in a finite element computation (23), and • method of weight functions with higher order (24).…”

Effect of Microstructure on the Strength and Fracture Energy of Bimaterial Interfaces

“…The observed bifurcation may be plausibly explained by this effect. Noticing that the singular term in (22) vanishes in crack flanks and, in particular,f,, (± a) = 0, we compute a,, using finite element used which are varied and refined to ascertain mesh insensitivity [see Sham (1991) [1,7]. Brittle mechanisms involve atomic 2.1.…”