Use of analytically decoupled near-tip displacement solutions for calculating the decoupled weight functions of mixed fracture modes

Abstract

A new approach for the efficient finite element evaluation of decoupled weight functions is presented in this paper for mixed-mode 2-D cracks. This new finite element approach uses the analytically decoupled near-tip displacement solutions (ADNDS), which are incorporated into a single colinear virtual crack extension (VCE) technique with singular crack-tip elements in the immediate crack-tip vicinity. The decoupled near-tip displacement fields are achieved by applying the analytical near-tip displacement solutions for an infinite medium to the singular elements with either K I = 1.0 and K II = 0 or K I = 0 and K II = 1.0 for the efficient finite element evaluation of Mode I and Mode II decoupled weight functions ( h I(II ) respectively. The validity of using the ADNDS approach for efficient calculation of the decoupled weight functions at all locations within a flawed Isotropic structure of interest is assessed by direct comparison with the earlier weight function results. These prior results on decoupled weight functions of a mixed-mode isotropic crack are obtained with the symmetric mesh approach in the crack-tip vicinity for the same crack geometry under identical constraint conditions. A remarkable agreement in the computed weight function vectors has been found for the ASTM three-point bending specimens of different crack lengths with two different approaches (symmetric mesh approach versus ADNDS approach). However, elimination of the symmetric mesh requirement in the crack-tip vicinity of the new analytical displacement approach can facilitate further extension of the explicit weight function evaluation to the anisotropic crack.