A new method for improving the approximations of stress intensity factors computed from pathindependent integrals is developed. The method uses Richardson's extrapolation. Numerical results are given to show the eciency and the stability of the present method. # 1998 John Wiley & Sons, Ltd.
KEY WORDS stress intensity factors (SIF); ยฎnite element method (FEM); reciprocal work contour integral (RWCI); path-independent integrals (PII); displacement correlation technique (DCT); quarter-point displacement technique (QPDT)
Introduction
The determination of SIF with numerical methods has received much attention in recent years because many fracture criteria use them. 1,2 In early studies, a highly reยฎned mesh near the crack tip was used to simulate the stress gradient and permitted one to obtain results with acceptable engineering accuracy (5 per cent). 3,4 However, owing to the fact that the highly reยฎned meshes necessitate high resolution near the crack tip, most researchers have developed techniques which permit them to ameliorate accuracy with fewer degrees of freedom in comparison with reยฎned meshes. 5ยฑ11 Whatever the technique used, the SIF may be computed using the PII 12ยฑ15 or method of virtual crack extensions. 16,17 In this paper, we propose a new numerical technique of estimating the SIF by using standard ยฎnite elements with high accuracy, without high resolution near the crack tip. This technique is based on the PII and Richardson's extrapolation. 18 Our technique derives from the new approach, using the PII, studied in References 19 and 20. For antiplane problems, we use one of the PII introduced by Eshelby and Knowles 21,22 and for plane problems we base our technique on that exhibited by Stern et al. in Reference 13 to distinguish contributions due to crack opening and those due to shear in the mixed mode.