Weight functions for a finite width plate with single or double radial cracks at a circular hole

This work develops accurate weight functions for a single crack at a hole in a finite width plate for various hole sizes. In order to develop an accurate weight function, we first obtain accurate stress intensity factors, using the finite element method (FEM), for a reference load case of uniform stress on the crack line. Following the earlier approach for developing a weight function suggested by Wu and Carlsson, we fit the reference stress intensity factor data from FEM to a smooth analytic function; however, for the open hole it is necessary to adopt a piecewise polynomial to fit the stress intensity factor data, in place of the single polynomial suggested by Wu and Carlsson. We validate the new weight function for the case of remote uniform applied stress, which induces a stress field on the crack line exhibiting the well-known stress concentration at the hole, and for which we have accepted stress intensity factor solutions. The new weight functions provide stress intensity factors that agree very well with results from two commercial fracture mechanics software packages. Comparing results from the new and earlier weight functions shows good agreement for some crack line stress fields, but errors of a few percent for other stress fields, with the new weight function providing more reasonable results. The improved quality of the new weight functions is due both to the new reference solution for uniform crack line stress and to the piecewise fit to the reference stress intensity data. Trivial changes to the FEM model allow us to provide additional weight functions for the cases of symmetric double cracks at a hole (by adding a symmetry plane to the FEM mesh) and a single crack at a hole in a square plate (by reducing the length of the FEM mesh).