FRACTURE-MECHANICS WEIGHT-FUNCTIONS IN 3 DIMENSIONS - SUBTRACTION OF FUNDAMENTAL FIELDS

A new procedure is presented for the determination of the fracture mechanics weight functions that are required for the evaluation of stress intensity factors in cracked solids. The procedure can be used with a standard three-dimensional boundary element code. The weight functions are proportional to the displacements on the boundary of the solid when the only loading is a pair of self-equilibrated point forces at the crack front. In previous work, the highly singular crack-tip fields that this loading produces have been modelled by replacing the crack front by a cylindrical cavity with appropriate displacement boundary conditions on the cavity walls. It is shown here that results are dependent on the cavity radius and that convergence of the results cannot be guaranteed. An alternative procedure, based on the subtraction of fundamental fields (SFF), is demonstrated herein. The high-order singularities are removed from the field before the reduced problem is solved numerically using a standard boundary element method. Since the reduced problem is equivalent to an unloaded crack in a solid subjected to boundary tractions, the usual quarter-point displacement elements and quarter-point traction singular elements can be used to improve the accuracy. Weight functions, so obtained, are used to evaluate stress intensity factors as a function of position on the crack front for a straight-fronted crack in a rectangular bar subjected to various loadings. Both edge and central cracks are considered and the validity of the technique is demonstrated by comparing the results with previously published values.