Weight functions and stress intensity factors for mode I cracks in arbitrary 2D geometries under general crack surface loading

Abstract

Stress intensity factors for Mode I cracks in arbitrary two-dimensional geometries under general crack surface loading are derived in closed form by boundary element calculations and approximate weight functions. The boundary element method was developed previously to deal with arbitrary two-dimensional crack problems involving uniform crack surface pressure. Reference stress intensity factors calculated by the boundary element method are used to derive stress intensity factors for the same crack under arbitrary crack surface loading with weight functions based on an improved Petroski-Achenbach crack surface displacement approximation. Various crack problems are studied and limitations of the method are discussed. The investigation shows that a self-consistency examination will effectively reveal the accuracy of the derived weight functions and the associated stress intensity factors.