Weight functions of the stress intensity factors K_1, K_2 and K_3 for a single radial crack emanating from a semi-circular side notch

Weight functions of stress intensity factors for a single radial crack emanating from a semi-circular side notch are derived for the loading modes I and II using the boundary element method (BEM) together with the complex stress function Z(z) applied at the crack tip and satisfying the Bueckner type singularity. The mode III weight function, being identical with the known solution of two symmetrical cracks emanating from a circular hole, is also shown to complete the present analysis. All weight functions, corresponding to particular modes, are represented in a unified form convenient to create the database suitable for rapid calculations of the stress intensity factors A' for any elastic stresses distributed along the potential crack path. Accuracy of the present approach is about ni-nete nine percent, verified by comparing the values of K obtained using the weight function method with particular solutions known from the literature and to the BEM results.