Stress intensity factors for through-thickness cracks in a wide plate: Derivation and application to arbitrary weld residual stress fields

Exact closed-form stress intensity factor (SIF) solutions have been developed for mode-I, II and III through-thickness cracks in an infinite plate. Centre-crack problems have been analysed comprehensively in the literature, but the focus has been on the effect of simple loading about the crack centre. In the current work, the formula of Sih–Paris–Erdogan was extended to consider the difference in SIF on the left and right crack tips under an asymmetric stress field. Mathematical manipulations were performed to derive exact stress magnification factors for SIF computations and simultaneously circumvent the problem of crack-tip stress singularity. The solutions so obtained are applied to derive the residual SIFs that would act on a crack growing under the influence of the residual stress fields associated with VPPA (variable polarity plasma arc) and friction stir welds, using measured residual stress profiles