This paper describes a computationally efficient weight function technique which can be used to estimate the opening-mode stress intensity factor around the perimeter of planar surface or embedded cracks. The accuracy of the weight function itself and of the numerical quadrature schemes adopted are verified for elliptical cracks with a wide range of aspect ratios. The technique is then applied to longitudinal-radial cracks at the inner surface, including crossbores, of thick-walled pressure vessels. The results obtained for a wide range of crack depths, aspect ratios and vessel diameter ratios agree well with the predictions obtained by others using finite element, boundary element and modified mapping collocation methods, as well as with previously unpublished experimental data. The paper also considers the applicability of the ASME Boiler and Pressure Vessel Code procedures for estimating K1 for these defects.

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