It is shown that the problem of evaluating the stress-intensity factor of a part-circular crack at the base of any through opening in a three-dimensional solid under general external planer loading conditions can be reduced to the resolution of three problems: 1) Analysis of the three-dimensional uncracked solid with the given opening shape under given loading conditions; 2) analysis of a two-dimensional solid with the given opening shape and a line crack under the given loading conditions; 3) analysis of a semi-infinite solid with the given crack shape under uniform stress. In fact, the given problem, identical to that of a pressurized crack at the edge of an opening, is reduced to the solution of an embedded circular crack with suitable pressure distribution which takes into account the presence of the opening. This pressure distribution is postulated as a product of initial pressure due to the application of external load on the uncracked geometry (Problem 1) with a function resulting from the analysis of a 2-D problem (Problem 2). Finally, the K values calculated using this modified pressure distribution on the circular crack, are corrected for the 3-D nature of the crack front through the solution of Problem 3. The methodology has been applied to part-circular cracks at elliptical openings in a 3-D solid under traction and moment loading. The method has been extended to treat corner cracks in quarter solids. A circular crack at a BWR-nozzle corner has been treated as an illustrative example. Finally, some generalizations of the method have been suggested.

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