Stress intensity factor solutions for arbitrarily shaped surface flaws in reactor pressure vessel nozzle corners

Extensive experimental results—based on the frozen stress photoelasticity technique for extracting stress intensities—for nozzle corner cracks in ITV and BWR geometries were reported by Smith et al.¹ Based on the above experimental studies, it was conjectured that if the crack shape inserted into a finite element model is not a real one, or if the inner fillet (for shallow flaws) or the outer boundary shape (for moderate to deep flaws) is improperly approximated, the obtained numerical results for stress intensity factors may differ significantly from the physical behaviour at the nozzle-vessel junction. On the other hand, almost all the numerical analyses published to date, based on finite elements, boundary integral equations or alternating techniques, considered only quarter-circular nozzle corner cracks.This paper presents stress intensity factor solutions for naturally shaped nozzle corner cracks in pressurised ITV and BWR vessels. Several actual crack geometries observed in the experimental work of Smith et al., cited above, are studied using the three-dimensional hybrid crack-element approach of Atluri et al.⁸ and Atluri and Kathiresan⁹ wherein the stress intensity factors and their variation along an arbitrarily shaped 3-D crack front are directly computed. In order to be able to compare the present results with the photoelastic experimental results (wherein the Poisson's ratio of the material is 0·5), some of the present numerical results are obtained for $\text{ν ? 0·5}$.In addition, some new solutions for stress intensity factors for pressurised thin (outer to inner radii ratios of $\text{～1·1}$) cylindrical vessels with belt-line flaws of semi-elliptical shapes of various aspect ratios and depth ratios are presented. Cases of surface flaws in the meridional direction—as well as in the circumferential direction—of the vessel are treated.