Three-Dimensional Stress Intensity Factors for Arrays of Radial Cracks Emanating From the Inner Surface of a Thick-Walled Spherical Pressure Vessel

Abstract

Some spherical pressure vessels are manufactured by methods such as the Integrated Hydro-Bulge Forming (IHBF) method, where the sphere is composed of a series of double curved petals welded along their meridional lines. Such vessels are susceptible to multiple radial cracking along the welds. For fatigue life assessment and fracture endurance of such vessels one needs to evaluate the Stress Intensity Factors SIF distribution along the fronts of these cracks. However, to date, only two-dimensional SIFs for one through the thickness crack in a thin spherical shells is available. In the present paper, mode I SIF distributions for a wide range of lunular and crescentic cracks are evaluated. The 3-D analysis is performed, via the FE method employing singular elements along the crack front, for three sphere geometries with outer to inner radius ratios of η = Ro/Ri = 1.1, 1.7, and 2.0. SIFs are evaluated for arrays containing n = 1–20 cracks,; for a wide range of crack depth to wall thickness ratio, a/t, from 0.025 to 0.8; and for various ellipticities of the crack, i.e., the ratio of crack depth to semi crack length, a/c, from 0.2 to 1.5. The obtained results clearly indicate that the SIFs are considerably affected by the three-dimensionality of the problem and by the geometrical parameters: the geometry of the sphere – η, the number of cracks in the array – n, the depth of the crack – a/t, and its ellipticity – a/c.