3-D stress intensity factors for arrays of inner radial lunular or crescentic cracks in thin and thick spherical pressure vessels

Some spherical pressure vessels are manufactured from 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. In a recent paper by the authors, mode I SIF distributions for a wide range of lunular and crescentic internal, surface, radial cracks were evaluated for a typical spherical pressure vessel of an outer to inner radii ratio of η= R_o/. R_i= 1.1. The present analysis is aimed to determine the influence of the spherical vessel geometry in terms of its outer to inner radii ratio η= R_o/. R_i on the prevailing SIFs. Mode I SIF distributions for a wide range of lunular and crescentic crack array configurations are evaluated. The 3-D analysis is performed by means of the FE method, employing singular elements along the crack front, for five geometries representing thin, moderately thick, and thick spherical pressure vessels with outer to inner radius ratios of η= R_o/. R_i= 1.01, 1.05, 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 0.95; 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 affected considerably by the geometry of the spherical pressure vessel-η, and by the following parameters: the number of cracks in the array-n, the depth of the cracks-a/. t, and their ellipticity-a/. c.