Analysis of Uniform Arrays of Three-Dimensional Unequal-Depth Cracks in a Thick-Walled Cylindrical Pressure Vessel

Abstract

The effect of crack depth unevenness on the mode I stress intensity factor (SIF) distributions along the fronts of semi-elliptical surface cracks is studied. These three-dimensional radial cracks pertain to large uniform arrays of unequal-depth cracks emanating from the bore of a pressurized thick-walled cylinder. The analysis is based on the “two crack depth level model,” previously proposed, and is performed via the finite element (FE) method employing singular elements along the crack front. The distribution of KIP-the stress intensity factor due to pressurization, for numerous uneven array configurations bearing n=n1+n2=8 to 128 cracks, a wide range of crack depth to wall thickness ratios, a1/t=0.01 to 0.4, and various crack ellipticities, a1/c1=0.3 to 1.5, are evaluated for a cylinder of radii ratio Ro/Ri=2. To increase the accuracy of the evaluated SIFs an existing improved version of the displacement extrapolation method is used. The results clearly indicate that unevenness, as reflected in KIP distributions, depends on both the number of cracks in the array as well as on the cracks’ depths and ellipticities. The “interaction range” for the various configurations of uneven crack arrays is evaluated. The range of influence between adjacent cracks on the maximal SIF, KPmax, is found to be dependent on the density of the array, as reflected in the inter-crack aspect-ratio, as well as on the cracks’ elipticity.