The Effect of Autofrettage on Uniform Arrays of Three-Dimensional Unequal-Depth Cracks in a Thick-Walled Cylindrical Vessel

The distribution of the mode I stress intensity factor (SIF), resulting from autofrettage, along the fronts of radial, semi-elliptical surface cracks pertaining to large uniform arrays of unequal-depth cracks emanating at the bore of an overstrained thick-walled cylinder is studied. The three-dimensional analysis is based on the “two-crack depth level model” previously proposed and is performed via the finite element method employing singular elements along the crack front. The autofrettage residual stress field is simulated using an equivalent thermal load. The distribution of $KIA$⁠, the stress intensity factor due to autofrettage, for numerous uneven array configurations bearing $n=n1+n2=8-128$ cracks, a wide range of crack depth-to-wall thickness ratios, $a1∕t=0.01-0.4$⁠, and various crack ellipticities, $a1∕c1=0.3-1.5$⁠, are evaluated for a cylinder of radii ratio $Ro∕Ri=2$⁠. The results clearly indicate that unevenness, as reflected in $KIA$ distribution, depends on all three parameters (i.e., the number of cracks in the array, cracks’ depth, and cracks’ ellipticity). The “interaction range” for the different combinations of crack arrays and crack depths is then evaluated. The range of influence between adjacent cracks on the maximal SIF, $KAmax$⁠, is found to be dependent on the density of the array, as reflected in the intercrack aspect ratio, as well as on the cracks’ ellipticity.