The effect of autofrettage on uniform arrays of 3-D 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 a overstrained thick-walled cylinder is studied. The 3-D analysis is based on the "two-crack-depth level model" previously proposed and is performed via the finite element (FE) method using the submodeling technique and, employing singular elements along the crack front. The autofrettage residual stress field is simulated using an equivalent thermal load. The distribution of K_IA, the stress intensity factor due to autofrettage, for numerous uneven array configurations bearing n₁=n₂= 4-64 cracks, a wide range of crack depth to wall thickness ratios, a₁/t=0.05-0.4, and various crack ellipticities, a₁/c₁=0.1-2.0, are evaluated for a cylinder of radii ratio R_o/R_i=2. The results clearly indicate that unevenness, as reflected in K_IA distribution, depends on all three parameters i.e., the number of cracks in the array, cracks' depths and cracks' ellipticity. The "interaction range" for the different combinations of crack arrays and crack depths is then evaluated. The effect of crack ellipticity on the "interaction range" is found to considerably vary along the crack front. Finally, it is found that both the submodeling technique and the improved displacement extrapolation have an impact on the accuracy of the results.