The beneficial effect of full or partial autofrettage on the combined 3-D stress intensity factor for an inner radial lunular or crescentic crack in a spherical pressure vessel

The distributions of the combined 3-D Stress Intensity Factor (SIF), K_IN=K_IP+K_IA, due to both internal pressure and autofrettage along the front of an inner radial lunular or crescentic crack emanating from the bore of an overstrained spherical pressure vessel are evaluated. The 3-D analysis is performed using the finite element (FE) method employing singular elements along the crack front. A novel realistic autofrettage residual stress field incorporating the Bauschinger effect is applied to the vessel. The residual stress field is simulated using an equivalent temperature field in the FE analysis. SIFs for three vessel geometries (R₀/R_i = 1.1, 1.2, and 1.7), a wide range of crack depth to wall thickness ratios (a/t = 0.01-0.8), various ellipticities (a/c = 0.2-1.5), and three levels of autofrettage (ε = 50%, 75%, and 100%) are evaluated. In total, about two hundred and seventy different crack configurations are analyzed. A detailed study of the influence of the above parameters on the prevailing SIF is conducted. The results clearly indicate the favorable effect of autofrettage in considerably reducing the prevailing effective stress intensity factor i.e., delaying crack initiation, slowing down crack growth rate, and thus substantially prolonging the total fatigue life of the vessel by up to twenty-fivefold. This favorable effect is found to be governed by σ_y/p - the ratio of the vessel's material initial yield stress to its internal pressure. The higher the ratio is, the more effective autofrettage becomes. Furthermore, the results emphasize the importance of properly evaluating the residual stress field due to autofrettage while at the same time accurately accounting for the Bauschinger effect, including re-yielding, as well as the significance of the three dimensional analysis herein performed.