Internally cracked, fully or partially autofrettaged, spherical pressure vessels are analyzed by numerically calculating 3-D Stress Intensity Factor (SIF) distributions along the fronts of radial lunular or crescentic cracks emanating from the vessel’s bore. The finite element (FE) method is used employing singular elements along the crack front. A novel realistic autofrettage residual stress field incorporating the Bauschinger effect is embodied in the FE model using an equivalent temperature field. The SIFs are extracted by using both the J-integral and the displacement extrapolation methods, and are calculated for three vessel geometries, a wide range of crack depth to wall thickness ratios, various ellipticities, and three levels of autofrettage. A detailed study of the influence of the above parameters on the prevailing SIF is conducted. The results attest to the favorable effect of autofrettage in reducing the SIF, delaying crack initiation, slowing down crack growth rate, and thus, substantially prolonging the fatigue life of the vessel. They also emphasize the importance of properly accounting for the Bauschinger effect including re-yielding, and highlight the significance of the 3-D analysis.

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