The Bauschinger Effect's Influence on the SIFs of a Semi-Elliptical Crack Emanating from an Erosion at the Bore of a Fully Autofrettaged Pressurized Cylinder

The benefits of autofrettage for thick-walled cylindrical vessels as a means of improving the vessel's durability and sustainability have been addressed in the published literature. However the presence of the Bauschinger effect complicates the overall effect of autofrettage, especially when complex three-dimensional crack geometries emanating from erosions at the cylinder bore are considered. In this paper, the Bauschinger effect's impact on the stress intensity factors (SIFs) on such cracks is investigated. The effect of various erosion geometrical configurations on the mode I tress intensity factor distribution along the front of a semi-elliptical crack, emanating from the deepest line of the erosion surface (DLES) at the bore of an autofrettaged, pressurized thick-walled cylinder of outer-to-inner radius ratio, R-0/R-i =2, is investigated. Both autofrettage with Bauschinger effect (BEDA) and Hill's ideal autofrettage residual stress field (BETA) are considered and simulated by an equivalent thermal load. The SIFs are determined for the semi-elliptical cracks of various crack depths to wall thickness ratio, a/t=0.05 to 0.25, and ellipticities, a/c, ranging from 0.5 to 1.5, emanating from the DLES via ANSYS software and the nodal displacement method. Three groups of erosion geometries are considered: (a) arc erosions of constant relative depth, d/t, equal to 5% and with relative radii of curvature, r'/t, between 5% and 30%; (b) semi-elliptic erosions of constant relative depth, d/t, of 5% with erosion ellipticity, d/h, varying from 0.3 to 2.0; and (c) semi-circular erosions of relative depth, d/t, between 1 and 10% of the wall thickness. K-IP, the SIF due to pressurization, is highly dependent on the stress concentration ahead of the DLES which directly relates to the erosion geometry. It is found that the absolute value of K-IA, the SIF due to autofrettage, is just slightly reduced by the presence of the erosion. Its change solely depends on, and is directly proportional to, the erosion depth. Thus, the combined SIFs of deep cracks are found to be significantly enhanced by the presence of autofrettage and might result in a shortening of the vessel's fatigue life by up to an order of magnitude. Counteracting this, the combined SIFs are found to be significantly higher for BEDA cases than for BETA cases. Therefore the vessel's fatigue life can be profoundly influenced by the presence of the Bauschinger effect.