Three-Dimensional Analysis of a Semi-Elliptical Crack Emanating From an Erosion at the Bore of an Autofrettaged Pressurized Cylinder

Abstract

The effect of various erosion configurations on the mode I stress intensity factor (SIF) 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, Ro /Ri = 2, is investigated. The three-dimensional (3-D) linear elastic problem is solved via the finite element (FE) method using the ANSYS 5.2 standard code. Hill’s autofrettage residual stress field is simulated by an equivalent thermal load and the SIFs are determined by the nodal displacement method. SIF distribution along the front of semi-elliptical cracks of various crack depths to wall thickness ratios, a/t = 0.05 to 0.25, and ellipticities, a/c , ranging from 0.5 to 1.5, emanating from the DLES, are determined. Three groups of erosion geometries are considered: (a ) arc erosions of constant relative depth, d/t , equal to 5 percent and with relative radii of curvature, r′/t , between 5 and 30 percent; (b ) semi-elliptic erosions of constant relative depth, d/t , of 5 percent 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 percent of the wall thickness. The effective SIF along the crack front results from the superposition of KIP —the SIF due to pressurization, and KIA —the negative SIF due to the autofrettage residual stress field. KIP is highly dependent on the stress concentration ahead of the DLES which directly relates to the erosion geometry. The absolute value of KIA is just slightly reduced by the presence of the erosion. Its change solely depends on, and is directly proportional to, the erosion depth. Thus, while deep cracks are almost unaffected by the erosion, the effective SIF for relatively short cracks is found to be significantly enhanced by its presence and might result in a shortening of the vessel’s fatigue life by up to an order of magnitude. Also, it is shown that 2-D analysis may lead to a nonconservative estimate of the vessel’s fatigue life.