Boundary element analysis of thick-walled spherical vessels with surface cracks

The boundary element method (BEM) is used for the elastic stress analysis of internally pressurized thick-walled spherical vessels with internal surface cracks. Spherical vessels with and without a radial crossbore are considered. The three-dimensional formulation of the BEM is first applied to the linear elastic fracture mechanics analysis of a spherical vessel without a crossbore with an internal surface crack. Normalized stress intensity factors are obtained for a number of geometric combinations, namely, spheres with radius ratios from 1.5 to 3, crack depths from 20% to 80% of the vessel thickness, and crack aspect ratios from 1 to 0.6. The normalized stress intensity factor around the periphery of an internal surface crack is observed to stay relatively constant until in proximity to the free surface. At this location, this quantity for small semi-circular cracks tend to gradually increase in magnitude, while for larger cracks with this form, the reverse is found to be true. This trend becomes more evident as the radius ratio of the sphere is increased. Decreasing the crack aspect ratio shows that semi-elliptical cracks exhibit an abrupt increase in the normalized stress intensity factor at the free surface. Polynomial influence coefficients are also obtained for all the cases, which permit stress intensity factors to be determined for any load case on the same crack geometry using the influence function method.Surface cracks initiated at the crossbore are also investigated. A three-dimensional analysis is performed to obtain normalized stress intensity factors for a representative set of possible geometries. For this study, a radius ratio of 2 is considered with a crossbore radius ranging from 10% to 25% of the internal radius, and circular cracks spanning 20% to 80% of the wall thickness. For the set of cases treated, it is shown that when cracks emanate from the crossbore at the internal radius of the sphere, the maximum value of normalized stress intensity factor along the crack front occurs at this intersection.The stress analysis of an uncracked spherical vessel with a radial crossbore is also performed using the axisymmetric formulation of the BEM. Spheres with the same radius ratios as mentioned above are considered, and the circumferential stress factor variation is determined for a crossbore radius ranging from 10% to 25% of the internal radius of the sphere. The maximum circumferential stress factor typically occurs at the intersection of the internal surface and crossbore. However, for relatively large crossbores, the maximum value can occur at the exterior surface.