Elastic crack opening displacements and rotations in through-cracks in spheres and cylinders under membrane and bending loading

Abstract

The elastic displacements at the centre of a through-crack in a shell under membrane and bending loading have been calculated. The geometries considered are: 1. sphere with meridional defect; 2. cylinder with axial defect; 3. cylinder with circumferential defect. The displacements considered are the opening displacement in the tangential plane and the rotation of the normal. The results are of interest in calculating coolant leakage rates, and in calculating whether crack closure will affect the stress intensity factor. The results have been calculated using both classical shell theory and Reissner shell theory, which includes the effect of transverse shear strain. These give similar results in membrane situations, but can be very different where there are large bending effects. The Reissner theory is to be preferred as being more realistic. Comparisons with results in the literature (mainly membrane situations) have been made as far as possible.