Abstract
Toroidal shells containing a surface crack and subjected to various symmetric and antisymmetric loading conditions are considered. A singular integral formulation of a through crack located along a principal line of curvature of a shell is used along with the line spring model to treat the surface crack problem. Transverse shear deformations are taken into account in the shell theory. Locating the crack along a line or principal curvature uncouples the symmetric mode I deformations from the antisymmetric mode II and III deformations, which are inherently coupled. Mode I loadings considered include membrane loading and bending, while the mode II and III cases include in plane shear, twisting and transverse shear. In addition to these loadings, residual stresses resulting in mode I deformations are considered. Stress intensity factors for the various loadings are given for shell geometries representative of spherical caps, cylindrical pipes and pipe elbows for a number of crack locations.
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