Numerical and analytical study of severity of cracks in cylindrical and spherical shells

Abstract

The present study deals with the severity of cracks in pressure equipments, where such defects are often involved. Our work is particularly concerned with the problem of cylindrical shells and also the little well-known problem of spherical shells, including all sorts of practical defects, namely axisymmetric or semi-elliptic, both internal and external cracks. The stress intensity factor in the linear elastic domain and the J integral in the elastoplastic range are performed using the finite element method and compared to the results provided by the application of the semi-analytical A16 or R6 simplified criteria, depending on a limit load calculation. The nocivity of the defects depends on the crack shape and size and other structural geometrical parameters. Use is made of a polynomial decomposition of the stress field in the vicinity of the crack in order to cover all industrial loadings. All the numerical results, for a wide range of shell and crack geometries, are depicted using appropriate tables and curves in order to check the fracture criteria more easily.