The effect of transverse shear and material orthotropy in cracked cylindrical and spherical shells

In this paper the effect of transverse shear and material orthotropy on the stress intensity factors in cylindrical and spherical shells containing a crack is considered. Unlike the classical shell theory in which the twisting moment and the transverse shear resultants are combined on the shell boundary through a Kirchhoff-type assumption, the particular theory used in this study permits the consideration of all five physical boundary conditions regarding moment and stress resultants on the crack surface separately. As a consequence of this it is found that the membrane and bending components of the asymptotic stress field near the crack tip become identical. In shell problems since the two fields are coupled, the difficulty in justifying the superposition of membrane and bending stresses and particularly of the related stress intensity factors when applying the results to fracture problems has thus been removed. In the solution given in this paper, in addition to the standard shell parameter a/(Rh)sup(1/2), the stress intensity factors are found to depend on the thickness parameter h/a where 2a, h, and R respectively are the crack length, the shell thickness, and the mean radius of curvature. The stress intensity factors are given for an isotropic shell and for two specially orthotropic shells. In isotropic shells the effect of Poisson's ratio is separately studied and is shown to be relatively insignificant. (orig.)