Stress Intensity Factors in a Hollow Cylinder Containing a Radial Crack

In this paper an exact formulation of the plane elasticity problem for a hollow cylinder or a disk containing a radial crack is given. The crack may be an external edge crack, an internal edge crack, or an embedded crack. It is assumed that on the crack surfaces the shear traction is zero and the normal traction is an arbitrary function of r. For various crack geometries and radius ratios, the numerical results are obtained for a uniform crack surface pressure, for a uniform pressure acting on the inside wall of the cylinder, and for a rotating disk. 1. Introducti on In this paper we reconsider the plane problem of a hollow cylinder containing an arbitrarily oriented radial crack and subjected to arbitrary normal tractions on the crack surfaces. Aside from its direct applications to plane problems such as cracked rings and rotating disks, the problem has potentially important applications to pressure vessels and piping containing a relatively long part-through crack in a meridional plane. In this latter group of three dimensional problems the plane strain solution provides an upper bound for the stress intensity factor in the mid-region of the longitudinal part-through crack in the cylinder wall. Because of the importance of the crack geometry, the problem has been studied rather extensively (see, for example, [1-7]). After Bueckner's early work in which the technique of complex potentials was used [1], most of the subsequent analytical studies were based on the {*} This work was supported by the Department of Transportation under the Contract DOT-RC-82007, by NASA-Langley under the Grant NGR-007-011, and by NSF under the Grant ENG. 78-09737.