The torsion of a hollow cylinder with an external circular crack

It is important to determine the stress intensifying factor accurately when a solid or hollow cylinder with a circumferential crack is subjected to various external load in relation to the strength design and the evaluation of fracture toughness of a pipe structure or a rotating shaft. In this study, the case of a hollow cylinder with a circumferential crack subjected to torsion is analyzed on the basis of three-dimensional theory of elasticity, and the stress distribution and the stress intensifying factor were clarified. In the analysis, considering the singularity around the end of a crack, the stress on the surface involving the crack was expressed with a Fourier series with unknown coefficients, and this problem was reduced to that of solving infinite simultaneous first order equations using the boundary condition of displacement. The stress analysis, the special case when internal radius is zero, and the result of numerical calculation are explained. The approximation formula given by Harris resulted in considerably small stress intensifying factor as compared with this result. This result approaches without unreasonableness to the exact solution obtained from the solution in case of a shallow notch and internal radius of zero. When the ratio of crack depth of wall thickness is constant, this result coincides with the exact solution when a band region with one side crack is subjected to shearing outside a surface when the ratio of internal radius to external radius is one. (Kako, I.)