An elastic hollow cylinder under axial tension containing a crack and two rigid inclusions of ring shape

This paper is concerned with the fracture of an axisymmetric hollow cylindrical bar containing rigid inclusions. The cylinder is under the action of uniformly distributed axial tension applied at infinity. The bar contains a ring-shaped crack at the symmetry plane whose surfaces are free of tractions and two ring-shaped rigid inclusions with negligible thickness symmetrically located on both sides of the crack. It is assumed that the material of the cylinder is linearly elastic and isotropic. The mixed boundary conditions of the problem lead the analysis to a system of three singular integral equations for crack surface displacement derivative and normal and shearing stress jumps on rigid inclusions. These integral equations are solved numerically and the stress intensity factors are calculated.