Problem of Cracked Infinite Hollow Cylinder With Two Rigid Inclusions

Abstract

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 hollow cylinder 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. Geometry and the loading is symmetric about z-axis. Along the rigid inclusions displacements are constant and continuous whereas stresses have jumps. The inner and the outer surfaces of the cylinder are free of tractions 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 shear stress jumps on rigid inclusions. These integral equations are solved numerically and the stress intensity factors at the edges of the crack and at the edges of the inclusions are calculated. Results are presented in graphical form.