Torsion analysis of infinite hollow cylinders of functionally graded materials weakened by multiple axisymmetric cracks

In this paper, mode III stress intensity factor for the multiple axisymmetric cracks in the infinite hollow cylinder made by functionally graded materials base on the dislocation technique is formulated. The shear modulus of the material of the cylinder is assumed to vary with the radial coordinate by a power law. It is assumed that the outer surface of the hollow cylinder is under the action of two distributed self-equilibrating lateral shear tractions and inner surface of the cylinder is free of stress. The solution of an axisymmetric rotational Somigliana ring dislocation in a functionally graded materials infinite hollow cylinder is obtained by means of a separation of variables technique. Next, the distributed dislocation method is used to formulate integral equations for a system of coaxial axisymmetric cracks, including annular, inner edge and outer edge cracks. The ensuing equations are of the Cauchy singular type and have been solved numerically to determine stress intensity factor. Numerical examples are provided to show the effects of material properties and crack type and location on the stress intensity factors and also to study the interaction of multiple cracks.