Torsion analysis of finite solid circular cylinders with multiple concentric planar cracks

Abstract

First, using the separation of variables technique a series solution for torsion of an intact finite cylinder under self‐equilibrating lateral shear tractions is given. Next, an integral form solution for torsion of an intact infinite cylinder under the aforementioned lateral loading is obtained. After that the solution of an axisymmetric rotational Somigliana ring dislocation in the infinite circular cylinder is obtained. The distributed dislocation technique is used to construct integral equations for stress analysis of the infinite cylinder with a set of coaxial axisymmetric cracks. These defects are penny‐shaped, annular and circumferential edge cracks. The infinite cylinder is under the action of the loading similar to the intact cylinder. The integral equations are solved numerically to obtain the dislocation density on the surfaces of the cracks. The stress intensity factors for the cracks are determined by employing the dislocation densities. The problem of a cracked finite cylinder is treated by cutting method. That is, a similar cracked infinite cylinder is sliced by extending two additional annular axisymmetric cracks. To validate the cutting method, the solution of the sliced intact infinite cylinder is compared to that of an intact finite cylinder which both of them are under the same self‐equilibrating lateral shear tractions. The solution is applied to several examples to study the effect of crack type/location on the resulting stress intensity factors at tips of the cracks.