Mixed-mode fracture analysis of infinite isotropic cylinder weakened by multiple cylindrical cracks

In this article, stress analysis of an isotropic infinite cylinder weakened by multiple concentric cylindrical cracks subjected to shear and radial loadings on the lateral surface of the cylinder is accomplished. First, relations for stress and displacement components are given in terms of the Galerkin biharmonic vector potential. Next, using these relations, the dislocation solutions for both Somigliana and Volterra dislocation are derived. Using the distributed dislocation technique, integral equations for the infinite cylinder with arbitrary number of the cylindrical cracks are constructed. The numerical solution of resulting integral equations which are of the Cauchy type singular equations leads to evaluation of Somiglianaand Volterra dislocation densities on the crack surfaces. Using related dislocation densities, the stress intensity factors of crack tips for some examples are attained and variations of them with lengths of cracks are discussed. For some special cases, validation of the results of this study with others available in the literature is done.