Tension analysis of infinite solid circular cylinders with arbitrary located axisymmetric cracks

• We obtain a solution to problem of axisymmetric Volterra climb and glide dislocations in an infinite isotropic cylinder.
• Using the dislocation distribution technique, we derive a set of Cauchy singular integral equations for analysis of a cylinder with a system of coaxial axisymmetric cracks.
• The cracked cylinder is under the action of two distributed self-equilibrating shear tractions on its surface.
• For some interacting cracks, we study the crack type/location on the ensuing stress intensity factors at tips of cracks and the interaction between the cracks.

This paper deals with the mixed mode crack problem in a long circular cylinder of elastic material. First, the solution of axisymmetric Volterra climb and glide dislocations in an infinite circular cylinder is obtained by making a suitable representation of the biharmonic stress function. Next, the distributed dislocation technique is used to formulate integral equations for a system of coaxial axisymmetric cracks, including penny-shaped, annular and circumferential cracks. The cylinder is under the action of two distributed self-equilibrating shear tractions on the curved surface of cylinder. These equations are solved numerically to obtain the dislocation density on the surfaces of the cracks. The dislocation densities are employed to determine stress intensity factors for axisymmetric cracks. Several examples are presented to study the crack type/location on the ensuing stress intensity factors at tips of cracks and also the interaction between the cracks.