Axisymmetric planar cracks in finite hollow cylinders of transversely isotropic material: part I—dislocation solution for infinite cylinders

Abstract

This paper presents the solution for the crack tip stress intensity factors of a system of coaxial axisymmetric planar cracks in a transversely isotropic infinite hollow cylinder. The cylinder is under uniform axial tensile loading at infinity. First, the state of stress in an infinite hollow cylinder with transversely isotropic material containing axisymmetric prismatic and radial dislocations is studied. To this end, the solutions are represented in terms of biharmonic stress functions. Next, using the distributed dislocation technique, the mixed mode crack problem is reduced to Cauchy-type singular integral equations for dislocation densities on the surfaces of the cracks. The dislocation densities are employed to determine stress intensity factors for axisymmetric interacting cracks. For validation, the problems including one single crack in an infinite hollow cylinder with a circumferential edge crack or an annular crack are reexamined.

Publication Title

Zeitschrift fur Angewandte Mathematik und Physik

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