Axisymmetric planar cracks in finite hollow cylinders of transversely isotropic material: Part II—cutting method for finite cylinders

Abstract

This paper is the outcome of a companion part I paper allocated to finite hollow cylinders of transversely isotropic material. The paper provides the solution for the crack tip stress intensity factors of a system of coaxial axisymmetric planar cracks in a transversely isotropic finite hollow cylinder. The lateral surfaces of the hollow cylinder are under two inner and outer self-equilibrating distributed shear loadings. First, the stress fields due to these loadings are given for both infinite and finite cylinders. In the next step, the state of stress in an infinite hollow cylinder with transversely isotropic material containing axisymmetric prismatic and radial dislocations is extracted from part I paper. Next, using the distributed dislocation technique, the mixed mode crack problem in finite cylinder is reduced to Cauchy-type singular integral equations for dislocation densities on the surfaces of the cracks. The problem of a cracked finite hollow cylinder is treated by cutting method; i.e., the infinite cylinder is cut to a finite one by slicing it using two annular axisymmetric cracks at its ends. The cutting method is validated by comparing the state of stress of a sliced intact infinite cylinder with that of an intact finite cylinder. The paper is furnished to several examples to study the effect of crack type and location in finite cylinders on the ensuing stress intensity factors of the cracks and the interaction between the cracks.

Publication Title

Zeitschrift fur Angewandte Mathematik und Physik

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