Plastic zones in a transversely isotropic solid cylinder containing a ring–shaped crack

Abstract

In this study, a problem of a ring shaped-crack contained in a infinitely long solid cylinder of elastic perfectly-plastic material is considered.The problem is formulated for a tranversely isotropic matrial by using integral transform technique under uniform load. Due to the geometry of the configuration, Hankel and Fourier integral transform techniques are chosen and the problem is reduced to a singular integral equation. This integral equation is solved numerically by using Gaussian Quadrature Formulae and the values are evaluated for various for discrete points. The plastic zone widths are obtained by using the plastic strip model. They are plotted for various ring-shaped crack sizes and transversely isotropic matrials. It is found that the width of the plastic zone at the inner tip of the crack is greater than the outer one.