Analysis of a crack in a disclinated cylinder

Abstract

In this paper, the stress intensity factors and the opening displacement of a crack loaded by a negative wedge disclination in an isotropic cylinder are numerically determined. The disclination axis coincides with the long axis of the cylinder, and one end of the crack coincides with the disclination location. The cylinder may also be subjected to equal and opposite line loads on its surface. An exact formulation leads to a pair of decoupled singular integral equations of the Cauchy type. Numerical solutions show that if the cylinder represents a grain in a polycrystal, (i) unstable submicroscopic cracks 10-5 to 10-1 times the grain size and stable microscopic cracks of the order of the grain size, are predicted, (ii) the submicroscopic crack length to grain size ratio decreases, while the microscopic crack length to grain size ratio increases, as the grain size increases, (iii) significant differences exist, even in the case of the submicroscopic cracks, between the predictions of the exact theory and the approximate theory which ignores stress redistribution, and (iv) the opening displacement is independent of the elastic constants and the crack profile is wedge-shaped.