The stress intensity factors and opening displacements were determined numerically for a crack which was loaded by a negative wedge disclination in an isotropic cylinder. The disclination axis coincided with the long axis of the cylinder, and one end of the crack coincided with the disclination location. The cylinder could also be subjected to equal and opposite line loads on its surface. An exact formulation led to a pair of decoupled singular integral equations of Cauchy type. Numerical solutions showed that, if the cylinder represented a grain in a polycrystal, unstable sub-microscopic cracks which were 0.00001 to 0.1 times the grain size and stable microscopic cracks which were of the order of the grain size were expected to exist. The sub-microscopic crack length to grain size ratio decreased, while the microscopic crack length to grain size ratio increased, as the grain size increased. Significant differences existed, even in the case of the sub-microscopic cracks, between the predictions of the exact theory and those of an approximate theory which ignored stress redistribution. The opening displacement was independent of the elastic constants, and the crack profile was wedge-shaped.

Analysis of a Crack in a Disclinated Cylinder. M.S.Wu, Z.Hong: International Journal of Fracture, 1996, 82[4], 381-99