Stress investigation on a Griffith crack initiated from an eccentric disclination in a cylinder

Disclinations are rotational line defects which may be introduced in metal wires during the manufacturing process. In this work, the relaxation of an eccentric (off-center) negative wedge disclination in a cylinder by nucleation of a Griffith crack is investigated. The nucleated crack is simulated with distributed edge dislocations. The stress intensity factors (SIFs) of the crack are evaluated by solving a set of singular integral equations. By enforcing the condition that the SIFs at the two crack tips should keep the same value in the nucleation process, the crack length growth on each side of the wedge disclination is determined. The critical disclination power and equilibrium crack lengths are then numerically determined. Some important characteristics of the Griffith crack nucleation are revealed. (1) The two tips of the nucleated Griffith crack grow asymmetrically when the disclination locates eccentrically. The tip closer to the cylinder edge travels a shorter length. This asymmetry is getting more severe as the normalized off-center distance increases. (2) The critical disclination power increases monotonically with the normalized off-center distance. (3) The normalized stable equilibrium crack length decreases as the normalized off-center distance increases while the normalized unstable equilibrium crack length shows an opposite dependence. The dependence of the critical disclination power and the equilibrium crack lengths on the disclination power and cylinder radius is also discussed in this work. It is believed that this work helps to predict the strength of disclinated metal wires at various length scales.