On the plastic zone correction of a Zener–Stroh crack interacting with a nearby inhomogeneity and an edge dislocation

Abstract

The investigation on the interaction among a Zener–Stroh crack, a nearby inhomogeneity/inclusion and an extra edge dislocation has been carried out. A Zener–Stroh crack is formed by pileup of net dislocations. With the existence of a nearby inclusion, an extra dislocation near the crack may be either absorbed into the crack (so the crack grows bigger) or repelled away by the crack and the inclusion. The result depends on the force on the dislocation from the crack and inclusion. In our current study, the plastic zone correction at the crack tips is adopted, where the plastic zone size (PZS) is determined by our newly developed generalized Irwin approach since the stress fields around the crack tips are mixed modes. With the distributed dislocation method, the expressions for the stress intensity factor, PZS and crack tip opening displacement (CTOD) are obtained for different sets of geometric and material parameters. Numerical examples show that when the extra single edge dislocation is located near the sharp tip of the Zener–Stroh crack, the normalized PZS and normalized CTOD become very sensitive to the position of the edge dislocation. It is also observed that the mixed mode problem usually has larger PZS and CTOD comparing to the pure mode I loading problem.