Generalized Irwin plastic zone correction for a Griffith crack near a coated-circular inclusion

Abstract

Elastic-plastic stress analysis on a radial crack interacting with a coated-circular inclusion in a matrix has been carried out with the aid of a generalized Irwin plastic zone correction. The crack line is assumed to be at the angle of 90° − θ from a remote tensile loading. In the mathematical formulation, the distributed dislocation method is used to simulate the crack. By solving a set of singular integral equations, three quantities, the effective stress intensity factor, the plastic zone size and the crack tip opening displacement (CTOD), are evaluated with the generalized Irwin model proposed. Numerical examples are given to show the influence of the key parameters such as the crack orientation angle θ, the normalized crack distance, the normalized coating phase thickness and the shear modulus ratio ( $\mu 2/\mu 3$ , coating phase/matrix) on the fracture behavior. The results indicate that the influence of angle θ is the greatest, while the effect of shear modulus ratio $\mu 2/\mu 3$ is relatively small. A validation checking is performed by the finite element method (FEM) for one case. The result obtained from the FEM simulation matches well with that from the current method.