M. Fan

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

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 ( μ 2 / μ 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 μ 2 / μ 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.

Fracture behavior investigation for a pileup of edge dislocations interacting with a nanoscale inhomogeneity with interface effects

Elastic-plastic stress investigation for a pileup of edge dislocations interacting with a nanoscale inhomogeneity has been carried out in the form of Zener–Stroh crack. The interface and size effects of the inhomogeneity based on the Gurtin–Murdoch model are considered. The fracture behavior of the crack with plastic zone correction is examined by the generalized Irwin model for mixed loading conditions, in which von Mises yielding criterion is fulfilled in the plastic zone area. The stress intensity factor (SIF), the plastic zone size (PZS), and the crack tip opening displacement (CTOD) of the crack are evaluated. For a nanoscale inhomogeneity (inclusion), the size and interface properties have great influence on the fracture behavior of the crack, which is completely different to a classical crack-inclusion interaction problem. Numerical examples are given to show the effects of the inhomogeneity radius, interface properties and crack-inhomogeneity distance, as well as the dislocation loading ratio on the normalized SIFs, PZS, and CTOD of the Zener–Stroh crack. It is found that for different intrinsic lengths, the normalized SIFs, PZS, and CTOD are very different. This influence will be even greater when the crack is closer to the nano-inhomogeneity. For the mixed-mode problem, the dislocation loading ratio does not have too much effect on the normalized SIFs, but does have significant influence on the normalized PZS and CTOD.