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The interface effect of a nano-inhomogeneity on the elastic–plastic fracture behavior of a crack with the influence of nearby edge dislocation is studied by applying the surface/interface stress model. When the inhomogeneity and the crack become nano-sized, the bimaterial interface contributes considerable stresses to the crack surfaces, which are usually ignored in the traditional micro/macro crack problems. With the existence of nano-inhomogeneity, 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 inhomogeneity. The Zener–Stroh mechanism is employed to model the nano-sized fracture behavior and the generalized Irwin plastic zone correction is taken to improve the fracture analysis at the crack tips. Using the complex potential functions and distributed dislocation method, the stress intensity factor, plastic zone size, and crack tip opening displacement are evaluated by solving the Cauchy singular integral equations. The numerical examples prove that the values of stress intensity factors, plastic zone size and crack tip opening displacement are sensitive to the interface properties of the current nano-scaled problem, especially when the inhomogeneity is small. When the extra edge dislocation is close to the sharp crack tip, the stress intensity factor increases significantly, which indicates the crack has a potential to absorb the nearby dislocation. Further investigations find that mixed mode loading conditions always induce much higher stress intensity factors, plastic zone size, and crack tip opening displacement comparing to pure mode I loading problem.

The elastic-plastic fracture behavior of a Zener-Stroh crack nucleated by a wedge disclination dipole interacting with a nearby circular inclusion is investigated. It is known that a disclination is a strong source of internal stresses and energy, one possible way for the relaxation of the stresses can be in the form of an initiated crack. In the current work, the nucleated Zener-Stroh crack is simulated by a series of edge dislocations with distributed dislocation method. The influence of the disclination is accounted through crack surface traction free condition. To improve the analysis accuracy, the Irwin plastic zone correction is employed to evaluate the elastic-plastic fracture behavior at the sharp crack tip. Von Mises yielding criterion is applied in the plastic zone area to judge the yielding occurrence. Numerical results are given to study the influence of the disclination strength, disclination dipole arm as well as material properties on the stress intensity factor (SIF), plastic zone size (PZS), and crack tip opening displacement (CTOD). It is found that the property of the wedge disclination dipole has great effect on the stress field and the elastic-plastic fracture behavior of the Zener-Stroh crack. Either disclination strength or dipole arm increases, the SIF, PZS, and CTOD will increase significantly. For the same disclination, if the nucleated Zener-Stroh crack has a longer crack length, the SIF, PZS, and CTOD could be smaller. For a Zener-Stroh crack nucleated between the inclusion and the disclination dipole, the interaction between the disclination and inclusion greatly influences the elastic-plastic fracture behavior. However, this influence highly depends on material combinations of the two phases.

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.

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 ([Formula: see text], 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 [Formula: see text] 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.