Crack interaction with a second phase nanoscale circular inclusion in an elastic matrix

The screw dislocation interacting with a nanoscale circular inclusion and a mode III crack is studied considering the importance of interface stress in controlling mechanical response of nanoscale composite structures. By using the complex potential function method, the image force and the stress intensity factor at the tip of the crack produced by the screw dislocation are obtained under an applied remote load. The results indicate that the shielding effect on the stress intensity factor due to the screw dislocation is enhanced (abated) by the negative (positive) interface stress, and increases (decrease) with an increase of the ratio of the shear modulus of the matrix over that of the inclusion (the relative length of the inclusion). The soft (stiff) inclusion promotes (suppresses) the crack extension. In addition, the surface of the nano-inclusion forms a tensional (compression) image force for the positive (negative) interface stress. It is also found that the interface stress generates strong size-dependence of the image force, comparing with the classical solution where this force is always constant.