Interaction of a wedge disclination dipole with interfacial cracks

Abstract

The elastic interaction between a wedge disclination dipole and collinear interfacial cracks in bimaterials is investigated. The general solutions of complex potentials to this problem are presented by using complex potential theory. As illustrative examples, the closed-form solutions for a wedge disclination dipole interacting with a finite interfacial crack and a semi-infinite interfacial crack are obtained. The stress intensity factors at the tips of the crack and the force acting on the disclination dipole center are also given. The shield and anti-shield effect of the wedge disclination dipole upon the stress intensity factors is evaluated, and the equilibrium position of the disclination dipole is discussed for various crack geometries and material mismatch. The results indicate that the shielding or anti-shielding effect to the stress intensity factors increases acutely when the disclination dipole approaches the tip of the crack. If the center of the dipole is fixed, there always exists a critical value of angle of the dipole arm which the shielding or anti-shielding effect to the stress intensity factor is maximal. In addition, the length of the dipole arm and the material mismatch have significant influence on the stress intensity factors. The results also show that the interfacial crack always attracts the wedge disclination dipole and an equilibrium position of the disclination dipole may be available near the interface, which differs from the case of a perfect bonded interface, when the dipole approaches the surface of the crack from infinity. The present solutions contain a series of new and previously known results which can be shown to be special cases.