A screw dislocation in a three-phase composite composed of an anisotropic elastic half-plane bonded to an isotropic elastic half-plane reinforced by a circular inhomogeneity

Using complex variable techniques, we solve the problem in anti-plane elasticity associated with a screw dislocation in a three-phase composite which is composed of an anisotropic elastic half-plane perfectly bonded to an isotropic elastic half-plane containing a circular elastic inhomogeneity. Analytical solutions are obtained for three typical cases: a screw dislocation in the isotropic half-plane in the exterior of the circular inhomogeneity, a screw dislocation inside the circular elastic inhomogeneity, a screw dislocation within the anisotropic half-plane. Explicit expressions of the image force acting on the screw dislocation are derived for each of the three cases. The numerical results indicate that at least one equilibrium position for the screw dislocation co-exists in each phase under certain conditions on the elastic constants.

Automated summary

In this study, the problem of anti-plane elasticity associated with a screw dislocation in a three-phase composite material is solved using complex variable techniques. Analytical solutions are obtained for three typical cases and explicit expressions of the image force acting on the screw dislocation are derived. Numerical results show that at least one equilibrium position exists for the screw dislocation in each phase under certain conditions.