Exact Solutions for Periodic Interfacial Wedge Disclination Dipoles in a Hexagonal Bicrystal

Abstract

In this paper, exact closed-form solutions for the elastic stress and strain energy density of an infinite, periodic array of interfacial wedge disclination dipoles in a hexagonal bicrystal with arbitrary in-plane c-axis orientations are derived by the method of image dislocations. These solutions are shown to be of the form of the logarithm of hyperbolic and trigonometric functions of complex parameters. The strain energy of the dipole array is also calculated by numerical integration of the density field. The results show that the stress, strain energy density and strain energy all depend significantly on the orientational and material inhomogeneities, and the importance of using an anisotropic bicrystal model over a homogeneous model for calculations is emphasized. For bicrystals with symmetric c-axis orientations, it is also shown that the strain energy of the dipole array can be a strong function of the orientations, with the maximum and minimum at specific orientations that depend on the bicrystal materials.