Stress and strain energy of a periodic array of interfacial wedge disclination dipoles in a transversely isotropic bicrystal

Abstract Analytical closed-form solutions are obtained for the elastic stress and strain energy density fields of a periodic array of interfacial wedge disclination dipoles in a bicrystal. The adjoining crystals are transversely isotropic with maximum dissimilar in-plane crystallographic orientations (0 and π/2). The solutions are obtained by the method of image dislocations. The strain energy per unit area of the bicrystal interface is also obtained numerically. The results show that significant discrepancies can exist between the bicrystal and the isotropic homogeneous solutions. The rates of decrease/increase of the strain energy density and stresses from the interface are smaller in the crystal whose larger stiffness direction is perpendicular to the interface. Also, the strain energy of the bicrystal boundary is a function of the dipole arm length (2 a ) and period ( L ). The maximum strain energy occurs at a / L =0.25 and is estimated to be ∼8.9 J/m 2 if the dipole period is 10 nm and the disclination strength is π/2.