Interfacial Wedge Disclination Dipole in a Hexagonal Bicrystal with Arbitrary In-Plane c-Axis Orientations

Abstract

The stress field of a wedge disclination dipole located at the boundary of a hexagonal bicrystal is investigated under plane strain. The c-axes of the adjoining crystals are restricted to be in-plane but can otherwise be arbitrarily oriented. Exact closed-form solutions for the stress components, obtained by the method of continuous image dislocations, are of the form of the logarithm of the ratio of the functions of spatial coordinates and disclination and crystal parameters. Numerical results show that the characteristics of the stress distribution depend significantly on the c-axis orientations. Also, the interfacial stress components, plotted as functions of the two c-axis orientations, possess extrema and saddle points. The occurrence of, and the stress magnitude associated with, the extrema and saddle points are dependent on the crystal elastic anisotropy and the bicrystal inhomogeneity.

Keywords

Disclination dipole hexagonal bicrystal c-axis orientation

References

[1] Li, J. C. M. : Some properties of the disclination structure of grain boundaries, The Nature and Behavior of Grain Boundaries, 71-82, ed H. Hu , Plenum Press, New York, 1972.

[2] Kolesnikova, A. L. , Ovid’ko, I. A. and Romanov, A. E. : Misfit disclination structures in nanocrystalline and polycrystalline films. Solid State Phenom., 87, 265-275 (2002).

[3] Shenderova, O. A. , Brenner, D. W. , Nazarov, A. A. , Romanov, A. E. and Yang, L. H. : Multiscale modeling approach for calculating grain-boundary energies from first principles. Phys. Rev., B 57, R3181-R3184 (1998).

[4] Wu, M. S. : Exact solutions for a wedge disclination dipole in a transversely isotropic bimaterial. Int. J. Eng. Sci., 38, 1811-1835 (2000).

[5] Wu, M. S. : Stress and strain energy of a periodic array of interfacial wedge disclination dipoles in a transversely isotropic bicrystal. Int. J. Eng. Sci., 40, 873-897 (2002).

[6] Stroh, A. N. : Dislocations and cracks in anisotropic elasticity. Phil. Mag., 3, 625-646 (1958).

[7] Yu, H. Y. and Sanday, S. C. : Dislocations and disclinations in transversely isotropic elastic solids. Phil. Mag., A 70, 725-738 (1994).

[8] Hirth, J. P. and Lothe, J. : Theory of Dislocations, reprint edn, Krieger Publishing Company, Malabar, 1992.

[9] Hahn, S. L. : Hilbert Transforms in Signal Processing, Artech House, Boston, MA, 1996.

10.

[10] Weertman, J. : Dislocation Based Fracture Mechanics, World Scientific, Singapore, 1996.