Dislocations and disclinations in the gradient theory of elasticity

Document Type

Article

Publication Date

1-1-1999

Abstract

The results of application of gradient theory of elasticity to a description of elastic fields and dislocation and disclination energies are considered. The main achievement made in this approach is the removal of the classical singularities at defect lines and the possibility of describing short-range interactions between them on a nanoscopic level. Non-singular solutions for stress and strain fields of straight disclination dipoles in an infinite isotropic medium have been obtained within a version of the gradient theory of elasticity. A description is given of elastic fields near disclination lines and of specific features in the short-range interactions between disclinations, whose study is impossible to make in terms of the classical linear theory of elasticity. The strains and stresses at disclination lines are shown to depend strongly on the dipole arm d. For short-range interaction between disclinations, where d varies from zero to a few atomic spacings, these quantities vary monotonically for wedge disclinations and nonmonotonically in the case of twist disclinations, and tend uniformly to zero as disclinations annihilate. At distances from disclination lines above a few atomic spacings, the gradient and classical solutions coincide. As in the classical theory of elasticity, the gradient solution for the wedge-disclination dipole transforms to the well-known gradient solution for a wedge dislocation at distances d substantially smaller than the interatomic spacing. © 1999 American Institute of Physics.

Publication Title

Physics of the Solid State

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