A revisit of the elastic fields of straight disclinations with new solutions for a rigid core

Abstract

The classical solutions for straight disclinations in an infinite elastic solid have been obtained by integrating the results for disclination densities. In this paper, the equilibrium equations are solved directly for straight twist and wedge disclinations, subject to the boundary conditions of the defects and rigid body translations/rotations. For a twist or wedge disclination in an infinite solid, the current solutions, based on a core fixed at a point to remove rigid body motion, differ from the classical ones by the constant $-\hbox {log }r_{i}$, where $r_{i }$ is the radius of the disclination core. For a wedge disclination in an infinitely long cylinder, additional terms of the form 1 / r in the radial displacement and $1/r^{2}$ in the stresses appear in the solutions. The dependence of the current and classical results on the Lamé constants highlights significant differences near the disclination line, which will impact studies of disclination relaxation such as crack nucleation and core amorphization. The energy of a singular wedge disclination in a cylinder without a core mostly underestimates that of a wedge disclination with a core.