Dislocation Dynamics — Phase Field

Abstract

Dislocation, as an important category of crystal defects, is defined as a one-dimensional line (curvilinear in general) defect. It not only severely distorts the atomic arrangement in a region (called core) around the mathematical line describing its geometrical configuration, but also in a less severe manner (elastically) distorts the lattice beyond its core region. Dislocation core structure is studied by using the methods and models of atomistic scale (see Chapter 2). The long-range strain and stress fields generated by dislocation are well described by linear elasticity theory. In the elasticity theory of dislocations, dislocation is defined as a line around which a line integral of the elastic displacement yields a non-zero vector (Burgers vector). The elastic fields, displacement, strain and stress, of an arbitrarily curved dislocation are known in the form of line integrals. For complex dislocation configurations, the exact elasticity solution is quite difficult. A conventional alternative is to approximate a curved dislocation by a series of straight line segments or spline fitted curved segments. This involves explicit tracking of each segment of the dislocation ensemble (see “Dislocation Dynamics — Tracking Methods” by Ghoniem). In a finite body, the strains and stresses depend on the external surface. For general surface geometries, the elastic fields of dislocations are difficult to determine.