Three-Dimensional Dislocation Configurations

To have any hope of honestly addressing the dislocation-level processes that take place in plastic deformation, we must consider fully three-dimensional geometries. Though we earlier made disparaging remarks about the replacement of understanding by simulation, the evaluation of problems with full three-dimensional complexity almost always demands a recourse to numerics. Just as the use of analytic techniques culminated in a compendium of solutions to a variety of two-dimensional problems, numerical analysis now makes possible the development of catalogs of three-dimensional problems. In this section, we consider several very important examples of three-dimensional problems involving dislocations, namely, the operation of dislocation sources and dislocation junctions. 

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An alternative to the full machinery of elasticity that is especially useful in attempting to make sense of the complex properties of three-dimensional dislocation configurations is the so-called line tension approximation. The line tension idea borrows an analogy from what is known about the perturbations of strings and surfaces when they are disturbed from some reference configuration. For example, we know that if a string is stretched, the energetics of this situation can be described via... 

Another important class of three-dimensional dislocation configurations are those associated with the cross slip process in which a screw dislocation passes from one glide plane to another. The most familiar mechanism for such cross slip is probably the Friedel-Escaig mechanism, which is illustrated schematically in fig. 8.37. The basic idea is that an extended dislocation suffers a local constriction at some point along the line. This dislocation segment, which after constriction is a pure screw dislocation, can then glide in a different slip plane than that on which is gliding the parent dislocation. This mechanism, like those considered already, is amenable to treatment from both continuum and atomistic perspectives, and we take them each up in turn. 

Elastic Forces for Three-Dimensional Dislocation Configurations Use isotropic linear elasticity to compute the elastic forces of interaction between two dislocations oriented as (a) two perpendicular screw dislocations, (b) two perpendicular edge dislocations. 

From the standpoint of the phenomenology of plastic deformation, one of the most important classes of three-dimensional configuration is that associated with dislocation intersections and junctions. As will become more evident in our... 

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