3-D Mesoscale Plasticity and Its Connections to Other Scales
There is a dislocation theory but there is no dislocation theory of plasticity. The reasons for this situation are multiple. By definition, a dislocation is a linear defect that ensures compatibility between slipped and unslipped parts of a crystal. The motion of this defect propagates microscopic shears and is responsible for the plastic (i.e., permanent) deformation of crystalline materials. A dislocation line can be viewed in two different manners. From an atomistic viewpoint, it consists of a highly distorted region, the core, which surrounds the geometrical line of the defect and has a diameter of a few lattice spacings. In the continuum, a dislocation consists of a singularity line to which are associated long range stress and strain fields. The line energy of a dislocation is mainly located outside the core region and can conveniently be calculated by elasticity theory. This allows treating all the elementary dislocation properties that derive from their self and interaction energies to any desired degree of accuracy. However, the properties of dislocation cores also govern important properties, like dislocation mobility or the selection of the dislocation slip planes. Although our current knowledge of core properties has significantly improved in the past years, it is still far from being just satisfactory. Thus, dislocation theory has not yet been able to bridge the gap between atomic scale properties and mesoscale properties (the mesoscale is understood here as the scale of the defect microstructure).
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