Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density

Classical plasticity has reached its limit in describing crystalline material behavior at the micron level and below. Its inability to predict size-dependent effects at this length scale has motivated the use of higher-order gradients to model material behavior at the micron level. The physical motivation behind the use of strain gradients has been based on the framework of geometrically-necessary dislocations (GNDs). A new but equivalent definition for Nye's dislocation tensor, a measure of GND density, is proposed, based on the integrated properties of dislocation lines within a volume. A discrete form of the definition is applied to redundant crystal systems, and methods for characterizing the dislocation tensor with realizable crystallographic dislocations are presented. From these methods and the new definition of the dislocation tensor, two types of three-dimensional dislocation structures are found: open periodic networks which have long-range geometric consequences, and closed three-dimensional dislocation structures which self-terminate, having no geometric consequence. The implications of these structures on the presence of GNDs in polycrystalline materials lead to the introduction of a Nye factor relating geometrically-necessary dislocation density to plastic strain gradients. (C) 1999 Published by Elsevier Science Ltd on behalf of Acta Metallurgica Inc. All rights reserved.