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

Classical plasticity has reached its limit in describing crystalline materi al behavior at the micron level and below. Its inability to predict size-de pendent effects at this length scale has motivated the use of higher-order gradients to model material behavior at the micron level. The physical moti vation behind the use of strain gradients has been based on the framework o f geometrically-necessary dislocations (GNDs). A new but equivalent definit ion for Nye's dislocation tensor, a measure of GND density, is proposed, ba sed on the integrated properties of dislocation lines within a volume. A di screte form of the definition is applied to redundant crystal systems, and methods for characterizing the dislocation tensor with realizable crystallo graphic dislocations are presented. From these methods and the new definiti on of the dislocation tensor, two types of three-dimensional dislocation st ructures are found: open periodic networks which have long-range geometric consequences, and closed three-dimensional dislocation structures which sel f-terminate, having no geometric consequence. The implications of these str uctures on the presence of GNDs in polycrystalline materials lead to the in troduction of a Nye factor relating geometrically-necessary dislocation den sity to plastic strain gradients. (C) 1999 Published by Elsevier Science Lt d on behalf of Acta Metallurgica Inc. All rights reserved.