A Crystal Plasticity Analysis for Accumulations of Geometrically Necessary Dislocations and Dipoles around Shear Band

Abstract

In this paper, generalized geometrically necessary (GN) dislocation density and GN incompatibility are newly defined by extending Kröner’s dislocation density and incompatibility tensors. A new model of dislocation-crystal plasticity coupling a deformation field with a dislocation field is developed by introducing these dislocation densities into the hardening modulus matrix of crystal plasticity through the Bailey-Hirsch relation. The corrected Seeger model for the dislocation mean free path is extended to the third stage of strain hardening. Moreover, a finite element simulation is carried out for an f.c.c. single crystal under plane strain tension. It is numerically predicted that the shear band can be regarded as a subgrain.