A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations

A two-dimensional nonlocal version of continuum crystal plasticity theory is proposed, which is based on a statistical-mechanics description of the collective behavior of dislocations coupled to standard small-strain crystal continuum kinematics for single slip. It involves a set of transport equations for the total dislocation density field and for the net-Burgers vector density field, which include a slip system back stress associated to the gradient of the net-Burgers vector density. The theory is applied to the problem of shearing of a two-dimensional composite material with elastic reinforcements in a crystalline matrix. The results are compared to those of discrete dislocation simulations of the same problem. The continuum theory is shown to be able to pick up the distinct dependence on the size of the reinforcing particles for one of the morphologies being studied. Also, its predictions are consistent with the discrete dislocation results during unloading, showing a pronounced Bauschinger effect. None of these features are captured by standard local plasticity theories. (C) 2003 Elsevier Ltd. All rights reserved

Bending of a single crystal: discrete dislocation and nonlocal crystal plasticity simulations

We have recently proposed a nonlocal continuum crystal plasticity theory that is based on a statistical-mechanics description of the collective behaviour of dislocations. Kinetic equations for the dislocation density fields have been derived from the equation of motion of individual dislocations and have been coupled to a continuum description of single slip. Dislocation nucleation, the material resistance to dislocation glide and dislocation annihilation are included in the formulation. The theory is applied, in this paper, to the problem of bending of a single-crystal strip in plane strain, using parameter values obtained previously from fitting to discrete dislocation results of a different boundary value problem. A numerical solution of the problem is obtained using a finite element method. The bending moment versus rotation angle and the evolution of the dislocation structure are analysed for different orientations and specimen sizes with due consideration of the role of geometrically necessary dislocations. The results are compared to those of discrete dislocation simulations of the same problem. Without any additional fitting of the parameters, the continuum theory is able to describe the dependence on slip plane orientation and on specimen size

Bending of a single crystal: discrete dislocation and nonlocal crystal plasticity simulations

We have recently proposed a nonlocal continuum crystal plasticity theory that is based on a statistical-mechanics description of the collective behaviour of dislocations. Kinetic equations for the dislocation density fields have been derived from the equation of motion of individual dislocations and have been coupled to a continuum description of single slip. Dislocation nucleation, the material resistance to dislocation glide and dislocation annihilation are included in the formulation. The theory is applied, in this paper, to the problem of bending of a single-crystal strip in plane strain, using parameter values obtained previously from fitting to discrete dislocation results of a different boundary value problem. A numerical solution of the problem is obtained using a finite element method. The bending moment versus rotation angle and the evolution of the dislocation structure are analysed for different orientations and specimen sizes with due consideration of the role of geometrically necessary dislocations. The results are compared to those of discrete dislocation simulations of the same problem. Without any additional fitting of the parameters, the continuum theory is able to describe the dependence on slip plane orientation and on specimen size.