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.