Multiple slip in a strain-gradient plasticity model motivated by a statistical-mechanics description of dislocations

We have recently proposed a nonlocal continuum crystal plasticity theory for single slip, which is based on a statistical- mechanics description of the collective behavior of dislocations in two dimensions. In the present paper we address the extension of the theory from single slip to multiple slip. Continuum dislocation dynamics in multiple slip is defined and coupled to the small-strain framework of conventional continuum crystal plasticity. Dislocation nucleation, the material resistance to dislocation glide and dislocation annihilation are included in the formulation. Various nonlocal interaction laws between different slip systems are considered on phenomenological grounds. To validate the theory we compare with the results of dislocation simulations of two boundary value problems. One problem is simple shearing of a crystalline strip constrained between two rigid and impenetrable walls. Key features are the formation of boundary layers and the size dependence of the response in the case of symmetric double slip. The other problem is bending of a single crystal strip under double slip. The bending moment versus rotation angle and the evolution of the dislocation structure are analyzed for different slip orientations and specimen sizes.