A non-local continuum crystal plasticity theory was proposed that was based upon a statistical mechanics description of the collective behavior of dislocations. Kinetic equations for the dislocation density fields were deduced from the equation of motion of individual dislocations, and were coupled to a continuum description of single slip. Dislocation nucleation, resistance to dislocation glide, and dislocation annihilation were included in the formulation. The theory was applied here to the bending of a monocrystalline strip in plane strain; using parameter values which had been obtained previously by fitting the discrete dislocation results of a different boundary-value problem. A numerical solution to the problem was obtained by using a finite-element method. The bending moment versus rotation angle, and the evolution of the dislocation structure, were analyzed for various orientations and specimen sizes; with due consideration being given to the role of geometrically necessary dislocations. The results were compared with discrete dislocation simulations of the same problem. It was found that the continuum theory was able to describe the dependences upon slip plane orientation and specimen size.

Bending of a Single Crystal - Discrete Dislocation and Non-Local Crystal Plasticity Simulations. S.Yefimov, E.Van der Giessen, I.Groma: Modelling and Simulation in Materials Science and Technology, 2004, 12[6], 1069-86