Since the mid 80s various gradient plasticity models were developed for obtaining the plastic response of materials at the micron- and submicron- scales. In particular, gradient terms were proven to be crucial for understanding size effects in constrained plastic flow, which were related to the emergence of plasticity boundary layers near passive (plastically not deformable) boundaries. In spite of the success of gradient theories in modelling boundary layer formation, there remain unresolved issues concerning the physical interpretation of the internal length scale involved in the theoretical formulation. Physically, boundary layer formation was related to the piling up of dislocations against the boundaries. This phenomenon was investigated by performing discrete dislocation dynamics simulations on a tri-crystal with plastically non-deforming grain boundaries. Strain distributions were derived from the discrete dislocation dynamics simulations and matched with the results of gradient plasticity calculations, in order to identify the internal length scale governing the boundary layer width.

Discrete Dislocation Dynamics Simulation and Continuum Modeling of Plastic Boundary Layers in Tricrystal Micropillars. K.E.Aifantis, J.Senger, D.Weygand, M.Zaiser: IOP Conference Series - Materials Science and Engineering, 2009, 3[1], 012025