Boundary layers in constrained plastic flow: comparison of nonlocal and discrete dislocation plasticity

Simple shear of a constrained strip is analyzed using discrete dislocation plasticity and strain gradient crystal plasticity theory. Both single slip and symmetric double slip are considered. The loading is such that for a lo cal continuum description of plastic flow the deformation state is one of h omogeneous shear. In the discrete dislocation formulation the dislocations are all of edge character and are modeled as line singularities in an elast ic material. Dislocation nucleation, the lattice resistance to dislocation motion and dislocation annihilation are incorporated into the formulation t hrough a set of constitutive rules. A complementary solution that enforces the boundary conditions is obtained via the finite element method. The disc rete dislocation solutions give rise to boundary layers in the deformation field and in the dislocation distributions. The back-extrapolated flow stre ngth for symmetric double slip increases with decreasing strip thickness, s o that a size effect is observed. The strain gradient plasticity theory use d here is also found to predict a boundary layer and a size effect. Nonloca l material parameters can be chosen to fit some, but not all, of the featur es of the discrete dislocation results. Additional physical insight into th e slip distribution across the strip is provided by simple models for an ar ray of mode II cracks. (C) 2001 Elsevier Science Ltd. All rights reserved.