A gradient theory of small-deformation, single-crystal plasticity that accounts for GND-induced interactions between slip systems

This paper develops a gradient theory of single-crystal plasticity based on a system of microscopic force balances, one balance for each slip system, derived from the principle of virtual power, and a mechanical version of the second law that includes, via the microscopic forces, work performed during plastic flow. When combined with thermodynamically consistent constitutive relations the microscopic force balances become nonlocal flow rules for the individual slip systems in the form of partial differential equations requiring boundary conditions. Central ingredients in the theory are densities of (geometrically necessary) edge and screw dislocations, densities that describe the accumulation of dislocations, and densities that characterize forest hardening. The form of the forest densities is based on an explicit kinematical expression for the normal Burgers vector on a slip plane.