Driving forces and boundary conditions in continuum dislocation mechanics

Abstract
As a guide to constitutive specification, driving forces for dislocation velocity and nucleation rates are derived for a field theory of dislocation mechanics and crystal plasticity proposed in Acharya (2001, J. Mech. Phys. Solids 49, 761–785). A condition of closure for the theory in the form of a boundary condition for dislocation density evolution is also derived. The closure condition is generated from a uniqueness analysis in the linear setting for partial differential equations controlling the evolution of dislocation density. The boundary condition has a simple physical meaning as an inward flux over the dislocation inflow part of the boundary. Kinematical features of dislocation evolution, such as the initiation of bowing of a pinned screw segment and the initiation of cross–slip of a single screw segment, are discussed. An exact solution representing the expansion of a polygonal dislocation loop is derived for a quasilinear system of governing partial differential equations. The representation within the theory of features such as local (dislocation level) Schmid and non–Schmid behaviour as well as (unloaded) stress–free and steady microstructures are also discussed.