Driving forces and boundary conditions in continuum dislocation mechanics

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.