  An asymptotically exact continuum dislocation theory of single crystal bars
under torsion is proposed. The dislocation distribution minimizing energy of
the bar with zero torque is shown to be uniform. If the applied torque is
non-zero, the minimizer exhibits a dislocation-free zone at the outer ring of
the bar's cross-section. The non-uniform distribution of dislocations in
equilibrium as well as the twist angle per unit length are found in terms of
the given torque. With the energy dissipation being taken into account, there
exists an elastic core region, while dislocation are concentrated in a ring
between two dislocation-free zones. This leads to the change of the stress
distribution increasing the critical threshold of the torque.
