Distribution of dislocations in twisted bars

Abstract

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.