Distribution of dislocations in twisted bars

TL;DR

This paper develops an asymptotically exact continuum dislocation theory for twisted single crystal bars, revealing how dislocation distribution and stress profiles change with applied torque, including the formation of dislocation-free zones.

Contribution

It introduces a new continuum dislocation model for twisted bars, capturing dislocation distributions and stress changes under various torque conditions.

Findings

Dislocation-free zones form at the outer ring under non-zero torque.

Dislocation distribution varies with applied torque, affecting the twist angle.

Energy dissipation leads to an elastic core and dislocation ring, increasing the critical torque threshold.

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.