On torsion of a single crystal rod

The paper aims at calculating the dislocation distribution inside a single crystal rod loaded in torsion within the framework of continuum dislocation theory. We construct an explicit analytical solution of this problem in terms of the modified Bessel and hypergeometric functions. The interesting features of this solution are the energetic and dissipative thresholds for dislocation nucleation, the translational work hardening, and the size effect. The comparison with experimental results shows quite good agreement of the torque-twist curves for small up to moderate twists.