The structure of coaxial (Eshelby) dislocations was computed using isotropic elasticity for arrays of up to 500 dislocations. The energies of the arrays were determined in order to predict the lowest-energy configuration, and multiple metastable configurations were often found. The results of these elasticity predictions revealed good agreement with molecular statics simulations of aluminium. From these simulations, the torque-twist curves were predicted and compared with molecular dynamics simulations. The structure of Eshelby dislocations resembled the distribution of charges confined to a disk. However, the structure was more complicated due to the various types of interaction included in the model. As the number of dislocations was increased, the dislocations appeared to distribute themselves uniformly throughout the cross-section. The plastic twist per unit length appeared to converge to its continuum limit as the number of dislocations was increased. The energy of the distribution of Eshelby dislocations scaled approximately the same as a grain boundary with respect to crystal size. An additional logarithmic term containing the radius could make these dislocations more energetically favourable at smaller wire radii. The energy of Eshelby dislocations appeared to scale linearly with twist over a larger range of twist values when compared with grain boundaries. Grain boundaries always exhibited an energy that returned to zero after a finite twist, of at most one revolution, which was not the case for Eshelby dislocations. The relationship between the plastic twist per unit length and the dislocation density was a function of the number of dislocations in the array, and the applied torque. This relationship had two limits: a diffuse limit where the dislocations spread out across the entire area, and a compact limit where the dislocations were confined to the center of the rod. The diffuse limit had the same dislocation density plastic twist relationship as did a rectangular array of screw dislocations while the compact limit, which was representative of a high torque, was similar to a single Eshelby dislocation. As the density of dislocations increased, the diffuse appeared to be the more appropriate relationship to use in gradient plasticity theories. Discrete dislocation dynamics models of the plasticity of these wires showed that, under the assumption of constant nucleation stress, the torque dropped continuously during plastic straining. This occurred because, during unloading, the proportionality between the torque drop and surface stress drop was not the same as that during elastic loading. The presence of dislocations already in the cylinder tended to enhance further dislocation nucleation. In comparison with recent work by Kaluza and Le (2011), some similarities and differences in the simulations were noticed. Those authors pointed out that their analysis revealed a dislocation-free boundary layer near to the surface of the cylinder in torsion. The present zero-torque data did not show this explicitly. However, under applied torques the dislocations gathered into the center; yielding a similar effect. The above authors also pointed out that their torque-twist curves should be reversible. The present results did not agree with this, in the quasi-static case, in the absence of thermal fluctuations. It was noted that these results, and previous work (Weinberger and Cai, 2010), pointed to an arbitrary number of Eshelby dislocations being in equilibrium within a torque-free wire. However it was clear that, during unloading, some of the dislocations could escape from thermal fluctuations; allowing the dislocations to overcome the energy barriers associated with escape. Finally, the torque-twist curves also differed. This could also be related to the different nucleation treatments in the two models. This suggested that a thorough comparison of the two models might lead to a better understanding of the behaviour of plastically twisted rods.

The Structure and Energetics of, and the Plasticity Caused by, Eshelby Dislocations. C.R.Weinberger: International Journal of Plasticity, 2011, 27[9], 1391-408