The effect of the integration time-step and the introduction of a cut-off velocity for dislocation motion was analysed via discrete dislocation dynamics simulations of a single-crystal micro-beam. Two loading modes, bending and uniaxial tension, were examined. It was found that a longer integration time-step led to a progressive increment of the oscillations in the numerical solution; which eventually diverged. This problem could be corrected, in simulations carried out in bending, by introducing a cut-off velocity for dislocation motion. However, the long integration-times and cut-off velocity for dislocation motion did not recover the solution using very short time-steps in uniaxial tension. That is, the dislocation density was over-estimated and the dislocation patterns were modified. The differing responses to the same numerical algorithm were explained in terms of the nature of the dislocations generated in each case. Geometrically necessary dislocations were generated in bending and statistically stored ones were generated in tension. The evolution of the dislocation density in the former case was controlled by the plastic curvature of the beam and, was independent of the details of the simulation. However, the steady-state dislocation density in tension was determined by a balance between the nucleation of dislocations and their annihilation or exit from the beam. Changes in the dislocation dynamics, imposed by the cut-off velocity, altered this equilibrium and the solution. The results indicated a need for detailed analysis of the accuracy and stability of the dislocation dynamic simulations in order to ensure that the results were not affected by the numerical methods used to solve the problem.

Computational Issues in the Simulation of Two-Dimensional Discrete Dislocation Mechanics. J.Segurado, J.Llorca, I.Romero: Modelling and Simulation in Materials Science and Engineering, 2007, 15[4], S361-75