Line Dislocation Dynamics

Abstract

In the preceding chapters we have discussed several computational approaches focused on the structure and motion of single dislocations. Here we turn our attention to collective motion of many dislocations, which is what the method of dislocation dynamics (DD) was designed for. Typical length and time scales of DD simulations are on the order of microns and seconds, similar to in situ transmission electron microscopy (TEM) experiments where dislocations are observed to move in real time. In a way, DD simulations can be regarded as a computational counterpart of in situ TEM experiments. One very valuable aspect of such a “computational experiment” is that one has full control of the simulation conditions and access to the positions of all dislocation lines at any instant of time. Provided the dislocation model is realistic, DD simulations can offer important insights that help answer the fundamental questions in crystal plasticity, such as the origin of the complex dislocation patterns that emerge during plastic deformation and the relationship between microstructure, loading conditions and the mechanical strength of the crystal. So far, two approaches to dislocation dynamics simulations have emerged. In the line DD method to be discussed in this chapter, dislocations are represented as mathematical lines in an otherwise featureless host medium. An alternative approach is to rely on a continuous field of eigenstrains, in which regions of high strain gradients reveal the locations of the dislocation lines. This representation leads to the phase field DD approach, which will be discussed in Chapter 11. Line DD has certain similarities with the models discussed in the previous chapters, but, at the same time, is rather different from all of them. For example, the representation of dislocations by line segments in line DD method is similar to the kinetic Monte Carlo (kMC) model of Chapter 9. However, having to deal with multiple dislocations on large length and times scales necessitates a more economical treatment of dislocations in the line DD method. Thus, line DD usually relies on less detailed discretization of dislocation lines and treats dislocation motion as deterministic.