Dislocation dynamics studies are based on the elastic theory of dislocations together with specific non-elastic local rules when needed, to predict how a system containing dislocations evolves dynamically under the application of a load. These rules are generally obtained by computation at atomic scale very often by MD calculation.This provides a description of how the piece of material under study deforms plastically under given conditions.
2D dislocation dynamics models are still widely used for specific applications, including radiation damage. Specifically, a Foreman-Makin-type model has been used to provide an estimate of radiation hardening in RPV steels, within FP6-PERFECT. Recently, the development of three dimensional (3D) simulations, in which line tension effects and long-range interactions can be allowed for simultaneously, is becoming a reality.
In a DD model, dislocations are described as lines of discontinuity in a (generally) isotropic elastic medium, constructed as sequences of segments and subjected to the laws of elasticity. The effect of the atomic core structure is taken into account, if needed, via ad hoc local rules, acting only on the dislocation segment(s) concerned. In most existing approaches, the dislocation is described as a sequence of straight segments. These can be either perpendicular to each other, or slanted at an angle, in an attempt to better reproduce the actual elastic behaviour of a continuous curved line (mixed simulations).
In these approaches, the fundamental law used to calculate the force acting on an oriented dislocation segment (whose module is its length), with Burgers vector, is the Peach-Koehler equation, where both applied stress and the internal stress appear explicitly. The former is the external load, assumed uniform in the whole volume; the latter is the sum of the stress fields due to all dislocation segments present in the volume (as well as defects, if present), e.g. evaluated at the centre of the segment, depending on the approach used. The force calculated with is then projected onto the glide plane and corrected by adding: (i) the contribution due to the curved shape of the dislocation, neglected by the discretisation into segments; and (ii) the friction due to the lattice and to the presence of solute atoms, if any.
The total stress thereby calculated is used to determine the corresponding dislocation segment velocity and displacement, by means of appropriate equations, whose choice depends on the material studied, especially on its crystallographic structure, as well as on the conditions of interest (e.g. temperature).
In addition, a number of local rules must intervene to manage situations for which elastic theory is inadequate. Calculating the forces acting on the dislocation line segments is inevitably an N-body problem, as a priori all N segments interact with all others. Thus, the computing time for 3D-DD simulations scales as N2. Since the total dislocation line length increases dramatically as soon as a load is applied, 3D-DD simulations represent a formidable challenge from both the numerical and computational points of view. In addition, the volumes that can be studied remain relatively small: 3D-DD simulations remain limited to portions of single crystals, or single grains.
Despite these limitations, 3D-DD simulations have produced important results that have helped to understand the work-hardening process and in general the plastic behaviour of metals. 3D-DD simulation methods have therefore, in general terms, the potential for directly connecting the physics of dislocations with the plastic behaviour of materials, as described by macroscopic continuum models. However, to apply 3D-DD to the specific case of radiation damage, it becomes necessary to introduce all the mechanisms of interaction between each type of dislocation (edge, screw) and all the microstructural features formed in an irradiated material in terms of local rules.