No abstract

Analysis of large scale discrete dislocation data requires the characterisation of complex dislocation networks by suitable average quantities. In the current work, we suggest dislocation alignment tensors and closely related curvature tensors as easily extractable and intelligible measures of geometrical and topological characteristics of dislocation distributions. We provide formulae for extracting these measures from discrete dislocation data based on straight segments. Examples for interpreting and visualising these measures are provided for a simple configuration and two more involved results from discrete dislocation simulations. We suggest the alignment and curvature tensors for wider use in plasticity research.

Dislocations are the main contributors to plastic deformation of crystalline materials. An important step towards the description of hardening behavior is the consideration of cross slip, as it drives the exchange of dislocations between slip systems, thus playing a major role in dislocation multiplication or annihilation. In density based continuum theories of dislocations, dislocations are usually considered closed curves within their slip planes. Recent discrete dislocation dynamics simulations, however, suggest that only a small fraction of dislocations is actually closed on a single slip system, due to cross slip and dislocation reactions. We therefore investigate how the kinematics of moving open curves can be considered in dislocation density based models. The assumption of open planar curves leads to modified evolution equations for the dislocation state variables. These extended evolution equations are presented for the theory of geometrically necessary dislocations (GND) and for the higher dimensional continuum dislocation dynamics theory (hdCDD). The resulting equations are checked for plausibility by numerical calculations using the finite volume method.

Since crystal plasticity is the result of moving and interacting dislocations, it seems self-evident that continuum plasticity should in principle be derivable as a statistical continuum theory of dislocations, though in practice we are still far from doing so. One key to any statistical continuum theory of interacting particles is the consideration of spatial correlations. However, because dislocations are extended one-dimensional defects, the classical definition of correlations for point particles is not readily applicable to dislocation systems: the line-like nature of dislocations entails that a scalar pair correlation function does not suffice for characterizing spatial correlations and a hierarchy of two-point tensors is required in general. The extended nature of dislocations as closed curves leads to strong self-correlations along the dislocation line. In the current contribution, we thoroughly introduce the concept of pair correlations for general averaged dislocation systems and illustrate self-correlations as well as the content of low order correlation tensors using a simple model system. We furthermore detail how pair correlation information may be obtained from three-dimensional discrete dislocation simulations and provide a first analysis of correlations from such simulations. We briefly discuss how the pair correlation information may be employed to improve existing continuum dislocation theories and why we think it is important for analyzing discrete dislocation data.