Analysing discrete dislocation data using alignment and curvature tensors

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.