Graph representations of dislocation networks

Gaurav Lathiya, Markus Stricker

The mechanical response of a crystal is governed by the evolving network of dislocations it contains, yet quantitatively linking the `state of that network' to its yield stress remains challenging. Here we represent the dislocation networks obtained from discrete dislocation dynamic simulation as graphs, using five distinct graph representations, characterize each network through a compact set of topological properties, and predict the yield stress from these graph properties and the applied strain rate using a standard random forest model evaluated with strain rate stratified cross-validation. The model predicts the yield stress with $R^2\approx0.86-0.90$ across all box sizes and $R^2\approx0.91-0.94$ for larger box sizes, and this accuracy is consistent across all five representations, indicating that the topology-stress relationship is a robust feature of the graph properties rather than an artefact of any single graph representation. We propose graph topology as a compact and robust route for connecting the microstructural state of a dislocation network to its mechanical response in addition to established variables.