Persistent Homology on Electron Backscatter Diffraction Data in Nano/ultrafine-grained Metallic Materials

Nano/ultrafine-grained stainless steel was produced by severe cold deformation followed by annealing. The effect of annealing temperature on additional structural parameters, including the fraction of high-angle grain boundaries (HAGBs) and the kernel average misorientation (KAM), are revealed through electron backscatter diffraction. HAGB and KAM values provide a mechanistic understanding of the impact of structure on mechanical properties, including hardness, strength, and ductility. In this study, a novel application of persistent homology (PH) was employed to reduce the dimensionality of the information describing the complex processing-structure-property relationship. PH emphasizes the relationship between processing (annealing temperature), structure (distribution of the Schmid factor) and property (strength). Specifically, the PH formalism translates multidimensional data sets into clusters, distinguished by common PH features. In this analysis, two clusters emerge. First, at low annealing temperature, incomplete reversion of austenite results in materials with a greater fraction of grain boundaries, resulting in high strength and low ductility. Second, at high annealing temperature, fully reversed austenite results in lower, though still acceptable strength and superior ductility. The PH approach is applicable for identifying salient features in complex processing-structure-property relationships and is amenable to analysis of large data sets based on machine learning.