Persistent homology-based microstructural feature extraction and its correlation with mechanical properties in Mo–TiC alloys

In this study, we applied persistent homology (pH) analysis to scanning electron microscopy backscattered electron (SEM-BSE) images of Mo–TiC alloys to extract topological descriptors and quantitatively evaluate their correlation with mechanical properties at room temperature, including 0.2% proof stress, Vickers hardness, and fracture toughness. While proof stress and hardness generally increased with increasing volume fraction of the hard TiC phase, fracture toughness exhibited a minimum near the eutectic composition and showed only a weak correlation with TiC volume fraction alone (coefficient of determination, R 2 ≈ 0.09). In contrast, the incorporation of PH-derived topological descriptors substantially improved the description of fracture toughness, resulting in R 2 ≈ 0.74, thereby revealing critical microstructural features not captured by phase fraction alone. These results demonstrate that persistent homology provides an effective means of characterizing microstructural features that govern mechanical performance, particularly for toughness, and offers a promising tool for microstructure-sensitive property prediction in multiphase materials.