Interpretable machine learning for intrinsic mechanical properties of γ′ phase in cobalt-based superalloys

The presence of γ′ phase establishes Co-based alloys as promising candidates for next-generation superalloys, stimulating intense research interest in the development of γ/γ′ Co-based superalloys. Although elucidating the intrinsic elasticity of γ′ phase is crucial for designing novel γ/γ′ superalloys, acquiring a large amount of elastic data of multicomponent γ′ remains a bottleneck. In this study, we proposed an interpretable strategy for predicting the elastic properties of γ′ phase in multicomponent Co-based alloys using density functional theory (DFT) and machine learning (ML) methods. A 1,674-sample elastic dataset was first constructed via high-throughput DFT calculations. By utilizing this dataset, a predictive model with strong interpretability was successfully trained in terms of sure independence screening and sparsifying operator (SISSO) techniques. The accuracy of the well-trained 2D model for bulk modulus ( B ) reached 87% while that for shear modulus ( G ) and Young’s modulus ( E ) exceeded 95%, respectively. The SHapley Additive exPlanations (SHAP) analysis revealed mechanisms: part of compositions, mixing enthalpy, valence electron concentration, and electronegativity yield significantly effect on the mechanical properties, in which Co elevation, Cr reduction, valence electron concentration (VEC) > 8, and standard deviation of VEC (DVEC) lowering enhance G and E values; smaller DVEC/Atom (Average atomic radius), larger average bulk modulus (Bulk), and Fe > Ni enhance B values. Using the well-trained and low-cost predictive model, we predicted the mechanical properties of γ′ phases across 151,796 samples in the unknown compositional space. The statistical analysis revealed that W, Fe, Mo, Nb, Ti, Ta, V, and Ni play dominant strengthening roles. Excluding W and Fe, promising candidate systems include Al-free Co-Mo-Ni-Nb/Ta/V and Al-containing Co-Al-Mo-Cr/Nb/Ta/V alloys. These systems warrant further research to advance the optimization of novel γ/γ′ Co-based superalloys. • A large reliable elastic dataset is constructed by high-throughput DFT calculations; • A high precisely Interpretable mechanical model of γ′ phase is developed; • Critical performance-related features are explored and revealed by SHAP analysis; • Several promising candidates are screened from >150,000 unknown compositional space.