Identifying determinants of γ’ phase coarsening behavior in Co/CoNi-based superalloys with explainable artificial intelligence (XAI)

The coarsening of γ’ phases in superalloys is influenced by multiple factors and significantly impacts mechanical properties, such as strength and creep resistance. While classical kinetic theory delineates the coarsening mechanisms of γ’ phases, it has limitations when excessive coarsening occurs. The challenge of identifying the pivotal factors that markedly affect the kinetic behavior of γ’ phase coarsening remains largely unresolved. This study utilized eXtreme Gradient Boosting (XGBoost) models to identify the CP and CPAE features that characterize the coarsening behavior of γ’ phases in Co/CoNi-based superalloys. Through meticulous analysis of CP features [aging temperature (T ), the atomic fraction of the Ti element (c Ti), the atomic fraction of the V element (c V), and the atomic fraction of the Ta element (c Ta)] and CPAE features [T , Young’s modulus (E ), electronegativity (EN ), atomic radius (r ), c Ti, the differences of atomic radius (σr ), and the differences of electronegativity (σEN )], we derived explicit mathematical expressions using symbolic classification approach, which offers improved interpretability compared to traditional black-box models. Our findings indicate that T , c Ti, c Ta, E and σr are dominant factors influencing γ’ coarsening behavior across different Co/CoNi-based superalloys. Notably, T , c Ti, c Ta and σr exhibit an inverse correlation with the γ’ coarsening behavior, whereas E shows a positive correlation. These insights provide valuable guidance for determining whether coarsening occurs in newly designed alloys. Furthermore, they facilitate the design of innovative anti-coarsening Co/CoNi-based superalloys. This knowledge is instrumental in enhancing alloy formulations, ensuring their performance and longevity in demanding environments where thermal stability is paramount.