Prediction of temperature-dependent yield strength of refractory high entropy alloy based on stacking integrated framework

Abstract

Refractory high-entropy alloys (RHEAs) are promising materials for high-temperature applications. This study introduces an interpretable prediction model for the temperature-dependent yield strength of these alloys, utilizing a stacking ensemble algorithm. The Kolmogorov-Smirnov (K-S) test results ($$ P $$ = 0.873) confirm the model's reliability. Key features are analyzed from global and local perspectives using accumulated local effect (ALE) and SHapley Additive exPlanations (SHAP) methods. The analysis reveals that an atomic size difference ($$ \delta>0.049 $$) and a bulk modulus (K > 150) positively influence yield strength. Bivariate partial dependence plots (PDP) demonstrate that yield strength increases with both K and the shear modulus (G). At high temperatures (1, 000 and 1, 200 ℃), the stacking model, combined with the Dung Beetle optimization algorithm, predicts improved yield strength in various alloy compositions. For example, the alloy Cr$$ _{0.275} $$Nb$$ _{0.215} $$Mo$$ _{0.349} $$V$$ _{0.161} $$ shows a 19.90% improvement compared to the original dataset. Using parallel coordinate plots and iterative analysis, promising concentration regions for high yield strength were identified, such as in the Al-Cr-Nb-Mo-V system, where lower Al and Nb content and higher Cr content enhance performance.

Keywords

Refractory high-entropy alloy / temperature-dependent yield strength prediction / stacking ensemble algorithm / model interpretation / dung beetle optimization algorithm