Evolution analysis of γ' precipitate coarsening in Co-based superalloys using kinetic theory and machine learning

The coarsening of γ' precipitates in superalloys involves multiple factors and impacts the performance of mechanical properties, such as strength and creep resistance. Classical kinetic theory describes the coarsening of γ' under limited conditions, as it shows deficiencies in γ' precipitation with excessive coarsening. Finding effective factors underlying the kinetic behavior significantly affecting precipitate coarsening remains largely unsolved. We address this by using machine learning models to identify materials descriptors describing γ' precipitate coarsening in Co-based superalloys. Using descriptors that include Young's modulus difference and valence electron number, we obtain an explicit relation assisted by symbolic regression that fits the experimental γ' size data far better than classical kinetic theory in describing γ' coarsening. We infer that the Young's modulus difference dominates γ' coarsening mechanism in different Co-based superalloys. Moreover, alloys containing additional elements with large Young's modulus should favor smaller γ' precipitates size, thus providing guidance for designing advanced multicomponent Co-based superalloys with high γ' coarsening resistance. [Display omitted] We utilize a computer vision framework incorporating the deep learning-based convolutional neural networks to extract accurate microstructural information from γ/γ' microstructure images for analysis in classical kinetic theories and machine learning (ML) models. Coupled with the classical kinetic theory analysis, it can well fit the earlier coarsening of regular γ' precipitates in some Co-based superalloys. However, the classical kinetic theory can not give a reasonable fitting and explanation on the fast coarsening of irregular γ' precipitate, which fully exposes its deficiency in dealing with practical problems. We use ML models and proposed descriptor selection strategy by fitting experimental γ' size data to describe γ' precipitate coarsening using descriptors such as Young's modulus difference (σE) and valence electron number (VEN), which we identify from ML models. The relation we propose for γ' size prediction equation in terms of aging temperature (T), aging time (t), σE and VEN is far superior in fitting to the data than classical kinetic theory, and Co-based superalloys with large σE value tend to follow the γ' coarsening predicted by LSW theory. For strengthening materials, this model for γ' size, which inversely depends on σE, predicts that