Combined approach to capture the evolution of oxidation of Nickel based superalloys using data driven approaches

Nickel-based superalloys are an exceptional class of materials that are indispensable for high-temperature applications in the aerospace and power sector industries worldwide. The prolonged application of these materials in a demanding environment is hindered by the increased oxidation rates and deformation due to mass gain at high temperatures and the presence of corrosive agents. Calculating the oxidation properties using experimental techniques is laborious and highly cost/time intensive, which presents a considerable challenge to reducing the oxidation in these materials. In this work, we establish an extensive database consisting of the specific mass gain due to oxidation ($\mathrm{\Delta }m$) and the parabolic oxidation rates (${\mathrm{k}}_{\mathrm{p}}$) of nickel-based superalloys spanning all the superalloy generations. Highly accurate machine learning (ML) models are developed to predict ($\mathrm{\Delta }m$) using artificial neural networks and tree-based XGBoost. The ML models are extended by unsupervised $k$ means clustering to improve the accuracy of the models and generate insights on the composition-property linkages. Additionally, the ML model for ${\mathrm{k}}_{\mathrm{p}}$ developed utilizing XGBoost yields unprecedented results with errors of 0.04. The ML model is analyzed using the SHapely Additive exPlanations parameters to determine the effect of individual features on the model. Further, we employ a genetic algorithm-based approach utilizing the developed ML models to minimize the ${\mathrm{k}}_{\mathrm{p}}$ to improve the performance of the superalloys at high temperatures. The genetic algorithm-assisted optimization successfully yields several compositions for new Ni superalloys with up to 20% reduction in the ${\mathrm{k}}_{\mathrm{p}}$. This work presents essential advances for accelerating the targeted discovery of new materials for highly specialized and demanding applications.

Figure 1

Schematic of the present work. Initially, a database is established for corrosion properties, followed by feature engineering and machine learning.

Figure 2

Learning curve for (a) $\mathrm{\Delta }m$, (b) ${\mathrm{k}}_{\mathrm{p}}$. The learning for $\mathrm{\Delta }m$ although converged shows considerable variation for the test data.

Figure 3

(a) Variance of data captured by successive principal components. The first ten principal components capture 80% variance, hence they are selected for describing the database, (b) Identification of ideal clustering. The inertia (error) reduces considerably until the $6^{\mathrm{th}}$ cluster. The error reduction after the $6^{\mathrm{th}}$ cluster is minimal, giving rise to the elbow plot.

Figure 4

Correlation of target property with the features for all the clusters. Blue (red) represent positive (negative) correlation of the feature of the cluster with the target property. Time and temperature are important parameters as the correlation is largley positive in all the clusters.

Figure 5

Summary plot for ${\mathrm{k}}_{\mathrm{p}}$ derived from SHAP. It represents the relation of the feature with ${\mathrm{k}}_{\mathrm{p}}$ as described by the best ML model for ${\mathrm{k}}_{\mathrm{p}}$.

Figure 6

Optimization of ${\mathrm{k}}_{\mathrm{p}}$ using genetic algorithm. The maximum, average and minimum values of ${\mathrm{k}}_{\mathrm{p}}$ for the initial and new population are presented. The average ${\mathrm{k}}_{\mathrm{p}}$ for the new population is considerably low as compared to the initial population. Further, the minima obtained for the new population is also an improvement over the initial population.