A K-means Clustering-Based Method for Quantitative Analysis of Stress Fields in Directional Solidification of Thin-Walled Hollow blades

Thin-walled turbine blades operate for prolonged periods under harsh service conditions involving high temperatures, elevated stresses, and severe corrosion. Directional solidification is a critical manufacturing technique for producing nickel-based superalloy blades and enhancing their high-temperature performance. In this study, a high-fidelity numerical model of directional solidification was developed using the actual blade geometry. The results reveal that slower cooling of the leading edge near the furnace wall—together with mechanical constraints from the ceramic shell and core—restricts free shrinkage and leads to stress concentration. To address the challenge of characterizing and quantifying stresses in thin-walled blades, a K-means clustering-based quantitative stress analysis method is proposed, utilizing stress-field images and three-dimensional numerical data to automatically identify and quantify stress concentration regions, with clustering effectiveness evaluated using the silhouette coefficient. In the 2D analysis, high-stress regions occupy 17.70% of the pressure side and 14.42% of the suction side, with the highest silhouette coefficients obtained at k = 4 (0.6901 and 0.6585, respectively). In the 3D analysis, the average silhouette coefficients for k = 4, k = 5, and k = 6 are 0.7301, 0.7346, and 0.7137, respectively, with k = 5 providing the best clustering quality. The number of clusters k can be flexibly adjusted to satisfy varying requirements for stress quantification. Overall, the proposed approach provides a flexible and robust framework for stress-field characterization and holds significant potential for extension to other physical fields, providing a quantitative and visual foundation for defect prediction.