The Characterization of Curved Grain Boundary in Nickel-Based Superalloy Formed During Heat Treatment

This study proposes a novel framework for quantifying curved grain boundaries that overcomes key limitations of existing methods. Unlike Fourier-based approaches that require labor-intensive sequential analysis of individual boundaries and selectively represent only high-amplitude regions, or spline-based methods that demand complex parameter selection for interpolation points, the proposed framework integrates curvature variance filtering with U-chord curvature calculation to enable automated, comprehensive, and noise-resistant characterization of grain boundary morphology. The curvature variance filtering adaptively determines smoothing parameters based on local curve properties, while the U-chord curvature method ensures rotational invariance and robustness against digitization errors. Four heat treatment processes were applied to GH4169 alloy, producing distinct grain boundary morphologies with mean curvature (MC) values ranging from 0.0625 to 0.1252. Controlled cooling alone (Process A) yielded predominantly straight boundaries (91.06% straight, 0.12% serrated), while re-dissolution treatment (Process D) produced the highest serration degree (58.81% straight, 3.53% serrated). The quantitative analysis reveals that dispersed δ-phase precipitation creates discrete pinning points, forming serrated boundaries with sharp curvature peaks, whereas dense, parallel δ-phase arrays at specific angles produce coordinated wavy undulations. This framework provides a reliable quantitative tool for optimizing heat treatment protocols to achieve target grain boundary configurations in nickel-based superalloys.