Freckle prediction model incorporating geometrical effects for Ni-based single-crystal superalloy components

A freckle is a grain defect frequently found in Ni-based single-crystal (SC) superalloy castings resulting in a high scrap rate. A precise prediction of the defect before production is of great importance, especially for the complex-shaped blades and vanes. Without reckoning geometrical effects, the state-of-the-art Rayleigh number (Ra) model fails to accurately forecast the freckle formation positions. In this study, a novel Ra-based mathematical model was proposed. It not only shortened the calculation period and eliminated the physically meaningless at the singularity of the existing model, but also quantified the geometrical effects. Using the model, the Ra at every position of SC castings was calculated, which can be used to evaluate the freckling tendency of the whole casting and locate the specific positions of the freckling risk zone. A freckle-free approximate critical Rayleigh number about 1.5 was determined. A highly consistent and accurate prediction of this model was validated by comparing it with the experiments using complex-shaped SC castings, which suggests its great prospects for industrial application.