Effect of cooling rate on carbides in directionally solidified nickel-based single crystal superalloy: X-ray tomography and U-net CNN quantification

X-ray computed microtomography (X-CT) and U-net convolutional neural network (U-net CNN) were used to characterize and segment the three-dimensional structure of MC and M₂₃C₆ carbides. The volume fraction of MC and M₂₃C₆ carbides, the percentage of MC carbides in all carbides, and the size of MC carbides were statistically analyzed. We found that the MC carbides were mainly distributed at the interface between γ dendrites and the interdendritic γ’ phase. The M₂₃C₆ carbide grows from the MC carbide to the interdendritic region. Combing with the finite element simulation of the directional solidification process, it was shown that the cooling rate had a significant influence on the carbide growth of superalloys. The faster the cooling rate, the smaller the MC carbides volume percentage and size, the larger the M₂₃C₆ carbides volume percentage, and the faster carbides growth. Based on the simulation results and thermodynamic calculations, we developed the relationship between the carbon addition, cooling rate, and volume fraction of carbides by regression models. The results show that the volume fraction of carbides in nickel-based single crystal superalloys increases linearly with the increase of carbon content and gradually increases with the rise of cooling rates.