The probabilistic distribution model of the γ′ phase in nickel-based superalloys

This study comprehensively analyzes the probabilistic distribution model of the γ′ phase in nickel-based superalloys . While the size distribution of the three-dimensional (3D) γ′ phase follows a log-normal distribution, the size distribution of the two-dimensional (2D) γ′ phase observed in transmission electron microscopy (TEM) images depends on the sample thickness t . As the thickness t approaches infinity, the 2D size distribution converges to a log-normal distribution. Conversely, when t = 0, it corresponds to the size distribution on the dislocation slip plane. Therefore, for polycrystalline nickel-based superalloys , strength predictions of γ′ hardening should employ the probability density function of the 2D γ′ phase size distribution on the dislocation slip plane, accounting for its probabilistic distribution.