Equilibrium partition ratios, densities, and transport phenomena in nickel-base superalloys

Abstract

To simulate transport phenomena, macrosegregation and segregation defects known as "freckles" during directional solidification of Ni-base superalloys, numerical modeling can be used; hence it is essential to have reasonably accurate values of the thermodynamic and transport properties for the alloys. In this research, therefore, the equilibrium partition ratios of the solutes in the Ni-Al-Ta-Cr quaternary system, as a model alloy, were measured, and the solid- and liquid-densities in Ni-base superalloys. were estimated. Also, the importance of these properties on the sensitivity of the results of numerical simulations was studied. The partition ratios apply to equilibria between melts and gamma-phase in the range of 1615 K to 1694 K, and it was found that the equilibrium partition ratio of Ta varies from approximately 0.6 at dilute Ta to 0.85 at 17 wt.% Ta. For the same range of Ta-contents, the partition ratios of Al and Cr vary much less and range from about 0.92 to 0.96. In addition to the partition ratios, the liquidus temperatures of the liquid in equilibrium with γ in the Ni-Al-Ta-Cr system were estimated with a multidimensional regression analysis. To calculate the densities of solid Ni-base superalloys as functions of temperature and composition, lattice parameters at 20°C and coefficients of thermal expansion (CTEs) were estimated by combining available data. The CTEs calculated from the regressions result in densities that are within 0.5% error or less for seventeen alloys. To estimate the densities of liquid Ni-base superalloys, the densities and temperature coefficients of density of the liquid transition-metals, which are used as alloy elements in Ni-base superalloys, were applied to a simple correlation. By using this approach, the estimates of the liquid densities of five Ni-base superalloys agree with the measured values to ±2.5%. Finally, the importance of using reasonably accurate estimates of the transport properties was illustrated by simulations of the thermosolutal convection and macrosegregation during solidification in a directionally solidified Ni-base alloy casting. In these simulations, the sensitivities of equilibrium partition ratio, solutal expansion coefficient and viscosity on the simulation of macrosegregation were determined. It was found that the segregation and convection are sensitive to the properties, especially to the equilibrium partition ratio.