An improved Rayleigh number criterion for freckle prediction incorporating the effect of carbides

Freckle chains are lines of equiaxed grains which may form during the directional solidification of single crystal Ni-base superalloys. In single crystal alloys freckles form as a result of convective flow of the lighter interdendritic liquid that tends to flow upward towards the heavier bulk composition liquid. Both the interdendritic liquid density and the permeability of the mushy zone affect freckle formation. The Rayleigh number, which is the ratio of the buoyancy to the drag forces in the liquid, is used to assess the likelihood of freckle occurrence. The addition of carbon has been shown to significantly reduce the number of solidification defects, including freckles. The formation of carbides in the interdendritic region will influence both the effective density of the fluid and the structure’s permeability. Using a combination of mesoscale solidification modeling and thermodynamic calculations, these two effects were incorporated into an improved Rayleigh number criterion and compared to experimentally observed freckles as a function of the carbon content. Introduction The formation of defects during the directional solidification of single crystal Ni-base superalloys can have a significant impact on fatigue and creep properties of some critical components such as turbine blades and discs for aeroengines. Freckles are chains of equiaxed grains preferentially appearing at the component’s surface. The formation of freckles has been attributed to the thermal solutal convection in the mushy zone. The evolution of convection currents in the semi-solid (mushy) layer is influenced by the component geometry, the alloy chemical composition and the primary processing parameters such as the thermal gradient and the solidification velocity [1]. The channels resulting from thermosolutal convection in the mushy zone are associated with a variation in density originating from interdendritic segregation. Lighter elements tend to segregate into the interdendritic liquid making it less dense than the bulk liquid. This leads to density-driven flow in the interdendritic region which was proved to initiate freckles. A widely accepted criterion for the assessment of the alloy’s freckling propensity is the calculation of a mushy zone Rayleigh number. The main advantages of using the Rayleigh number are that it combines the effects of alloy composition and processing parameters. However, it does not take into account the component’s geometry. A typical expression describing the Rayleigh number is given by [2]: