A Permeability-Based Model for Prediction of Freckling in Nickel Superalloy Single-Crystal Castings

Nickel superalloy single-crystal castings with dimensions representative of aero engine high-pressure turbine blades were manufactured to two casting conditions. Under conditions of low thermal gradient freckle chains of randomly oriented secondary grains arose on external casting surfaces. The number of freckle chains depended on the orientation of the crystal relative to the external casting surface. A permeability-based model of inward flow conductance through the semi-solid to sustain an upward rising plume of solute-enriched liquid at the mould wall forming a freckle is developed. The model accounts for both extrinsic casting and intrinsic material factors. It is discovered that by inclusion of the anisotropic permeability arising from the differing crystal orientations within individual castings and application of a new criterion for flow in the semi-solid, conductance to flow within the semi-solid local to the plume explains almost all variation in the number of freckles formed between individual castings. The model is applied to assess the effect of extrinsic and intrinsic parameters on flow conductance, ranking their relative significance.