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New freckle criterion for technical remelting processes
Bernd Böttger, Georg J. Schmitz, Franz-Josef Wahlers, Jutta Klöwer, Jürgen Tewes and Bodo Gehrmann
Freckles present a serious type of defects in technical solidification processes like Electro Slag Remelting (ESR) or Vacuum Arc Remelting (VAR). They limit the maximum ingot size for many grades of steels and superalloys. Modelling of freckle formation thus is an important task for optimizing industrial remelting processes. Essentially, most freckle models published by now are based on a Rayleigh criterion. They are inspired by the classical concept that freckles are caused by an inversion of the liquid density in the semisolid region. Plumes of the lighter segregated liquid evolve through perturbation of the metastable layering of the melt in the mushy zone, a mechanism which motivates its description via a Rayleigh criterion. Such models, however, are not suitable in case of alloys which do not exhibit a liquid density inversion. These alloys should have a stable layering in the mushy zone and, accordingly, should not be prone to freckle formation. However, freckle formation is observed also in technical remelting processes of such alloys as a consequence of curved solidification fronts. The present paper describes a criterion which – instead of using a Rayleigh number – is based on the evaluation of the non-isothermal component of an instantaneous down-hill flow of heavy segregated melt in a melt pool with axial symmetry. Given the knowledge of the exact pool geometry and the shape and properties of the mushy zone, the occurrence of freckles can be predicted. A preferred initiation of freckles at mid radius is found for typical ESR pool profiles, without the need of assuming an anisotropic permeability of the mushy zone. The model equations are derived and discussed for simplified pool geometries. The new approach is compared to classical criteria, and implications for a better understanding of freckle formation in technical remelting processes are discussed.
Keywords: Freckle, ESR, VAR, alloy 718, downhill flow, pool profile, liquid density.