A permeability model for hot cracking susceptibility prediction across near-equilibrium to rapid solidification conditions

The permeability of the mushy zone during alloy solidification is important for determining hot cracking susceptibility. The widely used permeability model is the Carman–Kozeny model, which is applicable under near-equilibrium solidification conditions when the secondary dendritic spacing is well-defined. However, its behavior becomes unknown when cellular dendrites without side arms form under rapid solidification conditions. In this work, we develop a permeability model for hot cracking susceptibility prediction over a wide range of solidification conditions with different mushy zone structures. A permeability formulation as a function of liquid channel spacing and liquid volume fraction is first obtained for uniform inter-plates. The formulation is generalized by considering morphology variation along liquid channels and is validated by direct modeling permeability of different microstructures including cellular, columnar dendrite, and grain boundary regions with CFD simulations and by similarity theory. This model is used to calculate hot cracking susceptibility in Al-Cu alloys under different concentrations, grain boundary energies, growth types, and grain size conditions by combining multi-phase field simulations and the RDG model. We show that in addition to the typical Λ -curve, a secondary peak is identified at larger grain sizes and higher concentrations, which is consistent with experiments. This secondary peak is related to single grain permeability which is hindered by the first peak induced by grain boundary when grain size is small. These results demonstrated that the permeability model is applicable to assess the hot cracking susceptibility over a wide range of solidification conditions.