Mold Surface Wavelength Effect on Gap Nucleation in Solidification

Abstract

A theoretical model that predicts the time and position of gap nucleation along the metal-shell interface during solidification of a pure metal on a sinusoidal mold surface is presented. The ratio of the mold surface amplitude to its wavelength is assumed to be much less than one and hence it is used as a perturbation parameter in the analysis. The molten metal perfectly wets the mold surface prior to the beginning of solidification, and this leads to a corresponding undulation of the metal shell thickness. A nonuniform distortion develops in the shell due to the lateral temperature gradient induced by the modest spatial variation of the mold surface. This causes a variation in the contact pressure so that the growing shell pushes harder on the mold in some places, but in other places it starts to pull away from the mold. Gap nucleation is assumed to occur when the contact pressure falls to zero. The conditions for gap nucleation in the surface troughs are examined since a corresponding increase in pressure at the crests signals the possibility of a growth instability in the shell at later stages of the process. A series expansion for the contact pressure is presented which is appropriate for early solidification times. This reveals how the contact pressure varies with the mold surface wavelength. This solution is compared with a numerical solution for the contact pressure that is not limited to early solidification times. Gap nucleation times are calculated for pure aluminum and iron shells for selected mold surface wavelengths. The associated mean shell thicknesses are calculated as a function of wavelength at selected mean molten metal pressures.