Combined effects of mold deformation and shell thermal capacity on growth instability during unidirectional solidification of pure metals

Abstract

Previous models of thermomechanically induced freezing front growth instability have neglected either the mold distortion or the thermal capacitance of the solidifying shell material. While these assumptions are useful in providing insight into solidification thermomechanics, they fail to account for the combined effects of the mold deformation and the thermal capacity of the shell material. In this paper, growth instability during solidification of pure metals is reexamined under the assumption that the shell material with nonnegligible thermal capacitance solidifies on a deformable mold with a mean finite thickness. The mold is assumed to have infinitely large thermal diffusivity, and a sinusoidal surface microgeometry for which the ratio of the amplitude to the wavelength in much less than one. This makes the aspect ratio a convenient perturbation parameter. The contact pressure in the troughs of the mold surface is calculated for different mold-shell material combinations that consist of pure copper, aluminum, or iron. The influence of mold surface wavelength and mean contact pressure on shell growth is examined for these cases. The effects of mold thickness on gap nucteation times for selected wavelengths are investigated. The role of the thermal capacitance of the solidifying shell material when combined with thermoelastic distortion of the mold is examined through qualitative comparisons between results from the present model and those from previous models. Conclusions are drawn about the relative significance of these factors on the unstable growth of the shell thickness.King Saud Universit