Existence of Critical Wavelength for Gap Nucleation in Solidification on a Rigid Mold

Previous theoretical models of pure metal solidification on a patterned mold surface neglected either the thermal capacitance of the solidifying shell material (which is equivalent to assume that thermal diffusivity is infinitely large) or interfacial coupling between the thermal and mechanical fields along the mold-shell interface. In the present work, however, we examine the combined effects of thermomechanical coupling at the mold-shell interface and non-negligible thermal capacitance (or finite thermal diffusivity) of the solidifying shell material during solidification of pure aluminum and iron shells on a rigid, perfectly conducting mold. It is assumed that the mold surface has a sinusoidal corrugation with a small aspect ratio, and the surface is perfectly wet by the molten metal which is initially at its melting temperature. The undulatory geometry of the mold surface lead to nonuniform heat extraction and hence initiated a nonuniform evolving distortion of the metal shell. This distortion produces a critical wavelength that corresponds to the situation where both the contact pressure and its time derivative simultaneously fall to zero. This critical mold surface wavelength serves as a cutoff between those wavelengths that lead to gap nucleation in the troughs and those that lead to gap nucleation in the crests. The conditions for gap nucleation in the mold surface troughs are examined since a corresponding increase in contact pressure at the crests signals the possibility of a growth instability in the metal shell at later stages in the process. Gap nucleation times, associated mean shell thicknesses, and critical wavelengths are calculated for pure aluminum and pure iron shells under identical process conditions. It is found that the iron shell nucleates gaps faster than an aluminum shell, with the associated critical wavelengths of iron being substantially larger than those for aluminum.