Critical Wavelengths for Gap Nucleation in Solidification— Part II: Results for Selected Mold-Shell Material Combinations

In this second part, we examine the contact pressure ratio, $Ptr,$ at the lowest points of the upper mold surface troughs in a directional solidification process using the theoretical methodology developed in Part I. Since there is ample experimental evidence that the mold surface topography affects gap nucleation at the mold-shell interface and the uniformity of the shell, we explore how the wavelength of the upper mold surface impacts the evolution of $Ptr$ for specific material combinations and process parameters. For this purpose, the mold-shell materials are assumed to be combinations of four pure materials, viz., aluminum, copper, iron and lead: these materials offer a wide range of thermal and mechanical properties. Critical wavelengths, for which $Ptr$ and its time derivative simultaneously equal zero, are predicted for all mold-shell material combinations. The theoretical model also predicts the existence of wavelength bands which are delimited by upper and lower critical wavelengths. All wavelengths that lie within the bands lead to gap nucleation, whereas all wavelengths that lie outside of the bands do not. The effects of distortivity ratio, which is a measure of the extent to which the mold-shell interface deforms under a given thermal loading, and selected process parameters (such as the mean mold thickness, contact resistance, and pressure) on bandwidth size, are considered in detail. Extensions of the present work to more sophisticated models that might lead to rudimentary mold topography design criteria are considered. [S0021-8936(00)03301-8]