SOLIDIFICATION OF A PURE METAL WITH FINITE THERMAL CAPACITANCE ON A SINUSOIDAL MOLD SURFACE

Abstract

Previous models of mold microgeometry-induced gap nucleation during pure metal solidification neglected the thermal capacitance of the solidifying shell: this is equivalent to the assumption that the shell has a small Stefan number. Although this assumption leads to steady heat conduction in the shell, and hence simplifies the solution for the thermal field, the corresponding assumption of a small Stefan number material is generally not appropriate for metals. In the present work, we remove the small Stefan number restriction used in a previous model for solidification of a pure metal on a rigid, perfectly conducting mold. The mold has a sinusoidal surface microgeometry for which the ratio of the amplitude to the wavelength is much less than one. This makes the aspect ratio a convenient perturbation parameter. Molten metal initially at its fusion temperature is assumed to wet the mold surface perfectly, which is held a constant temperature below the fusion temperature. The temperature field in the growing metal shell is numerically evaluated, and the instantaneous temperature field is incorporated into an analytical solution for the stress field in the shell. The evolving thermomechanical distortion of the shell is modeled assuming that the shell material follows a thermohypoelastic constitutive law that is a rate formulation of thermoelasticity. The contact pressure profile at the shell/asperity interface, which is indicative of shell distortion due to the asperity geometry, is obtained from the stress field. The effects of the mold wavelength and shell thermal capacitance on the contact pressure, temporal and spatial evolution of gap nucleation at the shell/mold interface, and mean shell thickness are examined for pure aluminum and iron shells.