A THERMOMECHANICAL MODEL OF SOLIDIFICATION ON A MOLD MOVING WITH CONSTANT VELOCITY
Titel:
A THERMOMECHANICAL MODEL OF SOLIDIFICATION ON A MOLD MOVING WITH CONSTANT VELOCITY
Auteur:
Howarth, John A. Hector, Louis G.
Verschenen in:
Journal of thermal stresses
Paginering:
Jaargang 24 (2001) nr. 10 pagina's 937-985
Jaar:
2001-10-01
Inhoud:
A thermomechanical model of pure metal solidification on a moving mold plate is considered. The goal of the model is to obtain a formula for the contact pressure at the shell/mold interface as the mold moves into the molten liquid. From the contact pressure it is possible to infer the effects of the mold velocity and the mold microgeometry on the time and location of gap nucleation which results from irregular distortion of the shell as it grows from the melt. The mold, which moves at a constant velocity into the molten liquid, has a sinusoidal surface with a low aspect ratio: this means that its wavelength greatly exceeds its amplitude. The mold is of infinite area and is assumed to be perfectly conducting and thermomechanically rigid. We therefore neglect the complexities associated with the physics of edge constraints and/or free boundaries of the solidifying shell and the interacting distortions between deformable mold and shell materials along their interface. The ratio of the velocity of the solid/liquid interface to the mold velocity is identified as another dimensionless parameter in the analysis. In order to arrive at an analytical solution for the contact pressure along the shell/mold interface, we assume that this parameter is small. This makes the velocity ratio a convenient perturbation parameter for the analysis of thermomechanical distortion of the thin shell material as it grows from the melt. This necessarily limits the analysis to situations where the mold moves at faster rather than slower speeds. It is assumed that there is zero tangential shear stress between the fluid and the solidifying shell. As the molten liquid flows over the mold, it perfectly wets the surface. This precludes wetting effects due to surface tension. A hypoelastic constitutive law, which is a rate formulation of thermoelasticity, is assumed to govern deformation of the shell as it grows from the molten liquid. Latent heat liberated at the freezing front is extracted across a constant contact resistance at the shell/mold interface. Peculiar fluid motion at the tip is neglected. A solution for the contact pressure that is valid near the liquid surface (i.e., the meniscus) is derived from the main theoretical developments. Beyond the time of gap nucleation at the shell/mold interface, the model is no longer valid since it cannot account for gross distortion of the shell (i.e., distortions that greatly exceed the spatial perturbations considered in the model).
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