Growth Instability During Nonuniform Directional Solidification of Pure Metals

Solidification of a pure metal against a flat mold surface is examined using a nonuniform thermohypoelastic beam. Heat is removed with a spatially periodic heat flux superimposed onto uniform cooling, which leads to irregular growth of the casting. The associated nonuniform temperature field also produces nonuniform deformation in the casting which in time may lead to air gap nucleation along the mold/casting interface. Air gap nucleation is defined as the circumstance where the local mold/casting interface pressure falls to zero. Unstable growth occurs when such air gaps nucleate beneath thickness minima, thus further reducing heat transfer at these positions, and dramatically amplifying the existing thickness nonuniformity. The time to onset of instability depends upon material properties such as density, latent heat, thermal conductivity, elastic constants, and coefficient of thermal expansion as well as upon process parameters such as cooling rate, fluid pressure, and wavelength of the periodic heat flux.