Freezing Range Effect on Shell Growth Instability During Alloy Solidification

During metal casting, nonuniform thermal strains due to small spatial perturbations in the cooling profile may lead to a condition of growth instability. This condition is one where the metal shell thickness becomes highly nonuniform due to the formation of microscopic air gaps along the mold surface. Documented experimental work with iron-carbon and aluminum alloy systems provides qualitative evidence that the freezing range width has an important influence on the macromorphology of the freezing front and hence the shell thickness. In this paper, we develop a thermomechanical model which points to a possible mechanism for growth instability during the solidification of a three-phase system where a small, spatially periodic cooling profile is superposed onto uniform cooling. This extends earlier work on two-phase (pure metal) systems. Temperature fields and shell growth are first calculated using perturbation theory, and then the associated thermal stresses and strains are determined from a hypoelastic constitutive law. The evolution of the shell/mold contact pressure beneath a shell thickness minimum is examined as a function of the freezing range width, and the onset of growth instability is assumed to occur as the contact pressure drops to zero indicating possible air gap nucleation. Under fixed cooling conditions, instability increases with freezing range width at small liquid metal pressures, decreases with freezing range width at somewhat larger liquid metal pressures, and disappears at still larger pressures.