Lg. Hector et al., FREEZING RANGE EFFECT ON SHELL GROWTH INSTABILITY DURING ALLOY SOLIDIFICATION, Journal of applied mechanics, 63(3), 1996, pp. 594-602
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 be
comes highly nonuniform due to the formation of microscopic air gaps a
long the mold surface. Documented experimental work with iron-carbon a
nd aluminum alloy systems provides qualitative evidence that the freez
ing range width has an important influence on the macromorphology of t
he freezing of the freezing front and hence the shell thickness. In th
is paper, we develop a thermomechanical model which points to a possib
le mechanism for growth instability during the solidification of a thr
ee-phase system where a small, spatially periodic cooling profile is s
uperposed onto uniform cooling. This extends earlier work on two-phase
(pure metal) systems. Temperature fields and shell growth are first c
alculated using perturbation theory, and then the associated thermal s
tresses and strains are determined from a hypoelastic constitutive law
. The evolution of the shell/mold contact pressure beneath a shell thi
ckness 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 wi
dth at small liquid metal pressures, decreases with freezing range wid
th at somewhat large liquid metal pressures, and disappears at still l
arger pressures.