A Simpliﬁed Three-Phase Model of Equiaxed
Solidiﬁcation for the Prediction of Microstructure
and Macrosegregation in Castings
KNUT OMDAL TVEITO, AKASH PAKANATI, MOHAMMED M’HAMDI,
COMBEAU, and MIHA ZALOZ
Macrosegregation is a result of the interplay of various transport mechanisms, including natural
convection, solidiﬁcation shrinkage, and grain motion. Experimental observations also indicate
the impact of grain morphology, ranging from dendritic to globular, on macrosegregation
formation. To avoid the complexity arising due to modeling of an equiaxed dendritic grain, we
present the development of a simpliﬁed three-phase, multiscale equiaxed dendritic solidiﬁcation
model based on the volume-averaging method, which accounts for the above-mentioned
transport phenomena. The validity of the model is assessed by comparing it with the full
three-phase model without simpliﬁcations. It is then applied to qualitatively analyze the impact
of grain morphology on macrosegregation formation in an industrial scale direct chill cast
aluminum alloy ingot.
Ó The Minerals, Metals & Materials Society and ASM International 2018
is a severe defect in DC
casting of aluminum alloys. It refers to the solute
inhomogeneity at the scale of the casting and is a direct
result of microsegregation at the scale of the dendrite
arm spacing. As the solubility of solute elements in the
solid phase is lower than that in the liquid, solidiﬁcation
is accompanied by rejection of the solutes into the liquid
phase. Rejected solutes are transported due to the
relative motion of solid and liquid phases, which
eventually results in macrosegregation. Diﬀerent mech-
anisms contribute to this relative motion in DC casting:
solidiﬁcation shrinkage-induced ﬂow, thermal and solu-
tal natural convection, movement of the equiaxed
grains, and thermally induced deformations of the
mushy zone. For a detailed description of these mech-
anisms, the reader is referred to Reference 1.
Several modeling attempts have been made to
describe macrosegregation formation.
researchers attempted to numerically analyze the for-
mation of macrosegregation in DC casting
models based on the volume averaging method.
commonly agreed that accounting for grain motion is
important in order to provide a sound description of
macrosegregation formation. Reddy and Beckermann
made the ﬁrst attempts to account for the impact of
grain motion on macrosegregation formation assuming
spherical grains. In DC casting, both globular and
dendritic grain morphologies can be observed.
Simpliﬁcations of the dendritic morphology by consid-
ering globular grains in numerical models resulted in
large discrepancies between model predictions and
Rappaz and The
were the ﬁrst
to propose a multiscale diﬀusion model to numerically
simulate equiaxed dendritic solidiﬁcation in castings
accounting for grain morphology. To accurately
describe the growth of dendritic grains, they introduced
the notion of the dendrite envelope and of three
hydrodynamic phases—solid, intragranular (also called
interdendritic) liquid, and extragranular (also called
extradendritic) liquid. Wang and Beckermann
introduced these ideas into volume-averaging multi-
phase models and proposed the ﬁrst model of equiaxed
dendritic solidiﬁcation that accounted for grain mor-
phology in the presence of convection and grain motion.
Wu and Ludwig
proposed a 5-phase solidiﬁcation
model by adding two hydrodynamic phases to the three
thermodynamic phases. Vreeman et al.
KNUT OMDAL TVEITO and AKASH PAKANATI are with the
Department of Materials Technology, NTNU, 7491 Trondheim,
Norway. Conatct e-mail: firstname.lastname@example.org MOHAMMED
M’HAMDI is with the Department of Materials Technology, NTNU
and also with SINTEF Materials and Chemistry, 0314 Oslo, Norway.
COMBEAU and MIHA ZALOZ
NIK are with the Institut
Jean Lamour, CNRS – Universite
de Lorraine, 2 Alle
BP 50840, 54011 Nancy Cedex, France and also with the Laboratory
of Excellence on Design of Alloy Metals for low-mAss Structures
de Lorraine, Lorraine, France.
Manuscript submitted January 8, 2018.
Article published online April 19, 2018
2778—VOLUME 49A, JULY 2018 METALLURGICAL AND MATERIALS TRANSACTIONS A