Alloy casting solidification processes
involve many physical phenomena such
as chemistry variation, phase transformation,
heat transfer, fluid flow, microstructure
evolution, and mechanical
stress.1 Simulation technologies are
applied extensively in casting industries
to understand the effects of these
phenomena on the formation of defects
and on the final mechanical properties
of the castings. As of today, defect prediction
is still one of the main purposes
for casting solidification simulation.
In this paper, we will first present the
commonly used microstructure simulation
methods, then discuss the predictions
of the major defects of a casting,
such as porosity, hot tearing, and macrosegregation.
The modeling of casting
solidification can be chained with
later stages of heat treatment such that
the resultant microstructure, defects,
and mechanical state will be used as
the initial conditions of the subsequent
processes, ensuring the tracking of the
component history and maintaining a
high level of accuracy across metallurgical
|HOW WOULD YOU...
…describe the overall significance
of this paper?
In this paper, some commonly used
microstructure simulation methods on
casting processing are reviewed. The
predictions for the major defects of a
casting, such as porosity, hot tearing,
and macrosegregation, are discussed.
…describe this work to a
materials science and engineering
professional with no experience in
your technical specialty?
The commonly used models on
casting solidification processing
are reviewed. This includes the
predictions of microstructure and
defects. Hopefully it will give a
general idea how modeling is applied
in casting industries.
…describe this work to a
The brief introduction on the
solidification process and its
modeling can give some overall
ideas on the integration of new
technologies and old processing.
The purpose of solidification micromodeling
is to predict the microstructure
developed during the casting
processes. Understanding the solidification
process and the resultant microstructure
will greatly facilitate casting
design and quality control and eventually
to predict mechanical properties.2-6
There are several ways of simulating
the microstructure formation during alloy
solidification, such as the deterministic
method and the stochastic method.
For the deterministic method, the density
of grains that have nucleated in the
bulk liquid at a given moment during solidification is described as a deterministic
function (e.g. a function of
undercooling). The stochastic method
uses probabilistic means to predict the
nucleation and growth of grains, including
the stochastic distribution of
nucleation locations and the stochastic
selection of grain orientation, and so on.
Modeling of solidification processes
and microstructural features has benefited
from the introduction of averaged
conservation equations and the coupling
of these equations with microscopic
models of solidification. When
conservation equations are averaged
over the liquid and solid phases, the interfacial
continuity condition automatically
vanishes and average entities (e.g.
mean temperature or solute concentration)
appear. Rappaz et al.7–9 proposed
a model using averaging methods to
predict the growth of equiaxed grains
under isothermal conditions. Rappaz
and Boettinger2 studied the growth of
an equiaxed multicomponent dendrite.
In their study, for each element, the supersaturation
is described as Equation
1, where j=1, n is the solute element,
cl,j* is the tip liquid concentration, Co,j is the nominal concentration, and kj is the partition coefficient. The Peclet
number is defined as Pej = Rv/2Dj,
where Dj is the diffusion coefficient, R
is the tip radius, and v is the tip velocity.
The Ivanstsov function is defined as:
Iv(Pe) = Pe × exp(Pe) × E1(Pe), where
E1(Pe) is the first exponential integral.
Assuming growth at the marginal
stability limit, the dendrite radius is
calculated by Equation 2, where Γ is
the Gibbs–Thomson coefficient, and m is the liquidus slope.
Please refer to the original Reference
2 for details about the derivation
of the equations above. The secondary
dendrite arm spacing (SDAS) is calculated
by Equation 3 and Equation 4.
Based on the equations, the solidification
of multicomponent casting can be
predicted. The averaged microstructure,
such as grain size and secondary
dendrite arm spacing, can be calculated
based on the chemistry and cooling
An experiment of an A357 sand casting
with chills on some locations is performed
to validate the micromodeling
above. Figure 1 illustrates the experimental
setup. Six cast iron chills are
used, and they are coated with a light
layer of sand to prevent blows from
gasses and condensation in this model.
With such a setup, cooling conditions
dramatically varied for different locations
throughout the casting.
Based on the micro-model presented,
the solidification process is simulated.
As mentioned earlier, because
of the use of chills, the solidification
times are very different across the casting.
For the chilled section, the solidification
time is as fast as 29 seconds. For
a location which is not chilled but with
similar wall thickness, the solidification
time is 242 seconds, which is one
order of magnitude longer. Because of
the different solidification rates, the
microstructure varies in the casting.
For this prediction, it is assumed that
only equiaxed dendrites are formed in
the primary phase, which is the case
based on the experimental observation.
Figure 2 shows the primary dendritic
grain radius. For a faster cooling rate,
the dendrite grain size is smaller.
The secondary arm spaces were
measured in the experiment. For comparison,
Figure 3 shows the measured
and predicted secondary arm spacing at
two locations, one on the chilled section
and the other one on an unchilled
section. The exact values can be found
in Table I. For the chilled section, the
measured SDAS is 0.00132? and corresponding
prediction is 0.0014?, a difference
of only 6%. For the unchilled
section, the SDAS is larger but the difference
between the measured and predicted
ones is even smaller, being 4.3%.
Based on Equation 3, the secondary
dendrite arm spacing is proportional to
the one third power of the solidification
time. This can be verified by the values
of the secondary arm spacing and solidification
time at those two locations
numerically as well. The solidification
time is around 9 times different, which
corresponds to roughly three times difference
of secondary arm spacing
There is a large amount of eutectic
phase formed during solidification for
this A357 alloy. The current micromodeling
can predict the microstructure of
the eutectic phase as well. Because of
the limitation of the paper length, these
results are not presented here.
Based on the microstructure, the ascast
room temperature yield strength
can be calculated, as shown in Figure
4. With the finer microstructure in the
chilled section because of the faster
cooling, the yield strength is higher.
But the difference is relatively small
compared to that of SDAS and solidification
time. The yield strength difference
between the chilled section,
83.8 MPa, and the unchilled section,
74.8 MPa, is less than 10 MPa, around
10%. Even though most in service castings
are heat treated, the prediction of
as-cast microstructure and mechanical
properties are still important. First, the
as-cast microstructure and properties
affect the final structure and properties.
And more importantly, as-cast properties
are critical for stress analysis during
the casting process.
Beside the deterministic micromodeling,
other models have been studied
extensively as well, such as the stochastic
method. One example is the
cellular automaton (CA) model. The
algorithm of CA models is to describe
the discrete spatial and/or temporal
evolution of complex systems by applying
deterministic or probabilistic
transformation rules to the sites of a
lattice. In a CA model, the simulated
domain is divided into a grid of cells,
and each cell works as a small independent
automaton. Variables and state
indices are attributed to each cell, and
a neighborhood configuration is also
associated with it. The time is divided
into finite steps. At a given time step,
each cell automaton checks the variables
and state indices of itself and its
neighbors at the previous time step,
and then updates the results at the present
step according to the pre-defined
transition rules. By iterating this operation
with each time step, the evolution
of the variables and state indices of the
whole system is obtained.
Several CA models have been developed
over the years for the prediction
of microstructure formation in
casting.10–14 The CA model is usually
coupled with a finite element heat flow
solver, such as the Cellular Automaton—Finite Element (CAFÉ) model
developed by Rappaz and colleagues.
CAFÉ is particularly well suited to
tracking the development of a columnar
dendritic front in an undercooled
liquid at the scale of the casting.12,13
The CA algorithm can be used to simulate
nucleation and growth of grains.
This model can be used to predict cellular to equiaxed transition (CET) in
alloys. Although these models do not
directly describe the complicated nature
of the solid/liquid interface that
defines the dendritic microstructure,
the crystallographic orientation of the
grains as well as the effect of the fluid
flow can be accounted for to calculate
the undercooling of the mushy zone
growth front. Two- and three-dimensional
CAFÉ models were successfully
applied to predict features such
as the columnar-to-equiaxed transition
observed in aluminum-silicon alloys,12
the selection of a single grain and its
crystallographic orientation due to the
competition among columnar grains
taking place while directionally solidifying
a superalloy as is shown in Figure
5,13 as well as the effect of the fluid
flow on the fiber texture selected during
columnar growth.14 Coupled with
the macrosegregation that has been developed,15 it thus provides an advanced
CAFÉ model to account for structure
formation compared to purely macroscopic
models developed previously,
e.g. References 16–18.
While the CA methods produce
realistic-looking dendritic growth patterns
and have resulted in much insight
into the CET, some questions remain
regarding their accuracy. For example,
the independence of the results on the
numerical grid size is rarely demonstrated.
Furthermore, the CA techniques
often rely on relatively arbitrary
rules for incorporating the effects
of crystallographic orientation while
propagating the solid–liquid interface.
It is now well accepted that dendritic
growth of crystalline materials depends
very sensitively on the surface energy
An alternative technique for investigating
microstructure formation during
solidification is the phase field method.
Phase field models were first developed
for simulating equiaxed growth under
isothermal conditions.21,22 A desirable
extension of the model was to study the
effect of heat flow due to the release of
latent heat. A simplified approach was
proposed in which the temperature was
assumed to remain spatially uniform
at each instant, and a global cooling
rate was imposed with consideration
of the heat extraction rate and increase
of the fraction of solid.23 The attempt
to model non-isothermal dendritic solidification
of a binary alloy was made
by Loginova et al. by solving both the
solute and heat diffusion equations and
considering the release of latent heat
as well.24 Besides equiaxed growth in
the supersaturated liquid, the phase
field model was also applied to the
simulation of directional solidification,
under well-defined thermal conditions.25,26 The phase field model has
also been used to simulate the competitive
growth between grains with different
misorientations with respect to
the thermal gradient.27 Further development
in phase field models includes
the extension into three dimensions,28,29
and multi-component systems.30,31
Usually a regular grid composed of
square elements is used in the phase
field models,22,23 but an unstructured
mesh composed of triangular elements
has also been used, which enables the
phase field method to be applicable in
a domain with complex geometrical
shape and also in a large scale. From
a physical point of view, the phase
field method requires knowledge of the
physical nature of the liquid–solid interface.
However, little is known about
its true structure. Using Lennard–Jones
potentials, molecular dynamics simulations
of the transition in atomic positions
across an interface have suggested
that the interface width extends
over several atomic dimensions.32 At
present, it is difficult to obtain usable
simulations of dendritic growth with
interface thickness in this range due
to the limitations of computational resources.
Thus the interface width will
be a parameter that affects the results
of the phase field method. It should be
realized that in the limit as the interface
thickness approaches zero the phase
field equations converge to the sharp
interface formulation.33,34 In contrast
to CA models which adopt a pseudo front-tracking technique, phase field
models express the solid–liquid interface
as a transitional layer which usually
spreads over several cells.
The diffusion equation for heat and
solute can be solved without tracking
the phase interface using a phase-field
variable and a corresponding governing
equation to describe the state in a
material as a function of position and
time. This method has been used extensively
to predict dendritic, eutectic, and
peritetic growth in alloys, and solute
trapping during rapid solidification.35
Figure 6 shows one such example. The
interface between liquid and solid can
be described by a smooth but highly
localized change of a variable between
fixed values such as 0 and 1 to represent
solid and liquid phases. The problem of
applying boundary conditions at an interface
whose location is an unknown
can be avoided. Phase field models
have recently become very popular for
the simulation of microstructure evolution
during solidification processes.36–40
While these models address the evolution
of a solid–liquid interface using
only one phase field parameter, interaction
of more than two phases or grains,
and consequently the occurrence of
triple junctions, needs to be included
into the multiphase field approach.41–44
The deterministic model is capable
of tracking the evolution of the macroscale
or average variables, e.g. average
temperature and the total fraction of
solid, but it cannot simulate the structure
of grains. CA models can simulate
the macro-scale and meso-scale grain
structures, but they have difficulty resolving
the microstructure. The phase
field method can well reproduce the
microstructure of dendritic grains.
However, with the current computational
power, phase field models can
only work well on a very small scale
(up to hundreds of μm). The typical
scale of laboratory experiments is
1 cm, and the scale of an industry problem
can be up to 1 m. Both of them are
beyond the capability of the phase field
method. In industry, for larger castings,
deterministic micromodeling still is a
Defects reduce the performance and
increase the cost of castings. There are
many kinds of casting defects. Those
defects are dependent on the chemistry
of alloys, casting design, and casting
processes. Defects can be related to
thermodynamics, fluid flow, thermal,
and/or stress. For most cases, all of
those phenomena are intertwined. It is
necessary to consider every aspect in
order to minimize defect formation.
In this section, we will discuss some
common casting defects in foundries,
which include porosity, macrosegregation,
and hot tearing.
Porosity formed in castings leads to
a decrease in the mechanical properties.45–51 This porosity may be a combined
result of solidification shrinkage
and gas evolution. They can occur
simultaneously when conditions are
such that both may exist in a solidifying
casting. One of the most effective
ways to minimize porosity defects is to
design a feeding system using porosity
prediction modeling. In such a way,
the model can determine the location
of porosity so that the feeding system
can be redesigned. This process is repeated
until porosity is minimized and
not likely to appear in the critical areas
of the castings.
There are many models which can
predict the shrinkage porosity from the
pressure drop during inter-dendritic
fluid flow.49–57 A comprehensive model
should calculate the shrinkage porosity,
gas porosity, and pore size.
As for many casting defects observed
in solidification processes, the
mushy zone is the source of porosity.
The basic mechanism of porosity formation
is pressure drop due to shrinkage
and gas segregation in the liquid.46,47,49 The liquid densities of many
alloys are lower than that of the solid
phase. Hence solidification shrinkage
happens due to the metal contraction
during the phase change. The dynamic
pressure within the liquid decreases
because of the contraction and sometimes
cannot be compensated by the
metallostatic pressure associated with
the height of the liquid metal. The decrease
of pressure lowers the solubility
of gas dissolved in the liquid. If the
liquid becomes supersaturated, then
bubbles can precipitate.58 Most liquid
metals can dissolve some amount of
gas. The solubility of gases in the solid
phase is usually much smaller than
that in the liquid phase. Normally the
rejected gases during solidification do
not have enough time to escape from
the mushy zone to the ambient air. Being
trapped within the interdendritic
liquid, the gas can supersaturate the
liquid and eventually precipitate in the
form of pores if nucleation conditions
are met. The formation of bubbles requires
overcoming the surface tension.59 Homogeneous nucleation is
very difficult. In castings, nucleation of
pores can be expected to occur primarily
on heterogeneous nucleation sites,
such as the solid–liquid interface and
Generally speaking, there are two
ways to predict the level of porosity in
castings. One is a parametric method
derived from first principles by using
a feeding resistance criteria function
combined with macroscopic heat flow
calculations.61–64 Parametric models
are easy to apply to shaped castings
and have been mainly directed at the
prediction of centerline shrinkage.
Another approach is a direct simulation
method.53–57,59 They usually derive
governing equations based on a set of
simplifying assumptions and solve the
resulting equations numerically. By
combining the cellular automata technique,
some models can not only predict
the percentage porosity but also
the size, shape, and distribution of the
In order to predict porosity defects
in casting processes accurately,
the following factors should be
considered: macroscopic heat
transfer, interdendritic fluid flow,
gas redistribution by diffusion and
convection, microstructure evolution,
and porosity growth.
Pores will form in a solidifying alloy
when the equilibrium partial pressure
of gas within the liquid exceeds the
local pressure in the mushy zone by an
amount necessary to overcome surface
tension. Hence gas porosity develops
as shown in Equation 5, in which Pg
is Sievert pressure, Pa is ambient
pressure, Pm is metallostatic pressure,
Pd is pressure drop due to the friction
within the interdendritic liquid, P8 = 2σ/r is surface tension, σ is surface
tension, r is pore radius.
Volume fraction of gas porosity can
be calculated based on Equation 6,
where fv is volume fraction of gas porosity,
α is gas conversion factor.
A set of castings with different initial
hydrogen content using an iron
chill plate was simulated and compared
with experiment for an A319 casting.45
The initial pouring temperature was
750°C. Initial hydrogen contents were
0.108 ppm, 0.152 ppm, and 0.184 ppm.
The experiments and simulation results
were taken at different distances from
the chill end. The comparison of the
value of percentage porosity against
local solidification time and hydrogen
content between simulation and experiment
is shown in Figure 7.
It shows that increasing solidification
time and hydrogen content increase
considerably the percentage of
porosity. Numerical simulation results
give excellent agreement with the measurements
of percentage of porosity.
Macrosegregation is another defect
for a lot casting processes. Modeling
and simulation of macrosegregation
during solidification has experienced
explosive growth since the pioneering
studies of Flemings and co-workers in
Beckerman did a comprehensive review
of recent macrosegregation models
and their application to relevant
casting industries.68 There are numerous
factors that can cause macrosegregation
during casting solidification
processes. Those include thermal and
solute induced buoyancy, forced flow,
solid movement, and so on. Macrosegregation
models have been applied extensively
in the casting industry, such
as steel ingot castings, continuous and
DC castings, nickel-based superalloy
single-crystal castings (freckle simulation),
and shape castings as well.
Freckles have been the subject of
intense research efforts for about 30
years due to their importance as a defect
in alloy casting.69,70 They represent
a major problem in directionally solidified
superalloys used in the manufacture
of turbine blades.69–73 Upward
directional solidification provides an
effective means of producing a columnar
microstructure with all the grain
boundaries parallel to the longitudinal
direction of the casting. In conjunction
with a grain selector or a preoriented
seed at the bottom of the casting, directional
solidification is used to make
entire castings that are dendritic single
crystals. During such solidification the
melt inside the mushy zone can become
gravitationally unstable due to preferential
rejection of light alloy elements
into the melt. Since the mass diffusivity
of the liquid is much lower than its heat
diffusivity, the segregated melt retains
its composition as it flows upward and
causes delayed growth and localized
remelting of the solid network in the
mush. At the end, a pencil-shaped vertical
channel forms in the mushy zone.
Highly segregated liquid flows upward
as a plume or solutal finger into the superheated
melt region above the mushy
zone. This flow is continually fed by
segregated melt flowing inside the
mushy zone radially toward the channel.
At the lateral boundaries of the
channel, dendrite arms can become detached
from the main trunk, and those
fragments that remain in the channel
are later observed as freckle chains.
The complex convection phenomena
occurring during freckle formation represent
a formidable challenge for casting
simulation.68,74–76 In 1991, Felicelli
et al. simulated channel formation in
directional solidification of Pb-Sn alloys
in two dimensions.77 Since then,
numerous studies have been performed
to simulate and predict freckling in
upward directional solidification.78–87
Neilson and Incropera performed the
first three-dimensional simulations of
channel formation in 1993.81 Three-dimensional
simulations have also been
performed by Poirier, Felicelli, and coworkers
for both binary and multicomponent
Figure 8 illustrates the freckle formation
for a Pb-10%Sn binary alloy
directional solidified in a simple geometry.
A temperature gradient is imposed
initially in order to simulate a directional
solidification system. Cooling
is achieved by lowering the temperatures
of the upper and lower walls of
the cavity at a constant rate such that
the overall temperature gradient is
maintained over the height of the cavity.
The lateral walls of the cavity are
taken as adiabatic. Figure 8a shows the
final composition of Sn. In order to see
the freckles clearly, a cut-off view of
the same results is shown in Figure 8b.
There are five freckles for this case.
Four of them are in each corner of the
domain, and one is in the middle.
Hot tearing is one of the most serious
defects encountered in castings. A
lot of studies have revealed that this
phenomenon occurs in the late stage
of solidification when the fraction of
solid is close to one. The formation
and propagation of the hot tearing have
been found to be directly affected by
the cooling history, the chemical composition,
and mechanical properties
of the alloy, as well as the geometry
of the casting. Various theories have
been proposed in the literature on the
mechanisms of hot tearing formation.
Detailed reviews on the theories and
experimental observations of the formation and evolution of the hot tearing
can be found in References 89 and 90
and the references therein.
Most of the existing hot tearing theories
are based on the development of
strain, strain rate, or stress in the semisolid
state of the casting. For strainbased
theory, the premise is that hot
tearing will occur when the accumulated
strain exceeds the ductility.91–93
The strain rate-based theories suggest
that hot tearing may form when the
strain rate, or strain rate related pressure,
reaches a critical limit during
solidification.94,95 The stress-based criteria,
on the other hand, assume that
hot tearing will start if the induced
stress in the semi-solid exceeds some
critical value.96,97 Although these theories
were proposed independently as
distinct theories, they can, indeed, be
considered as somewhat related due to
the relationship between strain, strain
rate, and stress. It is such a relationship
that motivates the development of
a hot tearing indicator which uses the
accumulated plastic strain as an indication
of the susceptibility of hot tearing.89 This considers the evolution of
strain, strain rate, and stress in the last
stage of solidification. A Gurson type
of constitutive model, which describes
the progressive micro-rupture in the
ductile and porous solid, is adopted to
characterize the material behavior in
the semi-solid state. The proposed hot
tearing indicator has been validated by
different alloy castings.
The constitutive model used to describe
the material behavior in the
semi-solid state is the Gurson model,98–100 which was originally developed
for studying the progressive micro-rupture
through nucleation and growth of
micro-voids in the material of ductile
and porous solid.
When the material is considered as
elastic-plastic, the yield condition in
the Gurson model is of the form shown
in Equation 7, Where F(σ) = (3(s–x) : (s–x)/2)1/2 is the Mises stress in terms
of the deviatoric stress s = σ – (trσ)I/3.
κ represents the plastic flow stress due
to isotropic hardening, χ denotes back stress due to kinematic hardening.
The Gurson coefficient Gu is defined
as Equation 8, in which q1 is a material
constant. Here, fu = 1/q1,fc is the critical
void volume fraction and fF is the failure
void volume fraction. Their values
should be different for different materials.
The evolution of the void volume
fraction is described by the nucleation
of the new void and the growth of the
existing void, i.e., Equation 9.
In this study, the nucleation of the
void is assumed to be strain controlled
and is written as Equation 10, where
Equation 11 is defined as our hot tearing
indicator (HTI). tC represents time
at coherency temperature and tS denotes
time at solidus temperature. It
is observed that the hot tearing indicator
is, in fact, the accumulated plastic
strain in the semi-solid region and it
corresponds to the void nucleation.
Therefore, it should provide a good indication
for the susceptibility of the hot
tearing during solidification. The value
of the hot tearing indicator is determined by the finite element analysis.101
For materials described by viscoplastic
or creep models, a yield condition does
Cao et al. performed some experiments
to study the hot tearing formation
during solidification of binary
Mg-Al and ternary Mg-Al-Ca alloys
in a steel mold,102,103 which is shown in
Figure 9. A hot cracking susceptibility
(HCS) was introduced which is a function
of maximum crack width, crack
length factor, and the crack location.
It was found that it is easier to have
cracks at the sprue end than at the ball
end. It is less likely to have a crack in
the middle of the rod. Also, the longer
rod is easier to crack. Figure 10 shows
the simulated results of hot tearing indicator
for a Mg-2%Al alloy casting.
The computed hot tearing indicator
agrees very well with the experiments.
From experiment as well as from
simulation, it can be seen that the hot
tearing is less severe as the Al content
increases from 2% to 4% and then to
8% at the same location for the same
casting with the same conditions. The
susceptibility rises sharply from pure
Mg, reaches its maximum at Mg-1%
Al, and decreases gradually with further
increase in the Al content.
The hot tearing indicator is calculated
at the end of the sprue for the longest
rod with a different alloy composition.
For comparison, the hot tearing indicators
as well as a crack susceptibility
coefficient (CSC), which is defined as
the temperature difference between
fraction of solid at 0.9 and at the end of
solidification, are shown in Figure 11.
As in the experiment, the susceptibility
of hot tearing rises sharply from pure
Mg, reaches its maximum at Mg-1%
Al, and decreases gradually with further increase in the Al content. Similarly,
different ternary Mg alloys have
different hot tearing susceptibilities.
The alloy chemistry, casting geometry,
and cooling conditions all contribute to
the formation of hot tearing and they
are included in the model directly or
Experimentally, Li systematically
studied the effects of various casting
conditions, such as mold temperature,
pouring temperature, and grain refinement,
on hot tearing of different cast
aluminum alloys.104 In Li's study, an
instrumented constrained rod mold
was developed such that it can be used
to simultaneously measure the load/
time/temperature during solidification.
The set-up is shown schematically in
Figure 12. Figure 13 gives the dimensions
of the studied casting. A detailed
description of the experimental setup
for quantitatively measuring hot tearing
onset and contraction during solidification
of aluminum alloys can be
found in Reference 104.
In one of the experiments, three
mold temperatures were used, 200°C,
300°C, and 370°C. The cracks in the
hot spot region of alloy M206 for those
three mold temperatures are shown in
The results clearly suggest that the
mold temperature has a significant effect
on hot tearing susceptibility of this
206 alloys. The hot tearing susceptibility
decreases with increasing mold
Based on the experimental casting
condition, the simulations were
performed. Figure 15 shows the hot
tearing indicator distribution for those
three mold temperatures. Table II lists
the actual values of the indicator. Increasing
mold temperature can reduce
hot tearing formation for this situation.
It can be concluded that modeling can
predict the hot tearing susceptibility
for this aluminum alloy casting very
well. As there are additional experimental
results in Li's work,23 further simulations
are under investigation to validate
the current model, such as the effect of
melting temperatures and grain refinement.
Modeling of casting and solidification
has been used extensively in
foundries to solve routine production
problems. Casting defects such as
those related to filling, solidification,
stress, and microstructure can be predicted.
As always, better understanding
and accurate material properties,
including mold materials, lead to improved
predictive capabilities. Further
development efforts should emphasize
the enhancement of the accuracy of
predicting various casting defects. Further
coupling of heat treatment simulation
with casting simulation can then
predict the final mechanical properties
of the part in service.
1. J. Guo and M. Samonds, Casting Design and Performance (Materials Park, OH: ASM International, 2009),
2. M. Rappaz and W.J. Boettinger, Acta Mater., 47
(1999), pp. 3205–3219.
3. W.J. Boettinger et al., Acta Mater., 48 (2000), pp.
4. J. Guo and M. Samonds, J. Matls. Engrg. and Perfor.,
16 (6) (2007), pp. 680–684.
5. J. Guo and M. Samonds, Matls. Sci. and Technol., 3
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Jianzheng Guo and Mark Samonds are with ESI
US R&D, 6851 Oak Hall Ln, Suite 119, Columbia,
MD 21045. Dr. Guo can be reached at email@example.com.