numerical determination of heat distribution and castability simulations of as cast mg-al alloys
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DOI: 10.1002/adem.200800269Numerical Determination of Heat Distribution andCastability Simulations of as Cast Mg---Al Alloys**
By Shehzad Saleem Khan*, Norbert Hort, Janin Eiken, Ingo Steinbach andSiegfried Schmauder
[*] Dr. S. S. Khan, Dr. N. HortInstitute for Materials Research, GKSS Forschungszentrum GmbHMax Planck Strasse 1, 21502 Geesthacht, GermanyE-mail: [email protected]
Dr. J. Eiken, Prof. I. SteinbachRWTH Aachen, ACCESS e.V., Intzestraße 5, 52072 Aachen,Germany
Prof. S. SchmauderInstitut f€ur Materialpr€ufung, Werkstoffkunde undFestigkeitslehre (IMWF), University StuttgartPfaffenwaldring 32, 70569 Stuttgart, Germany
[**] Authors are grateful to GKSS Research Centre Geesthacht,MagIC (Magnesium Innovation Centre) for funding andProf. R. S. Fetzer and his research collaborators for assistingin acquiring thermodynamical data for magnesium alloys.
162 � 2009 WILEY-VCH Verlag GmbH & Co
Magnesium alloy offers an outstanding combination of
light weight, ease of manufacturing, and good engineering
properties.[1] The most common method to manufacture
magnesium alloy products is die-casting; however, the defect
rate for magnesium alloy die-casting is still relatively high.
Especially in the case of thin-sectioned die-casting, mold
filling may not be accompanied occasionally due to its fast
solidification rate. As a result, fluidity (i.e., the ability of filling
a cavity) becomes very essential. In this paper, a concept of
‘‘feeding effectivity’’ is discussed. Previous works emphasize
more toward macroscopic behavior of the cast alloy. Less
attention is given to the growth of nucleants (solidification). A
bifurcation of the solidification and fluidity is not established.
A cast alloy is said to freeze when it solidifies which is not
entirely correct. This paper connects fluidity with micro-
structure attributes for particular cast alloy [two-dimensional
(2D) microstructural simulations]. It discusses in detail the
acquisition of experimental parameters to simulate fluidity
(using finite difference based Magmasoft1) and microstruc-
ture (using MICRESS Micro Structure Evolution Simulation
Software). Fluidity is a complex thermocoupled fluid flow
process. Cast alloy andmold are interactingwith each other all
the time. It is also very significant to optimize this interaction
and suggest new mold design based on the determination of
temperature distribution around the fluidity channel.
As cast alloys 12, binary magnesium–aluminum binary
alloys were undertaken (with 1–12 wt% Al in Mg), and the
resultant microstructures have been simulated and then have
been compared with the experimental output. The tempera-
ture distribution and the heat dissipation during casting has
been simulated and compared with experiments for different
geometries. Numerical determination of heat distribution
refers to the heat extraction rate during solidification and
dissipated heat during the cast process at the interface
between the cast alloy and the permanent mold.
Experimental Procedures
Fluidity tests have been developed and are used commer-
cially as quality checks to determine the flowing qualities of
molten metal [2]. Fluidity is an empirical measure of the
distance a liquid metal can flow in a specific channel before
being stopped by solidification [3]. Under gravity casting
conditions fluidity is inversely proportional to the solidifica-
tion interval of the alloy.
This channel may be straight or it may be in the form of a
spiral. The cross-section may be round, half round, trapezoi-
dal, or rectangular. In this work, a fluidity spiral has been used
(Fig. 1) [4]. The channel was wound into a spiral, thereby
simplifying handling and leveling problems. Steel was chosen
as the material to keep the mould influence free. Usually sand
moulds are used but the probability of a reaction (with the
binders) is higher. The evaluation has been carried out in three
phases given below:
– E
. K
valuation (experimental and simulated) of the mold filling
ability values of all binary Mg–Al alloys containing up to
12% of aluminum by weight at various pressure heads
(metallostatic) and superheats (heating beyond liquidus).
(These binary alloys have been used to simplify the phases
formed in the ternary alloy systems.)
– S
tudying the influence of process parameter on mold fillingability of these alloys.
– O
ptimization of themold geometry andmold parameters tomaximize mold filling ability values.
The alloys were cast in cylindrical chills, producing
castings with 17mm diameter and 160mm length. After
casting, samples were prepared for light microscopy, inter-
ference layer microscopy, and scanning electron microscopy.
All castings have been subjected to a melting temperature of
100 8C above respective liquidus of the alloy. Cylindrical
specimens for differential thermal analysis (DTA) were taken
from the casting billet. Cylindrical specimenswith dimensions
– F4� 22mm2 – were fabricated for the dilatometer
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Fig. 1. The mold made of steel, maintained at constant 250 8C for all casting exper-iments. (Left) shows the CAD modeled geometry of the mold. (Right) Real worldgeometry in a glance.
experiments. Specimen preparation grinding, polishing, and
etching according to Voeker et al. [5].
Figure 2 shows the microstructure changes with increasing
aluminum content. A small addition to puremagnesium leads
to a morphological change of the primary phase from a
cellular or columnar to a dendritic structure. Rosette-like
globular equiaxed grains form with aluminum-rich solid
solution between the dendrite arms. As the aluminum content
is increased further to 5 wt%, dendrites with pools of eutectic
phase between the dendrite arms start to develop and when
the aluminum content is further increased, a fully developed
dendritic structure with sharp tips is observed. The grain size,
Fig. 2. Micrographs of magnesium–aluminum alloys with increasing aluminum content.
Table 1. The experimental calculation of magnesium/aluminum binary alloys.
wt% Al in Mg Tsolidus [K] Tliquidous [K] Freezing ran
0 924.1 924.1 –
1 902.9 917.9 15.02
2 893.1 912.7 19.68
3 875.1 907.6 32.54
4 848.0 902.5 54.51
5 816.2 897.3 81.18
6 794.5 892.2 97.72
7 790.9 887.0 96.14
8 767.0 881.8 114.82
9 763.9 876.5 112.65
10 748.5 871.2 122.72
11 731.4 865.8 134.41
12 738.6 860.3 121.73
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denoted as the mean grain diameter, was analyzed by a
modified line interception analysis, which features an
evaluation in horizontal and vertical direction of the
micrograph.
Experimentally it is possible to determine specific heat
using the differential scanning calorimetry (DSC) equipment.
For the determination of the coefficient of thermal expansion
(CTE), NETZSCH Dilatometer 402 8C device was used. The
dilatometer was operated over a temperature range from
room temperature to 450 8C, at heating rates of 5Kmin�1, with
programmed heating, cooling, and isothermal sections, under
either air or a protective atmosphere. Samples up to 25mm
long and with a diameter of up to 12mm, with a maximum
shrinkage/expansion of 5mm, were measured. Latent heat of
fusion can also be determined using the DSC equipment.
Solidus and liquidus temperatures for each individual
alloy were also determined using DSC equipment. From
these temperatures the freezing range (Tmelt�Tsolidification)
was calculated below (Table 1). There is no thermodynamic
reaction occurring prior to solidus temperature. The heat flow
measured by DSC is almost constant till the solidus
temperature, beyond which an endothermic reaction occurs
and the melting starts. The onset at this point is referred to
solidus and the peak is taken as liquidus (Fig. 3). A very
essential experimental data that is needed for the simulation of
ge Grain si
ag GmbH & Co. KGaA
the microstructure is the cooling rate. Soft-
ware being used to simulate microstructure
(MICRESS1) takes the cooling rate data in the
form of heat extraction [6]. To determine
cooling rate, melt was poured in the two
crucibles (moulds) at the same time. There are
two thermoelements for thewhole setup, thus
yielding two cooling rates, the lower cooling
rate and the higher one. The final cooling rate
is the average of both.
Prior to simulations, the calculations of
feeding effectivety is a must, provision of a
value at this point that defines the range of
feeding is vital. This value describes the
solidified fraction of the melt up to which
ze average [mm] H [J g�1] latent heat of fusion
406.13 309.32
190.46 289.83
128.76 235.99
120.0 250.04
114.0 265.13
86.3 249.23
95.3 229.11
96.3 229.52
99.66 198.10
63.66 201.34
70.33 227.24
69.33 205.39
71.33 199.10
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Fig. 3. DSC curves for Mg–5Al till Mg–12Al.
macroscopic feeding can occur. The solidified fraction is
expressed in percent and is strongly dependent on the
solidification morphology. This refers to the temperature after
which the fluid ceases to flow through the mold cross-section
even there is a good amount of liquid still present in the
semi-solid mushy region. Figure 4 reveals the significance of
feeding effectivety. Solidus temperature is not the point where
the melt freezes but it happens far later.
Phase Field Method
For the simulation of microstructure evolution, in solidi-
fication processes phase fieldmethod has been used. One of its
main features is the description of moving phase or grain
boundaries using a continuous phase field parameter,
corresponding to the diffusion interface. The phase field
equation, expressing the evolution of the phase field
parameter in time and thus the movement of the solidification
front, can be derived in a thermodynamically consistent way
by local minimization of the Gibbs free energy. Extensive
work in this regards has been done by Steinbach et al. [7]. In
this paper, the multi-phase field code MICRESS1 is used
which can be online coupled to thermodynamic databases.
Fig. 4. Casting parameters versus Al content.
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Model for Heterogeneous Nucleation
The phase-field method presented addresses the evolution
of phase regions with time, but it does not care for nucleation
of new grains or phases. An independent nucleation model is
integrated for this task. A new nucleus is set if the local
undercooling at a nucleant position exceeds the required
nucleation undercooling. The required undercooling for
heterogeneous nucleation is determined according to the free
growth model inversely proportional to the radius of the
nucleants [8,9]
Tundð~xÞ � Tnucð~xÞ (1)
DTund ¼DGðci
a;TÞDS
(2)
DTnuc ¼2s
DSr(3)
where DGij is the driving force, Tund the undercooling
temperature, Tnuc the nucleation temperature, ca refers to
composition, DS the transformation entropy, and s the surface
energy.
The local undercooling of the nucleus at this position is
evaluated as function of composition and temperature. A
nucleation event during simulation is technically performed
by direct manipulation of the local phase-field parameters at
the nucleation position [10]. The combined model has been
applied to simulate equiaxed solidification of magnesium-
based alloys using the phase-field code MICRESS. The
software has been connected via the Fortran TQ interface of
ThermoCalc (Themodynamical Insitut Stockholm) to a
Calphad database [11,12]. Simulations have been carried out
in 2D.
After its nucleation, the grain starts to release latent heat.
Assuming the temperature diffusion length to be much larger
then the calculation domain, heat diffusion is not simulated,
but both heat extraction and growth-dependent latent heat
release are averaged over the calculation area [12]. Their
interaction typically leads to a temperature decrease in the
beginning and a subsequent reheating to the local liquidous
temperature. Only nucleants with radius larger then the one
corresponding to the maximum reached undercooling are
activated, while the others will simply be overgrown.
In this paper, heterogeneous nucleation is being modeled.
As input, information about the distribution of nucleant
particles in the melt is needed. These particles may be either
grain refiner particles or just impurities. Usually, there will be
a high number of small particles and the density will decrease
with size. This can be described by a density radius function in
exponential form as shown in this example. Following the free
growth model of Greer et al. [8]. It is assumed that the critical
nucleus radius for free growth equals the radius of the
nucleant particle and based on this assumption the critical
undercooling for nucleation can be evaluated as function of
the nucleant particle radius.
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Numerical Simulations
Microstructure Simulations
At the beginning of a simulation, the nucleant distribution
function is read and according to it, nucleants with different
radii are positioned. As a function of the radius, the required
critical undercooling is evaluated and only if the local
undercooling, which is a function of local composition and
temperature, is higher than this critical under cooling, a new
nucleus is set during the simulation. Depending on the
process condition (thermodynamic) it may either grow or
shrink. If it grows, it will redistribute solute and release latent
heat and will thus effect further nucleation. To simulate
realistic equiaxed cast microstructures, additionally hetero-
geneous nucleation of the primary phase as well as nucleation
of secondary phases is simulated.
First nucleation is simulated and then the growth of the
hexagonal magnesium phase and finally the precipitation of
the eutectic gamma phase. Input for such a simulation is the
nucleant distribution, the heat extraction rate, and the alloy
composition. As output the grain size and morphology are
evaluated.
While attempting to simulate the microstructure evolution
there are some properties, knowledge of whom is vital. These
properties are as follows:
– n
AD
ucleation density,
– h
eat extraction,– la
tent heat of fusion,– s
Table 2. Input parameters for Mg–12%Al.
Property for Mg–12%Al Values
Cooling rate 14.16K s�1
Specific heat 1.275 J g�1 K�1
Specific heat capacity 2.218 J cm�3 K�1
Effective heat capacity 3.595 J cm�3 K�1
Heat extraction 50.90 J s�1 cm�3
pecific heat capacity.
Nucleants have to be placed on the simulation window
(lower right hand window, refers to the area considered for
nucleation). Provided they satisfy a certain thermal require-
ment (Eq. 1), then they start growing. Now, the quantity of
these nucleants have either to be based on assumption or
compared with the experimental results. As in this case the
simulated results and the experimental ones are compared, so
the nucleant density was altered iteratively.
For the prediction of grain sizes, nucleation has to be taken
into account. Statistical models starting from a given size
distribution of inoculant particles which are based on free
growth control of grain initiation have been applied success-
fully for magnesium alloys.[8,9] Amultiphase field approach is
being used to equiaxed dendritic growth is presented which
allows for direct coupling to thermodynamic databases with
an arbitrary number of phases and components.[6,13] The
nucleation model has been adapted and spatially discretized
to describe the influence of seed density distribution,
segregation, and thermal boundary conditions on the grain
size. Special care has been taken as regards the release of latent
heat and its proper correction for 2D simulations. Themodel is
applied to the binary magnesium alloys.
A cooling rate of 14.16K s�1 was achieved experimentally
and with it the heat extraction of Mg–12%Al was calculated.
The heat extraction then was taken to be constant for all the
alloy composition (1–12%Al), Concept of effective specific
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heat, which includes the effect of latent heat is introduced (Eq.
4). Keeping in view the extensive work involved in the
simulation of each alloy only three combinations Mg–2%Al,
Mg–5%Al, and Mg–10%Al were considered
zCp� ¼ z Cp þ L
DTF
� �(4)
where z is the density of the particular alloy, Cp the specific heat
[kJ kg�1 K�1], z Cp the heat capacity[kJ K�1 m�3], L the latent
heat of fusion [kJ kg�1], and DTF the freezing range of the alloy
[K]
Q ¼ jCp� � DT
Dt(5)
where Q is the heat extraction [kJ s�1 m�3], DT/Dt the cooling
rate, determined experimental [K s�1], and z Cp� the effective
heat capacity.
The properties shown in Table 2 were updated in the
MICRESS driving input. Here, it is worthmentioning that it was
possible through a series of iterations that the scheme (Eq. 5) of
having constant Heat of Extraction was adopted. Formerly, the
cooling rate was kept constant for all the alloys but the
morphological trend showed unrealistic and adverse effect.
h ¼ Q
TAlloy12 � Tmold
� � (6)
where h is the physical heat transfer coefficient.
QAlloyX ¼ h TMeltAlloyX � Tmold
� �(7)
(Tmelt�Tmold) is constant for all alloys.
Heat extraction of any alloy can be determined using
Equations (6) and (7). Nucleation curve is used to determine
the cooling rate of all the required alloys and the thermo-
dynamical properties of the alloys (specific heat) are different.
In Figure 5, the grain size is plotted versus the change in
concentration of Al (wt%) and as it can be seen that until 5%Al
there is a reduction in grain size. Results have been compared
with literature and there is some scatter. The seen difference is
because of different casting conditions and different sizes of
the crucibles. Here, a small chill was used and the average
effect of Al was determined. There have been some peaks but
in general the results were satisfactory and expected.
Morphology
Figure 6(b) shows the development of the solid fraction or
diminishing of liquid fraction as a function of temperature. At
any point in the plot, it is observed that the lower content of
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Fig. 5. Grain size and the fluidity values (experimentally) versus content of Al. Comparison of the simulatedgrain size to the experimental.
Aluminum liquefies or freezes at a relatively higher
temperature then the higher ones. This effect is due to higher
solidus and liquidus temperatures of the alloy. Besides the
grain size, we can evaluate the morphology of the equiaxed
grains while the solidification progresses. The term morphol-
ogy refers to the ratio of the surface area of the particular grain
to the surface area of a sphere of equal volume (smallest area
of the grain of equal volume). While keeping the emphasis on
grain size, grain morphology is necessary to address also.
Figure 6(a) reveals the result obtained and it can be seen that
Mg–2%Al having less Al concentration and a bigger grain size,
attains lower morphology values. With the increase in Al
content (wt%) the morphology values increase too. This is
because that at higher Al concentrations the grain is restricted
to grow because of the solute redistribution, as described by
the grain restriction factor (g.r.f).
As the grain size ofMg–2%Al is higher then that ofMg–5%Al
and Mg–10%Al, it can be stated that the results are understood
and were expected too. The trend has been identified and it can
be seen that after reaching a maximum value, the grains reduce
their size a little and then mature. This phenomenon was
observed in the simulations and is due to the Ostwald Ripening
of the grains. If this process continues, eventually fewer and
larger crystals from inside the solid that have smaller and
smaller surface-to-volume ratios compared to the smaller
Fig. 6. The grain morphologies of Mg–5%Al, Mg–10%Al, and Mg–2%Al, and the development of the liquidfraction w.r.t temp.
166 http://www.aem-journal.com � 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
particles, thus reducing the energy of the entire
system.
Fluidity Simulations
With grain size fluidity have been the
major areas of consideration in this work.
Below in Figure 5, fluidity values and grain
size have been presented all together in one
plot. There are numerous factors effecting
fluidity. The salient being the following:
(i) m
etallostatic pressure head,(ii) d
egree of superheat.The height of the pouring level was
calculated to be 25 mbar, this is the pressure head but as
discussed formerly the human error might hinder accuracy.
Fluidity Results
It isalsoseenthat the increase insuperheat increases themold
filling ability values, these results have been presented in
Figure 7. In thepresent investigations, thedegree of superheat is
limited to 100 8C. Due to practical considerations, it is not
desirable to go beyond this superheat since magnesium alloys
have a higher oxidation tendency then other commonly used
alloys. Increase in superheat increases the total heat content of
the alloy.
Figure 7 shows the effect ofmetallostatic pressure head and
degree of superheat on the simulated fluidity. Three different
sets of simulations were done on the alloys:
– S
imulations with 25mbar pressure head and 100 8C super-heat (100 8C above liquidus).
– S
imulations varying the pressure head only and keeping thesuperheat constant at 100 8C.
– S imulations with varying superheat (150 8C) and keepingthe pressure constant at 25mbar.
The simulations show the following trends in the fluidity of the
alloys:
– Rise in superheat temperature by 50 8C(from 100–150 8C), increased the fluidity up
by almost 15%.
– Elevated pressure head of 15 mbar (from
25–40mbar), caused the fluidity to increase
by 10%.
– For lower concentration of Al (wt%) in Mg,
the superheat and pressure have no sig-
nificant change as the freezing range is
very short.
Determination of the Heat TransferDistribution
The reservoir feeding systemwas effective
in controlling the turbulence because of its
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Fig. 7. Fluidity comparison of different metallostatic pressure head and degree ofsuperheat versus Al content.
ability to allow fixed quantity ofmass to themold. At the same
time a portion of the cast alloy got solidified in the feeding
system itself, thus, hindering the path of the casting into the
cavity (Fig. 8).
To optimize the die, the aspect for consideration is the heat;
heat should not be allowed to dissipate by the casting to the
mold in a high rate. To find out the rise in temperature caused
by the hot melt 28 holes were drilled and Cr–Ni–Cr (capable of
withstanding high temperatures) thermocouples were placed.
These thermocouples are connected to a data acquisition
device which, in return, gives the temperature profile of each
point during the experiment with a very high frequency.
Based on this information and the heat gradient inmold filling
simulations, feeding system along with the mould was
optimized (Figs. 9 and 10).
Fig. 8. Temperature distribution in the old feeder cross-section.
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Conclusions
Based on grain morphology and feeding effectivety of the
alloys it was known that a cast alloy does not freeze on the
advent of the solidus temperature but a lot before that.
Feeding effectivety is known by the 2D microstructure
simulations. Properties like heat transfer coefficient and
viscosity are vital for a fluidity simulation; there have not
been precise devices available offering reliable measures. For
these simulations, the Magmasoft database for AZ91 was
taken and applied to all the under considered binary alloys.
The following points summarize the deviation:
– T
ag
he assumption of thermophysical properties like viscosity
and heat transfer coefficient.
– T
he metallostatic pressure head calculated might not be thesame value as used for simulations.
– I
mpossible to simulate the mold with the Aluminum Boxate(releasing agent) affecting heat transfer rate significantly.
On the basis of the results extracted from the simulation of
the virtual thermocouples and the experiment, the mold
geometry was optimized and a better fluidity was achieved. A
reservoir feeding system though controls the turbulence and
let themelt flowuniformly but as it accommodates themelt for
some time, the melt freezes in it which hinders fluidity. By
controlling the casting parameters the degree of damage
caused by these defects can be minimized.
Experimental grain size possessed scatter but the samewas
not seen in simulations. The disagreement between simula-
tions and the experimental data is definitely due to the canvas
of assumptions taken while calculating the input parameters.
The number of grains increases with increasing aluminum
concentration, while the grainmorphology becomes dendritic.
For lower concentration of aluminum, an equiaxed globular
microstructure was achieved (as shown by experiments). The
GmbH & Co. KGaA
low concentration alloys may be character-
ized equiaxed dendritic in some way. To
quantify that distinction the morphology
factor was introduced.
Figure 5 compares simulated microstruc-
tures for Mg–1%Al till Mg–12%Al. It can be
seen that the number of grains increases with
increasing Al concentration, while the grain
morphology becomes slightly more dendritic
(Fig. 11). Both effects can be explained by the
solute pile-up ahead of the growing solid,
which is increasingwith increasing concentra-
tion.
Grain being a 3D entity should be
analyzed in 3D. In future, if the feeding
effectivety is known by the 3D microstruc-
tural evolution that would yield more precise
results. The presented simulations are still in
2D approximations, which already give
qualitative results, but the absolute values
of the permeability in 3D will be different
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Fig. 9. The optimized geometry with the new feeding system.
ig. 10. The increment in fluidity with the application of the new mold. The experimental fluidity done in GKSSompared with the simulated results from Magmasoft. The error limit is 10%.
Fc
Fig. 11. The simulated grains for Mg–10%Al, the dendritic, microstructure can be seen.
from the given values. The main conclusion from this is that
the dependence of the grain size on the alloy composition is
weak compared to the dependence of the grain size on cooling
168 http://www.aem-journal.com � 2009 WILEY-VCH Verlag GmbH & C
rate. Comparing these results to experiments we must state
first, that, in particular for Mg alloys, the grain size is
dominated by the seed distribution which is predominantly
influenced by the alloy preparation. Systematic variations, for
the time being, can only be investigated if the alloy
preparation is well controlled and reproducible.
Microstructure results were extracted from a straight
channel die whereas fluidity results were done on a spiral. An
assumption that the flowing front of the cast alloy in a spiral
shall have the same microstructural attributes as that of a cast
alloy in a straight channel have created scatter when
compared (as happened in this paper).
o. KGaA, Weinheim
Received: August 21, 2008
Revised: September 22, 2008
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