FUNDAMENTALS OF SOLIDIFICATION IN ALUMINUM CASTINGS
Geoffrey K. Sigworth
GKS Engineering, Dunedin, FL, USA
Copyright © 2014 American Foundry Society
A version of this paper was previously published in 2013 AFS Transactions.
Abstract
In this paper the foundation is laid for a fundamental understanding of what happens during solidification. This knowledge is then used to derive practical conclusions about commercial casting alloys. Important phase diagrams are given.
These describe, in the form of easily read graphs, what phases form and the relationships between the phases. The nonequilibrium process of solidification is then discussed. The
formation, growth and coarsening of dendrites is described
and correlations given for secondary dendrite arm spacing
(SDAS) as a function of local solidification time. Finally,
segregation is considered and models which describe the
segregation are reviewed. Example calculations are made
for solidification paths in Al-Si casting alloys and suggestions are made to optimize casting alloy compositions.
Introduction to Phase Diagrams
where
p is the number of phases present
f is the number of degrees of freedom
n is the number of components present
The foundry industry is primarily concerned with the solidification process. This is essentially a phase transformation
from the hot, liquid state to a colder, solid state. Phase diagrams tell us a great deal about how this transformation occurs. For example, they inform us about:
1. 2. 3. 4. what phases form;
at what temperatures the phases form;
the relative amounts of each phase
the composition of phases, and how solute elements are distributed between the phases and
5. how difficult or easy it will be to place a specific
alloying element into aluminum.
These are important considerations, which affect the castability of an alloy, as well as the properties in the finished
product.
One starts by considering pure aluminum. If pure metal is
slowly heated, it remains solid until a temperature of 660C
(1220F). It then starts to melt, but remains at that temperature until all the metal is molten. Once it is fully liquid, it can
be heated to higher temperatures.
For a pure metal (or pure water) the number of components
(n) is equal to one. When both solid and liquid are present,
the number of phases (p) is equal to two. Therefore, the number of degrees of freedom (f) must be equal to one. However,
in practice the pressure is fixed by the prevailing atmospheric pressure, so this ‘uses up’ the one degree of freedom. In
other words, the melting temperature is not free to vary or
change, as long as two phases are present in a pure material.
If a pure metal was melted in a high pressure furnace in a
laboratory, the melting point would increase. There is a volume increase of about seven percent when aluminum melts.
Higher pressures would make it more difficult to melt metal
by opposing this volume increase. Therefore, the single degree of freedom means that, as long as the pressure is fixed,
the melting point is also fixed.
This situation is illustrated by the phase diagram shown in
Fig. 1. In this figure the temperature scale is indicated schematically by a thermometer.
The situation is exactly analogous to melting ice or placing
ice cubes in a glass of water. Ice and liquid water coexist
only at a single temperature. This temperature is called the
melting point. Only the liquid is above this temperature and
below it is the solid.
Now the addition of a second element to aluminum, to create a binary (two element) alloy, is considered. According to
the phase rule, if there are two components there will be two
degrees of freedom. This means that the melting point may
change in a two component system.
One way to describe the situation is to use the phase rule.
The phase rule is defined by the equation:
Those who live (or who have lived) in cold climates are familiar with the practice of adding salt to icy sidewalks and
driveways to melt ice in the winter. Salt dissolves in water,
lowering its melting point. This makes it easier to remove
p+f=n+2
Eqn. 1
International Journal of Metalcasting/Volume 8, Issue 1, 2014
7
the ice, as long as the temperature is not far below the freezing point of water.
The same thing happens in aluminum. Adding a second element to pure aluminum usually lowers the melting point.
This effect can be illustrated by considering the Al-Si system. Silicon lowers the melting point of aluminum, but aluminum also lowers the melting point of silicon. The two
curves for the melting of Al and Si meet at a eutectic—at a
composition of 12.6 weight percent Si and a temperature of
577C (1071F) (Fig. 2).
1. Hypoeutectic alloys
These alloys have a silicon content less than the
eutectic composition. Most of the common hypoeutectic alloys have between 5% and 10% silicon.
Some examples: C355, 356, 357 and 359. These
alloys are designed primarily for high strength applications where good ductility is also required.
At the eutectic composition and the eutectic temperature,
this phase transformation occurs during solidification:
Liquid → Solid (Al) + Solid (Si)
Eqn. 2
It should be noted that this transformation occurs at a single, constant temperature. This can be anticipated from the
phase rule:
f=n+2-p=2+2-3=1
Eqn. 3
Therefore, at constant pressure three phases can coexist in
a binary (two element) system only at a single temperature
(and of course, at a single composition).
An appreciable amount of silicon dissolves in solid aluminum at higher temperatures. The maximum solubility is
seen to be 1.65 weight percent at the eutectic temperature.
However, only a negligible amount of aluminum dissolves
in silicon.
Figure 1. Phase diagram for pure aluminum is illustrated.
Liquid aluminum and liquid silicon are completely soluble in
one another and form a single phase field represented by the
‘L’ in the diagram above the eutectic temperature. Using the
standard terminology for this behavior, the two liquids are
said to be miscible (or mixable). At temperatures below the
melting point of the pure metals, but above the eutectic temperature, there are two phase fields of solid in contact with
liquid. These are labeled ‘S + L’. On the left hand side solid
aluminum is in contact with liquid. On the right hand side, it
is solid silicon in contact with liquid metal. At temperatures
below the eutectic temperature, there is another two phase
field. It contains two solids: aluminum and silicon.
If one looks at phase diagrams for the Al-Si system proposed
in the literature over the years, it will be found that there is
disagreement as to the exact eutectic composition and to a
lesser extent, the eutectic temperature. This is because the
formation of the Al-Si eutectic is sensitive to small amounts
of impurities, especially P, Na and other alkaline earth elements. The phase diagram given here is based on a study
conducted at Alcoa.1
There are three classes of foundry alloys, which are grouped
together based upon their silicon content. They are:
8
Figure 2. Phase diagram for Al-Si system is shown.
International Journal of Metalcasting/Volume 8, Issue 1, 2014
2. Eutectic alloys
These alloys have between 10 and 13% silicon, and
consist mainly of Al-Si eutectic in the cast structure. They have a narrow freezing range, excellent
fluidity and are easy to cast. They also have good
wear resistance and are quite ductile when not alloyed and heat treated to high strength. Eutectic
alloys, containing Cu, Mg and sometimes Ni, are
used extensively for pistons.
3. Hypereutectic alloys
These alloys have between 15 and 20% silicon, so
their cast structure is composed of primary silicon
particles imbedded in a matrix of Al-Si eutectic.
These materials have remarkable wear resistance,
and are used where this characteristic is desired:
for pistons, liner-less engine blocks and compressor parts. They also have good high temperature
strength but are difficult to machine. Diamond
tools are necessary.
A more detailed look at the Al-Si phase diagram provides a
better understanding as to what these characteristics mean
in practice. The most important portion of the Al-Si phase
diagram for the foundry worker is shown in Fig. 3.
As solidification continues the silicon concentration in the
liquid portion of the casting increases. Silicon segregates
to and accumulates in the liquid phase. This segregation
during solidification is best described by a distribution coefficient:
Therefore, the phase diagram tells us that, at equilibrium,
the silicon content in solid aluminum is 13 percent of that
found in the surrounding liquid. The other 87% remains in
the liquid, where it accumulates. And as the silicon content
increases in the liquid, its melting point decreases. Hence,
the composition and temperature of both solid and liquid
phases follow the arrows in Fig. 3. This segregation continues until the liquid contains 12.6% Si and cools to the eutectic temperature. At this point, a eutectic mixture of solid Al
and Si forms.
Another important factor which can be determined from the
phase diagram is the depression of the melting point of aluminum. This is defined by the slope of the liquidus curve and
by this equation for the Al-Si system:
Now, consideration is given to the solidification of a typical hypoeutectic alloy, containing 7% silicon. The molten
metal alloy is taken from a furnace held at 760C (1400F).
This metal cools in the mold to a temperature of about 615C
(1139F). At this temperature the first solid forms: aluminum
crystals containing one percent silicon.
Eqn. 4
Eqn. 5
For silicon in aluminum, m is equal to 6.6° C per weight
percent Si.
The last important factor is the solubility of the element in
liquid aluminum at typical furnace temperatures. For silicon
this maximum concentration is equal to the eutectic composition, 12.6 weight percent Si.
These three factors have been tabulated for a number of
important or interesting alloying elements.2 The results are
shown in Table 1. The elements are listed in order of the
value of the distribution coefficient (k).
Several important and interesting things may be gleaned
from the above tabulated values:
•
Figure 3. Detail from the Al-Si phase diagram is shown.
International Journal of Metalcasting/Volume 8, Issue 1, 2014
Ni, Fe, Si and Cu segregate very strongly during
solidification.
• Zn and Mg segregate only moderately.
• Mn hardly segregates at all. The concentration of
Mn in solid aluminum is 94% of the liquid. This is
an important factor in the improved performance of
die casting alloys, where Mn replaces Fe to prevent
die soldering.
• The elements below Mn have a value of k greater
than one. This means there is a ‘negative’ segregation—the equilibrium concentration in the solid is
greater than that in the liquid. As a result, the melting point of aluminum increases.
9
For those who are curious to know the reason for the last
statement, a thermodynamic explanation is available.3
Up to this point binary systems have been considered. When
another element is added to a binary alloy, there is a ternary
(three element) system. It is somewhat more complicated to
read ternary phase diagrams, but it is often useful to consult
them. Therefore one will be presented to become familiar
with the procedure.
Figure 4 shows the liquidus surface for aluminum-rich alloys in the ternary Al-Zn-Mg system. This diagram is similar
to a topographic map, used for hiking or hunting outdoors.
The contours show the temperature (°C) at which solid aluminum begins to form during solidification.
A full ternary diagram is an equilateral triangle, but since
the interest here is in aluminum-rich alloys, the top portion
of the triangle (corresponding to Mg-rich compositions) has
been removed. The key to ternary diagrams is understanding
how to read the composition coordinates. There are two ternary eutectics in this diagram. They will be used for instruction in the correct procedure.
Ternary eutectics are similar to the binary eutectics, discussed previously. However, since there is an additional
component (3 instead of 2) there is an additional degree of
freedom according to the phase rule. Thus, a ternary eutectic
occurs only with this reaction:
Liquid → Solid1 + Solid2 + Solid3
Eqn. 6
The formation of three solid phases in the eutectic means
the reaction occurs at a fixed temperature and composition.
At the top left of the phase diagram there is a ternary eutectic
at 447C (837F). If a line is drawn from this point parallel to
the sloping left edge, this line intersects the scale at the bottom at about 13% Zn. If a horizontal line is drawn parallel to
the bottom edge, it intersects the left edge at about 31% Mg.
Thus, this ternary eutectic contains 13% Zn, 31% Mg and
(by difference) 56% Al.
often possible to find a used copy on the internet. Another
useful source for binary and ternary diagrams is the compilation by Phillips.5
For four-component and higher order systems, it becomes
exceedingly difficult to represent the phase equilibria. One
remarkable contribution worth noting is the study by Phragmen.6 He conducted an extremely detailed study, and presented the results for several quaternary and quinary systems. This paper is not easy reading, but would certainly be
worth consulting by anyone wishing to do any serious alloy
development in aluminum.
Dendritic Solidification
Some years ago, the author of this paper read a wonderful
book on snowflakes at the Carnegie Library in Pittsburgh.
This was a large, coffee table-sized book, with many photographs of individual snow flakes. In his introduction,
the author claimed that each snowflake is unique, and no
two crystals are alike. This claim may be true, in spite of
the incredibly large number of snow flakes that form each
winter. The variety of the snow flakes in this book was
mind boggling.
Something similar happens every time metal solidifies in
the mold. The liquid-to-solid transformation involves the
formation of many small, individual crystals of solid aluminum. This is a fascinating area, one which has received a
great deal of study. Only a brief overview will be given here,
touching on the aspects of solidification most important to
aluminum foundry industry. For those who wish to study
and learn more about solidification fundamentals, two excellent books are available.7,8
Table 1. Alloy Constants for Several Elements
Calculated from Phase Diagrams2
There is a second ternary eutectic in the lower right hand
side of the diagram, at a temperature of 475C (887F). A
similar procedure shows that this eutectic contains approximately 61% Zn, 13%Mg and 26% Al. As an exercise, these
results can be determined.
There are a number of useful sources of phase diagrams that
may be found in a good research library. Important commercial binary diagrams are also easily found on the internet.
However, the ternary diagrams are more problematic. The
best source found for these is the book by Mondolfo.4 It is
unfortunate that this book has gone out of print. It is a fantastic reference for anyone seriously interested in the technology of aluminum and aluminum alloys. Fortunately, it is
10
International Journal of Metalcasting/Volume 8, Issue 1, 2014
The solid aluminum crystals forming during solidification
are like snowflakes. The metallurgists first observing these
crystals thought they resembled trees. They were therefore
called dendrites, after the Greek word for tree (δενδρον or
déndron). Dendrites were first observed by polishing metal
samples or by etching the polished surface. More recently
real time X-ray studies have observed the in situ formation
of dendrites in Al-Cu alloys.9 Because the aluminum crystal contains much less copper than the surrounding liquid,
they appear lighter in X-ray images. Examples are shown in
Fig. 5.
The formation of dendritic crystals is a curious phenomenon; so many scientists have studied them. The technical
literature in this area is extensive. However, a relatively
simple explanation will suffice to understand what is happening.
One important clue is that pure metals do not form dendrites. But when silicon or other elements are alloyed to
aluminum, dendrites appear. From the Al-Si phase diagram, only 13% of the silicon in the liquid metal remains
in the first solid. This means that the silicon atoms ‘pile
up’ in front of the growing solid crystals. The situation is
shown schematically in Fig. 6. In keeping with the snowflake analogy, the growing aluminum grain by a snow plow
is represented. The top half of the figure gives a side view;
the bottom a top view.
Figure 4. This diagram shows the liquidus surface for aluminum-rich alloys in the ternary Al-ZnMg system (temperatures are given in °C)
Figure 5. These are dendrites found in Al-20% Cu Liquid.
(Pictures were taken (a) 110, (b) 139 and (c) 360 seconds
after the first grains appeared.) (Photo courtesy of Henri
Nguyen-Thi, Aix-Marseille University, Marseille, France.)
International Journal of Metalcasting/Volume 8, Issue 1, 2014
Figure 6. This shows a schematic view of silicon atoms
in front of a moving aluminum crystal.
11
The author of this paper grew up in Jamestown, New York.
Winter storms often left 30 to 40 in. (0.75 to 1 m) of snow
on the ground. So, a lot of shoveling was experienced. When
a shovel is pushed, the snow quickly piles up in front, so
one can go no further. When the author was a child the city
plowed our sidewalks. A man came by in the night, or early
morning, with a horse-drawn plow. This plow had a “V”
shaped blade the width of the sidewalk. This blade easily
cut through the snow, pushing it to the sides of the walkway.
This is shown schematically in Fig. 7. Dendrites act much
like this “V” shaped plow. Therefore, growing aluminum
crystals adapt a dendritic shape as a response to the alloy
composition.
Growing solid crystals adapt a planar or a non-planar (dendritic) shape depending on the interaction of two factors.
•
•
result, the dendrites in the final casting are thicker. he spacing between arms also becomes larger.10
It has long been known that the spacing of arms of the
dendrite in the casting depends on the solidification time.
One of the first detailed studies was published by Alcoa
researchers in 1963,11 who related dendrite cell size to the
solidification time.
Many of the early papers reported cell size in their studies. However, it is now known that a better measure is the
secondary dendrite arm spacing (SDAS). The easiest way
to measure SDAS is to use the linear intercept method.
This is illustrated in Fig. 9 for a modified Al-7% Si alloy. Lines are drawn on a micrograph where well defined
The growth rate of the crystal. This is usually defined as the velocity of motion of the solid/liquid
interface, in microns per second (R), and is controlled by the thermal gradient in front of the crystal (G).
The rate at which the ‘piled up’ solute elements
can be removed, by diffusion, from the solidifying
front.
For a binary system, the relevant factor for non-planar crystal growth has been shown to be:7
Eqn. 6
Figure 7. Schematic view of silicon atoms in front of a
growing dendrite tip is shown.
The factors m and k are the slope of the liquidus and the distribution coefficient, as determined from the phase diagram
and given in Table 1. C is the concentration of the solute.
DL is the diffusion coefficient of the solute in liquid. So the
shape of the solidifying aluminum depends on the amount
and type of solute dissolved in the alloy.
The grain size is also influenced by the presence of growthrestricting solutes, like Si and Cu. This may be seen by
comparing the grains of different Al-Cu alloys in Fig. 8.
These alloys were solidified at an average cooling rate of
1ºC (1.8ºF) per second. All four figures are shown at the
same magnification. It is instructive to compare the crystals
shown in Fig. 5 and in the bottom half of Fig. 8. In Fig. 5,
the crystals are just forming and are ‘new.’ The arms on the
branches of the dendrite are fine, much like needle-shaped
leaves on a Christmas tree. Also, the dendrites are growing
freely into liquid metal. They are still largely unimpeded by
neighboring grains.
At some point, however, the ‘trunks’ of the dendrites come
in contact with neighboring grains. (This time of contact
is called dendrite coherency.) After this time any further
solidification (and growth of dendrites) can occur only by
thickening of the leaves and branches on the dendrite. As a
12
Figure 8. These micrographs show grain morphology in
a) Al-5% Cu; b) Al-9.6 %Cu; c) Al-16.2 %Cu and
d) Al-25 %Cu. (Micrograph courtesy of David St. John,
University of Queensland, Brisbane, Australia.)
International Journal of Metalcasting/Volume 8, Issue 1, 2014
dendrite arms can be observed and the average spacing
between the centers of adjoining arms is measured. Typically, a number of measurements are made and the results
averaged.
The SDAS can be used to determine the local solidification time at any point in a casting. The results of many
commercial and laboratory measurements on Al-Cu alloys have been reviewed.10 The author of this paper has
developed correlations of his own based on measurements
of SDAS and the local solidification time measured by
thermocouples in the casting. These measurements were
in commercial castings and in thermal analysis samples
cast from 356 and 319 alloys. The results are plotted in
Fig. 10. The curve for Al-Cu alloys in this figure was taken from reference 10.
It can be seen that, for a given freezing rate, the copper-containing 319 alloy has a somewhat smaller SDAS than 356
alloy. The correlation for most other foundry alloys would
probably lie somewhere between these two curves.
Segregation
When a metal is liquid, it is homogeneous. That is, the metal
properties (especially composition) are the same everywhere.
However, there is a different situation in the solid casting.
During freezing there is a redistribution of alloying elements
and impurities. This redistribution is called segregation.
Microsegregation
There are two types of segregation. Microsegregation is the
variation in composition on a very small scale: between dendrites and dendrite arms.
Al-Cu alloy system will be used to illustrate how segregation occurs. This alloy system has been examined in great
detail by researchers. It also forms the basis for the high
strength family of 2xx casting alloys.
The ability to measure SDAS and the correlations, shown in
Fig. 10, represents a useful tool. It can help in learning about
the thermal history of a sample from an ‘unknown’ casting
(e.g., a competitor’s product) or from one’s own castings. It
may not always be convenient to place thermocouples in the
mold, but the solidification time at various points in the casting from the SDAS can be estimated.
The dendritic structure is often visible if you look carefully
into pores on the fracture surface of tensile bars. An example
is shown in Fig. 11. The rounded ends of the secondary dendrite arms are sticking out from the left hand side of this
picture. The SDAS in the sample appears to be between 40
and 50 microns, which corresponds to a local solidification
time of about two minutes (for A356 alloy).
Figure 9. Measuring SDAS by linear intercept is shown.
(Micrograph courtesy of Reza Ghomashchi, University
of Adelaide, Adelaide, Australia.)
International Journal of Metalcasting/Volume 8, Issue 1, 2014
Figure 10. SDAS versus solidification time in aluminum
casting alloys is graphed.
Figure 11. This is a SEM micrograph of secondary
dendrite arms in a large pore (A356 alloy).
13
Figure 12 shows the complete Al-Cu phase diagram.
This is a complicated system. A number of intermetallic
compounds form. Some of the phases in this system are:
q-Al2Cu, h-AlCu, g-AlCu2 and b-AlCu4. In the aluminum
foundry industry there is a concern with the aluminum-rich
portion of the figure and the formation of the q (Al2Cu)
phase. The relevant portion of the figure is shown in Fig. 13.
This diagram is based on data given in a recent study of the
system.12
If an alloy containing 4.5% copper is cast and is held near the
eutectic temperature, the casting will be in the single phase
field corresponding to solid aluminum. This is indicated by
the red box in Fig. 13. According to the phase diagram, this
alloy should be a single phase—aluminum with copper in
solid solution.
Looking at a sample from a casting of this alloy, it is found
to contain a significant amount of eutectic Al2Cu phase. This
eutectic should not be present, according to the phase diagram. So, it is called a non-equilibrium eutectic.
Also, if the distribution of copper in a sample of the casting is
studied by microprobe analysis in a SEM, the finding is that
the copper content in the aluminum phase varies. In the center
of dendrite arms, which corresponds to the first solid, the copper content is low. Moving towards the outside of the arms
which corresponds to metal freezing later, the copper content
increases. An example of this type of measurement is shown
in Fig. 14. (This figure was constructed from Gungor’s data.13)
Solidification scientists have studied this phenomenon for
many years, and have offered models to explain microsegregation. The first and most well-known was given by Scheil.14
This model is based on the following assumptions:
•
•
•
There is a local equilibrium at the solid-liquid interface. The compositions of the solid and liquid at
this interface as a function of local temperature are
described by the binary phase diagram.
There is no diffusion of solute in the solid phase.
Because diffusion coefficients are much larger in
the liquid, it is assumed that the liquid composition
is uniform.
Figure 12. This is the Al-Cu phase diagram.
Figure 13. Detail of the Al-Cu phase diagram is shown.
14
Figure 14. This diagram shows the distribution of Cu
in Al-4-5% Cu alloy (local solidification time is 750
seconds).
International Journal of Metalcasting/Volume 8, Issue 1, 2014
Based on these assumptions, one can derive this relationship
for the concentration of solute in the solidifying metal:
Cs = kCo (1– fs)k–1
Eqn. 7
where
CS is the instantaneous concentration of solute element
in the solid phase, at the solid/liquid interface;
k is the distribution coefficient of solute (wt % in
solid divided by weight % in the liquid);
Co is the original nominal composition of solute in the
alloy and
fS is the fraction solidified, on a weight basis.
Equation 7 has been used to calculate the lower (red) curve
in Fig. 15. The Scheil equation predicts the major features
of the results, but the actual copper content in the solid is
higher and the amount of non-equilibrium eutectic lower
than predicted by the Scheil equation.
ticularly thorough study was conducted by Sarreal and Abbaschian.16 They measured the amount of non-equilibrium
eutectic forming in Al-Cu alloys solidifying at cooling rates
over six orders of magnitude. Their experimental results are
shown in Fig. 17. The amount of eutectic is plotted as a normalized value. When this value is equal to one, the amount
of eutectic is equal to the amount predicted by the Scheil
equation. The approximate range of cooling rates found in
commercial casting processes is also indicated in this figure.
For the slower freezing rates, the eutectic is 70-80 % of the
value predicted by the Scheil equation. But as the cooling rate
increases, the Scheil equation is a better approximation to the
results found. At very fast cooling rates, found in splat cooling or other special processes, a different situation occurs. The
amount of the eutectic decreases as the cooling rate increases.
Various explanations have been offered for this behavior. (For
Brody and Flemings offered a correction to the Scheil equation, which accounted for diffusion of solute into the solid
phase during solidification.15 A simple equation described
the liquid composition during solidification, but to calculate
the final composition of the copper in the dendrites, it was
necessary to make numerical calculations. These calculations were made for an Al-4.5% alloy and their results are
plotted in Fig. 16, together with the experimental results13
and the Scheil curve. The calculations which include solid
diffusion are much closer to the actual microsegregation observed in castings.
Other people have studied microsegregation by measuring
the amount of non-equilibrium eutectic that forms. A par-
Figure 16. The experimental distribution of Cu in Al-4-5%
Cu alloy compared with two models is shown.
Figure 15. This plot shows the experimental and
theoretical distribution of Cu in Al-4-5% Cu alloy.
International Journal of Metalcasting/Volume 8, Issue 1, 2014
Figure 17. This plot shows the non-equilibrium eutectic
in Al-Cu alloys.
15
example, the discussions by Kurum, et al.12 and Sarreal and
Abbaschian16 should be read). It appears that local equilibrium
no longer applies at very fast freezing rates.
It will be instructive now to make some simple calculations.
A slightly different form of the Scheil equation is used:
Cl = Co (1– fs)k–1
Eqn. 8
and the equation derived by Brody and Flemings:
Eqn. 9
where
Cl is the composition of the liquid phase, as a function
of fraction solid (fS)
The term ak in the denominator of Equation 9 is a correction factor to the Scheil equation, which accounts for loss of
solute from the liquid by diffusion into the solid.
The model proposed by Brody and Flemings (B-F) can be
seen to work extremely well for Al-Cu alloys made by conventional casting methods. Unfortunately, this model involved some approximation which may cause problems in
some alloys, as noted by others.16, 18 When the value of ak
becomes larger than about 0.5, the B-F model produces erroneous results. Consequently, it cannot describe the segregation of elements having a high diffusivity, such as carbon in
iron-carbon alloys. For these cases, it is necessary to apply a
‘fix’ to the BF model.18 One may also consider an alternative
formulation.19 However, for the elements commonly found
in aluminum castings, and for all but extremely slow freezing rates, the B-F model appears to offer a perfectly satisfactory description of what happens in the castings. Therefore,
it will be used subsequently by calculating solidification
paths for Al-Si casting alloys.
Many models have been offered to account for the microsegregation observed during solidification. The review by
Kraft and Chang tabulated more than sixty different mod-
The factor alpha is defined by:7, 15
a = 4Dsts/d2
where
DS is the diffusion coefficient of solute in solid aluminum (cm2/sec),
tS is the local solidification time (seconds) and
d is the SDAS (in centimeters, not microns).
Once the local solidification time is known, the dendrite
arm spacing can be calculated from the correlations given in
Fig. 10. Also, the diffusion coefficient needs to be known.
Fortunately, a critical review has been made of the diffusion
coefficients in solid and liquid aluminum.17 The values for
the most important alloying elements in aluminum casting
alloys are shown in Fig. 18.
Another important element is iron. However, the diffusion
coefficient of iron in solid aluminum is two orders of magnitude smaller than the values for the shown elements. Also,
the distribution coefficient for iron is very small. This means
the factor ak in Equation 9 is essentially zero and can be
ignored. It also means the Scheil equation will be valid for
iron segregation. For these reasons, the diffusion coefficient
of iron is not plotted in Fig. 18.
One can now calculate the amount of non-equilibrium eutectic according to the model proposed by Brody and Flemings
(B-F). Equation 9 is used to calculate the composition of
liquid during solidification, and the fraction of solid at which
the eutectic forms (that is, when Cl is equal to 5.65%). Comparing the results of the B-F model to the amount predicted
by the Scheil equation produces the red curve shown in Fig.
19. (The conversion from cooling rate to local solidification
time has been made for the expected freezing range of the
Al-4.5% Cu alloy—100C [212F]).
16
Figure 18. Diffusion coefficients (cm2/sec) for elements
dissolved in solid aluminum are plotted.
Figure 19. This plot shows the non-equilibrium eutectic
in Al-Cu alloys. (Red curve is from Equation 9.)
International Journal of Metalcasting/Volume 8, Issue 1, 2014
els proposed in the literature.20 For most aluminum castings,
however, the situation is relatively simple. The Brody and
Flemings model for segregation and diffusion of solute in
the solid describes the microsegregation.
Calculation of Solidification Paths
Macrosegregation
Now that the equations for microsegregation during solidification have been established, it is possible to calculate solidification paths for casting alloys. An example calculation for the
commercially important Al-Si based alloys will be discussed.
Now consideration is given to the redistribution of solute
elements on a larger scale. In net-shaped castings this is
caused by the motion of fluid inside the casting and is usually related to feeding. Macrosegregation is most easily seen
in copper-containing alloys. An example is shown in Fig.
20. This X-ray shows a section of a cylinder head cast in 319
alloy. Two risers are visible at the top. Both show shrinkage
cavities. Underneath the risers are dark bands in the casting,
where copper-rich liquid has been ‘sucked into’ the casting.
The easiest way to proceed is to assume the distribution coefficients for the binary alloy systems can be used in ternary,
alloy systems. There may be some error associated with this,
but it usually is not serious. There are sophisticated thermodynamic data bases and programs that can be used to calculate phase relations in multi-component systems but these
are not foundry tools. Besides, the goal here is not to exactly
simulate what happens, but to provide a simple model that
one may use to understand what is occurring.
Risers are placed in the mold to ‘feed’ liquid to the solidifying metal, whose volume shrinks by 5-7% during solidification. When the risers are not sufficiently large, they will feed
the casting late in their solidification when the remaining
liquid is enriched in copper (and other solute elements).
The starting point is the aluminum rich corner of the Al-SiFe ternary. This was reviewed in detail in the compilation by
Phillips.21 The liquidus surface, shown in Fig. 21, is based
on his compilation. It should be noted that a rectilinear diagram is used to present the data, even though this is a ternary
system. This is useful, since it is easier to read compositions
on this plot.
Macrosegregation of this sort can also develop in Al-Si casting alloys, but it is more difficult to see this in X-rays of
castings. (The density difference between Al and Si is much
smaller than between Al and Cu.) A metallographic examination is usually needed to see macrosegregation in copperfree alloys.
The Al-Si-Fe system has also been considered in a recent review.22 Eleven different intermetallic compounds have been
identified. Four of them occur in the aluminum-rich portion
of the ternary presented in Fig. 21. They are:
•
FeAl3, which is found in the Al-Fe binary and in
alloys low in silicon;
• a-FeSiAl, which has a composition close to Fe2SiAl8;
• b-FeSiAl, which is usually represented by the composition FeSiAl5 and
• d-FeSiAl, which has the composition FeSi2Al3.
The compound which is of most concern here is the b phase.
This is the intermetallic compound normally observed in
commercial castings.
Now the solidification paths for an AA309 alloy having 5% Si
and various iron contents are calculated. (This alloy also has
1.2% Cu and 0.5% Mg, but this is ignored in the calculation.)
To simplify presentation of the results, the liquidus curves
are not shown, only the phase boundaries are shown. Also
a detailed section from Fig. 21 is taken. The result is
shown in Fig. 22 for alloy iron contents of 0.3 and 0.6
percent. Two segregation curves are given for each case.
The lower (red) curve is for a solidification time of 10
seconds. The upper (blue curve) is for a longer freezing
time of 1,000 seconds.
Figure 20. Radiograph shows the macrosegregation in
a cylinder head casting. (Radiograph courtesy of J. Fred
Major, Rio Tinto Alcan, Kingston, Ontario.)
International Journal of Metalcasting/Volume 8, Issue 1, 2014
From this result, it can be seen that 0.3% Fe is a borderline
case for this alloy. In rapidly solidified parts of a casting
17
there should be no primary b phase, only a ternary eutectic
according to this reaction:
Liquid → Al(solid) + Si(solid) + b
At slower solidification rates, however, primary b should
form. At higher iron contents (e.g., 0.6%) primary b forms
before any Al-Si eutectic regardless of the freezing rate.
This alloy was studied by Center for Advanced Solidification Technologies (CAST) researchers.23 They found that
casting defects were associated with iron contents that produced primary b. However, when they switched to a higher
silicon version of the same alloy, the defects went away. The
reason for this behavior may be seen by considering Fig. 23.
Similar calculations are made for the same two iron contents. In this alloy the higher iron content (0.6%) becomes
the borderline case. Therefore, 9% silicon alloy can tolerate
twice the iron content of the 5% silicon alloy.
In exactly this manner, the CAST researchers calculated solidification paths for numerous silicon contents. In this way they
derived a map of ‘safe’ iron contents for their casting (Fig. 24).
In conclusion, the results of related research, conducted by
Caceres and co-workers,24-25 should be considered. They produced castings in a number of alloy compositions and mea-
sured mechanical properties. Some of their results are shown
in Fig. 25. The tensile strengths for castings heat treated to
the T6 temper are shown on a quality plot (Ultimate Tensile
Strength [UTS] versus the log of elongation).
The red lines show constant values of quality index (in MPa).
The blue arrows indicate the change in alloy composition. For
example, iron was added to alloy 1 to obtain alloy 2. The result was a significant loss in casting quality—about 120 Mpa
according to the quality index. Silicon was added to alloy 2 to
obtain alloy 3. Nearly all of the lost quality was regained by
increasing the silicon content from 4.5 to 9 percent.
A similar result was found going from alloys 1 → 6 → 7,
except in this case copper was added along with the iron.
The loss in quality with the combined addition of Fe and Cu
was larger—about 200 Mpa—but that loss was regained by
increasing the silicon content.
By contrast, when copper was added by itself; in the
alloys 1 → 4 → 5, there was only a small loss of quality
found in alloy 4.
It is hoped that this illustration will make clear the importance of microsegregation during segregation and how higher silicon contents may be used to advantage in Al-Si based
alloy castings.
Figure 21. The ternary phase diagram for the Al-Si-Fe system is shown.
Figure 22. Solidification paths for Al-5%Si alloys are
plotted.
18
Figure 23. Solidification paths for Al-9%Si alloys are
plotted.
International Journal of Metalcasting/Volume 8, Issue 1, 2014
Figure 24. Solidification ‘map’ to avoid primary β is shown.
Figure 25. The plot shows the properties of heat treated
(T6) castings for seven different alloy compositions:
1) 4.5Si-1Cu-0.1Mg-0.2Fe; 2) 4.5Si-1Cu-0.1Mg-0.5Fe0.25Mn; 3) 9Si-1Cu-0.1Mg-0.5Fe-0.25Mn; 4) 4.5Si-4Cu0.1Mg-0.2Fe; 5) 9Si-4Cu-0.1Mg-0.2Fe;6) 4.5Si-4Cu-0.1Mg0.5Fe-0.25Mn and 7) 9Si-4Cu-0.1Mg-0.5Fe-0.25Mn
In this paper, the segregation of hydrogen was not considered. The diffusivity of H is 100,000 times faster than the
dissolved elements: Fe, Cu, and Si. Consequently, the segregation mechanism for hydrogen is very different. In this
case, one will have an equilibrium distribution of hydrogen
as given by the phase diagram.26
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20
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