Manufacturing Processes - Casting and Joining
Prof. Sounak Kumar Choudhury
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
Lecture - 07
Solidification of Metals and Alloys
Hello and welcome to the course on Manufacturing Processes Casting and Joining. Let
me remind you that in our last session we started discussing on the solidification after the
molten metal is poured inside the mold cavity.
(Refer Slide Time: 00:44)
We said that for pure metal, if you look at this slide, this is the cooling curve during the
casting; that means, here at this point it is the pouring temperature. This is the
temperature of the molten metal at which the molten metal is poured into the mold
cavity. As time elapses, the liquid started cooling off, but actually freezing begins from
this point .
And from that point when the freezing begins, up to the point where the freezing
completes, this is called the local solidification time. Whereas, from the time the molten
metal is poured, up to the time when the freezing is complete, this is the total
solidification time. The total solidification time is more than the local solidification
time. After the freezing is complete, this is the freezing temperature, then as the time elapses,
the metal is already solidified. And this solid metal is cooling down; and this is the slope
of the curve as shown here, it goes up to the room temperature. this is the entire cooling
curve, that is the temperature versus time; as the time elapses how the temperature
changes starting from the pouring to the freezing, and then till the total solidification
(Refer Slide Time: 02:38)
After that it cools down to the room temperature, but now in case of pure metal as we
said due to chilling action of the mold wall, a thin skin of solid metal is formed at the
interface immediately after pouring. As you understand that during the pouring, the
temperature of the molten metal is much higher than the temperature of the walls inside
the mold cavity.
Therefore, as soon as the molten material is poured, it gets in the contact with the mold
walls, and the mold walls are much cooler. So, the solidification begins at that interface
to begin with. This is what is said here. Now the metal which forms the initial skin has
been rapidly cooled by the extraction of the heat through the mold wall.
Now, this cooling action causes the grains in the skin to be fine and randomly oriented.
Fine, because the cooling rate is very high. Since as I said that walls are cooler, so the
molten metal will solidify very quickly at that interface, and therefore, the grains will be finer. And they will be randomly oriented. Now, this skin thickness increases to form a
shell around the molten metal as the solidification progresses.
Once the metal is solidified, this is the solid metal around the liquid metal, and that as if
is creating a kind of a shell. The thickness of the shell will be increasing as the
solidification progresses, as the time elapses.
Now, the rate of freezing depends on the heat transfer into the mold as well as the
thermal properties of the metal. Of course, that will depend on the heat transfer, how the
heat is transferred into the mold and on the thermal properties of the metal itself, because
different metals will have different rate of freezing. If it is aluminum, it is one slope; if it
is cast iron, it is another slope and so on.
(Refer Slide Time: 04:58)
Now, this is what is happening. This is the molten metal; the entire mold cavity is filled
up with the molten metal. As soon as it is occupying the mold cavity, it comes in contact
with the mold walls, and it rapidly cools down around the wall.
Now, since the cooling rate is rapid, so grains, as you can see, will be smaller, and they
will be randomly oriented. I am repeating that once again. This is the characteristic grain
structure in a casting of a pure metal showing randomly oriented grains of small size
near the mold wall, and large columnar grains oriented towards the centre of the casting;meaning that with further cooling as the time elapses, it goes away from that wall
towards the center.
It propogates in a prolonged elongated columnar grains form. This is how the picture
will look like. From here, it will go to the center. And these are the grains which will be
These will be large and the columnar grains because here the cooling rate is much less
than the cooling rate at the interface of the mold wall and the molten metal. However,
alloys freeze over a temperature range rather than at a single temperature . Here what we
have seen is a particular temperature.
(Refer Slide Time: 06:48)
In case of alloys, the phase diagram has been shown here. This phase diagram is for
copper and this is the temperature, and this is the nickel, and the copper – 50, 50; 50
percent each. There is a composition of the nickel and the copper, each of them is of 50
And here is the phase diagram. With the temperature, here we will have the liquidus and
this is the solidus. That means, in here we will have the solid solution, and in here we
will have the liquid solution. In between we will have a mushy zone, kind of mixed zone.
This is the liquid as well as solid phase.Now, here as you can see that as the liquid metal is poured, this is the pouring
temperature, the liquid is cooling. And in this, freezing begins when it goes to the
liquidus; it ends when it reaches the solidus point. As you can see that this is the liquidus
At that liquidus point, the freezing begins, and at the point where the solidus is there,
there the freezing completes. This is the slope of the curve from the beginning of the
freezing up to the end of the freezing. After it is solidified, solid metal cools down
according to this slope.
Therefore, the total solidification time, like in the case of the pure metal, will be from
the pouring temperature up to the point where the freezing is completed. So, this is what
happens in case of the alloy . As I said that this happens over a temperature range, and
that temperature range is from liquidus to solidus.
This is the phase diagram for a copper-nickel alloy system. Associated cooling curve has
been shown here. This is the associated cooling curve, temperature versus time as we
have shown in case of the pure metal.
(Refer Slide Time: 09:13)
This is what happens, as I narrated to you, as temperature drops freezing begins at the
temperature indicated by the liquidus and is completed when the solidus is reached. It
starts when this is in liquidus state; and it completes in the solidus. The start of freezing is similar to that of the pure metal, of course. A thin skin is formed at the mold wall
again due to the large temperature gradient.
Temperature gradient between the wall and the molten metal at this surface; freezing
then progresses as before through the formation of dendrites, that means, after that
thickness is achieved around the wall, then as the time elapses, the grains become larger,
because then the rate of cooling will be more and long and the columnar grains moving
towards the center will be seen in this case as well.
Those are kind of dendrites, because there are also sub divisions from them
perpendicular to the direction along which columnar grain is moving. Therefore, it will
look like dendrites, that grow away from the wall and moves towards the center.
However, owing to the temperatures spread between the liquidus and solidus, the nature
of the dendritic growth is such that an advancing zone is formed in which both liquidus
and solid metal coexist. I already told you that here we will have both the liquid and the
solid state of the metal.
(Refer Slide Time: 11:12)
The solid portions are the dendrite structures that have formed sufficiently to trap small
islands of liquid metal in the matrix. This solid-liquid region has a soft consistency.
Therefore, it is called as the mushy zone. Since it is soft because it has the solid metal
along with the liquid metal, this is called as the mushy zone.Now, depending on the conditions of freezing, the mushy zone can be relatively narrow.
If it is at a faster rate, the mushy zone will be narrower , or it can exist throughout most
of the casting, when the rate of freezing is relatively higher.
Now, the latter condition is promoted by factors such as slow heat transfer out of the hot
metal and a wide difference between liquidus and solidus temperatures. Meaning that, if
for example, this zone is quite wide, then the temperature at this point, that is at the
liquidus point, and temperature at the solidus point vary too much. In that case this is
Gradually, the liquid islands in the dendrite matrix solidify as the temperature of the
casting drops to the solidus for the given alloy composition. So, this is in brief what
happens - that freezing starts with the liquid and the solid both together, then it goes up
to the freezing point where the freezing completes, and then it becomes solid. During
that period, the temperature gradient between the liquidus and the solidus could be
narrower or it could be wider.
If it is narrower, in that case the mushy zone will be narrow or it exists for less time.
And it will exist for longer time, it will be more if the temperature gradient is more; and
if this is not so narrow, the liquidus and the solidus temperature gradient is higher.
So, this is what we can see. And inside you can see that this is the mushy zone. This is
the characteristic grain structure in an alloy casting showing segregation of alloying
components in the center of casting. These are the alloying components which will be
Here similar phenomenon happens like in the case of the pure metal, that means, there
will be smaller grains at the interface of the wall, and then the grains become larger, and
they get elongated and prolonged moving towards the center, away from the wall. And
here you will have the segregated alloying components. This is the difference in the
characteristic features between the pure metal and the alloys while solidifying.(Refer Slide Time: 14:38)
Now, let us talk about the solidification time, because solidification time is very
important, and we will see how important this is. We should have the ability to determine
the solidification time and should have the provision to control it. Let us see how to
control that .
Solidification of course, takes time. Total solidification time is the time required for
casting to solidify after pouring, that means, where the freezing ends. From the pouring
temperature up to the freezing ends is the total solidification time. Let us designate that
as the TST.
Now the TST – Total Solidification Time depends on size and shape of the casting of
course. If it is bulky, if its mass is more, it will take more time to solidify. And if it is less
bulky, it will take less time. Now, even in one casting, if there are thinner wall and
thicker wall, then the thinner wall will solidify at a faster rate than where the mass of the
material is more, where the thicker portions are there. There is a relationship, known as
Chvorinov’s rule.(Refer Slide Time: 16:15)
So, what is that Chvorinov’s rule? Chvorinov’s rule says that the total solidification time
is equal to a constant Cm into
. Cm is the constant and that is called the mold
constant. Now, the TST is the total solidification time. This is the mold constant Cm; V is
the volume of the casting ; A is the surface area of casting, and the n is the exponent;
usually that is taken as 2.
Normally if you see in the textbooks, you will find that the formula is given as
V TST C
= . That is, the value of the n is normally taken as 2 .(Refer Slide Time: 17:13)
Now, this Cm, that is the mold constant in the Chvorinov’s rule, depends on the mold
material, thermal properties of the casting metal and pouring temperature relative to the
Of course, it is obvious that it will depend on the mold material, what kind of mold
material is there, either it is a sand mold or it is a permanent mold, where the material is
metal. You understand that the property of the mold is different in case of the sand mold
or the metal mold. Therefore, mold material is important here.
Then the thermal properties of the casting metal. How much heat is transferred, heat is
taken out. And the pouring temperature relative to the melting point. Obviously, these
are the factors on which the mold constant will depend. Now, the value of mold constant
for a given casting operation can be based on experimental data from previous
In one word, what is said is that the Cm, mold constant can be tabulated depending on
the previous experience. That means, if we have a particular sand of a particular
composition or a particular metal, mold made of a particular metal, the Cm can be
calculated or Cm can be measured, and this can be tabulated. If you are using the similar
or the same kind of material, then you can take the value of the Cm from the hand book.This can be based on, as I said, experimental data from previous operations carried out
using same mold material, metal and pouring temperature, even though the shape of the
part may be quite different. Because as we said that Cm is a mold constant that does not
depend on the shape of the part, either it is a bigger part or it is a smaller part or it is a
Most important should be those three parameters, that is the mold material, thermal
properties of the metal, immaterial of the shape, and the pouring temperature relative to
the melting point. So, this is about the mold constant which is one of the most important
parameters in the Chvorinov’s rule as we understand that, because this total
solidification time is directly proportional to Cm .
Cm varies from mold material to mold material, because as we said that this basically
depends on the mold material. This is the first in this sequence. Therefore, if it is the
metal mold, this will be of a particular value, and if it is the sand mold then this value
will be different. As you understand that total solidification time, TST will be decreased
if the mold material is metal because the solidification is faster.
(Refer Slide Time: 20:33)
Now, what then Chvorinov’s rule tells us, let us see. This equation, that is total
solidification time as per the Chvorinov’s rule is equal to the mold constant multiplied by 2
. So, this says that a casting with a higher volume to surface area V
and solidifies more slowly than one with a lower ratio.
This is understood; because, once again, this total solidification time is directly
. Therefore, the casting with the higher volume to surface area
ratio cools and solidifies more slowly than one with a lower ratio because the total
solidification time will be more if the V
To feed molten metal to main cavity, total solidification time for riser must be greater
than the total solidification time of the main casting. this is one of the most important
parameters or most important statement that can be concluded from the Chvorinov’s rule,
that when you are feeding the molten metal to the main cavity, the total solidification
time for the riser must be greater.
Meaning that the molten metal in the riser should solidify later than the molten metal in
the mold cavity; and this I repeatedly I kept telling you in my previous lectures also that
the purpose of a riser is to feed the molten metal to the metal which is poured in the
mould cavity after the mould cavity metal is solidified because after the solidification
there will be shrinkages.
To compensate for those shrinkages, we should have some liquid metal present in the
riser, so that, that liquid metal can be fed to the to the mold cavity. That is why we call
the riser as the reservoir of molten metal. Therefore, it is obvious that the liquid metal in
the riser should not solidify at a faster rate than the liquid metal inside the mold cavity.
This is important.
And that the Chvorinov’s rule says how to design the riser because it already says that
the it depends on the
. So, you manipulate the V
in the riser with respect to the
mold cavity, and you can actually make sure that the molten metal in the riser solidifies
later than that of the mould cavity.Since riser and casting mold constants will be equal, design the riser to have a larger
volume to area ratio, so that the main casting solidifies first. This I told you already that
the idea is that the molten metal in the riser should solidify later. Therefore, it will be
riser to have the larger volume to area ratio that will actually solve the purpose.
Because the same molten material is poured inside the cavity and the riser, the riser and
the mold cavity Cm is the same, riser and the casting mold constants will be the same.
This minimizes the effect of the shrinkage, because it will be always ensured in that case
that the molten metal will be present in the riser and it can be fed to the shrinked portions
of the main cavity, the cavity where the casting is to be formed.
(Refer Slide Time: 24:38)
Now, I would like to discuss some of the numerical examples in which it will be very
clear how the theory that has been told to you, particularly the Chvorinov’s rule, the riser
design, how the riser can be designed in an appropriate way. How they can be
implemented in the in practice ?
Let us discuss few numerical examples towards this. Example number 1, riser in the
shape of a sphere is to be designed for a sand casting mold. This is the example. The
casting should be a rectangular plate let us say with length of 200 millimeter, width 100
millimeter, and thickness of 18 millimeter. This is the casting, final casting which is the
rectangular plate.If the total solidification time of the casting itself is known to be 3.5 minute, let us say
from previous practices, determine the diameter of the riser, so that it will take 25
percent longer time for the riser to solidify. Here this is the application of the theory in
the riser design area. You have to design the riser knowing that riser should be
solidifying 25 percent time later. Let us see how to do that.
Now, we know that the casting is the rectangular plate. The casting volume we can find
out. This will be length into width into the thickness. So, this will be 200 length, 100
millimeter is the width, and the thickness is 18 millimeter. So, this will be 360000 3 mm .
The volume being determined, the casting area has to be found out. Since it is a
rectangular plate, we can find out the area by 2 into 200 we have the length into 100 is
the width plus 200 into 18 is the thickness plus 100 width and the thickness 18 because
it is a rectangular. So, the area we can find out this way. This will be equal to 50, 800
mm . All dimensions are in millimeter and they are getting added up. Therefore, it will
ratio will be 360000 divided by 50800, and it will be equal to 7.0866 let us
say about 7.09. This is unit less because this is a ratio of V and A.
Now, the casting total solidification time can be found out using the Chvorinov’s rule
that is the mold constant into
we found out for the casting as 7.0866, Cm
. If the total solidification time of the casting is known, so the total
solidification time is equal to
which is equal to 3.5.
Now, from here, we can find out the value of the mold constant Cm which is equal to 3.5
minute divided by (7.0866)
. it will be 0.0697 2 min/ mm because 3.5 is given in the
minute. Now, that Cm has been found out, we will use it at a later stage and the riser
volume you can find out. Now you have to find out the riser volume. We said that the riser in the shape of a
sphere. Therefore, the riser volume will be
π D for sphere. D is given. We can find out
this volume and we can find out the area. About this in more detail, I will discuss in my
next lecture session.
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