Good morning. Last couple of classes, we looked
at one heat treatment process, that is called precipitation hardening, and in this particular
case what we saw that if you have terminal solid solution, and in that case heat the
alloy to a temperature, where it is a structure it is a homogeneous, it is a single face and
then you quench it. And when you cool it to a room temperature, what you do? You suppress
the precipitation process and subsequently you find room temperature or let it age room
temperature or may be you let it age or enhance the aging you keep it to a little higher temperature.
Then what happens? Very fine precipitates form and these precipitates are so fine that
they cannot be seen under optical microscope, but as a result of this process as a result
of this transformation that takes place in the super saturated solution, it is strength
increases and we look at this in some details. And today, we begin a new chapter that is
called heat treatment of steel, and steel that physical concept - basic concept was
already introduced. We looked at face diagram and we also know that also by changing the
composition, you can get varities of properties, and we will see and by giving heat treatment;
how the structure can be modified. So, what we are going to look at under this
next may be 6 to 8 classes is we will revise, look back something which has already been
covered, so that you are able to follow this lecture, we talked about face diagram; we
talked about time temperature transformation diagram. We will see that in this time temperature
diagrams; there are three distinct regions, you can an when basically a you can see that
you can get three distinct properties, microstructural features, say one is pearlite, another is
martensite and in between you can get bainite type of structure. We will look at how the
isothermal kinetics of the process, and any heat treatment that you do say, if you have
a steel at a room temperature and you have to give it a heat treatment, you will find
light in a solid precipitation hardening, you heat it to a temperature. So, that means
you take it to a temperature where steel transforms to a high temperature crystallography form,
that is austenite and this process is called austenitization.
We will look at austenitization, and what are the factors that determines the process
of austenitization, and how long should you heat sample at a particular temperature, so
that it becomes fully uniform or homogeneous austenite. We will also look at effect of
alloy elements on time temperature transformation diagram, and face diagram. And many often
and very often we do time temperature transformation, and these are drawn at the isothermal condition,
these blocks or these diagrams are generated experiments conducted in the isothermal condition.
But normally when you cool a steel when you quench at a temperature at a particular point
in the steel changes continuously. Now, we will see that what is continuous cooling transformation
diagram, is there a relation between CCT and TTT diagram, then we will look at few commercial
heat treatment very common heat treatment processes annealing, normalizing, hardening
and tempering and we will also look at hardening. Now, coming back you know it may be worthwhile
to look at one basic difference between precipitation hardening and the hardening treatment that
we are going to talk about steel, now in precipitation hardening, when you heat a metal to a high
temperature then quench it rapidly what happens, you trying to keep excess amount of solute
in the lattice. So, your solid solution strengthening may they are to a some extent, but your lattice
is not distorted very much or your actual strength does not increase, so the quench
to material may, so the lower hardness then the structure you had, initially you may have
a two phase structure, you take it single face region, quench it very fast you are retaining
more amount of solute elements. So, normally one would expect that since you have more
solute it should be harder, but it is not so you find that hardness decreases, but when
you age, you form a very fine precipitate all through the matrix and which gives it
high strengthening or now the situation is little different in case of a steel, when
you quench what happens? You hit it to a stage where that ferrite normally at a room temperature
steel is made up of. Let us say ferrite and cementite hit it to
austenite temperature that cementite or carbide dissolves in a matrix you have a single face
structure, and when you quench it you retain high amount of carbide no doubt, but we will
see in this case unlike precipitation hardening instead of going down strength goes up substantially
and we will try and see. Why this happens and in fact the reason lies
within the transformation processes that takes place in the steel during the treatment process
and we recall the part of here, what we have drawn is a part of the face diagram that is
iron meta stable face diagram. Now, why we have drawn a part because most of the time,
say we have a steel, say suppose we have a point 8 percent carbon steel, let us first
consider the process of heat treatment with reference to this particular steel and when
you this is called eutectoid steel and when you heat it to the austenitic region, what
happens you get homogeneous austenite. If you leave it above this temperature called
as a eutectoid temperature around 723 degree centigrade and if you heat it above thirty
to forty degree centigrade above in that case, it will become homogeneous austenite within
a reasonable span of time. And now, we will try to see what happens to the structure what
type of structure will it develop if you cool it on the different conditions and if you
recollect this idea this particular steel is known as eutectoid steel. This particular steel is known as eutectoid
steel and if you remember that structure that is when you cool this steel, so what you have
pearlite forming and pearlite is made up of alternate layers of cementite. So, this is
the way this pearlite forms, so this is a module of pearlite, in that way you will find
number of modules they develop, so when the cementite develops here can also develop austenite
grain on the other side. So basically, so what happens on this growth you know both
will grow parallel? So, within one grain you may find there will be several modules of
pearlite, which are made up of alternate layers of alternate layers of cementite usually in
the microstructure, what we see that normal microstructure steel that you… In that case,
the cementite touches the boundary cementite plate is so fine that it appears as a dark
line, so it will be hundred percent this will be hundred percent pearlite, so hundred percent
pearlite which is made up of roughly around fourteen percent cementite and rest balance
ferrite. So, you will see rest balance thickness of
cementite they will be 1 is to 7 around. Whereas, if you have a steel on this side which is
known as hypo eutectoid steel and here, the structure will be there will be some primary
or we will say that this is called pro eutectoid ferrite. So, ferrite which precipitates or
forms initially it may form on the green boundary and they grow these are the ferrite grains
and balance will gets converted once it reaches, will convert it
into pearlitic structure. So, the structure here will be made up of eutectoid ferrite
and pearlite and this pearlite essentially again will be made up of cementite plus ferrite.
So, in fact the amount of eutectoid ferrite, this will be maximum at this end and as you
pro eutectoid an amount of pro eutectoid ferrite goes on decreasing, so same thing happens
similar thing happens here what you have, when you cool this is called hyper eutectoid
steel and when you cool from this prostenitic region, initially the pro eutectoid cememtite
will form. And then this cememtite when it forms you will find along the grain broundary
first, and they often find a thin film around the grain boundary because these are the likely
places, and in fact and when it grows you know, you can clearly see, because normal
it ages only the boundary between the cementite and austenite cementite and ferrite.
So, you may find that there are quite this type of network quite network around this
and balance will be this portion will be pearlite, but interesting thing which you will find
in hyper eutectoid steel, because of this composition nature here, you know the amount
of ferrite increases this they from let us say, zero percent here at point two to around
hundred percent to close to 0.2 carbon, but in this case, the amount of pro eutectoid
cementite this will be proportional to this portion only this over that entire and that
means is portion is x eutectoid cementite. And this will depend on this is 6 point 6
7 amount of carbon in cementite somewhere in this side 6 point minus point 8 is larger,
so amount of proeutectoid which you have in steel is very less and that is why you know,
you will have only can expect only a thin network of cementite and cementite is very
brittle and this type of structure therefore, a brittle network at grain boundary is unwanted
and all heat treatment process we have to see that, we do not let this happen and we
know that you must recollect that this crystal structure austenite. This is face centered
cubic it has 4 atoms per unit cells. Whereas, in BCC it has 2 atom per unit cell, and then
carbon where does it go, amount of carbon it goes into the interstitial sites and which
we will see in subsequent. And we also have seen, define, you know what
is isothermal transformation diagram, we explain you know what is heat to, let us consider
this eutectoid steel that is 8 percent carbon steel and when you heat it above this you
know 723, the temperature is around 723 centigrade, you have heated it here and then what you
do after heating, you know once, you know that it is homogeneous cool it to a particular
temperature. Let us say, you have a bath, so a metal bath molten bath you have dipped
it a sample, and you are able to follow say, suppose you are and you are able to follow
say suppose keep it for certain different lengths of time and then you quench, say one
after this time, another after this time, another after this time and you can look at
this microstructure of each of these room temperature, what you will find, that structural
feature until this particular point is exactly same.
Say, similar identical feature but once it crosses a particular point, you find the pearlite
starts you do not from pearlite, if you quench from here, quench from here and then you start
seeing pearlite from this point pearlite goes increasing with time and somewhere here it
reaches 100 percent pearlite and after that if you go on quenching, no change in structure
and from this type of experiment, what you can find is when you cool it at a particular
temperature there is certain amount of under cooling. Let us say, this under cooling is
delta T we see that for different delta T, the transformation starts at a specific time
and it is completed after a specific time. So, this is start of transformation this line
represents end of transformation or completion of transformation this line represents end
of transformation completion of transformation and if you repeat the experiment at different
temperature and join these points you find you get like this. And similarly, you will
also find, you quench it for low, you get a different line here you start getting a
different type of structure. Nevertheless, here also it starts after a particular time.
So, this type of c type of curve similarly, what you kept during precipitation, hardening,
quenching also we talked about this type of C shape curve and you know, you must cool
it faster than a critical cooling rate to get specified structure. So, there also to
get a super saturated structure. Here also you will see, you will cool faster than a
critical cooling rate, then here also super saturated structure and we will know about
it little detail a little later. Now, difference here is unlike precipitation hardening the
super structure is extremely hard and brittle. So, this is the basic difference between precipitation
hardening and the hardening that takes place by rapid cooling in steel and we have also
defined, we have also shared that the structure you get becomes finer, as you go down the
transformation temperature goes down structure becomes finer.
Here, it is a little coarse pearlite, course pearlite means lamilar are wide apart, whereas
if you cooling somewhere here, these lamilar they are much fine sometime it may be. So,
fine that it may appear as the dark patch in the microstructure, but at a high magnification
the resolve and we can see that the also made up of alternate layers of cementite and ferrite
and as the structure becomes finer its hardness increases, this is the hardness features,
and when you come here the structural features changes. And this type of structure is called
bainite and when you quench rapidly it has a different types of structure here, you are
not allowing movement carbon atom taking to take place, so you get a super saturated structure
and this structure and this structure is called martensite. And now, let us quickly, there are little
differences in this we are just in coarse pearlite because this pearlite, these are
pearlitic structure, coarse pearlite in fine pearlite they will be much this plate distance
cementite to cementite plate distance will be much smaller something like this they will
be much smaller and entire portion will be filled up. If it is point 8 percent carbon
steel, it will be hundred percent, sorry this is the fine pearlite, we will come to this
bainite little later. So, this structure actually is, so this is where you have very fine pearlite.
So, beanite we have distinct type of beanite. Here, what is happening here under cooling
is much more so that means this is quite high so rate of nucleation will be very high. But
since, the temperature is low the rate at which carbon atom can diffuse this is low
so the distance through which carbon atom can diffuse is will be much smaller here and
these pearlite, where you have this long cementite, instead of that what you have
so may have this kind of structure these platelets, they may not be and they will all originate
they start from nucleation boundary, and they will always you know plates will be very fine
and this will be impossible to see under optical microscope. So, rest of the portion so you
will have such fine broken plateltes of cementite in ferrite matrix, so this will be the structure,
and since it is much finer much fine that pearlite it is stronger and again kind of
bainite. Here, what happens you have some platelets of some ferrite nucleating and then
you some types of acarbide these are meta stable carbide these are even fine and this
type of a structure called acicular bainite. So, you see so you will have some plates of
ferrite nucleating and within this, since this carbon atom they form a particular angle
to the direction of this; if this is the acicular means little light, if this is the shape of
a ferrite drain what happens you have this carbide like this these are precipitated,
and I think you mentioned this carbide here, and this cementite and this carbide is called
epsilon carbide, and we have seen that metastable structure is different competition different
crystal structures, and now when you see this, when you have this, when you have a martensite,
you do not allow the carbon to precipitate out what you have you have this austenite
drain within this austenite grain. You have this type of a needle type of a structure
forming an entire thing they cannot cross the grain boundary, but this entire thing
these are single face structure so will be their fineness will depend on how large is
this austenite grain some of these if grains are closer you can see this needle like structure
in optical microscope and this type of structure is called martensite.
It is, there is no precipitate what you have is no precipitate and here this is the type
of structure and quenching that is maximum hardness say R C scale it may be R C 64. So,
it this is an extremely hard structure you get on the steel; now the question becomes
why is it so hard, I mean what happens carbon atom go when you cool it very fast that answer
lies into that crystal structure, and the atomic size of the iron atom and carbon atom. And if you look back your these figures, see
this is the austenite structure you have face centered these are the potential sides and
if you go back to your earlier notes, how to find out the number of interstitial sites
and it was shown you have one interstitial site per atom. So, you have very large number
of sides available, but it may be worth looking at how many carbon atom you have so all sides
accommodated, if you have every side that is carbon atom then atomic, I mean in that
case percent solute will be you can go upto 50 atomic percentage which never happens it
cannot accommodate so many, because if you look at the dimension of this interstitial
sites these dimension of these interstitial sites are large enough to large enough to
accommodate carbon atom lattice distortion. So, if you accommodate carbon atom here, there
will be lattice distortion we have seen that lattice distortion here in this case is little
less, I mean it is symmetric in all direction you look at this atom, surrounding is exactly
same surrounding of all interstitial sites is exactly same look at these atoms these
site, it is exactly similar face centered cubic.
Now, if you join these, what you get is an octahedron 8 faces you can join similarly,
top and bottom and it is possible to show it was shown also that it is the dimension
in all direction the gap, in this direction the gap they are identical. So, this is, if
this carbon atom goes here it will only have an hydrostatic stress field. Whereas, look
at these atomic sides, so here so carbon goes into this octahedral sides, but which is octahedral
the all these surroundings we are seen if you try and find out that number of atoms
these interstitial sides in BCC structure. You will find, there are three sides per iron
atom so that means a number of atoms you have two iron atom whereas, you can accommodate
up to 6 carbon atoms the sides are available, but the point is if you look at this octahedron
here, so best way to imagine that octahedron here also you have similar it will be exactly
same say look at this octahedron, how does it say you join these they are all identical
so this is half octahedron and similarly, if you join this atom this iron atom layer
just above this you will find there is an iron atom centre iron atom in the next unit
cell and if you join this you get. Now, look you get this octahedron if you look
at this octahedron is much larger than this dimension and this is very small, it is so
small that there will be lattice distorted unevenly, it will be distorted in this direction
much more possibly in this direction, it is so large there would not be any rather it
will be this, will try to come or even it will come closer. Whereas, this side is less
than much less than the atomic diameter of carbon, so this side these atoms will be pushed
apart significantly. And this leads to an acetectic lattice distortion and which has
much stronger field than this it is not only hydrostatic will also have shear stress field;
therefore, these type of stress field can block the dislocation motion much more effectively. Now, a point about that how many items or
carbon atoms you have in steel say suppose, you look at this. How do you calculate say
atom fraction of carbon in eutectoid steel, so eutectoid steel you have 0.8 percent carbon.
So, to calculate to convert it into atomic fraction what you have to do this 0. 08 you
multiply by atomic rate of carbon multiply by atomic rate of carbon so this and if you
do that, you will find that even in eutectoid steel you have 4 atoms of carbon 4 carbon
atom within say, let us say hundred say roughly hundred iron atoms so ratio between is 4 and
hundred, so even within the unit cells so basically what is the if you have a face centered
cubic structure, you have very large number of sides so the position of the sides does
not arise, you have plenty of sides to accommodate carbon atom.
So, carbon atom and these and if at all a carbon atom is located here the lattice will
be distorted no doubts you keep 5 4, I mean some amount of carbon atom, but this distortion
and will be uniform in all direction so carbon concentration goes in so the austenite lattice
parameter is, but it will be it will not the lattice parameter, but what happens if you
do the same thing here what I mention is, if you have a side here gap is very less,
so this will try to expand whereas, this side is larger than this gap. So therefore, what
happens is lattice you keep, want to keep more amount of carbon that is lattice will
get distorted. So, carbon see 8 point 8 percent carbon is
fully soluble in austenite that is, if the temperature is greater than A 1 or if or greater
than this 723 centigrade, now imagine you have heated this to this, you have point 8
percent carbon so here also you have plenty of sides much more than what you have here
but this sides are smaller and if you want to keep this so many carbon atom by force
and mind you, if you have carbon solubility in BCC is very less point 0 2.
So, if you are trying to keep this much of carbon imagine the amount of to the extent
to which this lattice will get distorted and this distortion is so large that this crystal
structure also changes it is no longer this is BCC ferrite is BCC. But martensite is body
centered tetragonal is shown or people is shown saturated solid solution of carbon,
people often consider as a super saturated solid solution carbon in alpha iron we can
often, we write it as alpha prime and since it kept so many carbon atom by force that
lattice will be highly distorted, highly strain and you have so many carbon atom in the lattice
and this carbon atom will inhibit the amount of dislocation and that is why this microstructure
is extremely hard and with it is it becomes brittle as well this hard and brittle. Now, we in fact have talked about it, this
transformation diagram depending on the isothermal transformation, you get if you are transforming
somewhere here you get coarse pearlite structure somewhere here having a transformation, somewhere
here somewhere near the nodes, you have very fine pearlite; similarly, in this penitic
region upper benite called upper benite which is favoury you have broken cementite platelates
broken cementite platelates and here you have ascicular needle structure and within this
needle you have needle like this. And you have very fine epsilon carbide and in case,
if inside you have full needle like structure martensite, and you have increasing as the
structure becomes finer and you get maximum hardness over here. Now, the question comes so that means you
can get a wide range of microstructure in the steel depending on how you allow the steel
to cool. So, one can design and think of various types of isothermal heat treatment process.
Suppose, we say that various design the process of heat treatment where you will get mixture,
let us say in a eutectoid steel you can get some amount of pearlite, some amount of benite,
and balance martensite is possible. So, if you look at the diagram here, so then you
have what you have to do you have maintaining a bath a number of bath different temperature
say, one where pearlite can form and another temperature where beanite can form and another
path, where you can quench may be path this room temperature some water bath you just
quench in water this you have one bath mentioned at this temperature.
So, this path if you follow this path, let it remain over here and holding time should
be greater than the time at which pearlite transformation starts, it must cross this
and then keep it until then you quench to another path and when you quench mind you
even though it is passing this area does not mean benite will form because for benite to
form carbon will diffuse and when you are quenching you are not allowed knowing the
time, so even though it is processing the time looks it is passing through this, but
mind you this is isothermal transformation diagram. It represents this c curve is unless
you have a whole time here transformation cannot take place.
So, what you do you come over here then you hold until benite transformation starts, here
the benite starts keep it for sometime then you quench this transformation till part is
this portion is untransformed. So, then you get a mixture you get a mixture of pearlite
you can get benite, pearlite, benite and also martensite little and this property will be
you can see composite type of relationsip can use, that it will depend on hardness will
depend on how much pearlite, how much benite how much martensite you will have this will
have maximum contribution upto this stand, this will make minimum this will have intermediate
contribution. Now a critical look at, how a pearlitic transformation
actually takes place let us look at the mechanism by which pearlitic forms on forms in a austenite
matrix. So, here you have austenite drain how does this pearlite forms now pearlite
the pearlite to form you have to give a certain amount of under cooling and this under cooling
that is delta T, so you have to keep this steel at a temperature that 723 degree centigrade
and now here, the rate of nucleation depends on nucleation rate depend is proportional
to delta T. So, nucleation is the you can see is the stochastic probabilistic and this
is controlled by delta T. So, that means that is three factor that is nucleation process
that it has to overcome area and it talk about critical energy area that how it will that
free energy barrier for variation to take place that is the critical, and the energy
hump that is to be crossed and this is proportional to delta T.
If you have, let us say first cementite plate nucleus when cementite plate nucleus, if you
look back at this face diagram say, if you are looking at eutectoid steel see you have
come over here now, look at what will be the composition of cementite now, which can remain
in equilibrium with ferrite so here, you draw you will draw a line like this so cementite
is somewhere here 6.6 7. So, now the cementite concentration is 6. 67 ferrite is let us say,
around or virtually 0, let us say ignore this let us say, virtually 0 it will be very small
it will be let us say, 0 it will at this temperature say it is 0.01. So what happens when cementite
nucleus, it will withdraw say around it for cementite to form you will need so much of
carbon content, so if a cementite plate forms imagine it will capture all the carbon atom
from the nearing region, all carbon atom even nearing region goes here to form cementite
this carbon atom from this, so what happens the neighbouring region carbon drops down
drastically from so let us say, this carbon content is this carbon content is neighbouring
point 8 percent carbon here the carbon content is 6 point 6 7 percent.
So, it comes here when the carbon takes place here, so this the platelate of cementite where
cementite has been created. And now once this goes to a certain point this carbon content
decreases so much that a plate of ferrite nucleates and when a plate of ferrite this
is cementite this is ferrite, ferrite nucleates it will reject ferrite has hardly any carbon
content but astenite steel here you have 0.8 percent carbon. So, from point 8 it has to
reject the carbon the surrounding area is 0.8. So, if it rejects the carbon again at
the boundary therefore, the carbon content starts bending up and this process continues
this is rejecting carbon, carbon it is rejecting is all carbon from ferrite comes to this region
when it comes as this carbon concentration increases to 6.67 again a plate of cementite
it creates, so that is what is happening in the process two things are happening to diffusion
say carbon moving from here to here and carbon moving from ferrite to this place ferrite
here, here and with this process these can go in this direction can through nucleation
and subsequent grow in this direction. So, it will grow in this direction as well
as in this direction equally and ultimately what will happen in the microstructure what
you find say, if you have a drain of austenite you have this pearlitic regions growing, it
is growing in all directions, so it will be apparently they may look like this kind of
a circular thing and here different types of that arrangement sometimes from a site
also this plate can be created. So, this is the way and it will ultimately you will find
form into a module and this will grow and until after some time they will start impinging
and then the growth stops and finally, entire structure will be converted into entire hundred
percent, pearlitic structure so what we say for pearlitic transformation to take place,
we have two simultaneous things taking place one is a nucleation, second is growth nucleation
that is proportional to level of under cooling and growth is proportional or growth is a
function of proportional to the diffusivity of carbon atom and diffusivity, we know is
a strong function of temperature say activation energy say it is minus q over r t.
So, this will depend on the diffusivity of carbon atom, which diffuse much faster interstitial
atoms can grow much faster, so this growth will be primarily determined by the diffusivity
of carbon atom and this diffusivity is you know that the temperature goes down growth
becomes slower, so that is why what happens there is an optimal combination nucleation
and growth where the reaction is fastest and that happens near the nose of the TTT diagram.
So, this is the equilibrium A 1 temperature and we have seen this diagram like this so
this nose this is the optimum combination, where the nucleation and growth have optimum
combination which gives fastest reaction or fastest decomposition of austenite into pearlite
diffusion control transformation reaction. But if it exceeds martensite it is something
that the diffusion, we do not allow the diffusion to take place, so that is why we do not fast
there is no c curve, we do not see anything it is just parallel lines martensite start
temperature martensite finish temperature and as you will go, I mean look at the kinetics
of martensitic transformation and martensitic transformation is called where there is no
diffusion it is a diffusion less transformation this is the diffusion less transformation
whereas, in case of a benite structure, you know it is there is diffusion but you can
see the pearlite the carbon atom by large distance and in benite when this carbon atom
does not have to move large, and so that is why at a lower temperature when benite forms
you have such finite structure such small platelates of cementite or excellent carbides. Now, let us look at a little detail the kinetic
or pearlitic transformation, so we have seen that it is possible to follow the samples
from here and rate at a particular temperature, some temperature that means there is some
amount of under cooling that is delta T, that you maintain this bath try to follow this
transformation, and we can see that transformation starts after that particular point and it
is completed starts at t s and it is completed over t f, and how does this volume fraction
increases with time, if you generate a plot to get something like this fraction transform.
And if you plot this fraction transform often you find that this is at fixed temperature
isothermal is constant, t is constant and here this is how the type of plot that you
see that means initially the transformation is slow it picks up in between goes like this,
and what we will see you know how does this take place there is a process of nucleation
and growth. Now, it is often natural that we know that what type of transformation,
we control the degree of under cooling, and the transformation temperature. And what and know you have to visualize and
you have to imagine take place. Now, there will be 2 or 3 distinct cases which is shown
in this diagrammatically here and say suppose we make one assumption, there is constant
nucleation and growth rate which is diagrammatically shown here time at time you will be having
certain amount of nuclei forming, so right at the low t when you have a small amount,
so it is close to t s so many nuclei formed some intermediate what happens the nuclei
the stable nuclei which has overcome the activation energy become true. So, they have grown to
this size they have grown like this, I had the same time which nuclei can also form so
fresh nuclei form so you have 2 parallel processes taking place that and this very simple assumption
constant that means constant nucleation, constant growth rate which is possible to find out
what is the amount of transformation that is taking place that is fraction transform.
Similarly, there can be another stage where we can say that process takes place first
nucleation that all the number of nucleation there are certain specific sites, where nuclei
can form and once these sites gets saturated all these nuclei can form then only growth
can start, so this can be one way of looking at it so whenever to understand any transformation
process we do make certain assumption, how this is taking place and if we make this assumption
then derive an expression which can be connected to some of the parameters which can be measured,
and then we can know and if we are matching if they match according with these and the
derivation that you make with this. And you get one expression the derivation,
and if you make this assumption you will make another relationship fraction transform with
the temperature and time, and then you have to match which is represents the actual situation.
Now think happen as the process continues when f is very low, when f is nearly equal
to 0 this question does not arise, this question of impingement does not arise now here you
can see that here the nucleation here the question of impingement but when it is growing
when grow to this level growth in this direction will be limited and ultimately, what happen
then this can grow, so then this will grow in other directions this will grow. And ultimately
we have this kind of a structure the entire area is pearlite let us say, so
this is pearlite module and this is grown into this area so this is impingement area
and how do you calculate the impegement effect this is what we will go into. This is something like this which is shown,
so if it is you do not have an impingement calculation of volume fraction is quite easy
some of this is nucleus this is another nucleus add this true volume you get the net volume,
but if it impinges then the problem comes up if you add the volume so your volume fraction
added into 2 you get a wrong amount of volume fraction, because this area or this volume
you are counting twice and we look at it that with this concept that, how it is possible
to derive a expression or fraction transform like pearlitic transformation or any diffusion
control transformation this in fact will be even applicable to precipitation kind of transformation
and like even this type of transformation only thing is difference is precipitation
process in a super saturation precipitate is the volume fraction of precipitate is very
low very small. So, the question of this impingement is come
there, so that is volume fraction is so low that it will be necessary, so with this we
stop over here and what we did today is we just revise some basic. Concept face diagram and TTT diagram, we look
back at isothermal transformation, we looked at the effect of transformation temperature
on the structure and we also tried to decide nature of martensite or what should be the
crystal structure of martensite, the distorted BCC and in fact it is called body centered
tetragonal structure. We also talked conceptually concept of pearlite transformation diffusion
place a very important role and we also introduced the concept of nucleation and growth process.
Thank you very much.
