ah 
good morning ah last session i talk about
the role of chemistry of a steel grade how
does it affect quality so understand that
i have talked about ah the mode of solidification
the sequence of solidification which takes
place when the particular steel grade comes
during solidification comes from liquid to
solid state i have mentioned that you know
the solidification sequence can be of two
types is a delta or gamma or something in
between this is decided by the steel composition
now liquid may transform either to delta ferrite
or to austenite gamma so the possible routes
are liquid going through liquid plus delta
to delta and finally gamma another route may
be liquid going to liquid plus delta then
liquid plus delta plus gamma that means in
the liquid steel itself ah through peritective
gamma transformation is starting and then
finally will become total solid austenite
another sequence may be liquid going to liquid
plus gamma that means there is no delta and
finally going to solid gamma it is important
to remember that finally lets speak of the
chemistry the solid this thing solid type
is austenite whether we go through delta mode
delta plus gamma mode or gamma mode of solidification
finally we have austenite but how liquid to
austenite transformation takes place to different
stages that is what is important
so there are three possible routes depending
on the carbon ah equivalent for you know low
alloy steels or plane carbon steels and for
you know stainless steels again the routes
are similar but the criteria there is nickel
equivalent by chromium equivalent and not
carbon equivalent
so it is important to understand when delta
transforms to gamma here you see particularly
for this two and three delta rather in two
delta liquid is becoming liquid plus delta
delta ferrite and then liquid plus delta ferrite
is partly getting transferred to gamma through
the peritectic reaction
now this is important i have mentioned it
is important to understand when delta transforms
to gamma during solidification this route
there is no delta to gamma transformation
during solidification here also there is no
delta transformation only liquid going to
liquid plus austenite and then finally austenite
so delta to gamma transformation in the course
of solidification that means from liquid to
delta and delta to gamma in liquid stage itself
to express only in the medium range of chemistry
so there it is important to know when this
delta is transforming to gamma at what state
of solidification this transformation is possible
this is very important
so then i have mentioned that what stage of
solidification that means at what range of
solid fraction f s this is very important
because why this is important because the
strength of solid shell is different from
delta to gamma so the sequence of solidification
is important to understand what is the strength
of the solid shell what is the you know ductility
of the percentage area reduction of the solid
shell during solidification this is very important
then basically I talked about here from the
iron carbon diagram high temperature portion
that when the carbon or carbon equivalent
is less than point one this is plane carbon
iron carbon diagram or plane carbon steel
here we have carbon content allowing the x
axis but if you have a you know low alloy
steel where instead of carbon carbon equivalent
is important which i have talked about i will
discuss today also what is the formula for
carbon equivalent how it is determined from
the chemistry that means from carbon from
silicon manganese you know other alloying
elements so all this will finally chromium
this will finally determine what is the carbon
equivalently in low alloy steels
so if it is less than point one the solidification
takes place through delta only if the you
know carbon equivalent is between point one
to point five this is the range it is delta
plus gamma that means initially from liquid
delta will form and then there is a peritectic
transformation liquid plus delta giving rise
to gamma that means in the stage in the sequence
of solidification itself delta will transform
to gamma
now the question is depending on the chemistry
it is important to know at what stage this
delta to gamma transformation is taking place
whether at the early stage of solidification
or towards the final stage of solidification
that is very important
now when the you know carbon equivalent is
more than point five solidification takes
place liquid to liquid plus gamma and then
to only gamma so that means there is no delta
during any course of solidification any stage
of solidification so this is important that
how chemistry is playing a role in identifying
what are the solid phases what are the sequence
or formation of delta or gamma during the
course of solidification
ah then i have talked about the the modes
whether liquid to delta or liquid to delta
plus gamma or liquid to gamma there can be
three possibilities it depends on the carbon
equivalent and the relative amount of delta
and gamma during and after solidification
this is also determined by the chemistry that
means carbon equivalent
and i have talked about the concept called
ferrite potential which is given by this formula
two point five into zero point five minus
carbon equivalent for carbon and low alloy
steels the carbon equivalent can be found
out empirically through relationship this
has emerged after lot of experimentation done
by many metallurgists
so from the chemistry one can understand whether
it will be delta solidification mode delta
plus gamma or gamma mode when the carbon equivalent
is less than point one you see no gamma formation
takes place it is only liquid plus delta and
delta to after solidification only delta to
gamma takes place so during solidification
only liquid to delta
when carbon equivalent is between point one
to point five so ferrite potential is between
zero to one for this ranges of chemistry the
solidification mode is delta plus gamma that
means initially delta is forming and then
finally delta plus gamma is forming and finally
during solidification finally only gamma solid
gamma is here so if the chemistry or the carbon
equivalent is more than point five look at
this more than point five means this becomes
negative ferrite potential is less than zero
then the solidification sequence or mode is
only austenite there is no delta formation
then i talked about that in stainless steel
this carbon equivalent is of no consequence
this cannot determine you know what is the
mode of solidification so there what is important
is the ratio of chromium equivalent sorry
ratio of nickel equivalent by chromium equivalent
nickel equivalent is basically all alloying
elements which are similar to nickel in you
know making the stainless steel austenitic
that means austenite stabilizer these elements
like nickel manganese carbon nitrogen copper
these stabilizes the gamma austenite phase
so we can find out nickel equivalent from
this empirical relation where all these manganese
carbon nitrogen copper are austenite stabilizers
so they are club together along with nickel
in determining the nickel equivalent
similarly chromium equivalent consists of
chromium this is the ferrite stabilizer delta
ferrite stabilizer or moly silicon niobium
titanium all these elements are ferrite stabilizers
so these are been clubbed together along with
chromium and finally chromium equivalent we
can determine by this empirical formula
so if you know nickel equivalent by chromium
equivalent from this relationship you can
determine what is the ferrite potential you
know unlike for plane carbon and look low
alloy steels their carbon equivalent is a
criteria in determining the solidification
mode here since you have lot of chromium lot
of nickel lot of other alloying elements so
carbon equivalent is of no consequence in
stainless steel
here the ratio of nickel equivalent by chromium
equivalent is important that determines what
will be the solidification mode whether it
is delta delta plus gamma or gamma so the
ranges are basically point five five to point
seven four these are the ranges as you can
see from this figure if nickel equivalent
by chromium equivalent is less than point
look at here is point five so this is around
yeah point five five around that yeah so if
it is less than point five five look at that
transformation liquid to liquid plus delta
then delta and delta to gamma is basically
a solid state transformation so during solidification
there is no gamma
now when we go to a nickel equivalent by chromium
equivalent or more than point seven four this
dotted line point seven four from liquid it
goes to liquid plus gamma that means austenite
and then finally solid austenite there is
no delta ferrite for this range of chemistry
that have done point seven four nickel equivalent
by chromium equivalent
when nickel equivalent by chromium equivalent
ratio is between point five five and point
seven four then look at what is happening
initially liquid comes to liquid plus delta
ferrite and then these temperature this triangles
not that is triangle delta to gamma transformation
taking place at this points
so as the nickel equivalent by chromium equivalent
is increasing the delta to you know austenite
transformation is the temperature is also
increasing and they are taking place at a
relatively lower solid fraction that means
from delta austenite is becoming more and
more stable so delta to gamma transformation
is taking place relatively all in the solidification
stage
so if you look at the figure of say three
zero four you know stainless steel is a very
common stainless steel here what is happening
initially liquid then liquid plus delta and
this delta to gamma transformation is taking
place quiet at advance stage of solidification
that means when say delta to gamma that means
the solid fraction is around say point five
or point nine then only this gamma transformation
is starting this has lot of implication on
the toughness of the you know strand so this
is this will come to discuss subsequently
so what is important to understand is at what
solid fraction delta to gamma is taking place
at what stage of solidification delta to gamma
is taking place
now you look at the you know three zero one
stainless steel where nickel equivalent chromium
equivalent is less than point five five may
be it is point five two point five three so
here what is happening look at here initially
liquid then liquid plus delta and then solidification
is complete then also it is just delta so
gamma has not started solidifying started
forming during solidification which has started
you know forming only after solidification
is complete
so delta to gamma transformation is a solid
state transformation here and not during solidification
so three zero one here again four thirty these
are equivalent as far as the solidification
sequence is concerned liquid to liquid plus
delta and then solidification is complete
there is no gamma
here gamma since it is very you know low in
nickel equivalent chromium equivalent that
means chromium equivalent is very high nickel
equivalent is low four thirty that delta to
gamma solid state transformation takes place
at you know quite low temperature is around
may be twelve twenty or twelve thirty here
and the solidification is complete at say
fourteen twenty
so for quiet sometime so for our two hundred
degree centigrade only delta is present at
solid phase delta to gamma takes place on
the below this temperature that means during
cooling of the strand you know at the time
of continuous casting and after solidification
we have only delta and gamma is taking place
at quiet low temperature that means delta
will be grains are available dendrites are
available and it is possible that they will
be some grain growth because you know when
austenite forms at the grain boundaries of
the delta then only there is a illuviation
of the grain growth in solid state
so this is very important to understand at
what stage delta gamma is taking place whether
during solidification if during solidification
at what stage like three zero four at the
ah final stage almost at the final stage of
the solidification but if you look at three
one six it takes place when the solid fraction
is may be its a point three point three five
point four so its called early during solidification
delta to gamma is transformation is taking
place
three ten as initially liquid liquid plus
gamma and then solid gamma so no trace of
delta ferrite as i have told you beyond ratio
of nickel equivalent or chromium equivalent
of point seven four it is this only gamma
transformation during solidification liquid
to gamma only no austenite so every grade
if you know the chemistry you can find out
what is the solidification sequence so this
is very important
so as i mentioned that you know depending
on the chemistry you can find out nickel equivalent
by chromium equivalent more is high is the
nickel equivalent let it to chromium equivalent
so more will be the gamma solidification tendency
less is the nickel equivalent it will be delta
solidification more that means more ferritic
solidification and higher the nickel equivalent
by chromium equivalent more than point seven
four it will be austenitic solidification
gamma solidification
so this is important to remember that chemistry
plays a very play an very important role in
identifying the solidification sequence whether
it takes place through delta or delta plus
gamma or gamma that is austenite so this is
very important to remember
now let me talk about the concept of segregation
of alloying element this you know in every
preliminary fashion i have discussed earlier
that during solidification all alloying elements
steel is basically an alloy of iron and other
elements other alloying elements like carbon
three may be three may be silicon there may
be manganese there may be you know chromium
there may be nickel phosphorous sulphur all
sorts of alloying element that means solids
are there you know in the solution so it depends
what are the alloying elements are there you
know but one thing is common that during solidification
the solid has less amount of these alloying
elements the liquid becomes slowly more rich
and more rich in the solute elements this
is called segregation
segregation means the solute alloying elements
are segregating that means they are preferentially
moving from solid to liquid they are segregating
they are preferentially going from solid to
liquid so this is called segregation there
is a partition there is a diffusion there
is a you know movement of alloying elements
from liquid to solid just the reverse from
solid to liquid the liquid is more rich in
the aluminum yes it becomes more and more
rich
so micro segregation during solidification
they results in increase in concentration
of an alloying element except iron all other
alloying elements will undergo this you know
segregation so all alloying elements from
the if the original value is c zero in liquid
steel
suppose say we are ah taking we have taken
a steel where the carbon concentration is
say point one now during the original value
that means c zero for any alloying elements
say carbon further let us assume this point
one so initially the liquid has after solidification
the liquid after liquid you know ah after
it has become liquid that means when you heat
it up it becomes liquid so liquid steel the
concentration of initial concentration c zero
of that particular alloying element say carbon
it can be silicon manganese phosphorous anything
sulphur so that is c zero so during solidification
the value of you know carbon in the liquid
increases and the value of carbon in solid
decreases
so the last solidifying liquid if it becomes
if we denote it as c l it is much higher compare
to c zero and this is can be formed out from
the modified shell equation shell was the
first who try to find out how you know the
concentration will increase during micro segregation
during the course of solidification
so and finally original shell equation was
modified and that and then it becomes a modified
shell equation here just look at what are
the factors c zero is the initial concentration
of the alloying element c l is the concentration
of that particular element in the last solidifying
liquid c l so if there is a increase from
c zero to c l now c l it has increased from
c zero how it is related it is related by
the solid fraction f s small case the distribution
coefficient of alloying elements between solid
and liquid this k is is a thermo dynamic entity
it depends on the you know particular phase
diagram any phase say iron carbon if you look
at plane iron and carbon you can find out
what is the what is the value of k at different
temperature that means the ratio of solubility
of carbon in liquid in solid [divided] by
liquid that means k is always since the solubility
in solid it is less than the solubility liquid
so k is always less than one
so this k distribution coefficient of alloying
element if it is solid and liquid is the ratio
of concentration in solid divided by liquid
it is always less than one for all alloying
elements now this small a these are back diffusion
parameter that means whatever alloying element
is there in the solid you know so it will
try to be with the solid which is forming
later on during solidification it is rich
in relatively rich in the alloying element
compared to the solid which has formed earlier
and moreover the liquid is also having more
of that alloying element so there is a possibility
of you know back diffusion in the solid
so this is determined by this back diffusion
a is determined by the d as their diffusion
coefficient in solid t f is the local solidification
time that means time taken for local solidification
so it again depends on you know the temperature
difference between the liquidus and solidus
and the rate of solidification t l is the
liquidus t s is the solidus that means the
temperature difference between liquidus and
solidus divided by the rate of cooling local
rate of cooling at the particular you know
ah particular distance particular time of
solidification
so this given gives the local solidification
time and l you know is the secondary dendrite
arm spacing this l is again proportional to
the rate of cooling because this secondary
dendrites arm spacing gives the size or indicate
the size of the solid dendrite so thicker
the dendrites are the diffusion will take
more time so it becomes it takes long time
for diffusion to take place so thats why secondary
dendrite arm spacing l is important you know
diffusivity d s is important diffusion coefficient
you know ah local solidification time is important
because mode is this difference mode will
be the solidification time it of course depends
on the rate of solidification
so with all this factors it is possible to
find out c l with respect to c zero c l is
always more than c zero that means due to
the small value of k c l becomes more and
more rich in that particular solute so please
try to understand the segregation of alloying
elements will make the concentration of that
particular element in the last you know liquid
which is solidifying more rich compare to
the original value and because of this we
call it segregation
so the last liquid which is which will finally
solidify it is relatively more rich in the
solutes this is this is two for all solutes
carbon manganese silicon phosphorous sulphur
now to what extent you know the segregation
will take place depend on this value of k
will come to it more is the segregation means
lower is the small k because k is basically
the ratio of solid by liquid ratio of concentration
in solid by liquid for a particular element
it is always less than one
so suppose small k is point one for particular
element that means the liquid is becoming
more and more rich in that particular element
compare to the original concentration and
take another element where k is a point eight
so it is relatively les segregation you will
have less segregation of that particular element
so lower is the value of k more is the segregation
then liquid will become more rich in that
particular element so the final solidus temperature
will become more suppressed so the difference
between liquidus and solid become more wide
so this has segregation has lot of implications
during solidifications
what are the implications as i have told you
lower the value of k more is the segregation
so those element alloying elements whose small
k that means the segregation ratio or the
you know distribution coefficient is quiet
low those elements will create more segregation
more segregation means the concentration is
of the final liquid which is solidifying is
quiet rich much more rich compare to the original
value so what is going to happen more amount
of segregation and the because of the segregation
the solidus temperature is getting more and
more low so the temperature interval for solidification
temperature interval between liquidus and
solidus this solidus is becoming more and
more low as you know k is low more low is
k t s will become more low this i will discuss
in details subsequently so we will come to
know what are the implications of segregation
so please try to remember segregation is a
factor for all alloying elements it is a question
of whether it is relatively more or less
now another important thing is segregation
is not equal when solidification is taking
place between delta and gamma or gamma if
it is through delta segregation amount of
segregation is something if the solidification
mode is through gamma for that particular
element alloying element you know the the
k value that means the extent of segregation
may be different so we have to know what is
the k value for delta segregation ah delta
solidification what is the k value of that
particular element alloying element for gamma
solidification so lower is the k value more
is the problem of segregation more is the
suppression of liquidus temperature so you
have to keep in mind what are the implications
of these so this will be becoming more and
more clear as I go ahead with this concept
