Physical Metallurgy of Steels  Part 9
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Formal Metadata
Title 
Physical Metallurgy of Steels  Part 9

Title of Series  
Part Number 
9

Number of Parts 
14

Author 

License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
Identifiers 

Publisher 
University of Cambridge

Release Date 
2012

Language 
English

Content Metadata
Subject Area  
Abstract 
A series of 12 lectures on the physical metallurgy of steels by Professor H. K. D. H. Bhadeshia. Part 9 deals with pearlite, which involves the cooperative growth of ferrite and cementite at a common transformation front with the austenite.

Keywords 
Bhadeshia, Harshad Kumar Dharamshi Hansraj

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00:00
did again so we make a start today I'm going to finish of all the phase transformations and we're going to do what like it's the last of these transmissions and polite and you can see it's all about diffusion but it's unique amongst all the faces that itself that you have to face growing at the same time From the band facing a and semen that growing together cooperatively from the parent fate so the
00:41
time temperature transformation diagrams obviously because this is a transformation which requires diffusion it will happen at higher temperatures above around 600 degrees Centigrade at a reasonable rate of course you can get it forming at the low temperature but the the rate of transformation will be very slow so for example enough .period for carbon and the manganese and seconds still it put me 45 days you begin to produce power at 450 degrees centigrade so when diffusion is very slow low temperatures its rate of reaction of the incredibly itself especially appear below about 600 degrees recent so that the conditions required to form polite 1st that the common concentration of the Austinite must be sufficient to allow the Austin about fat and seeming to grow simultaneously and secondly that the temperature must be high enough to allow diffusion to happen so we decided that down so the actual
01:51
conditions needed for collective form number 1 is that everything diffuses during the growth of both like iron atoms carbon atoms and any the following elements that you can get to think about the number of cases but there is equilibrium in other words he simply do not get the case where substitution Allen elements not politicians during the growth of 4 alike so the 1st thing is that there must be sufficient diffusion the be sufficient diffusion generally at a reasonable rate that means you'll be at temperatures above 600 degrees centigrade so approximately greater than 600 degrees centigrade so iron atoms carbon atoms and manganese or whatever you have in your material we need to politicians during the growth of life and the 2nd is that the conditions must be such that works seamen died and there I can precipitate from the Austin it must be possible 4 of and the data the precipitate simultaneously from tonight not I explained to you that the happens in the vast majority of that are produced every year but it's usually dead in combination with the right because the vast majority of skills that make up fairly low stress so most of the state is that going to highrise buildings and so on that of the Order of 400 to 500 megabytes because strength and similarly when you make bridges the since all of fairly low and the seals there are certain Steelers which are fully politically and I'm incredibly strong so this is
05:03
what actually transform specimen of polite looks like the CDs nonJews over recalled colonies of Bud Light beach on a microscopic scale consist of a seaman died and fair growing together from Austin I and this role here is 1 of the strongest steals available you know this stance typically is between 2 and a half to 3 and a half .period bicycles so all the suspension bridges except that contain lots and lots of political life you transform at a low temperature and then you draw it out increases strength for the growing means called deformation to stretch it out and will coordinate and make the structure even finer get very high strength and in principle you should be able to get to find the bicycles that but you require the ability to draw the line a great deal and that means you have to have very pure steel that generally speaking the strongest of politics the analyzes is of the order of the the Abascal bicycles stuff that you see on suspension bridges on cable poster and cranes and so forth so that can be incredibly strong because you can make the spacing between the scene and that and very fine indeed I'll give you some examples of that later on but 1st let's go into the history of the bulllike transmissions and let me begin by the question what is a condition which ensures that you can precipitate boat seamen died and fired from the government precipitate both seamen died and fire yeah don't
06:59
worry just take a guess you know don't worry about getting things wrong I often do get things wrong they remember you corrected my mathematics so this is what the pinecovered phase diagram of like carbon temperature this is the last 90 lessons tonight Austinite love seemed and the concentration here is about 0 . 8 I repeat my question what is the condition that allows bold type and seamen died precipitate simultaneously from last nite right so the concentration there has to be at this new technology .period where all 3 phases can coexist in equilibrium so that temperature is about 7 23 degrees centigrade but let me ask you then Is it the case that I can only produce fairly fully politics deal when my carbon concentration is the effect of composition what do I need to do to represent that understand the condition is as follows if I want to precipitate seamen died from Boston 9 then my life must lie in the garment Placida faces if I want to precipitate varied from tonight then my fellow must lie in the upper class demonstrates but if I want to precipitate oratory that on this equilibrium phase diagram there's only 1 point that all 3 phases out In equilibrium and that's technology I if I extrapolate His fate boundaries to lower temperatures that's an extrapolation then any allied lying in this shaded regions can form fully political structure that because any ally in that region is supersaturated with respect to to the right and Siemens that is both in the office of less again and again and that's the decades feels so this region is known as the hood extrapolation the :colon so even if I have an ally which has only 0 . 4 with Percent Coburn divisive locally it's the last night sufficiently combination that extrapolated region and I can make a political steel when so what would be the difference between a fully politics 0 . 4 8 per cent carbon steel and affordability . 8 3 what do you expect to see as a difference between . 4 and point to a great extent governed fully predicted Steve exactly like the amount of statement that will be much smaller In the point fall weapons and carbon steel because carbon assuming that comes from God so all you do is you increase the spacing between the LAN if so that the volume fraction of seamen that is consistent with the concentration and similarly if I raise my carbon concentration to 1 weight Percent then I will get much more died then I would the point 8 of steel enough for the Ford so that's very good about what this diagram also tells us is that if I have a composition the lesson .period percentage that is my C then the equilibrium concentration in the fat which grows from the mean that would be given by the extrapolated out of the scandalplagued boundary and the equilibrium composition of the even that will be extrapolated them at the scene of the bombing so we use the same terminology as before the city Gamma Beta and see then alpha for the equilibrium compositions so
12:12
this is a Matthew drawing diagrams where you can see that if I'm holding was like at this low temperatures well below the effect of temperature then the composition of the Austinite which is in contact with semen that be given by an extrapolation of began seat his boundary and the composition of the Austinite which is in contact with that I will be higher given by the extrapolation of the gamma less out of place here if you want to phase is growing from us tonight then :colon intended use in the Austinite which is in contact with fellow the words the US nitrogen content consumer debt assuming that is observing that covered that so this is a schematic diagram of growth which is I think it's given you know somewhere then we have these lament of seamen died and leveling off when we look on a finding of scale and this is dependent on tonight and the 2 faces of growing together in such a way in anime carbon steel in such a way that the average composition of the borrower light is the same as the average composition of the Austinite so what does that tell you about the growth rate the average composition of people alike is the same as that of the US nite then what does that tell you about the growth rate we haven't got any yellowing editions other than cover but how do you expect the growth rate of wary this time yeah it would be a constant because there is no change in the composition of the Austinite as the polite grows the average composition of the light is the same as that of the US 9th the expected To do that integration with the growth rate is constant but this bed that diagram in mind the term ass here is what we call the intellect spacing and ass out and nasty clearly depends on the amount of carbon you have your steel because that is related to to the volume fraction of seeming so we mostly interested in this in the dilemmas spacing and the way in which Milagros is that the carbon that is rejected by the if users do us a seaman died which is observing the company and you can see that the diffusion not unlike all the transformations that we've discussed so far the diffusion parties parallel do the consummation the company's going from the farright 2 words that seemed begin putting Celeste the growth rate of so
15:25
I can do this in doing that can look at the growth rate of the the farright can work out the growth rate of semen that it doesn't matter does it because there were growing at the same rate so supposing we focus on the scene died then the meat which is the velocity of growth Her velocity times the rate at which the seamen dead is absorbing carbon because there will be a concentration profile this is CVR This is the composition in Austinite which in contact we perceive that and this is the composition of the same type which is in contact with us tonight so here we have seen in direct and serious ,comma we and as this interface advances the same that the absorbing that much cover gets 2nd right at the velocity times see the Dow minus C government freedom the deaths the rate at which seemed intent is absorbing carbon this is the right the bridge the tide absorbs carbon that must be equal during the flocks that is coming from the farright do the same in it that must be equal to the diffusion coefficient so we have the diffusion coefficient and the flux from the far to the seamen died in other words the Austinite that is in contact with the them so this is the game out minus C the government the day spearheaded by the diffusion distance which course In duets with it so far S is diffusion distance and yes is in the spacing we have a lot of here main diet and courage of the features and Alpha and the and the Lamela spacing here In France and the reason why I am using this parameter 5 is because Fuyuan distance is not exactly you know it could be from the middle of the far right to the same that in which case it would be half but you need to think of it more carefully because if region is happening from every point on the far too was assuming that it would be some sections of S 100 so we have a very simple equation that the rate Siemens is absorbing carbon from the Austinite here it is equally clear that diffusion coefficient of carbon in the OS 9 times the influx from the farright to was assuming so the concentration in the Austinite next to the far right is greater than the concentration in the Austinite next to the seaman died and therefore you get a flux parallel to the so we can simply write the velocity is equal to the diffusion coefficient divided by far at times s into the sea get 1 of the government figure divided by sea the minus gunmen so once again we have those from the phase diagram again so although the dynamics is taken care of all carbon infrared which is in contact with us tonight the solubility of governance even that we discussed in contact with the us and we have been in the Lamela spacing and we have a diffusion coefficient while isn't the volume French the average carbon concentration in it determines the dilemmas facing business yet so it's implicit in the determines the thickness of the Syrianbacked relative to to the thickness of the firm so far there is no time timedependent them here so the growth rate will the constant it's a constant growth rate look at that and we just not for that graph looks like that
22:08
led to the velocity forces in the Lamela spacing then I get a occurred which looks like this as in dilemmas facing decreases the velocity increases indefinitely because the diffusion distance decreases the diffusion is parallel to the transformation from decrease in dilemmas facing and the diffusion distance the printed so can you see that there is a problem here it's exactly the same problem that we had a weakness and I don't actually have a unique the last 2 years yeah yeah you know when Negroponte like the creating farright seamen died interface the and there is a cost which we haven't accounted for the let's quickly work out how much interface we are creating if I data Pumas of unless the site is and I have a lot Maryland of semen and the spacing here it is in the spacing then it was enough that you it is simply a threat so the volume sequel to include and the amount of between the seamen died and it is it you To a cube upon pass How do I get that well the area of the Lamela here the face is squared and the number of Islam I have for unit led he is right by that's but the s in dilemmas facing by dividing it by S I get the number of lamb unless I have interviewed but we have to interfaces but later decided that site and therefore we have affected to here so if I cancel out the dams which are common bond that comes to 2 upon S which is equal to the amount of surface freight unit volume this is the amount of the debt interface "quotation mark unit actually have been had set in a little bit of a simple way but this relationship is generally true that if you measure the man linear intercept for grain size then the amount of grain boundary airplane unit volume is still divided by the media Ewing said madam are much so that we have created as we've grown the polenta so the amount of free energy that's consumed in creating a statement that interface gene and recorded by his energy consumer creating the however in interfaces this is a 2 upon pants which is the amount of surface per unit volume multiplied by the individual energy it's a signal international energy the unit area so the units of there G. I which is the cost of creating those interfaces Jews but media cube because signatures for me this and as is a needed therefore when I was using up on that gives me the amount of energy locked up he interfaces inside because that's going to debate that's going to reduce the driving force for transmission so that if that is the .period chemicalfree change and the actual driving force is equal to that minus to stigma upon S so this is the actually French change not really get to a particular in the Lamela spacing Mitchell "quotation mark Astrid perceptive see of critical spacing all of the free energy is used up in creating interfaces so that achieving this but the critical spacing critical facing energy equals 0 and yet Dr. the living quarters Tuesday upon press C so I can really liked that the gene sequences this segment interior 1 1 S C minus 1 upon tests last season played In the letter spacing where all of the driving force is used up in creating interfaces and that Iowa property total is equal to so when 1 necessity of 1 s is the fraction Of the guiding force available drag the interface the 100 OK so I just take the question media derived earlier and multiplied by the Germans Quebec it's then we are we have taken into account the cost of creating interfaces because we know that velocity is proportional to driving force in the 1st approximation so for now rewrite the equation that we had on the previous page
30:59
this equation here then I will the last thing the sequel to the
31:16
diffusion coefficient divided by fighting in the past times seat gunmen were miners gone provided by please the program minus Gamma Beta and then multiply that by 1 minus that's the upon that's all we've done is we've taken that previous equation multiplied by the fraction "quotation mark the energy that's available to drive that will and fact that this equation out velocity was assessed that instead of getting Co which looks at group's today is that we just get rid of that the set of this speech which is not correct move yet because of which goes to maximum and the growth rate is 0 when the spacing is a critical spacing the girl to a maximum so the politely tried to find an optimum spacing not in the case of the mist and repay the maximum as a poultry plant because the experimentally measured values of the growth rate of weakness and that I was slightly higher than the maximum This is not actually the case for poor but we have 2 choices for picking Over the last working so we could simply as you s corresponds 2 maximum the last and in this case you know has to be equal to twice as you can prove that for yourself and the 2nd is the girl occurs at the parade which dissipates the maximum amount of free energies of the maximum free energy dissipation rate this year which leads to Mexico free dissipation rate so the most rapid decrease in free energy and you remember this equation where we had team into some but is different terminology here temperature times the rate of entropy production of entropy production includes a flux stand for what you remember that correct now it had little distance measure nice then the rate of and reproduction dance temperatures also the the energy stationary so there's some logic in choosing this my my own favorite is the 2nd condition where we get the maximum free energy dissipation rate and experiments seemed to confirm that but as I explained to you last and there is no fundamental theory we should tell you that there should be a figure that should the theory that is there is simply too complicated to represent real situations so if you want to do a calculation USA that used to the spacing S which leads to the maximum rate of free energy dissipation even if you try to do calculations of solidification innovative and that growth is not what you get when you get the rate of dendrite growth as a function of the dendrite did radius so you have to have some conditions to take the the action of last year which the would you agree at the transmission happens OK
36:32
that's enough of theory and this is what the natural growth rate calculations would look like for denying carbon steel where the growth rate of the the 1st of the order of you know when the micrometres per 2nd and in the Lamela spacing is below Michael that's quite difficult now we have dealt with alleged growth rates diffusion happening in in the Austinite parallel to the transformation from but there is also growing by of about interfaces here and interfaces are easy diffusion part so we can help dispel flux but also diffusing to the boundary at a much greater so all you have to do it is also a had another 2 which represents the flocks to the grain to the boundary between the but I between the prolife and the Austin so there is also an additional diffusion parts which we haven't taken into account and
37:59
just like we had the flaps going to the wall and suggested the volume diffusion coefficient and this term and then we had the diffusion distance we have a great boundary diffusion coefficient and a grain boundary thickness and this term here is exactly the same as that because we are assuming that the equilibrium that is also the same but this diffusion coefficient times the bonding thickness which is what we can measure experimentally he is actually a much faster diffusion so when you go down in temperature but the diffusion will dominate all you because while diffusion becomes much slower the activation energy volume diffusion is much greater then to the boundary boundaries using back structures of flux not only hasn't had a diffusion coefficient in it but also an area to which the flux happens and the area to which the bonding that happens is much smaller than the 1 of material ahead of Celulosa temperature even tho the volume diffusion coefficient is smaller than the boundary diffusion coefficients began to which 1 division can happen is greater and therefore at high temperatures when diffusion of at low temperatures boundary conditions don't let me just like that so the
39:38
transformation from itself front and if you thought so when we had the equation that the velocity and the rate at which president that is absorbing government sorry that's mine was due the diffusion coefficient in the Austin the Times said the Alpha Gamma minus the the can know so seed gamma alpha minus the gun avoided by S and there was a fighting here this is to the volume of us tonight recently added another which is going about it in the Norwegian backed the thickness of the bindery finds this a get out of minus the gunman feature divided by fire in s so did as units of meters per 2nd and times Delta which is the fitness of voluntary as units of squared per 2nd then there is the thickness of the boundaries and the diffusion coefficient the onemonth Austinite as units of meter square a 2nd reconsidered the dams that has the same units as the that according diffusion competition so I'm not going to go to you including gained In interface energy developments on it's fairly easy to add on a 2nd diffusion and by doing this you don't need to set my reaction is interface controllers while diffusion controlled this equation automatically does you how much flux goes to the boundary and how much flux goes through the wall as he ordered the transmission temperature but so
42:39
this is the same thing expressed again that we have flocks to the volume and the lasted about boundaries and the points you
42:51
represent experimental measurements on I'm governor this is a calculated growth rate but as a function of temperature assuming that diffusion only happens to the volume of material and this go here represents the growth rate calculated assuming that diffusion only happens to the boundary and the could In the middle allowing both of them to happen automatically To conclude but at low temperatures the problem models it's consistent with all the points and it's closer to the interface control diffusion because most of the flux close to the interface at shares that hightemperature as you have much more Austinite ahead of the transmission front so you have a great area to its diffusion can happen and therefore welcome diffusion dominance approaches but the use of public equation you don't need to worry about whether it's 1 diffusion controlled interface and you have just add that to fluxes of so it's possible to calculate the growth rate of the like using this simple the only problem that remains which I'm not comfortable with and which many people are not comfortable with how to select the Inter Lamela spacing from the function of the last versus the spacing if you have been use the maximum free energy dissipation rate as the charts for picking so did suggest that any new generation of the last Bond influx is greater at higher temperatures because you have a greater amount of Austinite to reach diffusion can happen them through the now
44:52
that papers in the literature which proposals also turned diffusion part because diffusion in fact is much faster than in Austin and diffusion of carbon so possible that carbon from the Austinite gets into the fat and then gets to the seamen died what I would predict is that assumed that thickness increases behind the transformation from and there is no evidence that that is happening but supposing you needed to do this calculation you just added that yeah that's not a problem but it's not believable that you're getting thickening of seamen died behind the transformation from when we quenched the specimen and we look at the shape of the seaman died is more less than but we can also take into account the system just like we did before and after moving further out in this case in the case of radio added manganese of substitutions on you can forget moreorless about volume diffusion the difference between volume diffusion and boundary diffusion is so large that all of these cases it's usually boundary diffusion controlled growth the substitution of solids are really happy to be and move about in the boundary compared with the volume of the Austin so the fact that they have to defuse dramatically slows down people like reaction In this case for chromium again let me to show
46:38
you I explained to you that strength depends on India Lamela spacing them and we can reduce that facing by drawing steel but obviously if you start with the finest facing then you end up and even find spacing when you draw the wire that How can I reduce the in the Lamela spacing this so I
47:06
just moved back there forget this light but equations allows you to to reduced in Lamela space but transformation you know what limits state dilemmas facing right what limits the finest basing that I can get what determines the value of the critical in the spacing at which good trade becomes ill inland what has abruptly become 0 at a certain into London spacing the going ahead no 1 knows the content sense here as wide as a growth rate becomes 0 when the spacing becomes the critical value SC yet so when discussing the concept find that all the driving force is used up in creating interfaces you get a 0 growth rate so how can I make it fine I provide stuttering .period no 1 they're providing extra falls is to use a magnetic field it is not coming back to your area of expertise it why would a magnetic field increase the driving force for the consummation of Boston but they cost nite pose a magnetic field on it why would that increase the driving force 4 consummation that so generally speaking Austinite is not magnetic strip yeah that handsome and work can be fair magnetic that they pose a magnetic field it favors the formation of the magnetic phases so that includes a driving force him so by applying a very large magnetic field
49:44
this slide shows you some we did a few years ago this is the steel transformed without a magnetic field as soon as he applied magnetic field you form polite instead the favouring the formation of violent and it had shown that transmission electron might you
50:06
get incredibly fine so this is a spacing of about 50 nanometers this had not been drawn it's just by phase transformation no I'm asking you again Turkey does allow magnetic field is that easy to predict there were difficulties huge new expensive red Is there any other way in which I can increase the driving newly acquired the power of smaller city consistently produce field of 30 thousand staff How can you also quoted the free energy difference between Austinite Hanford normally without magnets you temperature but we have a limited because diffusion must happen yet so we already actually the wires already transformed at about 450 degrees C by patenting according patenting the process for you we will to lend bottle of some of the but what about Halloween you know what elements can I add to the Austinite which remains the farright more stable and all Colorado that basically the only dueling that allowing elements which will increase the change so
51:45
this is completely without a magnetic field and here we also have a spacing of the order of 15 enemy but we drink the chemical composition of the steel just by natural cooling you get 50 centimeters basing that this data will come out soon in script regalia I'm not saying this is practical because God is expensive but it's interesting enough to start with the spacing 15 animators you know we don't even know all how much we could would get to it we now quiet so the letter who had a goal and hasn't had much attention in recent years but it could have some of the major technological advances if we can create without wide drawing the fine structure because then afterward if you draw it you that get it you will find that's all for today