Physical Metallurgy of Steels  Part 5
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Title 
Physical Metallurgy of Steels  Part 5

Title of Series  
Part Number 
5

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 

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 5 deals with the formation of Widmanstaetten ferrite in steels.

Keywords 
Bhadeshia, Harshad Kumar Dharamshi Hansraj

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the but then maybe we can make a start so this is our time venture transmission diagram and we have already discussed might incite we discussed Loeb a nite and of urbane and also how to use the information that we we have discovered so far in designing new steel so and the followup in temperature again but still remain with the displacing of transmissions and talk about commitments that in fact it's a hard as we mentioned by warm weather and the consequences on the structure and properties what no I explained to you several
00:41
times now that supposing we have Austinite with 2 different kinds of we can transform it into a different course of structure by 2 essential matters the 1st enrolls a homogeneous deformation of the crystal structure In view of the new shapes and as a consequence we get a macroscopic shape change which at the formal opening then plane staying with the larger component and there is an economic correspondence between the parent and brother faded because the neighboring atoms are not actually "quotation mark in their relative positions again on the other hand but when we have reconstructed consummation of the it achieved the change in the crystal structure by breaking all the bonds and rearranging the atoms so that there isn't a large amount of strain energy created and you can imagine this transformation do occur in 2 steps doesn't actually happen like that but you can imagine it happening in 2 steps that 1st we have a displays mentioned you got this part of and bring it over here and therefore you have diffusion which eliminates any shape deformations so that it down mechanisms and I'm going to prevent you these mechanisms in a slightly more entertaining manner this transformation is an extended disciplined transformation here the atoms move in a random manner so
02:18
supposing we imagine the displays of confirmation 1st and you have a queue of soldiers 4 out 18 at the bus stop where the military transport is going to take them to new military service or whatever and they have certain names when they boarded the bus stability in a highly disciplined manner so the Andean neighbors are still the same irrespective of whether they like each other and not have to say it but I don't think there's a lot of strain and you know that this is called a military transmission have a highly disciplined movement of patterns nor the 2nd scenario where we have a
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queue of civilians yeah waiting at a bus stop and the bus arrives and that OK on the bus in an uncoordinated manner and there going to sit next to people that they want to say it
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even tho the positions of the people in the queue a different but we lost all correspondence between the queue and positions in the bus and in that process that will minimize strain but of course this requires the chaotic movement of atoms which means that it must happen at a sufficiently high temperature To allow atoms to move about this trend and there is 3rd kind of transformation is so fast we had the military transformation and then we have the civilian transformation and in all countries you know in addition to the military and civilians we have paramilitary yet having heard that before military is not quite soldiers and they're not quite civilians there usually used for internal audits and there less disciplined than soldiers OK so I'll illustrate what I mean so imagine that we
04:15
have a few again here and there are a lot of atoms and small items not these larger items you know in a disciplined manner but the small ones will go unoccupied wherever they like to occupies of smaller items of defusing during transmission but the larger than the displaced so the change increases structure he is achieved by displays mechanism but smaller items for example carbon atoms which are in the interests these are able to partition between the parent and the product phases during transformation so that's called a paramilitary transmission
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and in technical language that's called upon equilibrium transformations alleges strapped on what what I
05:02
mean so pedigree this means that the change in crystal structure is achieved by displays of transformation the crystal structure there's a chance transformations In other words there will be no change in the iron and manganese atom ratio anywhere between the Austinite and the rich that got the ratio of the manganese atoms to iron Adams both of which are larger and remains constant during transmission so there is no change hand is to iron Adam ratio the it is a substitution of solutes however subject to that constrain the carbon atoms with use during transmission and end up in the face of the preferred to be In the case of skills to Coventry partition interest you however fast diffusing atoms such as problems partition during transformation exactly analogous to the few of smaller lighter atoms boarding a bus so this transformation will have all the characteristics of a display symptoms and that means we will see a large shape deformation that this year and there's been a lot of strain energy and because of that you will have a blank check and the reason why we are getting this kind of a mechanism is because you change the temperature to a higher temperature where the carbon atoms are to mobile To be captured as interface moves so let me now I assure you the list of characteristics of that does that mean listed
08:25
the characteristics of observed characteristics of innovate and modern side I'm going to go through what we mean by weakness and the notice also that because carbon politicians during transformation that means the Fed never has an excess concentration of problems this is not restricted performing below that is the temperature can you inform about that these irritant to the pedia temperature only defines the point where diffusion less transmission becomes possible if the weakness and 5 formation is not restricted by the pizza we confirm that higher than the teaser temperature OK so
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this is what we understand that looks like this is my Austinite structure and we get these characteristic plates at the dinner not covered by the rent adjusted shading we believe that characteristically triangularshaped sections and request that the wedge W. EDT and then they go directly from the Austinite 900 services that "quotation mark primary weakness that violence and supporting we already have some fun at the grain boundary and the plates growth from that then the "quotation mark secondary with 7 price that's just definitions there is no fundamental difference between this and this but the shape here is somewhat different from what we get in modern side and the nite that it is in the firm of a bad shape object so we need to explain all that not obviously I'm drawn this structure so that it looks great cost because you know an OS 9 grains size is about 30 40 micrometres then here we have plates which are growing rapidly the side of the Austin agreements and furthermore
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when we look at this in an optical microscope in partially formed conditions that means that we haven't transformed all of this is modern science this doesn't .period remember when he saw the optical my progressive a nite they were really dark compared with the mindset this does not edged up what does that mean primary explained that they might actually Dr. because it has a lot of structure inside what PC optically this does not this is keen it will appear right in your optical micrograph so you can distinguish this easily from May 9 From the way catches with his back to untempered Montes and you can see also the shapes of the plates here the there's a clue from the optical microscopy that there isn't significant structure inside what we observe as plates of missile obviously if the the change structure is achieved by a displays a mechanism then we should be able to pick up a shape deformation and what other methods we have used for characterizing the shape deformations holding on new shows that the transformation product producers this year what experimental techniques have been used so far what what How do we proved that is shame change experiments so you need some additional view the structure of exit 80 the line pipe and says What is this you won't be able to tell just by looking at it you've got to do a whole series of experiments to show whether the shape change accepted How would you do that but the solemnity of the clues had we had the interference microgravity remember that nice beautiful color showing the demand said plates then the remember that amount let me put it out so we politicians sample
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completely flat and then we
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allow it assembled
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Austinite completely flat American allow to transform into modern site and the services tilted area of modern and interference by cross Kabila lies on height differences so this is not an abstract believes that this is an optical interference might eventually could do an experiment by like but you're structure has to be optically desirable because this is about 50 micrometres In the case of a nite we can't do that right so what technique with what that means they're being used show the shape deformations yeah this is
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something yeah yeah so the atomic
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was microscope which basically the higherresolution method of looking at surface topology and scanning tunneling microscope is similar to that its use different kinds of signals From the from the sort of not inventive but the device which goes over the surface to record a topology so here this game is 1 like a media and Atletico's skaters 200 men Wright said what we see in their commitments that made of costs so
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we don't need to use them atomic force microscopy to
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characterize this the news article Michael Spinks and
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that drew methods hopes to methods illustrated here this is a different kind of interference microscope called Polanski interference might from the you have all of these techniques are available here where you look at the displacement of fringes which are formed by interference and from that you can measure the boosting the share except at a much simpler method is when you prepare your mental graphic specimen there will always be scratches and no scratches on deflected wherever you see the plate of weakness and from from the deflection of the scratch you can work out this year the nation's if you look at them a picture of the San Andreas fault in California yeah From From of the higher you can see that plantations of oranges here were displaced when the verdict slip so that's exactly the same thing this is the deflection of a scratch by phase transformations San Andreas Fault is on a much much bigger scale the so we have here a shape deformations reaches an amendment mainstream but unlike unlike the nite both of these are please give on both sides Of those countries which are displaced in opposite directions up plates of really stand for so
16:40
what's happening is that if we form a single played at the time as illustrated in then the strain energy is just too great to allow the weakness and tried to form at high temperatures close to the a threephase boundary because we raise the temperature of the driving force for transformation decreases and you cannot easily sustain such a large strain energy new to the shape deformation so instead of isolated plates forming you get the situation illustrated indeed where the other 2 plates forming together in such a way that the cancel out each other's shape deformation and that results in a dramatic reduction of strain energy just about 50 Jews from all compared with 600 Jews from or in the case of modern science thank so it's very clever you've got to play its growing together in such a way that they cancel out each other's shape deformation not completely because they don't have the same plane on which performed by the cancel out each other's shape the consequence of this is that you have to nuclear plates simultaneously would the correct shape changes right the probability of mediation therefore decreases and therefore you end up with a very costs like a structure the and that plates are not good for mechanical properties this much coarser than what you get with a knife because the chances of a new creating to appropriate plates simultaneously His of course less than isolated nuclear fission events there spoke from the good point of view witness and fire can grow very close to the 8th 3 temperature well above the 0 because of effect of the strain energy is dramatically reduced by the simultaneous growth or plates that also explains the shape because this plane is different from this plane but the crystal graphic Agrarians that means the same indices but arranged in a different way so clearly there will be a finite angle between these 2 plains and that is the reason why you get a bad shape yeah you cannot have 2 plates with exactly the same shape deformation the different playing it's because they're different shape deformations here and here that the the habit planes are also different and it predicts that there should be a single when you look at this In a transmission electron microscope I was happy with that and
19:31
indeed that's exactly what you see this is you can see this case here it's of course later you know would talk about what a quarter micrometres fall they nite and so forth here it is 1st marriage low angle bonding between the 2 latest reform an optically single plate of weakness and now of course said is this forms biped equilibrium transformation that means carbon mast diffuse during information than the growth rate of this plates will not be fast because the carbon has to get out of the way In order for the plane to to grow so I'm not going to go through the theory forward the growth rate of these things but if you can control problem diffusion controlled growth rate of weakness and the plates and that going each year he is simplified so it's not perfectly accurate accurate theory is available but it does you absolutely everything that you need to know about that nature of the growth process there is no point in doing things in a more complicated way than is necessary in a lecture somebody make approximations that for example the concentration gradient is constant at the interface rather than some kind of an Arab function and so forth yeah OK so the 1st thing is the
21:20
shape or weakness and as well the wedgeshaped is apparently the same as what we call a parabolic cylinder if I take a parabola and appreciate in this direction but that generates a play chess but so far sketch that the shape of a that of a parabolic cylinder that means it's like that he said it's like a parabola being pushed 2 space and Music characteristic radius at the gate of greatness let me just tell president of the more clearly so that is the model of a plate of weakness and everyone clear about that In this distance here we'll call L now as the plane grows companies is being partitioned into the Austinite and this is the free and the concentration and we have the votes the 3 energy because of plan and of the Federal a common tangent to these codes and that is me the equilibrium compositions of the right hand of Austinite which let's see gamma and see how the gamma where of Obama's is the composition that equilibrium compositions of is the company all have In equilibrium and seeing them and I was similarly is the composition all Austinite which is in equilibrium that and somewhere in between these values we have the average composition of steel which article BA it's a secede by it is the average concentration In the scale so this summer when Austinite is in contact with food the maximum carbon concentration it can tolerate is given by this value it which is the 8th phrase bonding and the composition of the firm that is given by this so if I did not draw the concentration profile at the moving interface then it will look something like that the this that distance which that and this is concentration then the composition firing from the interface is see this is our farm and this is Austin the thickness of the firm the length of the farright right has said staff it's a Z stuff it is the position of the offagain interface of again interface this distance here it is the investors not if I did this properly then the diffusion distance would extend much further because it's like an Arab functions but this is a very good approximation to take just a constant now that design an equation for the growth rate somebody regret this concentration profile after the interface has advanced a little bit this is again said and that said this is the initial positions and after certain time it advances that is the amount of carbon that has been pushed as the interface advances and if I may if I take this advances that Z and I have a velocity then that is the amount of carbon that had been pushed ahead of the interface yet because the Fed has this concentration here so I'm happy with that so I know that you need to
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go back if I liked being
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molested and is equal to gain that stock by the team it is the time there will velocities multiplied by this value and is see gamma out and this is Alpha Gamma so gamut of mine is the government is the rate at which some is being pushed ahead of the way yet the rate at which solid is being pushed ahead of him His everybody happy with that he said by the team he said stop by the king multiplied by how much so you we've got to get rid of all right yeah now if I carbon into the Austinite then this concentration C game out will increase from but that's not allowed so we've got to carry away by diffusion the problem from ahead of the interface the same rate at which it is being partitioned so the rate at which we carry aware that governed by the fusion is equal to the diffusion coefficient bank gradient of concentration reaches amount of the minus the divided by the diffusion distance said yeah that Pixar's 1st law diffusion yes we have the concentration gradient times the diffusion coefficient so see minus bar is the difference in concentration and right by the distance that gives you the flaps away from the face those 2 are different than the gun out of a change which is not allowed the in His would happy with that but but somebody
31:12
like that equation out again that the velocities the last thing to understand is the sense star by clean multiplied by by seed gamut of mine is the of again must mean more to the flaps away from the interface in the event of maintained a concentration of being responsible for the the money In them out my divided by said the those involving other related its solid his petition must be the rate at which it diffuses away from the interface if we we are to maintain the equilibrium at the end of that they were unhappy with that Red I'm not going to use it that along with a few distance that the EU is the same as the tip radius r so that is resumed that said Dean His name was you off because as this advances we're leaving behind and we are advancing into fresh Austinite it's a bit of ladies always advancing into fracture last nite so there's reason for carbon to build up the head of the interface apart from the division distance will approximate the diffusion distance as being that the radius so I'm not really rearrange this equation I get develop St His "quotation mark the times scene gamma of the minus he wanted by sea again but when sea of again if you want the the prettiest so you don't actually have an answer for we have the velocity of the function of the radius and this is a very common problems in face transformations that we don't get of Alaska but we get the velocity of the function of some dimensions that might not be velocity was his the radius then added get growth which looks by this spread This is the radius and this is the the last thing as Iranians goes to 0 the velocity goes to infinity so this doesn't really make sense In the 1st of all I don't know which lost debate and secondly I can't really Have a plate of weakness and that is infinitely would grow infinitely fast but it's that makes sense yet so we're losing their view you've got something missing from the theory and there's something missing Is that we have to account for In the facial area which is created as a plate you have a look at that cylinder that did we can work out the cost of creating interface as the plate Pickens so we need to do account for nearly we will the can't for all of creation "quotation mark In and the interpellation energy is Sigma June 4 meters square the signal "quotation mark the international energy "quotation mark unit area so the area cylinder the the cylinder is the cylinder at the pier extending into the broad yet the area of the cylinder head In area since it is illegal to buy the radius so do buy into the region Dubai our times than men so that the UAE my idea 4 other the area is equal to To buy fell into the and the number of problems in the cylinder and and is the number of veterans is equal to finance he held divided by only go home again is the 1 so I can write the land the to fire channeled into our all of Flamingo deal but allowed you divided by Omega .period liability of Japanese everybody happy with that so the changing area has an atoms replied he is given by the right this is 1 here by this 1 reaches some compiled will disappear we have a long way I see yeah divided by Omega it is stated greatest divided by so the rate of change so this area as had happened it is I divided by Omega red no I made a mistake the other way around only elementary mathematics is not my stance which so it's Omega upon our because we had dividing the whereby the and because remember that change of area with the number of items that we had is given by only got about 1 hour soviet creating that interface as the weakness and unfair victims but then so the
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energy cost of it does intervention area for you and people Unitarian multiplied by the so the energy cost His signal In 209 divided by the statement also intervention and deployment area she is the and I have mine the PNG good for us tonight and prefer it and effect of this term directions the free energy cut off to a different value where this difference here it is given by Sigma the only got 1 of which means that equilibrium at the interface to change because if I'm not going the common and will have different values yet so this is a common when the radius is infinite and it changes when the radius is by 90 so here we had the concentration gamma of and here we have a different concentrations he got out of it for final 2 radius so consuming some energy in creating an interface and if the driving force for transmission is that the when the interface radius is very large it does the gene it is the driving force for transformation then that the we are is a driving force for consummation we have a finite separated the is a good thing the Minor Sigma filmmaker divided by so we are removing some of the driving force to create interfaces that already have agreed that so far now at some point the radius will become so small that all of the time was accused of being creating interface and the growth rate will be 0 the device that blows equation 2 0 so critical radius we are seeing the energy is equal to 0 in other words strategy it's a good to signal only all will the critical radius so I can that this equation here as the Entergy the sequel signal if do well on policy minus 1 yeah he passed under substitutes for she yeah I'm just substituting for delta G in terms of the critical radius at growth the becomes 0 and this is the term coming from here yeah I'm happy with that so velocity is proportional to driving force so what we are saying is that when we have a radius which is not infinite we will have a reduction in driving force by this racket here To but blowback do my velocity equation which I wrote earlier yeah and I simply
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multiplied by that which reduces the driving force bye the effect which depends on the tip radius then I will have a more reasonable theory arrived that out again so
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seems velocity is proportional you don't see how far we can write the velocity is equal to the difference in cooperation that is seen again of miners Sieber divided by sea gamma alpha minus the Alpha Gamma if you want 1 contemporaneous This is the previous day and multiply by 1 of 1 city minus wonderful so that's a much more reasonable treatment of the growth of weakness and if I'm not this R and velocity then I get the Classico region is not just through for weakness and fire but also for generating growth for example and many other transformations so far here we have a velocity of 0 when the radius is the critical radius policies and this is the maximum velocity that maximum velocity is when the pope radius is included 2 see so I to prove that we don't differentiate this equation and fined the maximum and brewing for yourself right that the maximum occurs when the equal to us now I don't have any justification fundamental justification for doing this but I feel happy to say that the nature girl at the fastest rate possible but I cannot theoretically justified but let's assume that played girl at a maximum velocity another was that used radius Mitchell give the maximum growth last year the U.S. Navy had no solution at all and I'd like to know it this is an important equations because it contains this comes from the phase diagram In the equilibrium concentration and danger still positions he about it contains functional energy per unit area because the critical the radius depends on the individual energy and you got diffusion coefficient so there's an awful lot of hearing here do allow you to change the parameters for readers and further growth when you're designing a steel now when you mention the
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growth rate of even 7 fell and you compare against calculations so this is the calculated Brady Anderson's major so this rate is the maximum lengthening rate the at the peak of the view when it compare you get a pretty good correlation the calculated rate here is a little smaller spending measure but that's what I was saying I feel happy do choose the maximum rate because the UN mandate the maximum rate is slightly smaller than the actual rate and that's obvious why you know there are many approximations that we've made for example is taking a parabolic cylinder as opposed to a wedge shape and so forth and so on but you can pretty about that lived within 5 micrometres a 2nd you can calculate the growth rate function of steel for example but let me
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summarize them this is what we mean by the research firm but the mechanism of transmission is displacing that means you expect a plate shape you expect an American plane strange shape deformation but with the addition of a feature that took place grow at the same time so that it can happen at a higher temperature but there is absolutely no doubt that it can form a 0 temperature and therefore there must be a partitioning of province during the growth of the plates and indeed when measure the growth rate it's consistent with carbon diffusion program this is important because they when you have to have been of late growing together the probability of nuclear into plates at the same time in the same location and with the appropriate shape deformations is small and therefore the structure will always be costs and it is bad for your mechanical properties rent structures on I'm going to ask you if you have any questions I know nobody will ask any questions but if you do have questioned enough feel free you ask questions any time you can send me an email if you want but then again socalled today thank you