Physical Metallurgy of Steels - Part 2

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Physical Metallurgy of Steels - Part 2
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A series of 12 lectures on the physical metallurgy of steels by Professor H. K. D. H. Bhadeshia. Part 2 finishes with the phenomenological theory of martensite crystallography and aspects of the thermodynamics of martensitic transformation.
Keywords Bhadeshia, Harshad Kumar Dharamshi Hansraj

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some the but Hi stocks the lecture last time by emphasizing some difficulties that we have the first one is that plane on the my consent forms as strange indices for example 215 and even that is the rational in the sense that we 15 is just an approximate representation of the having played indices the real indices are cannot be expressed in terms of indigenous so why does mountainside form on strange habit planes we also notice that the orientation relationship it is a rational in other words you know the close inspect planes from the lettuces are not exactly parallel the approximate white why is that and I showed you some images all the shape deformation which happens when Austinite transformed the modern side and when you measure that accurately that's an invariant planes strain that means it appears to leave a plane undistorted and unrelated so what I'm going to do now is to show you that it's actually impossible to transform Austinite in verite of modern and leave a plane completely coherent another was an invariant that even know we observe that the shape deformation is an invariant planes strain it is impossible to transformed the crystal structure of Austinite into that of modern side by deformation which leaves a plane completely coherent right so these
are the crystal structure of Austinite and far-right and just to remind you know this is the far right and it's going and had them at the center of the unit itself and Austinite with Adams also at the center of the faces of units that I haven't drawn all the India just avoid confusion but this is what we call face and CU all QB closed because it's a close-packed structure and by standard cubic and we need to know how to deformed babies In this so that we can achieve that transformation without any diffusion there some kind of defamation which would change the structure into this it looks unlikely know then look quite different but actually this problem was solved back in 1924 by Bain not imagine if I take 2 unit sales Of
course the and for them next to each other for the suggests that do unit south of Austin inside that I can drill another unit still up for us tonight we haven't done any defamation and this is just a different unit-cell representing the structure of Austinite and you can see that is what he centered at Dragon but this is still Austinite you know you can we can represent a pattern by many different unit sales the only requirement is that whatever units selling shoes has to be able to to fill the space so just to illustrate that in 2 dimensions if I have ever
had in all somebody try this
new towing them but if I have a pattern in which I have a set of points letters points a the regular repeating set of points then you know the obvious units said here would be a square From the just joined the assault groups it's not quite a square who had had revived vent stack those squares into them a new dimension diving the group produced on the other hand I could also a cell which looks looks like this will say this is not working very well and inclined sell like this and still repeat the pattern of the on the border the it's easier so we got a set of points the 2nd a square itself I think the England inclined itself and there's actually an infinite set of cells that I could to represent the same pattern which use the cell which has a small athletic effective than the angles of 90 degrees just for convenience because that reflects the symmetry of the back and better than something like this so in the same way indeed Austinite can be represented as a body
sent it to tribunal we know was represented at the hearing but a about centered the track himself to the point of this is that now it's very easy to see how a change Austinite into interference the fight compress the US nite along this city's and uniformly expand along the horizontal axis taxis then I generate my body sent give itself but that deformation is called the bane defamation compression and uniform expansion in the horizontal plane it's a homogeneous defamation which would change the OS 9 in into far-right buoyed by news of the regulatory could alter the award centered at regular cell of modern site and the deformations required are a written here but this is just a ratio along the z axis we just have the ratio of the lattice parameters of American arsenic and along the sexes you can see that we had forming the 1 1 0 direction Of the arsenic into the 1 0 0 direction of terror so basically the defamation changes last nite in the interference is straightforward it's a compression and the uniform expansion along the other 2 axes it also implies that there is an orientation relationship between the Austinite and the migrants because clearly you can see the ZX seas of the 2 cells apparel so I could write the orientation relationship as 0 0 1 of gamma being parallel to 0 0 1 of and 1 by 1 0 of gamma being parallel to 1 0 0 of them exactly parallel obviously we don't observe that orientation relationship but there's still something missing from the main strength so this is not the orientation relationship use of the this is an exact orientation relationship note this is not an experimentally observed but let's let's put the of the brain information because many people have studied different kinds of defamation which transform Austinite into modern site other than the strength and cases you find that this has the lowest among the strain energy generated if it's the smallest defamation with changes Austinite into modern side so there's still something wrong here that the orientation readership isn't what we measure experimentally but let's just carry on and see whether this deformation can produce and invariant play and at the very least any produced an invariant lines because that's the minimum conditions for modern city transformation that you remember that from the last lecture them To get modern city transformation you must have at least 1 line understood and under-rotated so what I'm going to do them them would represent the Austinite there's this sphere what happens then to the sphere we applied administration what shape that fear become yet have you ever had an Eminem candy yet so if I think my sphere and that compresses ladies and uniformly expanded that becomes like an the an ellipsoid side of revolution about the axis somebody illustrate that now but this is how we
represent the defamation this is the defamation matrix and these are the principal defamation you knew the principal strange because it's a difference in the lattice parameter divided by the original let and this is a compression and these 2 are uniform expansion just expressed in terms of the lattice parameters now I'm not going to use maker speculation In the lectures that I give you in this course but you can download book from my website called geometry of crystals if we actually have to do all the calculations everything I'm going to say can be expressed mathematically rigorously and allow you to make many predictions but today I just want you to understand that might say not actually do calculations but the let's represent the Austinite as a yellow sphere but this is my and here and flooding the ZX cities and this is the x so replied compressed the Austinite then this becomes this ellipsoid here and we have expansion along the excesses right and what I wanted to notice it is written the mainstream we have these 2 lines here which are actually uh corns in 3 dimensions because we also have the Y axis pointing out of the plane of the board which has expansion along the way so always becomes dashed and Obie becomes will and they are all equal land so the land off lawyer is not changed by the brain's and similarly the land of all B is not changed by the fact there are unhappy with that Of those invariant lines ideas can I call those lines in various lines because the lands are unchanged why is that yeah you're absolutely right this is these are not in red lines there simply lines which are understood but there repeated and addition means that they don't represent coherent line between the Austinite and and there is no way I can't find even a single line which is understood that Enron retaliated by the mainstream it's of 2nd problem with the mainstream is that it does not leave any line invariant it does not any lines that means you know this is the fundamental requirement for modern city transformation that we you must be able to find 1 line in vary between the US nite and modern science and the Beijing does not do that so there is something missing From our analysis not surprisingly but I take my Austinite applied urbane straight and I generate this as my my consent and then I rotate stuck inside back the last nite so that 1 of these lines come into exactly that then the combination of urbane strain and a rigid body irritation gives me an an invariant line so if I play right the and the rigid body retention that gives me an invariant lines strings it is a rigid body irritation so the Bass Strait is only 1 part of the defamation the other party is the rotation which generates various invariant lines but there is no rotation which will give me doing their because the need to amend lines to define an invariant playing you knows this line has gone further out of coincidence by applying the rigid body irritations that there still an inconsistency With the shape deformation review of that which is an invariant plane straight everyone OK so far the combination of the base train and the rigid body revision is an air land string and this extra irritation that we have to put in exactly predicts the observed orientation so the bane orientation is all it into the experimentally observed orientation relationship by the rotation that is required to generate the Red Street so exactly the rotation by the by sang here required to convert the mainstreamed into a rigid body irritation predicts the experimentally observed the rational orientation relationship for this predicts he observed the rational for information prevention so 1 problem is solved completely if I give you the lattice parameters of us tonight in the lattice parameters of the deterrence then you can calculate the brain strain and you can calculate the rotation required to generate an invariant light and that gives you the exact orientation relationship between the US identifier in it's only a function of the lattice parameters of the hubris now it's quite important that we understand that the orientation relationship is only a function of the lattice parameters because the antibody irritation doesn't doesn't alter anything any vector just what does the direction of erected a noted the magnitude and all I have here is the latest parameters of the new crystals so when you alloy steel the latest parameter doesn't change very much so you don't expect the orientation relationship to change yeah so you're not going to get very different orientation relationship between Arsenal and might incite different steel that is what this prediction that is what you observed roughly speaking because closely packed planes in the 2 dresses are approximately parallel and the cloak like direction and to crystals are broken down so if in the same steel see slightly different orientations that cannot be because the modern said it's adopting different orientation initiative because it only depends on the left there must be some other factors that influence changes in orientation and more than likely the Austinite does not have a uniform orientation particularly BST on us tonight you find gradients of orientation in just 90 gradients of orientation is just you have gradients of fishing in the markets but even if the composition is and there are no all in homogeneity is India last nite then you will get the same orientation the relationship repeatedly so
what problem is solved we can predict the orientation relationship exactly and that is by ensuring that the combination of being strained and the region but invitation leaves 1 line completely coherent between the 2 vessels so it is OK so far you don't don't hesitate to ask questions if can right so just to summarize the area um result the orientation ship and this applies to any material a combination of mainstream and rigid body occasionally predict the orientations as long as you generated in their life but what we observe as a shape deformation is inconsistent with this because the shape deformation appears to leave you 1 plane completely understood that an unrelated where is this only leaves 1 line understood that an honorably and there is no way so that we could add any irritations which would generate 2 invariant lines and we haven't solved the problem of the strange habit planes either there is no explanation so far on why you know my consent forms on 2 to 5 and 2 5 9 in Sweden 15 gunmen and so forth so what I'm going to show you next is perhaps 1 of the most beautiful theories in all of metallurgy it solve all these problems in 1 go mathematically and the precise predictions and the important thing is to understand the basis of the cheery once you understand the basis of the tapes made the calculations are easy OK so I'm going to start where a single crystal of Austinite of a particular shape because that makes it easier to explain things so here I have a crystal of Austinite a single crystal of us tonight and when it transforms for modern science we get shape change is like a Shia that means believing a plane understood it and rotated so if I not transform that into modern this is is the shape it would become because she had it on those would complaining that change into a square-shaped but this the observed shape but it's got to be the wrong crystal structure because you cannot change us tonight in the mud inside by a share but we proved that the combination of Bass Strait and rigid body irritation and invariant lines you cannot actually of playing political so although we have the correct shape here this is what we observed it's the wrong crystal structure so there's something missing here and I'm representing this shape deformation by this matrix B now if I not shared on this plane on the horizontal plane then the combination of the 2 shares leaves a single line unchanged but because every line on this plane is unchanged by this year every line on this plane is unchanged by the share of the pie to share then there's only a single line that so combination of 2 shares on different planes is an invariant lines straight if someone to do that the croc here if I share on this plane then I generate the right course of structure because this this this is now an invariant lines strain but of course this is now the wrong shape because this is the correction but the problem is not completely sold out I need to correct the shape do this without changing the crystal structure so what kind of defamation and I use In order to change the shame without changing the crystal structure and ideas what kind of defamation during the 2 years in order to change the shape of the cutting the price structure you know when you when you deformities of steel said fair interstitial free steal it doesn't change its cancer from so what is the mechanism of the defamation it's not yet so we can see this crystal periodically so that it should become this Is there any other kind of defamation which doesn't change the crystal structure training but he can't do different modes which would alter the shape but not to change the crisis structure here is training so I periodically end this crystal and you can see the macroscopic shape now is correct and the price of structure is also practical training does not change the crystal structure just puts it in a different orientations and inside this modern said we should expect to see grain interfaces and the 2nd mechanism it is said I periodically slip this crystal I can't change its macroscopic shape into this without the all during the crisis and in this case I do not get any interfaces inside the modern but overseas slipped that so this is the complete solutions because even if these planes directional played like in a 1 1 1 0 1 0 1 the average playing here is not you know it's a combination of rational and the average playing with them and by how much slip what winning I need to correct the and that critics the observed habit planes if you do you understand what I dissent that these facets you might be rational method but the Everest playing here can be anything depending on how much what winning we add to the mountains so everything is now explained and furthermore the prediction is made before the observations that sometimes Martin said will have internal Prince and when the electron microscope we became available those trains were discovered actually a slight later on so all of this this is a complete theory of modern science that the change from last nite demand-side side the defamation is a combination of the veins trade and a rigid body rotation the rigid body irritation converts the bane orientation into the observed orientation and gives us 1 their language is the minimum requirement for my considered transmission but the shape here is wrong because when we observed the macroscopic shape change it's an American plane strain and to achieve the correct shape the crystal of modern secular periodically slip for such that you know this average playing on which it's actually forming he is not a rational playing even though the individual process here rational so
this is what a modern incite plate would look like if it slipped of course we don't have any structure inside the place if it is strange that privacy interfaces inside the plane
and this is 1 of the early observations of trains inside a plate of much inside look at the skating as the spacing areas of Europe 204 arms and the whole crystal is periodically twins this is actually the interface between the Austinite and modern science and concede the line features that I was talking about in the last lecture this is a transmission electron might micrograph wreck the 1st observation was actually done on a replica a :colon replica because I think was came later after the government applications but you need thin forests through proved that the the trains now the next question is when do we get training and when do we get and new you know if I can find before a piece of steel at an almost strain rate then it was slip if I put an explosive and they're blast the steel I don't see lots of mechanical so when modern site forms extremely rapidly the interface is much more mobile than we have training so much inside that forms extremely rapidly will between and modern site which has a dislocated interface and you have produced the slips that they tend to be slipped Martin said and if both of these processes happen perfectly you will not find dislocations in the market so you know 1 of the things you could have mentioned when I asked you about the characteristics of modern site is a high dislocation density what I'm saying here is that there should be a 0 dislocation that events In the modern and that is why get the shape memory you know the interface reverses without reducing the effects if it produces defects like dislocations than the interface would become blocked and you lose your memory and that's that's what eventually you know when of Memory Element many many times it uses its memory because the defects interfere with the moment of the interface so my desired perfectly will not contain a high dislocation densities the dislocations that you've seen In ordinary steel because the shaking relaxes by leftist please notify look at the shape deformation so this is mine so and the formation of modern science cause the surface let us get in there and then strained but if you are calling modern side at a relatively high temperature where both the parents and brother phrases are mechanically weak then this deformation is very large and it cannot be sustained elastically so what happens is we get this thing by then you get plastic accommodation this is out of crime and this is plastic accommodation in the US nite of the is not able to support that large Shia and that is what generates the dislocations because then when the modern said late becomes thicker it absorbs the for the best locations that the scene inside much insight but because of the plastic relaxation of the shape change the dislocation density the high dislocation density indicated last optional change and generally threatened the MS temperature is high ambassador is the modern says that temperature the 1st temperature at which might incite forms during the cooling of the US so it simply isn't true that might incite will have high dislocation density otherwise we would never get shape memory the effects now there is
1 further point which I haven't addressed which identified in the difficulties and that was that at silent much insight formed exactly on 1 1 1 it was not any rational and so forth and at silence is hexagonal close-packed so if I look at the close proclaims that they are stacked in the sequence a B a B AB and Austinite is because back and the same planes are stacked in the sequence ABC ABC NBC so it's very easy to see the deformation of the change off-night in view of silence or that to do is change the stacking sequence In due this stacking sequence by share 1 those close effect planes so to change the 2nd sequence we need dislocations whose bogus vectors and not let inspectors that means that when you operate the dislocation it would change affecting the enormously doesn't change the 2nd sequence because the voters factor is the latest it moves from 1 I've position to another identical position but what we want is a partial list of nations that but by draw that closed by plane protecting means the atoms touch each other this follows me around and think that it looked like planes and let inspectors goes from disposition to this position and that's an a bite you 1 1 0 but expected it so far removed from 1 point to the other according to that there is no change in stacking seats however if I removed the layer on top from disposition to this position that is not elected by the studies and nearby by 6 Drew 1 2 1 1 I think so that's called a partial dislocation fortunately the nation's because what is a change in the 2nd sequence from a to B. and this is also a partial dislocation and that is 3 5 6 if you want to 1 by adding 2 up against perspective so whatever they do is to pass 1 of the dislocations on every successive plane to change ABC ABC into a B B and that's exactly what happens during the formation of a silent might affect it's just like slip deformation where the bogus vector is not alleged it's 0 the at sign in modern society In a Silent Monk last and by 6 2 1 1 dislocations would have agreed successes 1 1 1 gameplay and that changes affecting sequence of gamma from ABC ABC aired changing stacking sequence of government which is really the the agreement now this injustice here and sheer leaves the plane on which the doctors completely unchanged so that's the habit plane of a planned that exactly the shape deformation that exceed so in the case of Upsilon Martin the
diagram that Andrew earlier it is extremely simple but I simply shared the Oscar nite on these planes and I get the correct shape and the correct structure and that is the reason why the habit playing off silent exactly 1 1 1 ,comma now let me ask you a question is the density of the silent might inside the same as as that of course tonight that was close so is the density identical you know what the structure of the iron in the middle of the year is solid hexagonal yet 1 yeah high-pressure now what does that imply that if silent is stable at high pressure with the 2nd left yeah that's has a higher density than us tonight that means that just as she had affirmation cannot describe the transformation because shared doesn't produce a wedding there must also be a small change in volume normally everything and this is a
beautiful experiment which was done in Birmingham University but when you look at the stacking fault in a transmission electron microscope it looks like this because it's inclined to the importance and these are just stepped fringes a 2nd he is like a thin layer of silent much insight but you have to to prove that because you can only be obtained Monday inside if there's also won him change and this experiment proved that encourages 2nd pole I also have a William change not supposing I look at this fall and I using G equal 0 I'm familiar with that 5 familiar with emitting bogus by using a reciprocal lattice vectors which are at 90 degrees to the displacement so there's is a technique in electron microscopy where you can make a dislocation disappear if you use an imaging rector which is at 90 degrees to the displacement because then the displacement is not visible similarly understanding 43 do an experiment Rijeka .period was 0 then they should disappear and look in this life he has disappeared the contrast of this criticism this important not there but not it's very carefully it hasn't completely disappeared and the reason why it hasn't completely disappeared is because of the volume change so to the fore so this is the 1st ever experiment which proved 1st of all that this single study .period can be regarded as a silent march inside the nucleus of the side and 1 of the few have a perfect location which is a bite to 1 1 0 and its associates into posture than inside in between the partial you've created a seven-month and in this paper they also studied a sequence of allies read the William change should be different but if you change the concentration of cobalt than the Williams change on the gamut of silent transmission changes and the contrast here changes in the way changes almost 0 the contrast disappears as the 1 in becomes bigger because just becomes so the real shape change when you get a dynamite it is not simply a share this is gonna like that of silence will lead 2 was a wanting change and this year and the shared dimension is simply given by distracted divided by West the spacing of the 1 1 so we've solved the crystallography all Alpha and silent much that you can predict every feature of the new transformations completely using the theory of crystallography there was OK with that so let's now look into the thermodynamics also demanded information so it is
that he does not transformation in steels that I know of where you can predict things so accurately that because of modern cited a very simple transformation there's no diffusion involved the modern that plates it never crossed and Austinite grain there you know if you look at what a lot to modify it to grow across enough migraine because it most acute their lost you lost the connection with the original Austinite enriching nuclear but might incite only grows in the grain in which its nuclear because it's displaced transformation not some of you might be familiar with this diagram but others may not somebody explain this is the I'm Coburn phase diagram of what the uncovered and this is their right this is the 81 phrase boundary and this is Austinite and on this side we have completely obstinately material on this idea completely freighted material and the way in which we can calculate the space bond rates is the plots the free energy cos apparent in Austin so you know if you have some motel eloquently data and so on you can obtain this PNG curves From From that the I'd familiar with that roughly if I then draw a common tangent to do to because that gives me the equilibrium composition of Boston and Barak at a particular temperature the 1 for which the screening process calculated for measures and the locus of these points as a function of temperature gives me the 81 phase boundary and the locus of these points as a function of temperature is maybe a fun so that's just the equilibrium phase diagram for equilibrium between Austinite and what I want to notice is something which is not listed on the equilibrium phase diagram and that is this point here where Austinite and variety of the same composition at the same if I plot the locus of the Green Point as a function of temperature then I get another line which is called the 0 line the importance of this line that if of composition greater than this -dash like it cannot transform far-right without the composition change because that would lead to an increase in but if I was nite of composition less than discreet .period then it can transform In 2 far-right without any composition changes and a reduction in Korea so diffusion less transformation is impossible if the Austinite competition lies beyond the 0 .period that's the important point might inside can only form at a temperature below but the 0 but the fire last nite of this composition it's possible for my consent form but if I was nite of this competition it's impossible for form because that would lead to an increase in the end I will use this 0 Co frequently when we come to other transformation so it's important to understand it and it's very easy to calculate it either using you know market candidate out you can download free software my website to allow you to do this as a function of the full chemical composition of the steel so my 2nd only performed below when the US composition lies below that the 0 line I'm not In this Sagarin we have nothing about staying energy and leaving now that the modern city transformation is dominated by where so we've got to allow for that strain energy so what exactly like form as soon as the OS 9 reaches below the you have been allowed for a greater under cooling which corresponds to the strain energy the interface energy that green interface energy when you add all the stones up you can define the under cooling and therefore you can define the MSN so just to show you the magnitude so involved to allow for the strain energy we can raise the free energy code of parents that this disparity strain energy and that will have the effect of shifting the Jericho to a low carbon concentrations
and that Italy the strain energy Peter Martins City consummation is obduracy 600 Vermont modern cited training than you but you allow for for the individual energy of the transmittal of Europe 100 for all but the gamma Alpha Prime In the facial it is really quite small when you have a macroscopic name because the service to William ratio is very small and in general the energy due to dislocation is much smaller in comparison so if I had all these up let's say comes to something like 700 Jews from all In total so I've got to cooled below the 0 under the free energy change between Austinite and verite without any change in composition becomes 702 all and that way I can calculate the MS temperature so just to repeat that on a diagram but flooding temperature over here and the free energy change transmission without any change in composition services energy change the "quotation mark Eugene telephone lines the government and not composition change and this is 0 we got downloads is negative then it starts at 50 0 temperature here His approximately linear at the 0 that the G 0 now the stored energy of modern less state 700 Jews from all add up all those so when investors become minus 700 go more so do that that is me my limelight stop and so if I know that effect of manganese and gold on the free energies of alpha and gamma then I can calculate the MSN all I need is that free energy because of alpha and gamma as a function of composition and all these suffering that I mentioned allow you to calculate the free energy as a function of composition there are complications here so the MS temperature doesn't just depend on the chemical composition if you reduce the size of the Austinite grains then the MS temperature decreases if uniformly Austinite before for transforming the much said he understands to be creative and so on but all of these effects can actually be taken into account and the Emirates temperature predicted but for other crimes might incite and for Salomon said and I don't know you know homes at the end but he ain't what all these factors together and there's some software which you can download from a website which will allow you to calculate and using a simple method as a function of chemical composition as a function of the OS 9 grain size and as a function of the amount of defamation that you put into the Austinite but it's roiling defamation wire drawing forging it doesn't matter what kind of defamation it's possible to calculate the effect of the crock before nite on the Anniston NRC is the modern sense that look at you need a little bit
more than just the MSM the unique in all the fraction of modern said changes as you go below the and there's a very famous equation called the question and mother the equation and 1 of I think something like 1953 which works extremely well so line the volume fraction of my consent sequel to exponential minus 0 . 0 1 1 into -minus so this next year is almost identical most this is simply the temperature below the modern science .period temperature and this is the 1 infraction of modern science the that if of a good estimate of how much much inside you will get the function of on the cooling the dollar amounts and there's no meaning actually the and have them that means the much insight finished just because if you look at this equation you will never get 100 percent Martin said but you can define you and temperatures said that you reach 95 percent mark but practical purposes you can define such things but fundamentally there's no meaning to and then you will always have a tiny tiny amount of regained Austinite let between the modern said later so this was a B a thermal consummation that somebody talked about it in the the 1st lecture so just imagine In the lectures you're able you know how how to calculate the complete crystallography of modern and also the transformation temperature and development of transmission below the Anniston you cannot do that for any other transformation instead so the last paper that was written on this at the title the complete theory for the modern test I and say that what onto paper after that there is no more research needed on this subject again I'm joking but you know that there's an awful lot you can do by calculation now instead of making measurements the can not in the next 2 lecture them would talk about what they and there is much more confusing as the transformations because forming at temperatures where it was simple that you might have some diffusion happening during transmission but we'll see we're going to that India and once we have dealt with year they I will be able to design some really nice feel so very lecture on the design of being in the steel which actually has led to commercial success do you have any questions


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