Physical Metallurgy of Steels - Part 3

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Physical Metallurgy of Steels - Part 3
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A series of 12 lectures on the physical metallurgy of steels by Professor H. K. D. H. Bhadeshia. Part 3 deals with the mechanism of the bainite transformation.
Keywords Bhadeshia, Harshad Kumar Dharamshi Hansraj

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about Chen OK so today's lecture
is about Bain and will do exactly what we did that might incite through begin by looking at the the characteristics of a nite and then tried to explain them quantitatively and From what you learned today we should be able to design some really good in the filing that connect me with it so everything that I'm going to tell you today is quite important if you want to design Benedict steel it OK so
once again are looking at transformation between Austinite which has a face and a cubic but it's a close-packed structures that we often call here close by into a body centered cubic crystal structure there's no difference Is the Alec topic transition is still going from space center cubic bodies and the CU but they might forms at a higher temperature than might inside so I explained to you that things get a little bit confused because it's possible for for some items to be more at the higher temperatures now I explained to you
that there are 2 classes of phase transformations the reconstructive transformations and the displays of Transportation's I'm going to explain that once again so imagine that we have all of us tonight and it has 2 kinds of atoms than it did Brown items and the square at that that could be for example manganese and iron and we want to change this unit south from the shape to shape which looks like this that's all phase transformation change the unit itself we can do it in 2 different ways the 1st is very simple that the homogeneously deformed this so that we create the correct this year we have lost tonight and this is the new crystal structure of Ferrari and since we have achieved this changing increases structure by a physical deformation there is no diffusion involved so here for example of this Adam has this neighbor in the product phase and it has the same neighbor In the current phase recall that anatomic correspondence an atomic correspondence between the parents and the product faces this Adam knows where it came from independent and that is why we get shape-memory factory displaced and machines because it just recreating the arrangement of atoms without losing the neighbors furthermore if you look at this the chemical composition of this region is exactly identical through that region the corresponding region the parents but the most important thing to notice here is that given that we change the pattern in which the AT and arranged the overall shape has also changed and that is the macroscopic shape deformation which recorded invariant plane strain if this plane undistorted Enron congregated on a macroscopic scale but it's also very large because if this is surrounded by other crystals then it's going to cause a lot of strain and so these are strained energy dominated transformation not imagine better forest transformed by a homogeneous deformation that means displacing I then take this corner cut it off and translated onto the site that is effectively diffusion I'm cutting off this corner translating it onto the site so that's diffusion and it's happening because strain energy is a bad thing you know the reasons the energy of the transformation products so if I do a displays events mentioned and also diffusion itchy what's known as reconstructed transmissions because we do not get a shape deformation apart from volume change so this is exactly like when a glass of water solidifies In 2 eyes you do not get the changing shape apart from the 1 in the red there's a lot of fluid flow which programs the formation or large strains now obviously if you have fewer people going on in the form of diffusion then if the square atoms prefer to be In 1 phase than the other then there was partition petition means you end up with more of the square comes in 1 side compared with the parent phase so here look we've got the largest concentration of square items then we started off with because square items 1 to be in the product phase in this case going so there will be a composition change because diffusion allows the system the approach equilibrium better than the displacement mentioned but there is no macroscopic shaved change apart from 1 and that will endanger the isotropic not just normal to the havoc plane as we did in the last election but there were unhappy about the difference between these 2 you can imagine that the reconstructive transformation happens like a displays of transmission but you have to transport matter In order to award the build of strain so these are obviously closer equilibrium but they require atomic mobility so the happen at relatively low temperatures and problem at bay nite you the reason why in the past few decades In the there's been a lot of discussion about how they might forms His is because it's forming at a temperature where there is a possibility of the fusion again now a lot of the discussion is quality if you look at the literature you know it's not really proving things quantitatively and what I wanted to focus on is the quantitative details because then you can actually make a prediction that you can verify experimental but if you just discussed like politicians know that if I do this this will happen the dismal Rio proved In that the proof of a theory comes when you make a prediction which is not known and then you do an experiment validated so I want to go to that process for the day-night transformation and at the end of that to see whether we can make predictions so once again Stop me if you have any questions now this is a
classical time temperature transformation diagrams and got this this is experimental where we have ironed .period full weight Percent covered and here we have ironed .period full weight same carbon and and mainly and I'd like you to focus on this for the moment the iron manganese covered phase diagram it's divided into 2 Seko's here and this is of course representing the modern sidestepped temperature Seiko which is at higher temperatures represents reconstructed transformations for example a lot to move the far-right and so on and this represents transformations we get the shape deformation which is an invariant mainstream that last year from Boniface displays of transmission and of course might incite is also displays not the problem is that when we reduced the following elements in our steel everything becomes very fast within the time scale here this is the 1 2nd so when you tried to measure of of ladies you do not pick them up a separate Co because that is happening too fast compared with your ballot on 3 but you will find that there is a retardation of transmission here corresponding to this break In the QC curves now can anyone explain I remembering this is a logarithmic scale here why does manganese have a smaller effect on displays of transformations compared with reconstructive transformations any ideas you know this is this is several orders of magnitude change independently compared with approximately 1 order of magnitude change their nappy headed to wake the scent of 9 that's what is so let me ask the question in a different way what is the role of aligning elements how do they work doesn't just apply to manganese but everything that we had to steal yeah correct high-visibility ability means you're absolutely right what does have ability mean no not not defamation nobility means the ability to harden the steel so if you can call it slowly and still get Martin said that is a high nobility if you can cool it if you have to cool very rapidly to get mountainside then that is a little harder than think this case for example to get might instead have could really fast yes but that's a little nobility and here I conclude relatively slowly so that a higher ability I still want to know how as manganese influence the ability any ideas what allowing elements very good so yeah the elements have partition between the phases after diffuse threat and the fusion can be slow so how does that explain the difference between reconstructive and yeah there isn't diffusion of displays so the effect is going to be a much smaller but there is in fact so where does that come from yeah you know even the displays of transformation is influenced by so how does manganese influence if it's not diffusing so diffusion is a kinetic effect the 2nd player Is there another effect the thermodynamic yet so if it influences the relative stability is of the US and fire that means a difference in the energy between last nite and character that will have an effect on all transformations the manganese will retire or transformations because it reduces the free energy change between Austinite and far-right so this is this is
quite important when designing steals there due
effects of yellowing editions here go then would try this the 2 that's quite correct and of solid solitude is the same as Alan division within the the first one is in influencing gene and the Gamma Alpha is the driving force for patents transmission the relative stability Of course tonight and all all transformations influence influence and the 2nd 1 is diffusion division is only happening with the reconstructed transformations and therefore there will be a much bigger effect of solutes on reconstructive transformations so it's only irrelevant reconstructive transformation look so let's let's carry on with him understanding that time temperature transmission diagram so if
your reaction is happening rapidly because there aren't enough solutes then you may not pick up this late between the 2 2 Koreas because there will be an overlap of information and generally speaking this place is at approximately 600 degrees centigrade because it's at that sort of a temperature that substitution of values and even iron become more by the difference between reconstructive and displays of transformation is pretty close to 600 degrees centigrade that's why when you want secondary hardened steel because secondary hardening requires a things like molybdenum Carbide and so on to precipitate that cannot happen at 400 degrees centigrade you've got to temper your steel at about 5 or 600 degrees centigrade to get substitution of solutes to move now we can actually calculate these diagrams that so you can just download the software would doing calculations of geeky diagrams from our website put in whatever following elements you want and the predict the relative ships 2 sets of sequels there is of course more detail and the up with Seiko here represents for example the formation of a lot more the ferret and talk about a lot to move it and later it's fact starts at the Austinite grain boundaries and polite as well and then we have to be we missed 7 variety here what's known as Upper Bay nite nobody nite and Mike and good luck to all of these during the 12 lectures but today we are going to focus just on the day-night reaction here OK so what is the bay
nite there has been some translation of notation from the from Macintosh of Microsoft this is not 1 to micrometres here the symbol does that represent micrometres in Korean or not at objected this is to give you an idea of the scale of the Microsoft shares this is 0 . 2 the plate of Benedict Ferro is 0 . 2 micrometres stick typically and it is about 10 micrometres in land the not usually that tells you that optical microscopy is not good enough the result I don't know what it is the resolution of an optical microscope "quotation mark it's actually bigger than that because the redolent of light is 509 yeah so to get any resolution below about 500 men managers disease yeah so there no way that you can just use optical microscope the result the structure of a nite To see whatever drawn over here you need a leader you know a good scanning electron microscope or preferably transmission electron microscopy conventional transmission electron microscope with nothing fancy so other late-night user forms at a relatively high temperature and we have plates of there I which are completely free From semen that precipitates but there's a lot of seamen died in between the plates of foreign and in the case of Loeb a nite you have some precipitation inside the plates of forever and a smaller amount of precipitation between the that is a classical my extremely well established we transform at a relatively low temperature you get a structure which looks like this is transform at a relatively high temperature you will get what's known as top of a knife and whatever theory you have you've got to be able to explain this is going to be able to explain this 1 did eventually get enactment of the Get up rain and why is it important that this is a very bad Mike structure because here we are not tampering not controlling the precipitation of semen assuming that actually forms during the course of consummation so that tend to be very big part of seamen died and that ruins the toughness if you're working on high-strength steel and that's why we know if you look at structural steel there have low-carbon concentrations if their accelerated that could generate need Microsoft isn't always have problems usually less than 1 0 5 8 per cent if you're doing accelerated cooling the strength comes from the very fine scale here you cannot achieve a quarter micrometres grain size by Phil mechanical processing or in the normal way here you just achieve it by phase transformations but this is about in fact nobody nite is stronger than that of a nite because form that the lower temperature and yet it is tougher than Overbay nite because all these particles are fine so if you have a higher carbon concentration than it's better to have Loeb nite than up a we haven't actually explained how the structures are generated but these are the facts we know about the MicroStrategy property relationship here
is an actually micrograph and noticed the scale here this is the 1 micrometres so the plates are typically about 0 . 2 micrometres in thickness and there is this phase in between the plates which can be seen this is simply the rest of the modern site it's been partially transformed yet 1 of the problems with the steel such as laying pipes views and the literature line 5 students is that people call it a name I call them my constructed name for that really looking at is material which had been transformed over a range of temperatures it and therefore are all the particles have grown attached to each other and shape no longer represents the shape during growth if you want to look at the mechanism of transmission you've got to look at Foshan transformation that uniform summit some consummation product and then you quenching so this is my in this case if I fully transformed this and particularly if it's the composition of lying that the problem concentration is very low then all of the grains will grow touch and change the shape because they have to fill space 2 people just give it a name that quality vesicular whatever without understanding how these crystals form so this is the upper Bay not where you can see that inside the plates there are no Carbide
In contrast this is Loeb a nite where in addition to the seamen died in between the plates again look at the scale business half of my permitted In addition to to the precipitation between the plates which is 1 of finest scale you have some of the carbon precipitated inside the plates of because this is a very characteristic way of distinguishing between the upper and lower brain nobody nite you also get semen that presentation inside the plates and the scale of the Carbide's is smaller and that's why nobody 9 tends to be careful then up of a nite even tho it is stronger normally when you increase the spread the toughness decreases did you understand why why do you expect you know in general and talking in general widely expect the strength of the toughness decrease if this trend so supposing that I
look at the flow stressed all fired because you get a tough material if it is able to to flow classically even those strong yet because plastic flow absorbed a lot of energy supply plot b I have been OK so I'm plotting here the temperature and here stress then the reason why we get about how brittle transition you know I am is that the flow stress of BCC iron is very sensitive to temperature there because it's a it's a relatively open structure the characters a relatively open structure so that the pilot barriers to dislocation motion is lodged its the variation groups look stresses very sensitive to temperature now if I blot on this the cleavage stressed that means stressed to break the crystal without much plastic deformation that doesn't absorb energy that's what we call brittle fracture but not on this the cleavage stressed and the key that stress is pretty insensitive you temperature so that means that below this temperature I have to do but in this region I have a clear and in this region have ducked out here is that this is brittle and the transition is of course the duct of Britain transition temperature now you you see what will happen if I increases strength but increases trends are so let me just naval the physical plastic floor and this is for for cleavage the fire increased their strength so stronger then you can see that the death of brittle transition temperature increases and the material will be In a brittle over a bigger temperature range so well received between upper and lower Bay contradicts this because when we have Loeb a nite stronger but it's still tougher because the particle size is small there are unhappy with now this is a beautiful
technique which allows you to look at the shade in 3 dimensions in the real looking at 2 different surfaces at the same time and of course this is you know that if you look at the scale this is using optical microscope but not is you can do this on a very fine scale right you know of a technique by which you could do this very easily and on a very high resolution looking at services at the same time if I ask you to protect their sample which is only 1 micrometres big but you're looking at services how would you do it some of you may already have used this technique How would you machine sample which is only 1 micrometres by 1 might from what 1 might we have the equipment here yeah focus on being yeah we heard of that so you just the name of wines to cut out a sample and then you can look at it uh normally we use it for the making pinpoint specimens but you can do the same to me here and the importance of this so this is again a nite and it's partially transformed Q of a of this very nite this is all much insight you can see that the Bay is late change in 3 dimensions so it's not a needle it's not a secular vesicular means needle-like like me like like yeah it's a plate in 3 dimensions can you tell me why the bay nite which is darker than insight that is a very good way of distinguishing nite from modern side in specimen which contained both even using optical microscope why does the midnight .period you go Carbide's here so this is this is underemployed might inside so there aren't many interfaces to attack we a chemical but this contains structure in the form of provides and so on therefore and natural attack it more and you can recognize optically the difference between 9 and might incite if you have both of them in your structure obviously this fully transformed you can't tell the difference of case but you can see the contrast is pretty spectacular now the next
characteristics characteristic that we need to look at when we are forming a picture of the atomic mechanism is whether the transformation producers a should change or not the church said James beyond and I tell you that you know the scale of urbane I played is about 0 . 2 micrometres in thickness so we cannot use the interference techniques that I showed you for might incite to look at the surface really caused by the reactor use another technique which does the same job so this is a crystal of Austinite which is polished completely flat and then it's allowed to transform into banal and then we look at it in an atomic force microscope or a scanning tunneling microscope so basically those are techniques to look at surface topology on a very high resolution you can get atomic-resolution but you can get quantitative information about the surface topology these are individual platelets of nite and you can see that there is a very large shear deformation here it just like much insight but there is 1 more thing I want you to notice this is the the adjacent Austinite here and that is relaxed yet member in the last lecture I talked about plastic relaxation Of the shape
deformation Of the quickest so if we have an elastically accommodated their shape change then you will get the full effect building off the surface and this is the modern inside under the surface so this is of and this is gamma gamma and this is elastically accommodated but this is quite a large deformations if had a high temperature where the Austinite is mechanically weak then it was time to relax goodbye plastic deformation so instead you get a shape deformation which is nice and clean where the but then then you get a relaxation and here we have but Cameroon and gamma and this is plasticity this is a very major consequence on the structure of a your memory said that the transformation interface has to be decided that means that you know the dislocations in the interface must be able to move without diffusion if you put obstacles in the way Of those specifications then they interface cannot move those obstacles can be precipitates that can be dislocation Bengals and so on so the plate of a nite simply stopped growing even tho it has not had anything else when this plastic accommodation builds up sufficiently the plate of a nitrogen growing simply stops growing that means you get very very fine plates much finer than with modern civic transformation but that's a good thing From the point of view of structure property relationships and I'll show you a transmission electron micrograph all the structure at the interface between May 9 and
Martin said nite and Austin
so this is the diagram that I just threw out where we looking at plastic accommodation indigenous and dust and cost 1 more thing this is very important is that if the I grows into this region then there would be a large orientation gradient within the bank because it's dislocation produced Miss orientation so this is a
transmission electron micrograph of that interface where this is Austinite and this is the varied look at the look at the dislocation structure indigenous endorsement huge numbers of dislocation by the relaxation of such a change and those basically kill at the moment of his interface so bayonet forms and even before it hits any obstacle in the skills itself and stopped growing again and
optical like Rupp and these are all as of late Sunday nite and this is the modern science and I'm going to show you now that this black color is produced not just by the covered by the but there is actually these things consist of thousands of small plates each of which has grown to assert late let's stop and then you form new plates so this is not actually a single played but the cluster of thousands of small place so I share your transmission electron micrograph which shows 1 of these objects so the Scania is 50 micrometres and we're not
looking at this scale which is 1 my community so 1 of these objects is this this is a among the important thing is that each of the state's grows too a certain size at which plastic accommodations stops its growth and then you can only propagate transformation by forming a new plan so these are the plate lentil were here is the same as the plate landfill here so they're all going to a finite size because of this plastic accommodation and that's very good for mechanical properties because you cannot get such a fine structure even that much if this was classic accommodated and this would be a single player the recall this cluster of plates machine of the nite Schieffer is just a collection do just like when you harvest wheat yet you don't hold individual strands but you tie them up endure cluster which is called a sheaf of wheat this is a Schiefelbein S H E I happy so now
let's look at whether that the Adams moved during transformation and we previously discussed an atomic method of doing chemical analysis it's the atom probe where you know you will out items 1 by 1 and you measure the time of flight between 2 points and from that you can tell what kind of man commits and you can even collapse only specific kinds of atoms that carbon of silicon and form an image of the distribution of those that so here is 1 of the earliest all the partitioning of allowing elements during the reign of transmission that this is called the feline microscope image where we're looking at individual atoms and on this side we have lost Austinite this idea distribution of iron distribution of silicon you can see there is no positioning officers and you can of course be the images but you have quantitative data to prove that but look at the company :colon seems to have petitioned into the Austinite when we can reduce the measurement common distribution is not uniform the far-right contains little problem compared with so we we might reach that conclusion but during the brainiac transformation the carbon diffusers france but let's think about that a little bit more less let's think about how long it takes carbon to diffuse at the temperatures of interest so what hypothesis is that problem diffuses during the course of transformation
but we could also have a scenario like this ribbon forms exactly like Mike inside the province supersaturated plate but at the temperatures where we are making no observations the carbon then escapes into the Austin and at high temperatures it escapes rapidly so you get precipitation between the place as you lower the transmission temperature here we have a plate of modern science the carbon is escaping but at the same time there is an opportunity to precipitate because the driving force for press stations inside varieties also large just like tempering of Martin said so given that you precipitate some problems here you will have less government between the place for such a such a theory would explain easily the difference between upper and they know where we need to prove that the initial growth event is like modern became the let's let's say calculate how long it takes for the carbon to escape from a plague of site at the temperatures were forms here
is a calculation and you know this is a difficult temperature range over which you might get big nite and this is the time required for all the problems inside the plague of modern science to escape In the infected there Quentin petitioning process is similar to this theory where you're taking might incite heating it up so that the carbon escapes from them so the times are of the order of seconds on less than a 2nd that means but by the time you do an experiment to measure the province at 11 right so by measuring the cabin concentration you cannot true that at 1st the transformation is deficient by the time you go to make a measurement things will change it looks really hopeless have been approved the role of private if we cannot examine it fresh this is 1 of the reasons why there has been a lot of controversy if somebody show you how to do this now you remember
this diagram where in the top half year plotting the free energy cos of of and Austinite at a particular temperature T 1 and to get equilibrium we draw this common tangent and that gives us the 83 and 81 phase boundaries when a lot of these points as a function of temperature but that's the way it Macao can empty data and so on calculated phase diagrams but this is an interesting point rare verite and Austin 9 of the same composition have identical free energy that the Greenpoint here and diffusion less growth it is only possible if the Austinite composition is less than indicated by the Green because then we have a reduction in the energy but on this site it's impossible because you increase the free energy forced nite transforms the far-right without a competition change this is everybody care about that this is a very very important diagram from point of view of designing steel so not the this is the opportunity again so have blocked the locus of these points as a function of temperature I get what's known as the T 0 Co diffusion less transformation is impossible here and it's possible in principle if the OS 9 has a carbon concentrations less than the 0 so now we would do an experiment in I had a thought experiment not
supposing so flooding carbon concentration here and the temperature let's assume that we have an ally with this carbon concentration which labor leaders next textbook the average carbon concentration of the steel and is that and we also have the 8th Rico which gives us the equilibrium carbon concentration of the Austinite OK now I'm going to take my steel and transform it to Bay nite at this temperature so far the former blade of a knife yeah just like modern science but the carbon can escape because it's a high temperature so the next blade of a knife form from Austinite which is richer in province yeah and that will also petitioned and this process can only continue until the point where the OS 9 compositions it's that the 0 voluntary it cannot happen once the concentration of carbon in the US nite creatures that Eurobonds on the other hand if we have partitioning of carbon during the growth of pain and then I don't even need to form the material formed the main I below the Gezira temperature these plates simply continue growing and the composition of the Austinite reaches the A 3 4 0 so if you measure the carbon concentration of the Austinite at the point where the reaction stops then we can determine whether the problem whether the day-night form like might incite or whether Coburn petitioning happened during the growth of so I'll illustrate that once more right so
if it is the case that the nite forms like modern side but the carbon then escapes then the reaction would stop at the Gezira Co this dashed on the P 0 simply represents a calculation they take account of strain but if Coburn politicians during the growth of a nite then you can see it's a big difference because these areas populations and the difference between this concentration and this is very large so I show you some experimental results
OK so they're dashed on the Kobe simply take account of the strain energy because when they forms we have a shape deformation this is a real
real measurements of the carbon concentration of the US Night at the point where the reaction stops and you can see this is a very large difference this is an atomic directions with so much about 20 to get the right so the difference here and here it's very large so this proves that's when they form the forms exactly like much side but then the carbon escapes from played it to the growth of the 90's diffusion that's where the problem then escaped because the operating at high temperature and these days you're trying to do that with modern science In designing the Quentin petitioning steel so that's quite an important result and From this result we make many predictions which we then have to verify experiment worst of all yeah since the reaction stops at the 0 and if we my average carbon concentration is this then I get to this temperature get 0 banal you know once once the average carbon concentration of the steel is equal to the 0 you cannot get they Nifong at all even tho the temperature will be well below the equilibrium transformation temperature of Boston so if you do the LAT dormitory this is a Korean
agreement of centigrade but you didn't optometry as you raise the transformation temperature you get less and less of a nite until eventually you get no and that's called Bay nights start temperature and it is always loaded the 0 temperature of the city yeah because the strain energy to account for and the amount of a nite also decreases as we raise the temperature because the composition of the last night hits that 0 Bondra sooner yeah so this this is a "quotation mark that incomplete reaction number because he had this plenty of driving force for last nite to transform the deferral but not for last nite to transform the far-right without a composition change the real rates 0 fractions Of the nite even tho we have well below the equilibrium that's why it's called incomplete reaction it hasn't reached equilibrium and inform you as long as the mechanism they know the 2nd so just to summarize
Grotius diffusion lesson of course in making all these comparisons we must take account of the strain energy you the shape deformation because that strain energy it's quite large Pete next prediction that you make is that if you measure the growth rate then the growth rate must be much greater than consistent with the the diffusion of province this mountainside forms without diffusion forms rapidly how do we measure the growth rate because you know ,comma vocal microscope is not good enough on Fogel laser might cost me if the resolution is actually slightly worse than optical might have been so you not going to be able to see the individual plaintiffs but there is a technique called for 2 emission electron microscopy please take a bulk samples and you excited electrons from the samples by shining light on and then you use those electrons to form an image just like in a transmission line but you can use about sample and high temperatures but that the resolution is much higher I'm
going to show you a sequence of 4 pictures this is from a four-day mission electron microscope and you see individual platelets of late-night growing so here the new seats 1 the the individual platelets of the nite
and by looking at these images we can calculate they
can measure the growth rate and it's about 3 orders of magnitude faster than would be permitted if we allow Coventry diffuse during image so that's assistant to remember whenever you have a theory you have to be able to make predictions which you can validate experimentally that's why you know nobody who works on string theory has won a Nobel Prize because they cannot make predictions which can be validated the observations have to be on the scale of 10 to the minus 34 meters to validate string theory OK can now explain this
quantitatively so all you have to do do predict the transition between upper and lower body is to compare the time for Colvin to petitions from the plate With the time for precipitation if if this precipitation fanatics are rapid then we will get they if they're slow then we will get out of so we put together a theory for the transition from opportune
and it make predictions which I wasn't comfortable that this with my students find with Takahashi but here we plodding temperature was government and are all calculations this is the main I start temperature in the modern sense that temperature and the strange thing is if I look at a problem constellation In this particular steel of less . 3 then as a lower the temperature I go from nite much insight is not obeying and you know all the textbooks would have told you including mine that you get know of a 19 Loeb nite and then margins have getting up of a 9 directly to my consent and as we go to these carbon concentrations you go directly from the overnight might this not forbade the narrow range of concentrations where you get hold of a nite Nobody nite and and my life so we didn't publish this for quite a long time because you're not comfortable with the predictions and Dale discovered the papers in the literature so this is work
than in Japan where they examined high-carbon allies and you can see that In this case we go from polite to Upper Bay 9 and then sorry but I like to Loeb a nite in then minds is known the the high the and then there work by Omori and honeycomb we chose that the low with low-carbon steers you go directly from politely of urbane said is no only it isn't true that in all spheres we'll get of a nite low a nite and my side if you have a low carbon concentrations than the carbon can escape before precipitation can happen the driving force of preservation is smaller than the carbon concentration is low if you have a high carbon content that is easy to precipitate inside the far right and for some province to petition so video covers the you may not actually get banality OK so
there are many other predictions that remain which can validated and in the next lecture we will use this theory In order to design some really nice steals we turn now commercial it's a very very simple calculation to dramatically change the toughness of the steel with think


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