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Physical Metallurgy of Steels - Part 1

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Physical Metallurgy of Steels - Part 1
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A series of 12 lectures on the physical metallurgy of steels by Professor H. K. D. H. Bhadeshia. Part 1 here introduces the martensitic transformation.
Keywords Bhadeshia, Harshad Kumar Dharamshi Hansraj

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but bond-market OK I'll start the lectures so there will be 12 lectures in old and nearly a 3rd all of the phrase transmissions that happened from Austin and it also used the theory that be developed to design new kinds of steel stressing how very simple theory can be used to design new kinds of steel this is a summary of all the different kinds of transformations that happened From Austin I guess I'm not including income by 5 because here although I refer to them later on and you can classify them into 2 essential kind of transformation the reconstructed terminations and displays transformations reconstructive transformation means that you have to to break all the atomic bombs and rearranged the pattern in which the atoms are arranged into a different pattern it so that's like water solidifies to ice you don't see a macroscopic changes shape but the crystal structure of the ice is completely different from that of water OK so that requires fluid flow or diffusion here we change the crystal structure by a physical deformations so this process does not require and the diffusion and all of these transmissions can happen at temperatures rare iron atoms cannot move within the timescale of the experiment so I really do it all of these transformations and we want to deal with them in such a way that we can do some calculations and design so I will give specific examples of the design of steel than the behavior of Sears as a function of these Mike structures and I'm going to begin with what is possibly the simplest all transformations which is modern said game might incite is right down over here is a very simple transformation because there is absolutely no diffusion no diffusion even of carbon atoms and some people With added Edmont side is not a nuclear and books phenomenon because lakes formed very very rapidly but the fact that you can identify might incite Blake coexisting with Austinite means that there must be a nuclear nations the incidence the same as any other transformations steal nuclear tension and grow the event so I'm going to begin by asking you some questions so tell me what you understand by my and don't worry about getting things wrong just answer give me some
characteristics of modern society there you have to participate in these elections so you're smiling so how could you you tell me what 1 characteristic of modern science OK let's let's make a note of that so much inside is so brittle see so I remember this is like a brainstorming session where if you get the answer wrong don't worry about it but then you must know much more about might incite it being brittle right so give me some more characteristics of modern society Hodge what else so the the physical properties of modern site what else do you know about my consent you less what else yeah so there is a clear crystallography isn't it because if you look at the structure of the year the plates are not forming on random planes forming on particular planes and with particular orientation relationship respectively last nite so there is a strong Priscilla graphic element to much insight there are some crucial details missing there you know you can buy spectacle but you can bend right and then you warm it up and go back to its where is the shape what is that yeah shape that is a shared memory effect but the transformation produces a defamation no just like when you do do a tensile test and you get defamation here the change in crystal structure produces a defamation so there is a shape change what about transformation temperature anything about that it's a yeah so what does it several mean you're right what does it mean excellent so it's an 8th film mile transformation that means that in order to get mountainside after Kudo said and I'll get a certain fraction of transformation To get more tense 90 cool further if I hold it at a particular temperature for a long time you will not get more what else so if I gave you a piece of steel and I said OK produced much inside what would you do no quenching so that indicates what need rapid cooling and we can think about many other characteristics I will show you now that almost all of these I'm not correct again so I'm going to now go to the characteristics of modern society and demonstrate to to you that almost all of these I'm not actually correct even tho we have it's ingrained in our brain that might incite is brittle and that it's hard and that it's a thermal and it requires a rapid cooling so let's go to the characteristics of incite now so this is what we
are doing here trying to discover what we think about might incite from everything we've studied so far and whatever its characteristics but the 1st
thing to note Is that modern society I need not be hard but so yeah a modern city transformations in a whole variety of materials these are steals this is a ceramic it's zirconium oxide this is a solid solution of organ and nitrogen and this is copper aluminium you can see that might side is not hard so why Is might incite hard In some for example here we have a Vickers hardness of 600 but not here Oh um wide said why is it the case that In some steals might inside is higher and in others it is not took cut carbon uh causes hardening and does anybody know why carbon causes hardening White common cause London said to be hiding take not expansion OK so why does someone not hardened us tonight so much but actually there isn't more space if you calculate the size of then interstates in Austinite it's not that much different from the reason is very wary
interesting the federal unit-cell cell of verite so these are my iron atoms and we have a body centering at them in the middle the that's the crystal structure of Ferrari Hang Coburn said so here it's an op-ed that he designed and this distance here the lattice parameter divided by 2 right this is hero it is the wrote to 0 at 2 it's half the face value so the holiday there is an updated but it's not a regular the strain in this direction is much larger than the strain this way or that way so it's at the tribunal distortion distortions if you look at Austinite it so this is at the center of this place here and our covenant communities located here this distance is important to you and this distance is also there .period to so it's a regular of the heeded government and causes a uniform expansion he sits like a hydrostatic strain strain and uniform expansion not if you have a hydrostatic strain but cannot interact with the shear stress you know when we do the pressing of powders the but with the powder into a mall and then the pressurize and then the pardon become standard but the shape remains the same because they're not shear stresses associated with pressure dislocations are about so dislocation strain fares has a very weak interaction with the uniformed strangers and that's why carbon in Austin I was very little hardening just like Mikaelian Austinite causes very little hiding because it causes a uniform expansion yeah but the dragon and strained for years has a very strong interaction with the Shia strain fields of dislocation that's because after all the dislocation is about sharing not about William Jennings Bryan so strong interaction with dislocations so unhappy about that the basic reason by common causes hardening of modern site in steals is because of this the tribunal distortions if we had the same amount of governing Austinite almost negligible hardening by comparison if the pact is like a substitution of solitude In Austinite it's causing a uniform expansion so cabin does not always cause timing if he had 0 carbon concentration and modern citing pure iron by cooling rapidly that would be soft we do not need :colon to produce might incite might inside is simply a change in price of structure to take your iron and and equally rapidly you will get Martin said now the other thing do not reach we haven't listed over here is normally think of modern city transformations happening at a low temperature but look here we have modern site in Zirconia which is forming at 1200 Calvin on the other hand this modern site formed at less than full Calvin so the point about this temperature is not that might incite all those forms at the low temperature but it can form at a low temperature that means that it cannot have diffusion during the transformation it need not formatted low-temperature but it can form at the temperature so much insight informed at a low temperature form at the low temperatures 1 I need not USA if I asked you about the speed at which might incite forms could you give me an idea in meters per 2nd set in a growth rate of Martin said Have you heard about acoustic emissions did he go to my Web site you can hear my considered transformation happening is a file I which you can use as a ring tone on your telephone yeah which is the sound of modern society now acoustic emissions happen when you get certain events and modern city transformation sometimes happens very rapidly and the speed of sound in the middle and the speed of sound in the metal is roughly how much thousands of meters per 2nd compare that with the fastest ever solidification rate which is about 80 meters per 2nd it because certification was diffusion where is a defamation the changes the course of structure can happen extremely rapidly so modern 2nd fall extremely rapidly expanding approximately 5 thousand meters per 2nd but it can also grow slowly for example in the shape memory scenario where you know you have growing and I'm growing modern at a slower rate so if need not do do so OK so the major characteristic of modern city transmissions is that when you get a changing crystal structure you get a change in the shakes so if you got pattern of atoms which is arranged in a square and then transformed into modern society then obviously there will be a change in the shape of your sample thank please just like the shear deformation or twinning defamation except that we also have a change in crystal structure now does anybody know
what this is this is a virus a particular kind of quiet and think of this as the body of the the virus which contains the DNA and these are some sort of arms and the virus goes in attaches itself to the surface of a material and then it operates this hypodermic needles so here you can see it's long and thin and here it is short and fat and by changing the shape it injects the bacteria DNA and then it can multiply the viruses don't don't have sex you don't make they multiplied by infecting something else this change in shape is actually a modern city countermeasures In a cylindrical crystals so this is actually a cylindrical crystal so effectively
two-dimensional Crystal Ridge by modern city transformation changes its crystal structure and in the process goes from a long thin for short fat and this
is an actual microgram showing this virus going to was a victory attaching itself and then infecting so of course In doing so the virus itself no longer is alive because it's lost its meaning you don't have DNA not alive but the but did you producers by infecting the victory so Maddon said happens in life and death as well again
this is a classic movie by Sugiyama from Japan where you can see the shared memory origami where origami is a paper artwork but thereby raising the temperature it falls into that shape that many included again to regenerate the original set of might incite variants it will unfold itself so this deformation that have drawn on the ball is a real defamation which you can physically measure because and it can in principle do well as well so many cozy deflected knocked him again so you can find this on you if you before want to watch it again OK so said her so we
have never said that you know it may not be hard and it is not hard it may not be brittle yeah so you know it if you look at moderating steel my aging still has almost no carbon in it the mountainside is produced by allowing this a lot of nickel and molybdenum and when you graduated it's not too hard materials actually extremely tough and to get the strength you then he treated to precipitate into metallic compounds and in my eyes he still is used for rocket casings so you can't have that Britain it's going to be really tough right now just imagine the stresses on the rocket motor when when it's fired so my dad said need not be brittle how do you know that its diffusion last if I asked you to prove to me that my considered transmission is diffusion less how would you prove it talks that it is diffusion less but if you had to prove that it is diffusion that's how would you do it yeah so we can measure the chemical composition and show that it's the same as that of last nite so how would you measure the composition what what other methods for measuring chemical composition on a fine scale so to be clear plate is about 0 . 2 micrometres wide yeah let experiment yet so yes said that that's a good good point because Coburn has a big effect on the left parameters yeah but it's not too sensitive what what methods do you know which we have in geography and prospect go on you can use energy dispersal vector analysis yet Richard uh examines basically about 1 cubic micrometres of material the company is difficulty moved co-author you have remained disperse erection analysis 1 thing I wanted to go 2 atomic analysis how would I do it so I want to measure atom by atom we have the technology and prospects a surface but it's good for and it's a surface analysis atom probe yet so we have the we have indeed manner center the machine where you can pull out atom by atom and measure how long the atom stake to fly between 2 points and from that determine its the chemical identification so on the finest possible scale you can chemically analyze and show that might incite is diffusion less we also have used this information you know at 4 Calvin there's no possibility diffusion even of In the timescale of experiments and it is growing at this speed there is no way that you can have diffusion of power so
so these are the tree matters is the fact that he can form at very low temperatures and it can grow very rapidly indicates that its modern city transmission that is diffusion and we have many techniques measure the fine scale chemical composition to prove that its diffusion that's were OK so far look at what
is the shape of modern society I can tell you that many many research papers that I read incorrectly identified the shape of so if you if you had a plate of much of the story of a given away the answer but hit it is wrong to say that might incite is needed shape yeah because what you're doing is you're taking them something that is a plate in 3 dimensions many section yeah a year looking at a projection so it looks like a meal but in the dimensions it cannot be a need the mechanism of transformation does not allow it to be anything other than a plate or a plate which is thinner in 1 dimension as sorry as is wider along here and showed a in which rate case we call it laugh In a lack ruler yeah so it has to have a large flat shape a flat plain and there is disco it has to have that later on but in 2 dimensions the shape of my concern is that of a plate for or a laugh so
this is a typical optical microgram and you cannot see any round sections right so if it was the media then the probability of seeing elliptical around section is very high you cannot see any this and when you look at your own mind set examples you will not find round or elliptical sections 1 inside is not needed shape it's wrong to call it needed shape it's a bit late a a lot in 3 dimensions now I'm giving you all of these characteristics of modern science we need to explain why we get all these characteristics so today's lecture I'm just summarizing what we need to explain and in the next lecture we will have the theory to be able to explain everything about my size it the price of the shape of Mike inside is in the form of tin plates all Blacks and the reasons
for this particular shape is as follows no I indicated to you that when we get a change in crystal structure by deformation there will be necessarily a change in shape Of the Austinite which transforms into modern said so here for example is a single crystal of us tonight and supporting there's nothing surrounding it then note is the shape deformation it is a combination of a sheer on this plane and I assure you later on that also won you change because it's not strictly speaking this year it's a bit more complicated than that but we'll get into that later so this is unconstrained that means there's nothing to restrict the changing shape is the single crystalline air but in the last majority of cases we're dealing with polycrystalline samples so there might be a grain of Austinite surrounded by more grains of last nite and that really pushes against this defamation so to minimize the strain energy adults the shape of a thin plate now this is what we call the habit plane of mine inside the plane on which the mountainside forms and the average it is the same as here because is the crystal graphic indices of the Emirates plane here is the same as a year but here you form at the end late because you cause a lot of strain energy by pushing against the surrounding crystals and by forming a very thin plate you reduce that strain energy again I will explain why didn't plate leads to a reduction in strain energy later on but a very simple explanation is as follows so supposing this is mine Austinite and I transform it into modern society and this is the habit planes you can see that the displacement increases as a mower from beheaded playing that the strain is the same because a stranger's displacement divided by height but the magnitude of the displacement is increasing as a move away from the other that that so if I restrict the shape "quotation mark the mud inside To me like this then you can see that the displacement here is what 0 so the reason White forms as a thin plate is to minimize the strain energy by minimizing the displacement at the tip of the blade that is why it gets down to a shout yeah the displacement is 0 thank so if you look at the optical micrograph you can see that the
plates are very narrow at the hip the recall this lenticular shape a landslide shape it lens like shape all no the lens a magnifying glass has a lens like shape and that's the shape of a modern side playing now
we have defined what the habit plane is it is basically the
interface plain between the Austinite and might inside the major interface playing between the US nite and Martin said if anybody has questioned you feel free to ask now yet so the habit planes it is a major interface the training last nite and modern types of gamma-rays last nite and Alpha Prime is my not when they talk about slip deformation there so it happens on a nice close-packed playing in Austin and break 1 1 1 plane of us tonight there is everyone familiar with that all and it happens in a particular close-packed direction it is 1 0 1 directions the Soviet the atoms are most densely packed it's very easy to slip and similarly for the state directions my side is extremely strange not
carefully the would approximate here again these habit plane indices are really strange 2 9 5 to 15 10 2 5 2 and even these numbers are approximate you cannot actually expressed the habit plane of modern side in terms of integers just like you cannot express the square root of In terms of inches just goes on for ever at 1 . 4 1 4 1 4 1 but that so similarly might incite forms on strange planes With rational indices a rational means you cannot express the indices in terms of vintages and you know you get quite dramatic changes in habit playing with the chemical composition so we need to explain all of this the only well-behaved every plane is Eppes Island much insight In stainless steel of silent Night insiders hexagonal close-packed reserve as the prime is the body centered cubicle bodies and that the dragon of might concern so this forms on exactly the 1 1 1 place it's not any rational explained it's in exactly a 1 1 1 so we need to explain 1st of all I know why does my consent form 1 really strange planes it's not nice packed planes this year happens and in some cases why it doesn't do so quiet forms exactly on the 1 1 somebody you in today's lecture when I finish yeah with a lot of confusion and everything will fall into place in that in the next election hopefully similarly
orientation relationships between the Austinite and my concern is not a straightforward relationship we have the close-packed planes approximately parallel the many reading the literature that but you 0 1 1 is to one-on-one alfalfa that is an approximate parallelism they're not exactly because there might be about . 4 6 of a degree the book and similarly the cloth bag directions From the 2 crystals the gunman Alpha I'm not exactly parallel so the when the orientation relationship is a rational and the need to explain that so the orientation relationship is I have explained and orientation relations here rational except in the case of the Eppes Island might incite transformation the purpose
of already said this when people talk about good theme of Saxony sharemylesson meant they don't really mean that that that stating that there an approximate relationship you can't really measure these accurately using the the BST or even straightforward electron diffraction in the transmission might have you got to do something called convergent beam electron diffraction very very careful measurements to pick up the rationality of the orientation to measure an orientation the difference of . 5 degrees you cannot do with ordinary electron diffraction because the zone axis can be this way or that way yet you know when you're using 10 follows you can get Bragg diffraction even when you're not at the exact Bragg orientation and similarly CBS-TV don't believe anything it says that the accuracy is . 5 of a degree you just measure on the Austinite itself you see a big range In the orientation of the OS 9
OK a settlement transformation would do we mean by itself was transmission is new find it very well that look if I out explain this equation later on but this is the volume fraction of modern science and this is the modern stock temperature that means temperature at which might incite 1st begins to form and this is the actual temperature which could be anywhere below analysts In this equation which shall 1 infraction of modern side the function of temperature there is no time that means that if I could do this .period I can calculate the amount of might inside but it remained constant on my time temperature transmission diagram no matter how how long I hold it at that temperature so it's what we call and a film of transformation that doesn't apply here if I if I hold my denied I get 1 per cent but like a hooded longer I get 50 per cent 95 per cent and so on so that's the difference between and a fellow transmission and transformation which depends on time the reason why this is not strictly true it is that things are happening very rapidly if he could observe something that's growing at 5 thousand meters per 2nd there would be a time dependent With right we need to
think about the structure of the interface between Austinite and much insight because that interface has to be able to move very rapidly without diffusion it so that's the basic condition for Martin said the structure of the interface on the interface between Denmark and trying must permit rapid concentration without diffusion that's a good thing you look at a grain boundary in a transmission electron microscope would reduce the yet he was saying something new supposing I look at the interface in a transmission electron microscope would you the by yes yeah if there is a perfect match then we would see nothing yeah but In general what would you say Ford and interface looks like in the transmission electron microscope there be a series of lines now do you know what those lines are but did not to worry let's create an interface with again so how do we create an interface rather stop a single crystal if I cut along here and did the 2 parts the suspect to each other by an angle the death I don't get any interface I get a gap here yes that is not yet an interface I need to fill that gap with something To make the 2 crystals connect with each other so what do we do
report dislocations inside that gap and those dislocations fill up the gap because In this case the edge dislocations and edge dislocations have an extra half blamed so if you look at the structure of an edge dislocation it like this this side is still stood with his back to the site that's the operation we did in the previous slide and this population is just filling up the space so unhappy with that so far I put enough dislocation in here than the gap disappears but these are dislocations and the spacing of the dislocation is indeed and simple geometry as you that the tangent all the debt is equal to the mother rector of the dissipation divided by the spacing so if I if I don't know then the spacing decreases so this is the dislocation model of an interface and that's exactly what you see when you look at the interface in a transmission electron microscope consists of a series of dislocations this is a particularly simple interface where we just is that the 2 halves of the press you could have a more complicated the relative orientation and in general you might have 3 sets of dislocations with different line represents to define an interface but interface is nothing more than a set of dislocations Rich allowed that do crystals to connect but and you can see this is the pigeons in a transmission electron Mike breath I bring along such a microbe effort in the next election and this is the very simple relationship between the Miss orientation between the 2 houses the character of the dislocation in terms of the bogus elected and the spacing and you know as you increase the debt eventually this model doesn't become meaningful because you start to get the overlap Of the cause of the dislocation France and that's when you have a completely incoherent boundary I OK with that OK now we need to think about what is a kind of interface that must exist between Austinite and my concern because it has to be especially in the face which allows rapid transformation and without any diffusion right
so yeah I do kinds of interfaces again dislocated structures this article Buechel because the brothers vector lies outside of the plane of the phrase so these dislocations can move you know if you liar stress so you called the the material with this in mind said has mentioned these can rule and cause the defamation without requiring any diffusion yes on the other hand this is a Cecile interface because for all these dislocations move you would require climb climb of the the that they're unfamiliar with Klein if so here we have a dislocation lying on this particular playing if I wanted to move on to another plane yeah and I'm going to use this material thank I would use it by diffusion that's called the climb of a justification so interface like this cannot move without diffusion where to translate this way or that way you need to add atoms or removed items from That Extra Half so this is the kind of interface that must exist for modern doesn't require diffusion it's basically the glide of dislocations that happened to be the face this efficient but it's the blight of dislocations so it must be this Klein requires diffusion I want to hear now again this is a very simple structure of the interface and I mentioned to you that in general I might need 3 sets of dislocations to accommodate the misfit between 2 crystals yeah because we only did a very simple operation very copped a crystal and did that the 2 halves by can do many other operations To give the relative orientation that so in general 1 set of dislocations is not enough to accommodate the misfit so we have to ask the question With might incite can we have more than 1 set of dislocations In the interface so from looking at the plane of the interface so we're now looking at the plane between Monday said region behind aboard an off nite which the head of the board should we have a structure with just 1 set of dislocation or is it possible to also have a structure like this With more than 1 set of specifications yeah so give me looking at the habit plainly to the Board of boat behind his mind inside and in front is Austin you look in a condition electron microscope is this what we should expect with modern side all something more complicated so let's try and answer question select clock is still not working is stuck at 2 30 kids so I might carry on lecturing and was too good for the so let's imagine we have to dislocation yeah this 1 is an edge dislocation is bogus vector is pointing at 90 degrees to the line and this 1 is as good as the patient where the bogus vector there is parallel to the line what happens when these dislocations cross well exactly what happens when a dislocation moves to a crystal you would create a step and on this dislocation here the direction of the step is the bogus rector of the B-1 yeah and on this dislocation the direction of the step is the displacement meeting them so when they cut each other you create steps we correspond to the bogus rector of the cutting dislocation yeah so these are called jobs and then there are the facts 1 dislocations caused by the intersection of the different expectations now a screw dislocations In rule on many different planes any blame which contains it's bogus vector it can move on that plane but once you have introduced this job that becomes impossible yet because his job is no longer a screw as saying this job is no longer as good the bogus bacteria still pointing this way but the line is different so this dislocation was decided and becomes Cecile by the cutting yeah now it will require diffusion to move so in the interface between Boston Ivan my said you cannot have more than 1 set of specifications very very important result In the interface the cream gunmen and Alpha Prime we cannot have more than 1 set distributions all this attention so this summer I saw
here this island face cannot contain more than 1 set of dislocations in the like this if you look in a transmission might but not like this and modern citic transformation is only possible if you can create such an interface between 2 crystals and you can only have 1 set of dislocations if there is no distortion along this line yeah yeah but if there is distortion along this line you will need another set of dislocations to accommodate them so this line we call invariant line invariant line that means that there is no distortion or rotation between the Austinite side along that direction there is no distortion or patient along that line no distortion for protection along that line the bus tonight in the modern site match perfectly along that line the atomic arrangement in the US and the modern match perfectly along that line so there is a perfect match along that line if you cannot find a perfect match along 1 line between the 2 crystals is not possible to get much insight if I gave you any crystal structures right whether it's in ceramic all brass or whatever and I ask you the question is modern city transformation possible between these 2 crystal structures they wanted monarch clinic and the other 1 is cu if you cannot find 1 line which is coherent between the 2 crystals it's not possible to get modern city transmission so now you're able to predict for any 2 crystal structures whether or not modern city transformation is possible In principle yeah so it's a very important result that modern city transmission is only possible if the deformation the changes the parent in our case Austinite into the product which is modern science use 1 line understood it and under-rotated an invariant like cannot find such a line that modern city transmission it's is impossible so that the formation which changes Austinite In Dumont inside Mussolini 1 line completely understood and rotated I don't want to hear about that this means that you can never get a fully current interface between us and modern because we're only leaving 1 line understood it really want plane understood it then that's a fully coherent but the minimum requirement is to find 1 line so that we can have just 1 set of dislocations in the interface so you know just in today's lecture we are not able to defining whether modern city transformation is possible in plutonium all these different crystal structures or in any other system you can find 1 line which is understood in an undirected it's possible invisible to get modern city transformation if you cannot find such a line it's impossible so the interface between modern side and Austinite must be semicolon here and in a special way that there is just 1 set of specifications this does
repeating the same thing which I drew on the board OK this
is the reason why the individual energy between modern inside and Austinite is really quite small yeah this is 0 .period do Jews for me to spread roughly and that compares with the twin boundary which is fully coherent and an incoherent boundary which is about 4 times that and the sofas energy of window glass here which is about 1 2 but meet spread the energy is low because there's quite a lot of coherency along this direction the this is an
interference micrograph it's called animosity to France my program and the color represents Hi so the specimen was Austin intake when he was punished completely flat and then allowed to transform into much insight and this is not we are looking at the deformation of the free surface caused by the formation of these migrants the plates it's a real physical deformations just like slip what winning except that we are changing the process structure at the same time and slip and winning you don't change the crystal structure but it might inside you default and you change the crystal structure so this is 1 method of looking at the changing shape and the
changes shape is not actually just this year supposing I take a crystal of beryllium the barium is a metal but it's blossoms ratio it is 0 so in fact quality then I only get the 1 change and on that the contraction I get of change which is normal do the habit playing here so this is just units here delegation if I share something then I get shoestring here but I don't get anyone hinting share does not go the right shares only to indeed stepping off the planes is not calling the 1 and if I add these 2 out that is what modern side does you have a share defamation and award change nor was do this plane going and this year defamation is very large it's about a quarter we can anybody tell me typical magnitude of inelastic strain In steel 4 of the 5 Blier stance over 200 megabytes schools what is the strain elastic strains was homogenous a steel but the guests what's the elastic modulus of steel the Young's modulus come on somebody must know what the Young modulus this what is the yeah so the Young's modulus it is 200 the Oscars and fire apply stress of 200 megabytes then the strain is equal to distressed over the modernists this is minus-3 so it's very small look at the size of this deformation huge so it's a strain of . 2 6 share and William changes of the order of 3 % of course it depends on the lattice parameters of the last nite and my consent but typically of the order of 2 % so this is a small don't compared with this but nevertheless there is a change in density might incite forms in steals so this is a Union accident inflation this year and this is what we call an invariant planes trains it use of plain understood and unregulated now you should be concerned yeah about sort of sad that the minimum conditions it is we should have an invariant lines but when we look at the shaking it looks as if there is a plane which is fully coherent between Martin inside in Austin you know that interference micrograph and many other experiments that you can do shows that there is a plane which is understood and rotated between us and modern science so it's as if we can produce a fully coherent interface but this is just to
show you that when I draw these diagrams you're looking at a macroscopic scale on a microscopic scale of course when the interface moves is producing a series of steps did so on a macroscopic scale this looks relatively smooth but actually there is steps he quoted above its vector of interface dislocations
right so going back to the strain energy the diagram that here the reason why the modern cited plate is to minimize the effect of these displays the strain is not wearing a long here but the displacement is very as you move away from the having played so having a thin plate minimizes the strain energy and this is a strain energy by unit volume this is the shear modulus of the Austinite this strain and the denigration of strength and the thickness over the land ratio so if I make my plate dinner then I reduce the strain energy what is the origin of this equation what is a strain energy by unit volume 1 that diagrams I'm just blank looks a lot stress was restrained What is a strain and but it was the area under the curve so this is a strain energy for you .period the "quotation mark too hard Sigma and yeah and Upsilon is equal to signal upon the modulus so is equivalent do Our actually I want to be the other way around on directs igniting homogenous over it closed modulus times of silence so that's equivalent to half 1 times Sundance Square it's from this year's C that the strain energy should be related to the modulus directly related to the modulus which is what we have here sorry about the terminology here this homogenous and this is trained and it should be related to the square of the strain so here in the square of the Shia strain and the this dome here the thickness over land of explained to you on this diagram but is due complicated to right there is a need special this theory Over last distinct do reach this simple equation the theory itself is very long and I'm not going to do it but you can find it in Christians theory of transformations in matter than but you can understand it by looking at stars that is the reason why might incite forms at this has been delayed actually this is also the reason why mechanical twins former Western plates because mechanical training is also a shear deformation like this OK
so just to finish and there are some difficulties in the data that are presented 1st of all you saw that we have very strange habit planes the 3 10 15 and even that is approximate the orientation relationships are not rational that means the cloth bag Close aspect planes are not exactly parallel neither of the clothes but directions the shape deformation is an inventor played that implies that there is a fully coherent interface between the off-night and modern and I assure you in the next lecture that's impossible it's impossible to get a fully coherent interface between Austinite and my but nevertheless when observe observed the shape deformation using the interference by 1st the or many other techniques it's an invariant plane straining the use of plane distorted and undertaking so these are the difficulties which led to a very very major breakthrough they in with theoretical metallurgy which explains everything everything falls into shape you can't exactly predict the crystallography of might inside the shape of my side and so on and that we will do In the next election at button