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Physical Metallurgy of Steels - Part 11

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Ch but I think it will make a start so in the last lecture I explained the defamation matrix for the shape change that accompanies might consider transformation so that for any direction you can work out the strain and just go to that again so we had a defamation matrix the 2 groups the
1 0 Record asses the shares strain this is 0 0 1 last Delta and Delta is the delegation of straight and if I multiplied by any rector and the example that we took was 1 0 1 then I get the results by taking role by column and 1 last 0 1 last day but this is our defamation matrix which is defined retrospective coordinate said this is an initial vector you and this is what happens to that wrecked after the defamation and draw little sketch if this is not the then the activity my point in a different direction and also have a different magnitude so the strain is approximately equal to the strain of Saturn 7 approximately equal to 1 minus the magnitude of the divided by the magnitude of you and if I take care the she strain as about 0 . 2 and the delegation of strain is about 3 per cent then I get the silence has approximately per cent inundation so the effect of modern city transformation in that coordinate system 1 of active 1 0 1 it is distracted by about 14 per cent not been trips fears produce stable last tonight but when we apply a stressed that Austinite decomposes into modern that's the whole basis of trips to you that we have some Austinite applied stress and trigger might consider transformation so what that stress is doing is adding a mechanical driving force and we need to work out the magnitude of the driving force so In Topsfield steals we have stable was tonight and the effect of the stresses India's modern city transformations and stress India says modern city transformation and it does that by adding a mechanical driving force if so just like we can trigger might acidic transformation by cooling that by cooling the increasing the chemical-free and interchange instead of cooling apply a stress and that adds a mechanical driving force which can trigger modern city transformation so we need to calculate I need to calculate In mechanical driving force so any ideas how I could do that if I give you a stress I don't work the energy per unit volume when the stress does work on the mountainside yeah so you remember that earlier on in 1 of the lectures I drew stressed it was strain grass you identified that the area under this graph is the work done by the stress in creating the strain at silence so is an energy per unit volume you know volume the only difference now is that we are not dealing with elastic strains modern city transformation is a plastic string so how does that modify the area the plastic strain is that yeah the stressed time this train wreck some of driving force will be simply stress multiplied by the straight OK so effectively autograph Of the 3 With his temperature analysts call this 0 and this is the driving force the then as a cool my example the driving force for the gamma to Alpha transformation will become more negative yeah that means there's a reduction in free energy but my consent forms and when that value reaches a critical point yeah if you called that the G S M S the trigger might inside and this is our definition all the modern science temperature so this is nothing new about do you that in the 1st a couple of lectures that when the driving chemical-free French change reaches a critical value trigger might said now if we are adding a driving force you to stress that the MS temperature increase or decrease that's a question added stress will hamas temperature increase of decrees increased so here it is the great will also had a mechanical driving force you to you it the mechanical driving force and this temperature here called M S signal therefore the MS temperature increases 2 and S Sigma and the quantity you it's simply a "quotation mark the enormous stress on the habit planes multiplied by Delta blast the she stressed on the heavy place multiplied by S this is the normal stress and this is the shear stress on the haven't played and because S & L got a plastic strains we don't have a factor of how often they simply stressed multiplied by industry I want happy with that so obviously if I'm pulling my sample along 1 axis I want to resolve that stress under the habit plane as the shear stress and also stressed normal to have thing so it's is very droll the habit playing here that this my plate of modern science an hour later stressed in this direction but I've got to resolve that stress In do enormous stress the Soviet 90 degrees this is Sigma and and she has stressed here which is parallel to the head so let's assume that the angle between the tensile axes and the normal to the habit plane is the death this so this anger here the green the enormous stress and the normal to the Harriet Lane between the stress and the knowledge of the habits Lanier cedar so angle between Sigma madam To the habit planes see cancel the
debt this tangle between tens stress and normally To be having this is my pencil stressed here this is the normal and this angle here the Peter it's like expressed my then cities In terms of the death of its leader be elected reach has coordinates signed the death in having plane costs does in the normal direction the tensile stresses of that is parallel to Sigma 2 signed the deal 0 "quotation mark the and I'm assuming now that the stress the habit plane normal and the she direction are lying in the same plane it so that a simplification they don't necessarily need to lie in the same place so that's my plans Alex's and I want to find the inundation in the whole of the sample transformed into my concern so how do they do that a defined the direction of my pants Alexis and I want to find a long duration In the end I sampled transforms into modern said given any vector the how finding nation along that direction and might consent forms the new ideas I simply take my defamation matrix and multiplied by the Directorate but 1st I need to also find the enormous stress and the shear stress so that I can work out the optimum value of the car so we need to find we need to enormous stress and the shear stress on To calculate the optimum value of the day yeah because if a plate it is like this then the Mecca of driving force of different from if a plate is oriented like this spring but there is certain plates which have the largest interaction with the applied stress and that is what we call variants selection that means the plates which that the most with the applied stress we'll be the ones that are favored for all other possibilities so that 24 possible orientations of modern and those orientations reach indirect the most with the stress will be the ones that are favored because that's what variants selection of the largest lanes with the data corresponding to largest mechanical free energy we'll be favored and this is known as variants selection but they let me just go
through that again so this is how we calculate that might incite stopped and checked the plot the difference between the GAM and out of the function of temperature when it reaches a critical value which is that the G at the mass then the triggered modern city transformation and depicted at the GM accident about a thousand Jews from all because in the 1st 2 lectures we worked out the strain energy and interface energy in the twin interface energy and roughly that comes 2 thousand to 4 more before any system for which you can calculate the free energy should be able to estimate the modern said satisfactory when we applied a strap we have to add another because of the interaction of distress great the fastest the due transformation and do you and that has the effect of raising the might says that temperatures so that the sample and be used to transform into modern side by a Dalmatian as opposed to buy cooling rack now here is a
beautiful experiment he chided case where in 1 single best I can look at the effect of stress changing stressed on my concern that said this is not a better location and you can see that it is a tapered age and yet so when I break the sample I will get a gradient of stress and indeed you can say that as a function of stressed I get more modern side as the stress increases because the mechanical driving force increases again and this is
what I mean by variants selection is that if I simply quenched this sample Beninese just migraine that the possibility of 24 different orientations of late but and say that these are forming at approximately 45 degrees to the entire Lexus defense Alexis horizontal why at roughly 45 degrees the shear stress is maximum at 45 degrees when you put the sample yes but the Catalan and saying approximately 45 because we don't just have shear stress we also have that deliberations so when you get fewer ready then the 24 because they're forming in a particular orientation favored by the stress you call that variants selections yet have come across that Gandalf or if you read the papers on trips the and so on you find that not all possible orientations of might in some form some of favored over others and that's what variants elections here those plates which are inclined at roughly 45 degrees are the ones that form OK so now I would
displayed distress the tensile stress into a shear stress an enormous stress as a function of the orientation of the place not you have a chance to look at the Moss Circle construction or have you done it before yet so I got to read very briefly so if a plate is at an angle Peter beauty can cities than on this block I draw a line in a circle whose diameter is signal 1 that's your answer stress again and from the center I draw a line which is at an angle to the care that figure is the angle between events Alexis and the normal right and then I can read or hear the shear stress experienced only habit planes and this value here is the enormous stress on behalf the 2nd right down my interaction energy they simply so the normal
stressed sequel to signal 1 upon president 1 is Europe is offense stress that and if I go back to the staggering you can see that on the horizontal axis of a signal 1 a point to end this valley here a signal 1 of 1 2 calls to the death rate just this this distance yeah signal 1 of 1 goes to the debt and assessing wonderful you therefore I can ride my normal
stress signal 1 . 2 1 last off the day and the shear stress it is go back to that diagram you can see on the word of the Lexus that signal 1 point you sign to the this height over here between that doctor and the poison polite is signal on a point to sign to the rent the signal 1 1 2
inches sign so my interaction energy becomes a simpler 1 1 2 this will be 1 of the normal stresses to be multiplied by Delta so I have dealt plus delta cause To the duck and this just as we multiplied by the shares trade so I have class induced signed To the so this now expressed in terms of the tensile stress sigma 1 so how do I find the optimum value of the the largest body of yeah somebody said it let us know now I can't hear very well yeah differentiate and fined the maximum so let's just do a differentiation and I might get a strong so check everything I'm doing but the user by the the death the was and the 1st disappears because he doesn't have a so it's just a single 1 upon 2 -minus signal 1 . 2 into the 1st sign To the death last uh sorry there should be a there as well right so up to signal 1 of there at the last set do signal 1 a point to induce s cause to the event and it is set to 0 and don't cancel out terms which matter then you find that the tangent of duty is equal to pass over therefore set it is equal to 0 and engine of the death is equal to press 1 delicate and that would be you'll find that the data is approximately 45 but not exactly 45 and the death comes to approximately 45 the means when asked is equal to 0 . 2 6 and that is include 0 . 0 3 2 adult plates which happened to be at that angle will be favored by distress right now the problem becomes simple nor the value of the car can be nodded the tensile exodus is located at the 1st sign the does 0 conceded that those of the coordinates of the and Alexis they remember that the stress sigma won his battle to sign the does 0 cost to think and we know the value of the death from that equation that could be right down to the day possessive about so all I have to do if multiply my defamation matrix bye this direction of the band selected and I've got the implementation so and see
if I have an exact value but you can work that out for yourself it so all I have to do is take my matrix 1 0 s 0 1 0 1 0 0 1 multiplied by the vector signs the 10 0 cost again this is my concern the direction of the tensile stress parent that will give you signed the last as cause the 0 1 last than in due course and you can substitute the value optimum value of the day in there and when you do that you will find there is also a lofty Austinite transformed into the most favored variance then you will get any longer nation of 15 per cent so that's the maximum amount of transformation plasticity but you can get get it although the last night transforms and transformed into it plates which are optimally oriented so substitute optimum value of the the value of the dollar and the nomination comes to approximately 15 per cent all gamma transforms injured optimum Martin said the gates modern said oriented the largest interaction energy you not how much retained Austinite does it an ordinary kid that still contained that is not something that's fully needed but the sort of things that you were gone commentary darndest In the persistent steel that you know Posco manufactures and many other companies make How much retained nite is yeah that's more than 20 per cent maximum so how can I calculate the the maximum nation that I should expect if that 10 per cent of course NYTimes on the 1 . 5 per cent you transformation plasticity because the scale of this by fraction of Austin so you only get 1 . 5 % inundations if all of the US 19 nuclear assistance to transformed into modern science so the idea that transformation plasticity itself gives the larger long-duration incapacitated still is wrong In a few years ago I wrote a two-page paper With the title Tribasa SA's dealers ?question mark because the transformation plasticity itself is incredibly small only 1 . 5 per cent and yet you get inundation of about 25 % when your last nite know the reason why we put arsenide there is because it increases the longer should read so why is that consummation bestest itself is dying but there is no doubt that you get more inundation if you have your 1st nite there yes let us just write it down because it's important so in steel 10 cent ,comma consummation induced persisted this 0 . 1 multiplied by 15 per cent which is 1 . 5 cent 1 . 5 per cent it is much smaller than the elimination of the steel so the consummation is doing something else what it is doing Is it is introducing work hardening inside your material now wives work hardening important if you get a plastic instability In your samples that means a little bit of a neck and the just Austinite transform their locally then it will harden that region and stop that nite from beginning so it's a composite effects Of the creation of inside the creation of this dislocations and so on which gives you the hardening in the region where you get necking and therefore stops the necking so it's not consummation last Tuesday by itself but the fact that you introduce work hardening in regions where you have a plastic instability small reduction of area compared with the rest of the sample so the real contribution retain just 9 the real contributions Of retained us tonight it is not transformation plasticity by itself but work the In other words preventing the onset of of plastic instability preventing on all plastic instability the 1st thing the
question
so this this was the calculation of the maximum strain that he expected the entire sample was fully asthmatic and transformed into the optimum orientation of the my concern I want happy with that but that's quite an important result which you don't normally find in papers or in books
but it problem is we've got 30 vapors and nickel and nobody's going to buy them steel because it be very expensive right so still development they created a still image you can retain Austinite With the cheapest possible airline element of which is the cheapest possible allowing come with it and do this has been known for 100 at least 100 years that yet silicon then stop semen that precipitation during the day-night reaction so all you do it is you take a steel you transforming partly into banality that partitions carbon and the problem remains in the Austinite and stabilizes the the US the silicon doesn't dissolve seamen died and that's a reason why seem intent is suppressed so you've got an incredibly cheap steel in which Europe paying us tonight without adding expensive Allen editions
and it looks something like this and it almost all of give us Steelers have roughly this composition 0 . 1 5 8 cent carbon 1 and a half silicon purely there this document that presentation during the day-night reaction and 1 and a half but Percent manganese to give you a hard nobility about 70 per cent of the microsurgery just a logjam of and the remainder is transformed into a mixture of the nite and carbon and retrieve data last nite and that retained last nite typically has a common concentration in excess of 1 weight cent so even tho your Steel has an average composition of 1 . 1 5 you partition the carbon and the Austinite is very rich in Koblenz and that's what stabilized it's very clever because you need a small amount of carbon if you want to wear the material otherwise you get brittle much insight forming doing spot welding so the oral carbon construction must be low and it is it said 0 . 1 5 but you distribute the carbon after genius inside your material by this very clever heat treatment but that the Austinite containing more than 1 break the center incredibly clever idea and you can produce this
in 2 ways to get the common man you start with a fully obstinate example you generate about 70 per cent of the locomotive verite at high temperatures and then you transform it into Bay 9 at around 400 degrees centigrade which is roughly also the temperature at which you might galvanize the material alternatively can start with the cold rolled steel and heated up into ending the critical zone where Austinite and fried can coexist so you have your immediate far-right and then you generated retained OS 9 and then transforming him into May 9 and then this this process itself takes a few minutes but this is a continuous production line you know you can produce hundreds and hundreds and thousands end of thousands of tons of this you haven't you think about this this is an absolutely brilliant technology much more much more clever think then even computers because the beautiful you don't need any human intervention the Steelers flowing through your continuous and line and producing your cars and you can that we
get a strength because we've got a mixture of hard and soft yeah and you get continuous yielding again because you got a mixture of soft and hard because when you have a mixture of soft and hard you have lots of free dislocation generated as soon as you start to deform so you don't get a .period affecting you .period effect is no good for former ability but my much much stronger than almost 2 years and still you get a very respectable inundation From the scale now I have a lot more that I
could about trip stands but unfortunately I don't have time today because I have to go to a meeting now where but we have 1 more election left so the color of the rest of it in the next election it would be a stopover earlier today Frank thank you
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Metadaten

Formale Metadaten

Titel Physical Metallurgy of Steels - Part 11
Serientitel Physical Metallurgy of Steels
Teil 11
Anzahl der Teile 14
Autor Bhadeshia, Harry
Lizenz CC-Namensnennung 3.0 Unported:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/18584
Herausgeber University of Cambridge
Erscheinungsjahr 2012
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Technik
Abstract A series of 12 lectures on the physical metallurgy of steels by Professor H. K. D. H. Bhadeshia. Part 11 deals with steels which undergo stress-induced martensitic transformation, the so-called TRIP steels or TRIP-assisted steels.
Schlagwörter Bhadeshia, Harshad Kumar Dharamshi Hansraj

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