Modern Steel Products (2014) - Strengthening mechanisms: lecture 16

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Modern Steel Products (2014) - Strengthening mechanisms: lecture 16
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16 (2014)
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Cooman, Bruno C. de
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Professor de Cooman talks about some of the strengthening mechanisms in steels. This is a part of a course of lectures given at the Graduate Institute of Ferrous Technology, POSTECH, Republic of Korea.
The Graduate Institute of Ferrous Technology (GIFT)
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I it's Scotland collect your favorites I just to repeat a little bit which we were talking about earlier this week on Tuesday the strengthening mechanisms are basically mechanism whereby we will introduce obstacles 2 dislocations To the movement of this locations so that we can increase the dislocation density in the material the incident where you have to think about it this you have the dislocation which is phone causing the plastic deformation of most of the material and and meets a an obstacle yes that the so we we discussed just defected to the obstacles are the not necessarily attractive but let's let's assume that did we followed theory 1 of the theories where the interaction is attractive so the dislocation of is prevented from moving here at this obstacle it's about and so it will continue to move on where it's not stock yes under the influence of distress you fly in and out of the obstacle will exert a force on this this location and I the more I had forced the more the more and apply force the more it this location and bulges out of the larger this forest becomes yes why do I know it becomes larger because the if the efforts to force on the exerted by the obstacle on the dislocation that I have I can't simply wrong before steady this location has on the obstacles under the form of the energies the blind tension 1 so as I as I increase this the bulge saved the ball smaller here defectors T are oriented like this to the sum of these factors become larger yes so and at 1 point but the force is large enough and that the dislocation is released when I reached this maximum force and that's basically what happens now so I can have strong obstacles we obstacles but and so on but in an obstacle usually is defined by if the forests distance Shane yes and depending on this obstacle and a particular interaction you have a theory that describes this and so we we have seen that in the case of solid solution when you add instance silicon aluminum all the elements to steal and the element is in solid solution informed precipitate then the lattice distortion is the main cause of the interaction between dislocation and the substitution all or the interstitial element has and you can buy the quantified this but distortion by means of this primary Delta has which which is it basically tells me how the lattice parameter changes with the concentration of the all you that's 1 thing and then I also have as a dependency on the concentration of the of the soul you know and usually does the available theory says it's proportional to a certain power of this concentration and ends and so 1 of the theories says its proportional to the square root of the carbon content and for example In uh we saw some examples where the for Martin site for instance where the the concentration serenely on the strength of the mark site is proportional to the square root of the carbon .period however of also told you that but we don't have enough theory to to work with in practice so we usually go for the engineering
solution and that the issue here basically say that
I do we going to use empirical equations that dissolute solutions strengthening is proportional to the concentration of a specific element and we're going to use a lot of experimental data to to know what it the strengthening for amassed Percent of an allergy elements this and we have seen also at certain allying elements such as phosphorus and silicon are very strong solid solutions Frank Winters and and we like to use them but that because of other reasons in particular the impact that the the negative impact of these elements on the toughness we will not be able to use more than I say a 700 ppm of phosphorus less than that and silicon a max of all . 5 so mass person wake what we used to have but because of toughness reasons but with manganese we don't have that problem we can add manganese because it doesn't impact the 1 the toughness actually it improves the toughest but for most of the elements you cannot add very large amounts before you start on the proper processes you see all the processes to occur in particular LaFrentz would manganese as you add more manganese you add 2 per cent 2 and a half per cent that's about the maximum people use for steel for the principal constructional steals are you you you rarely find out compositions that are higher than that why is that will as soon as you start adding 4 but the 3 per cent 3 and a half since then this steel becomes very hard animal that means it becomes very easy to turn it into markets I guess at 4 per cent the steel will be almost air hardened by means of any times you do 8 and heat treatment yes and the cooling rate is a little bit tight yes you get market such as that in many cases you don't want Arkansas and so that's a problem so you up with manganese again you you know it's it's a it's a good addition but there you are limited by the fact that its power it's and it makes still very hard Annabel 2 2 and a half per cent above the maximum you will use otherwise it becomes very hard and pardonable I think so and
and and and I had shown you
this craft to illustrate how difficult it was to but although it immediately it looks very simple to check the the which theory applies it's actually more complicated in practice because we don't have that we can't have these very large ranges of C in in in of concentrations in practice and and in these different uh exponents are applied in many in many
cases this is worthy
examples which we looked at it is 1 of the phenomenon that's it's important for you to realize is when we when we talk about them the solid solution hardening and we we we often forget that the properties of steel will vary with temperature and that is the same way who solid solution hardening with solid solution hardening you get temperature affects us and in particular when you go to higher temperatures the solid solutions the effect is last is lower is lower why would it be lower as well because I have 2 effects 1st of all my what this distortion is last year's and 2nd the elastic modulus becomes lower fares so again that creates but it is results in the fact that the solutes are less effective obstacles that's 1 thing the other thing that happens is that as we reduce the temperature there isn't special phenomenon that occurs and that is a phenomenon that we called solutes softening yes and it it basically means that at lower temperatures yes the for certain elements yes we get an alloy softening so the the the yield that instead of having a yield strength increase yes we get the yield strength the decreases do you you can measure what is the yield strength increased the mass per cent for words silicone has and you find out at at lower temperatures than it actually reduced and it becomes so what would visit me that means for instance if you have so you have a pure irony so this temperature and you measured the yield strength of pure irony as a function of temperature so and this is about to room temperature so this is what you find In this said this very strong increases in their strengths but at lower temperature because of the the screw dislocations dislocation mobility it is very low now if I had to silica knows what I see Is that so this is a room-temperature that at room temperature I had I get solid solution strengthening the material is stronger than as any this so also at higher temperature but as we reduce the temperature and this is what we find yes the material here yes this is actually softer then if you hadn't put anything in it and the reason why this happens for certain alloy element of all there's that it depends on the the concentration of allying element that she added but them it's an and and again but this is for BCC Arun grew up not not for Austin Texas and and so what's that this means basically that but something else is happening here and what is happening here is well is simply the fact that these following elements will increase the screw dislocation mobility and at low temperatures and the day will do this because the LRA elements so make double change nuclear fission for formation easier so there is no means dislocation mobility goes up the screw dislocation mobility goes up that's an important but point to know that solid solutions strengthening yes the function of of temperatures temperature dependence look at
so now so let's have a look at it on In another strengthening phenomena yes contribution to strengthening and that is the dislocation density and l the rest of very well known empirical observation that the flow strength what is proportional to the dislocation density square that basically means that 1 of them the when you measure aid the stress-strain curve yes you will actually increase the dislocation density the dislocation density increases so the dislocation that this is the strange dislocation density increases in a certain fashion and if you take this to data listed this data together yes you plot distress this as a function of the dislocation density square dance you find a straight line and this is a very useful and very famous relations In strain hardening stance but it is there the masks the number of points 1 of the things that if that happens is that so in the picture it is not that you go from a homogeneous distribution of dislocations With a certain density to higher density of homogeneously distributed dislocations knock what what happens very quickly with the dislocations is that they they will form patents these patterns which usually refer to them as cells the former cell structure we show you a picture of the cell
structure this is a cell structure here this is a variety for Riddick steel you well you can see the dislocations of the black lines this is the defamation here is 5 per cent and so that's not very much and you can still see dislocation assist 10 per cent of form as you can say you can barely make out this locations here which is C are very dark bands here which we call cell walls where all the dislocation seemed to be the confined and then sell interiors usually go quite a geometrical sell interiors with the dislocation density is very low OK so In it's as if you
if you wouldn't know it by instance in TM and make the analysis Of the total dislocation density here's what you find is that this total dislocation density consists of dislocations in the cell wall and you see most of the dislocations are in the cell wall and then a small amount of dislocations in the cell interior and and it is actually these there's uh dislocations that are responsible for the the plastic deformation because this once in the cell wall there basically immobile yes not that the
interactions that we have this between us dislocations can be what we have already discussed on the left which is what I would call the forest dislocation and action at this location on 1 slip plane that but comes across this locations on another slip planes yes and what is prevented from from moving because of what happens at the at the point where they meet and we've already seen it acts in certain cases at the point where they need you form jobs has and these jobs will add act as the as the pending .period literally very Street and even if it's a Sesil Ed job on the screw this so it's very very strong opening .period so that
we can that makes sense without the that the square root dependents of the dislocation density simply by noticing that if you have faith that the dislocation density of it is a role has been the the Inter dislocation distance is 1 over the square root of this dislocation densities
and this is this equation here into the theoretical for you've got stress is equal to a lot of struck the friction solid solution contribution and then you have you dislocation contribution and you dislocation conference dislocation density contribution has a constant the shear modulus B is the the burger specter of few dislocation and you dislocation density since and if if if if awful far-right you you know what Alpha is about .period 3 . 3 5 G is part of AT and dig Pascal and b is about . 2 5 nanometers you can calculate this this fact has and so you get this very simply very simple the dislocation of density contribution to strength and have you if you want I need this and there are many people who have looked at these the relation between strain and dislocation density so you know you even half of equations which will allow you to to calculate his contribution a very simply
this an example here who and what is the best increase in dislocation density while what you typically go from 10 to 12 the meters of dislocations cubic meters and then as you strain material the density goes up to USA of few you have like 30 % information goes to about close to tentative 15 meters per Q meter of material Kenny can then just basically using this year the calculate true stress as a function of true true strain has and and and and plot and values of some strain hardening values uh that you obtain and and calculate even want to uniform strain will be that's very convenient
for now I again and there is this some example here of this
calculation and a table that gives you typical dislocation
densities that you have but that but said
dislocations that it did is we usually don't use this you would we don't usually the former material to get strength in products has however and and the strengthening by dislocation is basically your standard work harder but what we can do and uh that gets a lot of attention in technologies is reducing grain sizes because grain sizes at grain boundaries Excuse me are very efficient In an increasing this strength yes and in addition the the negative impacts on other properties are minimal and there is actually 1 very positive impact is is a great size reduction always leads to an increase in tough and so that's In many applications structural applications in enough petroleum and gas industry In the shipbuilding industry Wine pipe industry it's very important to have very tough materials so Grain engineering grain size engineers very important for this problem so that you can see here what happens is that in your material when you you generate dislocations I promised dislocation they will distributional moved and then they'll have to bring boundary yes and then it's not against them in contrary to a single crystal where as you perform the singer Chris dislocation can move out Of the single crystal in this case it is stuck stuck literally stuck at the grain boundary and because the sources of dislocations emits always the same dislocations you get pilots pilots and these pilots In order to Bush more dislocations and create more dislocation it becomes increasingly harder To do this and that was the reason is very simple is because these pile-ups the dislocation all these dislocations exert repulsive interaction on each of the more dislocations that have in the pilot the larger the the repulsive interaction and the harder it is to make more dislocations make the this location source created more discipline and you can see very nicely on this micrograph here that the and the stresses increase in the pile up because the distance between the dislocations become gradually larger so basically these pilots generate with what are called back stresses that communities back stresses strengthened the material and that we're not going to go into
the theory but you know that the strengthening from grain boundaries is is the inverse of the the grain size the grain diameter now what about the real reason 4 the strengthening US and would seem like but I think the the wheel and interest in grain boundary grain size engineering dates from about 60 years ago that's when it was a big topic of the people you know discovered and and try to work out in a big way but but that this still many things and we don't know yet and and and it's certainly holds for seals about what what is it actually that makes the heart of the grain boundaries several it's especially in the in the strengthening of because don't forget the square root dependence on is very easy to derive From the modeling point of view of the couple of models for 5 models out there that are readily give this 1 all 4 square root of D the relation theirs but they're very different models of 1 of the models is that I'm OK you have these huge pile-ups and 2 grain boundaries and that these pilots at the tip of the boundary to the tip of the pile-up you have very high stresses his Andy's high stresses will propagate this slipped from wandering to the other great and that's a that's a very nice theory and there are many I'll be there are alloys such as the 1 I showed you here that's
where you can see the pile-ups in and out and you say Well that's it that's a very reasonable theory however these pilots you don't see them and steel there are no pilots and and so it's of it's the distillery that you probably heard mentioned good trailed theory of a grain size strengthening and is a very nice theory but it it's you know 1 of its basic elements that you need to have pile-ups but you don't have pilots in in
Ferris the Ferret excuse
reason why you don't have pilots is because of the dislocation properties the dislocation of properties are such that I've told you that when the the dislocation and far-right meets an obstacle which is moved to another like play this so you don't have buildup of these very high stresses and so on what it's probably have is the fact that the grain boundaries themselves are active in the In the end the process Of this strengthening of that's I'm and and a people who have discovered this in this waiver is simple way they are lot the yield strength of this as a function of the inverse off into the square root of the diameter and they do this for different compositions and in particular they do this for different carbon contents have 0 carbon 30 ppm ,comma 60 ppm ,comma and what you see is that what you have an increased slow In other words that for the specific diameter grain size you get a higher strength yes so that points 2 the fact that what what obviously if the if it was a pile-up effect that this the grain boundary has nothing to do with it here we know that at this level of carbon concentration the carbon it's been grain boundaries is the segregates to grain boundaries and changes this is what we know at strangers the cohesive strength of grain boundaries for instance does but it also changes apparently have the the emissions of dislocations by the grain boundaries look at alternative theory says what happens is it's actually did this look the intimate degree boundaries that generate dislocations and I that's it grain boundaries acts as location sources and when they get stronger it becomes more difficult to to generate dislocations and you get increasing the flow stress right
envisages a number of examples here I think you I do want to point out that this this
equation in this equation here this this whole this would
we call the whole batch coefficient here has is is not a universal
constant right so if you if if if you measure this the slope here for different steals it will be different this time and and it will also differ 4 for instance your friends with the composition from here we added phosphorus phosphorus is added phosphorus is courses and you see that the strength increases the reason is because you know phosphorus very efficient a solid solutions training but the grain boundary strengthening becomes less efficient as I add more phosphorus so there are
many other people have looked at this and there's quite a variety of
K values out there that you can the fight but ended the year these are for and the number of style steals actual steals and you can see that in the middle of 4 IS deals it's very low yes and for the commercial quality steel the cart basically a low-carbon steel which much higher about 4 4 times higher and what this basically means is that this is a reflection again of the fact that In the commercial quality steel you have carbon yes and a common can influence the strength of the grain boundary whereas in an IDF steel there's no free carbon so that the grain boundaries very clean yes and apparently it's very easy for them to emit dislocations and this is
also for the whole batch equation at higher stories
are so it's very into it again so that the grain boundary the the more grain boundaries you have the better for the strength and that's that's basically the work so but usually during thermal treatments grain boundaries will have a tendency to move yes and so as to increase the grains are dense and so are we prevent this by having particles In the wake of the moving grain boundaries because if you have a grain boundary that's moving and it cuts a precipitate another precipitate is in the grain boundary as the it added just just this fact is enough to pin the grain boundary underpins the grain boundary because you see the drain very energy is reduced by this surface yes and so this there you know when the great battery wants to past it's got to increase the the surface area by this mountainous and that X it exerts a restraining force on indeed on the boundary and you can see here France's this is a little particle at a grain boundary yes and this is around the grain bound the grain boundary here is not and it it has moved whereas at the particle stated so but there is a very
convenient equation which recall the Zena equation which reason relates the maximum grain diameter very simple parameters the radius of the precipitate and the volume fraction of the precipitate as the the ratio of these 2 part of these 2 parameters times 4 divided by 3 this is called the Zena equation has basically says that if I plopped the diameter yes both my uh maximum the maximum diameter they'll have in mind Mike rastructure still might concern have over the ranges of the precipitate Is it will go down yes in Lovelock Monteverdi this linear relation when daily the amounted to India volume fraction of the precipitous so I'm having a lot of small particles In you might rastructure will prescient train growth yes now this equation this theoretical equation is a little bit that this actually apply for steals right away but I if you replace this the 4 thirds by 0 points 17 yes it applies perfectly and this is an example here for so this would be the new equation yes and that he's here you have the for each only steel micro alloyed steels if I have precipitates of the 5 nanometers 50 Angstrom stance on the grain size the Mexican can calculate the maximum grant size on just by using this this equation as the grain size will vary from 5 micron Max 2 a half a micron used for a density volume fraction that is not that large No 10 to the minus 3 10 to the minus 4 and this is actually what we do when we make it has only steals it is weak controlled the grain size bye adding Carbide's yes in the Microsoft rupture now the
question is that Of course if you can the strengthened steals by reducing the grain size yet I note that you don't have to do anything with the chemistry yes except maybe add a little bit again using the volume from the very small a little bit of a Carbide's and Mike restrictive but why not and go all the way you know why not make extremely small grain sizes much smaller than the Micro or have like what happens that while the problem there is that you get collapsed in plus if you take In and I have steel so interstitial free steal you and you I look at the strength Of this steel as a function of the and grain just 1 over the square root Of the grain diameter right so what you expect to see of course it is your whole patch equation right and and this is your whole batch equation so this fine yet and there is a whole batch equation for the yield strength and there is a whole batch equation for the tensile strength however you can see here that the 2 meet up they meet so what does this mean if you have the stress-strain where did to meet up well it's life right it's there is the goal uniform the formation that's because that's basically when you have a stress-strain curve say this is the yield strength and this is the tensile strength when these 2 are while this no more you this is a uniform elongation right is no more uniform along the nation's this the material Will the net this will never very quickly and then bring so you lose all your plasticity you have huge struck back to their use nude strength because it Niasse steel will typically have if it's well annealed will have you'll strains of less than 200 made Oscar but you can increase the strength up to close at Giga Pets just by reducing the grains so that's amazing what value but not the material is there you cannot deformity anymore no yield strength and it is no defamation you can see here this is the unit this is that the total elongating you can see as soon as you had 1 micron you get to the collapse of the the illumination is it that it doesn't go to 0 by the way this there is still post uniformly along Daishin yes but if you concentrate on the uniformly longer nation's basically that so this is 1 of the 1 micron and this is a half a microbe that that in the range of 1 to have my grown you know more uniform elongation but so that right you you
cannot really use this I but today we cannot use this method To make former materials we make Wikinews is meant to make extremely strong steals but that's it but there are ways to address this problem but and then you have to make more complexity I'm in literacy but
because I'm and talking here the idea will all come back to this the small very small grain size and also show you that you do get increase in strength as I live in general you get a reduction in uniform vision but the other thing that's positive of course for a reduction of grain sizes is the toughness of that that's usually improves as you reduce the grains of sand in it will will talk about this in but precipitation
strengthening in steals usually that it also involves the the following so if the precipitates a or softer they can be cut shared by dislocations Nos if they're very strong you they're bypassed by the dislocation so they let me show you what
bypassing means say this is obstacle yesterday but now it's a very very strong obstacle it's it's extremely strong obstacle so that when the dislocation arrives here yes it will bulge out yes bulge out and typically in steals these for for for many steals such as speeches only steals these precipitates are very hard carbide particles so there's no way the dislocations can share them there's no way and so the dislocation will just wrap around this precipitate like this and I now do that if this is a screw dislocations indeed 2 arms Of the screw dislocations years past the obstacle I have become too edge dislocations and if I look at these 2 edge dislocations from a point of view of the extra have claimed then 1 of them looks like this and the other 1 looks like this so they can annihilate each other because there they will they attract each other there is an attractive interactions and they can annihilate simply moved towards each other and they form a perfect lattice again him and this 1 and this 1 broker so basically L the dislocation the pinched off we so you end so this is before the pinch and this is after the pinch of after the pension you have the obstacle which has a small dislocation loop around and and dislocation here which continues its motion so this is their interaction which is very common in high-strength steels with carbide precipitates is is is called the moral warning mechanism let
me show you this is an example here some TM images you concede this location close to a precipitate you and you can see it being dependent on us he receives this location is spent and there the dislocation pushing on it and this is a precipitate where this location a few dislocations have passed it and you can see it's surrounded by dislocation yes at an end and that every time you come to lose that's there and the number of dislocations that have passed now
depending on the situation where went what it so if you can
shear the the the
precipitate the relation between the strength of US the strength and the precipitate radius it's given by this equation of businesses for tactic the so-called precipitated can be cut we don't encounter a situation in steals most of the time but we need most of situations we encounter disk relations and where the strengthening is proportional to the density although the volume fraction rather of the precipitates to the square root and divided by the radius of the person so that means that and if we have cost precipitates we get less strength so we want to have a very small precipitates this parent and we want to dispose dead certain density of him right and again in this
series worked out and inferences if you would want to calculate it 4 the particular situation that did you have this would be yet another new you do strengthening due to precipitation of Carbide's is 10 times the square root of the volume fraction so that would be France's 10 to the minus 3 as of precipitate volume fraction of DP here and here is the the precipitate diameter In microloans as this equation here can readily
be put in it the Graf yes which shows you How much strengthening you can get from precipitates so here's this this equation and adjusted the terms increases the yield strength and this is the size of the particles and undersized decreases so we see that as the the size of the particle decreases get increase the strength and and that the more before the end of the week and volume fraction of these particles increases I will get more strength alterations this same equation here you can presented as the increase of the strength as a function of the precipitate fraction as in this case are you getting cleaner guy plots you have of course if it has to be a long long long plot to get linear equations linear plot and in the region for the ages of ladies steals the shown here so we typically try to achieve of particles that are 0 . 0 5 microns 0 5 nanometers and are the so are density typically I'm I going to do ministry the fault that Syria should send volume fraction and so what can we expect in terms of strengthening yes we can expect about 100 make a Oscar and that's that is the contributions from the no precipitation strengthening yes and assuming all the particles are in the matrix at the same time we've just seen that these carbide particles can also reduce the grain size yes so anytime you add now you'll be in Carbide in the microscope trip of its sizzling you get to affects you get strengthening by grain size reduction and strengthening by precipitation the of
it's it's not the only system but where we get to where we get precipitation hardening and and this is another system in steel where we use small copper particles yes and with pure copper particles in our steel matrix yes 2 To obtain precipitation hardening this system of of Hahn is different from the 1 which is those particles as copper actually soft particles and the hardening caused by these particles is but is not the oral 1 Hardin you can cut you can cut the copper particles the effect is actually I it's been studied in detail that'd be the effect of strengthening effect is due to a difference in elastic modulus between the copper industry and as copper and precipitates are used In end Copper strengthens fervor right but also in certain markets citic steals it's used to strengthen the Sara now again this
situation is a little bit more complicated because if we look at the yield strength also the copper added steel so the yield strength as a function of the mass per cent of copper what we see is that copper does more than just those increases strength by precipitation hardening 1st of all it leads to a reduction of grain stocks yes and you can see here the contribution of the reduction in grade is actually considerable yes 2nd copper when you add comparable to the steal it will form precipitates but some of the copper will remain in solid solution and I will get a solid solutions strengthening effect you can see here this is the contribution here it's I believe that lasts forever you will live at all for 50 make a basket depends of course on the amount of copper has added and then you have the contribution of the precipitation hardening yes so the way you put to cooperate is very simple on did you can see here that copper and that about 800 deg C yes you can easily dissolved up to about 1 and a half per cent of copper in eyes and so you just at the typical of copper strengthen steel will contain about 1 man's Percent of copper yes and if you quench yes you will keep it in solution and then you do reheating at around 500 deg C that will precipitate out the Copper that is in the Super saturation and that's the gives you all these particles and that there is strengthening so going back
to the these precipitates as the the controlling the volume fraction is not really a big issue and you control the volume fractions of a precipitate by you know how much now you'll be a man carbon you've added or how much copper you've had it's basically a concentration of related it's important is that is the distribution of the sizes so for instance is here is the image of a Carbide's in any of the money will be amended by by Tania added steel but these very large precipitates have no effect whatsoever I because it way too large to impact this strength has so it's very important that the use of the particles art do not cost yes do not cost to be efficient in both in in both situations of whether the particles are can be shared all whether they cannot be shared it's important for
them to be Standard it's not it's small enough right to this again plenty of it things we can have To get from theory and from experiments for instance if if if you if you know what the volume fraction is of your precipitated and what the sighs as of your Pacific you you you can determine what is the distance between the particles and and the strengthening is proportional to the inverse of the particle spacing so that they are going to discuss this the smaller the particles spacing the leaders of the larger the 1 Overland of the larger district that's what you we
expect right so in a nutshell for far-right yes
when we look at the the strength contribution it's important to know that we are at room temperature and we are in the region where the but there the yen and the strength properties of the steel arch temperature dependent yes there are certain strengthening contributions which are not much temperature dependence and which 1 of these wells so if you can see here I can discourage here I can consider it temperature independent strength part of the strength and the temperature dependent part of distress this found look at what parts are not temperature dependent as but you don't have to worry about looking for a temperature dependence this location dislocation interactions this location solutes interactions so having said this book and you'll be aware of the fact that there may be you should check for a solid solutions softening but that's for lower temperatures and apparel stressed that that's the order lattice friction that's pretty much Seu that's a constant value and then we have the the process of double King formation yes which is the what we called it the Double Creek Formation nuclear nation has which allows screw dislocations to move in bcc that is very much temperature dependence and in its hands and you cannot really ignore it even at room temperature because it wherein the tale of this temperature dependence on Of these of course that you know that it's a low temperature on the high-temperature part with which we see is that both of the 600 deg C as we get a quick collapsed if assistance was purely this puerile using a very quick collapse of the Of The year of the strength of courses because we are at home in it and then you get into the creek area of the behavior now in OK so
we will all tinkle stop here which will


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