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Mechanical properties of steel 15: single to polycrystal

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"quotation mark concurrent and its Letson and start so we had been discussing the yeah it concept of part of stressed last week so you remember what hollow stress that you assume that an entire dislocation jumps from 1 Charles Valley To the next Charles in 1 go this picture and I am at room temperature the interim complete and absolute 0 you can tap to calculate what what it takes yes and which seen that it's very different whether you have grew more edge dislocations and whether you look at firing of gamma and we know from this is that school locations require very high apparel stresses look now 2 herself the center of room temperature I hope we will measure things like the critical result shear stress and we'll see in a moment that this idea of the do this this the screw dislocation jumping from 1 Charles fell into the other ones as as a whole arm isn't that really home but would steal it as I said complex it was his 1st let's look at which we measured experimentally you take a single crystal you oriented but in there in the way that you make sure there's only once listed slip system that works for instance case 1 Burgers vector and 1 1 1 all claim was true you find they what you actually find when you when you actually measure if you measure they a tensile strength in compression of the body not attended to yield strength in compression that is equal to 38 mega pasta and then you have to recalculate there to know what the critical the shear stresses you do this with the cement factor and you find 19 major Pascal is the sheer power of stress critical shear stress scandal low-value knows now let's have a look at With would would have to be be on the yield .period now perhaps a few new slides here just to uploaded to him this morning so you will will not this 1 but the few that I will be discussing in a moment of so make sure you you check the new the new file on the class so rights this is another of the measurement but that it's a similar type of measurement you see that material he starts to yielded you know between 10 and 20 Pascal 20 but those who make Pascal being a a good value and we see that the material to the States and crystal hardens and will be discussing that when we discuss strain hardening that is due to this location dislocation and that but if we look at the at the temperature dependence of this critical shares so at around room temperature with around 20 the major Pascal and then as we decrease the temperature you can see very strong increases yes and it's the measurements don't go as low as OK but you can you can see from the data if you would like to extend the straight line there at that time you know you would be far from the 400 may get passed so the idea of that and this was assessed correct at this locus actually jumps at low temperature from 1 part solely to the other ones as well as as a set for a four-hour fire and for for excuse such it's a little bit more complex that's not what's happening what's the reason why it increases so strongly it's due to the fact that the core Of the dislocation is spread out this this
spread out and and that kind of keeps you because it gives me very high critical shear stresses about that of the dislocations and so we discussed the subsystems and and how but there are also odds really special because not only do you have a spread-out call for you and as a consequence you have a so-called gnomes summit behavior non Schmidt behavior and that in that the normal stresses on the slip plane are important not only to shares stresses and you have other effects of course very strong thermal temperature dependence and then you have it depends on what direction the Burgers vector is oriented if you going into the twinning direction all and you have slipped 1 1 1 2 types planes it you'll have a slightly different stress in the and Dutch winning and then there were there were complications but with the slipway and turns out that in pure Al-Faran the plane is 1 1 0 only at very low temperatures but that in steals this low temperature but because of the low-temperature slip system actually prevails also at high temperatures In the case of Steele's we're probably looking at always 1 1 0 slipped yes but that's been much less surprisingly much less studied and she's very few people have gone up the good work on binary alloys of Byron and look at slip systems there and actually some of this work that I show here has only been done very recently and the reason is because it's very hard to make high purity Irish without having any of the bits of the particularly carbon or any other and is again you know looks surprising considering that we can make our silicon and semiconductor crystals with extremely high purity that it's actually extremely uh it's even if it is to be difficult to find an equivalent of a single crystal for Arron or any other matter for that matter but that's a fact of life but it had submitted the data here you know for those who want to look carefully at the data show you'll see that are you know the critical serious stress that's not always the signing itself somewhere between 10 and 20 Apr . it's the lot of scatter and that's true yes so I'm your question may be sold in or if I do it calculation what value should I use while know a good values 20 minutes that would be the value of would be using if I were to do calculations and there's no reason to use anything anything else and the way you did you actually determined that the critical distress in practice it is also a challenge an annual sum wiser challenges like such a simple experiment to do the trouble is not only is a difficult to music to make single crystals of metals extremely high purity like you would do this for the semiconductors but is also very very hard to make single crystals of iron ore metals that do not contain any dislocations and the level of purity and if that is achieved in the semiconductor industry yes or like the silicon or any other semiconductor is extremely high and there the defect level in these dispersal is incredibly law but it's extremely was almost impossible with the current state of technology because there's no application for single crystals of and said that a union to achieve extremely low levels of the dislocation so as a consequence you get Michael plasticity when you start to but stressed a single crystals you sure it's not there is there are no 0 0 per cent of dislocations in there so I missile bases already present there would can give you what we say Michael plastic effects that will start moving but quickly and and so that it looks like it yields very early so that if you out in
practice if only go back
when you measure the when you actually measure the critical Sears you don't measure here you you look at this 1st stage of hardening and you extended to 0 strength but that would be a way to do this and that's why I'm saying you know
20 make a Pascal is a good critical resolved shear stress for pure Paris now L
but so and of course you say I Wally OK so we've come this far and we noted the 20 meter Pascal is a critical result should stress work of art that they were happy with that but we don't work with Al-Faran 80 and and in the end be we work with which stealing their Pollack crystallize so hot you know what do I do With that the value of 20 or 19 as you have been a few slides back said I don't know when that when will be pure irony starts to yield yes and there and then and that's a big challenge in as you know how you could connect which you measure to single crystal with the public purse and it's 1 of the let the people spending their whole research on this most Hollycrest crystallizing plasticity and and the reason is because you have different oriented single crystals yes and up on and down they will have different the behavior of course because of the slip systems will be different and so we need some kind of averaging procedure was complete and I so you couldn't have averaging procedure that Francis assumed that there is isotropic In all parts of the crystal of the Polly crystallography site that we have all very large number of graves so we can really average and that there is no preferred orientation and that there are no grains grain size effects but that so well these are actually quite a lot of strong condition and then the usually you will not apply for for steals you take sheet steel for instance we we already discussed this you have pronounced the crystal graphic orientation and so the this this may not whole having said this but
there is an additional complication is that how are you going to do the averaging procedure and that there is a union of the origins of you may already be familiar with that it is always to Strobl and father if you have a single crystal results which are basically shear stresses and sheer and cheers there's on a single slips of the other 2 ways to to the do the averages and 2 extreme ways and if you can say Well I have equal stress conditions or you can say I have equal strained condition and nobody can really say you know who's right with wrong however we we know that equal strain calculations give give results the very close to reality that's and that's not the case with equal stress condition I think this kind of cartoon of what he stressed conditions mean it's as if the grains would all be in the role women you get equal stress conditions and you can have a different strains and if you have equal strained conditions you your grades again all parallel to each other and parallel to the EU's distress axes lights and what will see instead if we have equal stress conditions we can calculate the stress From the single crystal data by dividing but the show list Schmidt factor Amin Schmidt factor yes if we use equal strained conditions we can calculate the stress-strain conditions in tensile stress tens of repression by using our single crystal later and multiply it using a single crystals tell value and multiplying with which we call the tight Taylor factor the tale of OK so I so if you
consider very tensile stresses are constant news for all the grains no but then you'll have yielding and you don't worry about the strains the strains are totally independent yes but the grains do can do whatever they want us in that model and so the yielding more than occurred when the resolved shear stress Of the select system there are reached reach a critical value critical resolved shear stress and then each grain all yield when you reach there critical the result shear stress of that audience that particular orientation right so would you basically do as well you just randomized you just calculate which would be if I had all possible orientation what would be the end value which would be the Brenda M. value answers and it's it's it's it's a relatively simple Sigma is Tao critical resolved shear stress in this case divided by this mean and value which is 2 . 0 8 4 Alpha so somebody went out there and as you know went through all possible orientation and calculate the mean value talks would assist friends anyone you want to know the yield strength of our if you have 19 make Pascal there's a new find 39 about 40 megabytes of of it's a little bit different just last week I calculated the same value the fact that the value to yes that was for a walk for its specific orientation yes In this case it's the mean value conflict using the mean and in Galway Ireland it's slightly different value is 2 . 2 3 to 10 but that's that's valid way of calculating ever and averaging procedure and all the other way as the Taylor approach and there you have the same strain same strength and so on right and and so you get different because of the stresses you have this deformation that you so you have to achieve accommodate the possibility of multiple slip not a single slipped in each grade In this brings oriented different way the the have you say you have to strain the same way yes you don't you don't say the stresses are the same you have to deform the same way it and you have to be for the way the whole crystal the whole of steel to 4 so so you cannot you understand that if it if you have a single subsystem In in each grain like you have in the case of same because we just illustrate what I mean here so you have to grains here right and in being so it in the 1st the approach where you say the stresses of the same answer but there and in all so you have this slip system here has and you have this system here if this guy goes like this and this guy goes like this there will be holes in Europe press there will be hope you going to start making holes in it because that's not the case in in them With Taylor with the Taylor system because the strains have to be the defamation has to be I know this has to be the same defamation the grains in every grain you have to take more than once ellipsis that's that's the 1st complications and ends of course that the reason is because each grayness limited by the presence of the neighboring graves during deformation and so you need to assist you take more slip systems into the equation to say you have a macroscopic Shearer 1 of your Pollack Christo is given by the incremental slip contributed by the individual active subsystems of the you have more than 1 slip system in and the contribution this is the sum of the contributions from the individual slips the site as it is to make things a little bit of it's it's complex of patients and and kind of squashing things all the time on 1 slight use of state were interested in Union actual tests and we have a randomly oriented Alpha our public resources so we applied stress in the x axis and expects and there an in your stress and we know there is a small incremental in the constraints the X X as events achieved by subsystem many different slips isn't in each grade there look at the end the way that the theory approached is you look at the work that you do you calculate the work that's being done with this information so so if I had this stress and with this strain the small strained this is the work yes this is the macroscopic work yes this is also what you measure right this distressed and the strain that those are the things that you will physically be met in the crest in at the Crystal level we've got all the crystals contributing a little bit to just the strain of idea Shearer has and is more than 1 subsystem program so so we have the macroscopic at work is equal to do in my cross make macroscopic was acquitted of microscopic words which is the work of each slip system so the times the German I think tank now if we're looking at it we simply looking at the at the yielding than the critical results here stressed we assume it to be a constant how about critical resources that we see that we can make a ratio of Sigma expects divided by 10 because the equal rights likened Phi segment expects to buy tower the critical results here stressed is equal to the gamma this here is divided by the epsilon Texas and this ratio but that's the that's too Taylor that
so again on this there still a factor was and is a number turns out that you know you can go to all the mathematics you know that in the case of a Ne actual tensile test but it turns out to be a number that you can give that to be relatively but you know when you can calculate it and you and you find values and of course depending it depends on the slip systems Lawrence said you you sue them for instance in gamma you only have 1 Taylor factor that's 3 . 0 6 7 because we only have 1 1 1 1 1 old glass In in Al siren if you can assume 1 1 0 0 1 1 1 guy but you can also have a go at Glide planes 1 1 2 yes they have a different and value but you can assume pencil glide in and around and you can also measure it experimentally so would you find values that are close to the story In general OK so what's really important if so far in our case with the cost we're interested in the street you know that examining properties and then measuring them in a tense salt tests so we're happy with this factor and we will go very far with this factor of 3 yes 3 .period all of 6 or 2 . 9 we like as I told you 4 steals we have 1 1 0 1 1 1 slipped it's 3 points all 6 7 is this the value we will remember for that but for tensile test but if you start looking at other defamation laws for instance you your interest in rolling all you did was interested in playing the plane stress situations or any other complex then what that you should always remember that M is a function of the the the crystallographic texture with the shape change and in Inderjit the General Juma arrangement of 2 stepsisters we think for instance here this is the well known yes With their of very formal steel and you can see the gamma fiber here with maximum here and here close to 1 1 1 1 1 2 the texture components of and this year yes is the distribution of the M values as in ODS space 4 the specific what type of deformations namely playing straight that would be for instance the ODS you would use the activity of the and values you would use to study rolling and then you can see for instance that that in this region near for these orientation here you have high and values and other orientations like your friends in the corners you have very low and values to what would assist physically mean no and 1 of the things it's really important to remember Is that high and values the grains that have high and values of grains with orientations with high and values mean that they will deform more yes so if you looking nowadays with the BST for instance systems and all that but you can easily calculate the killer factor but what does it physically mean it means physically that these grains will have more information they will have hired dislocation densities and always also remembered it and is not only a function of the crystal to crystal orientation yes but distressed debt stressed it is also important so if if if we had that if this would be not playing strain but the union actual strained would be look different OK when the collected and end the and and and then there was the detail here just because it's a calculated factor and because you allowed it you assume more than once with step-sister per Grain you have to I know that in general the the and values calculated for specific orientation that you haven't stressing assuming that you have 5 independent subsystems and the suffice independence this system to accommodate 2 strains and they are the ones that give you it the least work for the specific defamation and that's how you select so it's it's the in the Taylor approach of averaging is much more complex than the equal stress approach and but that's the 1 that's closer to reality so what what does it
really mean in practice for the for the rest of the course as as we as we go well in you will see in certain cases in the courts we will be will will have data that looks like this which we calculate friends and gives shear stress yes the plots is sheer stressed as a function of shares and and you don't have a stress-strain curve you have a share share her as to how do I go if I had this data can I easily go for began for the unity actual tensile test case ordered Union actual compression test very simply I think this the show this year stressed the multiplied with amp yes I'd take for every point the share divided by em but to find respectively the stressed in the stretch the truth stress and the truth so you can easily go from if you have a pencil tests data from single crystal which you or calculations the shear stress share you can always get stress-strain curves from them simply dismiss the factor is 3 . 0 6 7 right so that was just about the
averaging so let's continue here about
it gets so they will now say something about it the dislocations and dumped this location lost and it's a kind of and all the way 2 to proceed but you'll see that in the end it kind of makes sense but To introduce strained right "quotation mark so when you make measurements of this year's summation you make measurements on a single crystal of fire with the 6 atomic per cent silica Will you see when you if you're ever going through the literature on properties mechanical properties of irony you very rarely actually meet the get data of thought of pure iron you get lots of data on Our and the reason is because of the transformation and that's actually 1 of the big challenges when you want single crystal data for Byron I usually when mixing critical to high temperatures has and I you make a single Crystallex silicon at high temperatures and equally talented and here we know that at 900 deg C it doesn't matter how good you single crystal West when you when you go through the other Tropic transformation You're beautiful single crystal turns into goes so attractive face transformation at 900 deg C I knew basically destroy your single crystals him with people that have gone is it studied a lot of the iron silicon Alice because when you add about a few per cent wanted to percents of silicon euro there is no face transformation and you go from high-temperature variety to low temperature without any case transformation that's very interesting but you know it's a big limitation and that's where the people get the single lots the single crystal were so anyway this is the Orient you single crystal here and you you you measure the French critical results here stress as a function of the due the temperature and this would you find so you have a low temperature range room temperatures around here never like flat plateau and then it increases and so on what we have here idealizes behavior is as follows we say there is a thermal part and that a thermal part and this thermal part is often called effect so you have an effective stressed and temperature independent or a thermal part 2 do just to distract reported to critical resolved shear stress I'm right and so this a thermal pod is due to long-range stressed dislocations dislocation tangles grain boundaries hard incoherent precipitates suggests Carbide's tonight and it is and this part has 8 we usually when we make schematics we will make put this horizontal in practice it's it's he it has a little downward slope that's because of the temperature dependence of the elastic properties the shear stress becoming softer as we go to higher temperatures and this is what we're interested in this this this
effective share stress the fact strength but and so we have to do this change over From there for school back so this
change over from of flat behavior to very strong temperature behavior that occurs the siren around 77 degrees From then end the
the cost structure yes after dislocations has already said it is is the reason for that and in particular Infratech steals I'll fire and this is a very this thermal Partis effective stressed this very a very strong temperature dependence Informatics steals this the dislocations our extended but it's the core is extended in the core is extended in Nong glide playing on 1 extension is in the glide plane and 2 other expenses are not in the occurred and so the temperature dependence of the strength of steel is due to this the lattice friction that results from this spreading In the case of the Austin medic steals referring mainly to low stacking fault energy all Semitic steals there we have also the chorus also extended but in a different way we have the stacking faults only the glide but I don't have extension away from the glide so there will see that the temperature dependence part is not influenced by the the cost structure or by the lattice written but is mainly influenced by the dislocation intersections so if I
could this schematic is like
best "quotation mark In sporadic steals this is the process of the dislocation going from 1 part as well into the next part of Valley that's the process that controls the dislocation With the strength and that the and in a moment of dislocation velocity In the case of Austin antics steals these I think it glided the resistance to motion but it is what it is mainly the result of dislocation interaction and this this particular way of looking at this year's this is what how does this look well the dislocations with which the glide dislocation interact are forest this location we call the forest destruction because it looks as if the glide dislocation have to cut through these trees incident the plane His the forest these are trainees we now move in Korea and disappears has to cut through this traced it to to move him because of that's the process that firm controls the the motion of dislocation
get so we need to have some we need to deprive fundamental simple fundamental equation and so we can start talking about this location velocity and again it'll look like we're going off on a tangent to suddenly start talking about velocity of dislocation and strain rates which which you'll see in a moment you know with everything comes back to stresses and strength of crystals but so so let's look at this this this block that originally but look like this you and and I introduced 1 2 3 4 dislocation said introduced 1 dislocations in this case so and I like this dislocation move through the crystal when it comes out this this is what it is .period right it's it's it's the form to this no the shape here this this volume to let's say we have no small amount of material here indicating crystal and the size of it is the X-1 1 X to adapt and DX we in the height so and there are dislocations in this volume I think will say there are and dislocation just this parameter will go away animals so but so what is the dislocation density in this a little bit of crystal and of dislocation density now I put a little em here yes and the Emory 1st the mobile some and and I may be a little bit sloppy sometimes I writers sometimes went on Friday but in general it not in general not in this but dislocations you always knew have this location which are mobile has and have not abuse on not for instance in the in the previous slide I said you had forest dislocations and have dislocation that cut through it the forest dislocations we kind of assumed in that picture that they were not the slip dislocations of mobile and because those are the ones that really contribute to plastic deformation again so that at this location and status is is the length of the dislocations divided by the volume right so end times the and then be there all edge dislocations and the parallel to each other's all have the same birthday the system make it easy and times the X so too is the life and the volume of this thing is of course the X-1 leaves the soaring so and that is and then can be calculated as location and the times the X wanted the X 3 what is the sheer now which the sheer here this year please well In this particular for this particular drawing rights I had 1 2 3 4 5 and this locations that let go through this little bit of Crystal said the sheer here is equal to the end times B so that's in this value here and times being divided by that's the X 3 can the excellent definition of this year but right in now way substitute this equation that I had 4 N In here and I get the share is density of dissipation times their Burgers vector times the X water in other words dish the few yes and not knowing the generalized there's this equation here for this year is equal to the dislocation density times be times the average displacement of the dislocations In way divide this by time the time it's taken to do this fifa divide is by time I get the change in the this year with time is the sheer rate and a change of the dislocation position with time is their velocity and I get this equation here the sheer rate is dislocation density mobile dislocation the time their burger Specter times the velocity and it's a fundamental various central equation In plasticity and we'll you will little pop up quite a few times In In the lectures right so when the dislocation stated dislocation densities constant now "quotation mark of course and and B is usually constant also purpose but then the strain rate is determined by the secretion velocity right so so I take a piece of steel you put it in this the tensile machine you pull it yeah you pull it at a certain rate yes the deformation rate there will be the function of the dislocation density of course but it will be a function of the velocity of dislocation and so what does the velocity of dislocations and depend on quality depend on the forests I have of working on a dislocation and the mobility of the dislocations and what is that it basically means reflects the ease with which all the difficulty which which dislocations segments of dislocations can move around obstacles and again so so what does this mean for our fire infotech steel that means the lattice friction certainly at lower temperature and 4 Boston epic steals stainless steel it means the forest dislocation so this location velocity will strongly be influenced by doing this the physical nature of these obstacles Walk obstacles can be anything really and we'll see that's going to be the central idea of strengthening mechanism yes yes to put obstacles in the way Of the dislocation to reduce their basic mobility I their velocity right and so in steals and certainly infotech steals arrest this pronounced dependence of low-temperature dislocation lost on the crystal structure and again and said that there is a fundamental difference between Hellfire far-right and Austin at steals what happens in Austin systematic steals is that we have the process of moving yes yes by the
double kink nuclear nation and sideways propagation of these things yes that is the way the dislocations move and surmount the perils barriers and the interesting thing is that that processes thermally activated and that's why we have a very strong temperature dependence at 0 OK yes we don't have any thermal activation and that's 0 OK the dislocations do indeed go as a whole they jump from 1 slowly to the next parts yes now so that your kid is did you use disagrees moment when Europe your share stresses heightened apparel stressed on this occasion was as a whole without any I think formation and if the distress is too small yes this no motion of the dislocation and in the sporadic steals these screw this up is because they lie along paths Valley and they can you haven't missed the coordinates extended over the a number of blight planes nose and they will have very high the perils potentials but if the temperature is high enough we conform kinks there's and and that way we get this pronounced temperature dependence on decrease of distress To move dislocations in the infotech states of this text the this year I think a little bit about it this location velocity probably I don't think you can calculate dislocation blast is that you can know we could just use the formula which is the right and say Well let's make a few of those assumptions and see if we can get couple at this location velocities that took it will it will just assume that we have a certain strain rate and and we have specific dislocation density so we should be able to calculate what dislocation velocities princess we say at this location lost district density of 10 to 13 per the square meter that you may not know to that know some of you may be familiar with dislocation density values but that that would be like a a reasonable reasonably low dislocation density and strain rates a 5 . 5 10 to the minus that's the reason of strain rate you would have been a tensile test that's a rather slow tensile test and so on so where this might share strain rate in this case well this is a this strain rate is 80 macroscopic strain rates if I want to translate it into a shear strain rate I can always use them I am value right To get because of its easy it's the value about 3 OK and I just apply this formula but my share strain range here that I think I did this really but this year's venerated status the term the shares strain rate is and times the I the applied their share that the strain rate and and then I did I just use this year the uh dislocation density yet and this is the Burgers factor In times the velocity of this so what do I get the obvious 6 . 7 to 10 to the minus 80 cm the sec OK that's the the velocity of dislocation that means that if you want to get that kind of defamation and it's a kind of velocities you dislocation must have if we have this density there so what do we know you can actually do measurements on dislocation velocities and as I said earlier the dislocation the velocity is a function of distress you apply and the mobility I'll do dislocation so here I illustrate the fact that when you do the experimental measurements you can actually see the stress dependence and distressed dependent is very often we presented by this empirical function as of the velocity Of the dislocation is equal to they it is proportional to the To the power at and in order to avoid complications with units it's he usually presented as the dislocation velocity of this will be divided by a reference velocity is equal to tower over a reference to the shear stress to the power and so on these if the 0 Renault is the it Is the velocity of 1 centimeter per 2nd and 2 out not is the shear stress required to achieve this this location lost talk so people have done measurements yes measurements for single crystals of Al-Faran for Bayern 3 per cent silica measuring dislocation lost it as a function of the resolved shear stress this you have to be very very patient to do this kind of measurements and what they've done it for edge dislocation and screw dislocations as a function of the results shares of these are some examples here at room temperature you can see here for instance for single crystals of irony you get different values in a different situation and for firing 3 % silica you can see for instance that the Tao 0 is this dress for the velocity of 1 centimeter per 2nd principle that would be around here you see that single crystals that you have a much lower value then for this basilica of reasons Of course solid solution hardening and you also have a very different and value the stressed this and values called the stress exponent and in particular the the stress exponent is much higher for the day the high silicon the situation and will this is empirical value added empirical equations will come back to this stress exponent later on but check this stage it's important for you to know that this equation exists but you can write stressed there is proportional to it the loss dissipation is proportional to the shear stress too but power and so that's that so
said that the control now of the velocity we we already know that in and it's lattice resistance in gamma it's forest dislocation how does this look here what what do we mean with this lattice resistance when the this location in Alpha iron moves years last year the distribution is fully determined by the velocity or mobility led with his immobility of the screw dislocation and this screw dislocations moves in the process that's called the double kink the process double King nuclear nation and propagation so what happens is that have epa's Valley and other parts Valley it a 1 1 1 direction another 1 1 1 Valley against and this location jobs locally not the entire dislocation but makes a little bulge and then this bulge jumps to the next valley and in the process it creates too edge bits of dislocations and you can see because the bird factors in this direction rights of these on edge this locations that cross this the Carl's barrier His and these moved sideways and they move sideways very rapidly so the reason is the following if you look at the core of the screw dislocation here yes it's Cecile it hasn't extended core yes and the the bank that has moved to do the next part of Valley also has an extended cordial success but the bet that crosses Over the perils Hill here hasn't Gless I'll call it's it's it's not extended in 3 dimensions and that's what this beds can move very quickly laterally and achieve the motion of this look let's look now at the process In more detail so that you can refer to this drawing here perhaps the 1st to form a little belch yes that happens by thermal activation this location moves back-and-forth in deposit money and 1 moment has enough thermal energy to cross this barrier and a new form a kink pair yes it's another to King Paris are a small edge dislocations with opposite Burgers vector so initially when they're very close to each other but they will be attractive yes it will be attracted to it and that's balanced by the forests on the dislocation which pulls them apart but the activation energy for King formation is full to the formation of a king is much higher than the energy for kink migration to the energy for the the king to migrate here is much much smaller and the reason is the core structure is not spread and so they will move very fast once therefore there so the rate of pink nuclear nations is very important in this whole process because that's the limiting that's the factor that will be a determining the velocity because once you have a kink the 2 edges the "quotation mark next going the limiting step is the king formation the nuclear fission rate of King the place is low compared to King velocity the king density but of course is also small on my dislocations and there will also be kink annihilation processes when went to kinks meat from opposite side of me and the Kinks moved to the end of the dislocation where there may be penned usually pendant and and that their therefore curved segments so let's let's draw this little bit larger 1st step is I have this location bulges then I formed kinks and 2 assuming that the former news crew segment in the next borrows money and they have used to edge kings and these edge kings of very high velocity and they moved laterally and when it moved to the end my dislocation has has jumped from 1 the personality the next witness but not in 1 6 in 1 single got theirs let's
see how we can describe this OK so L what it what
happens in the during the double King process will have applied some stress on my material pulled material or I pressed compressed what would happen as well 1st of all I have an external force that works on my I think yes the shares fast times the that's the peach-colored formula the kinds X X is that the dimensions the length of the and then I need to look at the the activation energy for forking formation so at 0 OK indeed King formation energy is 2 times the formation energy for 1 which is speech can then there is an attractive interaction between the 2 segments which has a certain for than there is an that externally applied stress which drives the Kinks apart as of the equation for the activation energy looks like this there is a term think formation of 0 OK an interaction terms between the 2 kinks yes and then the effect of the stressed the externally applied stress on the case
itself I in think the To make a long story a bit shorter then that it is not To make a long story short and this is this is the the the the way you have to look at it so personnel to make bulges yes you To make bulges you need activation energy which is reduced by the applied Stewart it's easier to make a bald if we reduce the if we if we applied shear stress and at 0 OK yes it's 0 OK I need to apply the Powell stressed yes 2 To make the dislocation move OK this involves formation kink pair formation activation energy is equal to so I have 3 terms like that of the 1st term there is the King formation energy 0 OK In this term which is the interaction term which looks like this and then we have to be the the peach-colored effect as the stress on the became part which is my nostalgia in the Times H time suspects so this is energy right so I need to have the forests is tout and be times the length of the dislocation suspects times H H is the distance that be over which the dislocation is is moving so this is the equivalent of the energy but then don't by the external forces OK so 1st the let's say a few words but this interaction terms this a correction term is not that important it's only important at the very 1st there moments where you've made a tank when the 2 this locations are interacting strongly and and and this is the interaction so at the beginning so the this is the activation energy as a function of the distance this distance here will be will have their share of so we have this location bulge in fact than we have this stage where did the deed to edge is a very close to each other and there is the strong interaction there but what we're interested in is the stage where we have independent kinks independent King stage and that's where we we have this effect the effect of the applied stress and you can see here that in this case this term here this interaction term that doesn't work anymore when the when to edge dislocation of forward so we reach a maximum and then there is a decrease and the idea is to they think will spread yes once we reach this this critical this is critical size if you want this critical and you can we can calculate this critical
size because it we just make a derivative of the the activation of the With distance this as being that of the West the width of the the size of the king and we find this square root value here 4 X C and this and the maximum activation energy is and that's OK so once a dislocation working chronic achieves this critical energy audits critical size the kinks will very quickly move apart rapidly that's the that's the point and that is of importance so if we know this yes we can calculate the braids of King pair formations at the rate of King Paris is personal is the attempt frequency How often per 2nd that's the dislocation attempt 2 to swing from 1 part of it to the next we use we set this equal to the buyer frequency this in natural for the vibration frequency of Microsoft then the length of the of time give the length the dislocation divided by the critical length so How many pieces are critical can can have had the correct length has and then multiplied weight how many of the jobs are successful basically expressing that the thing is the process thermally activated and so in here the activation energy is what we do right here so and and you can
see that at a certain temperature and for a certain a double King formation energy the higher the stress I apply he the higher the number of successful attempts will be to form cakes it is a defect in and recalculate this this equation is based on the number of simplification and in particular related to this attempt frequency 1 if you if you want to take into account the fact that you should use the natural vibration frequency of the crystal but you should use the vibration frequency of the dislocation itself in the form of looks very slightly different he added term be over the critical west of the decay so the dislocation velocities and very simply the Burgos factor times the attempt frequency yes saw it as the Burgos factor times that the nuclear nation right because indication to Burgos factors the distance that you travel and the the nuclear nation Ray tells you how often you travel that distance 2nd 2 If you make this product you find the dislocation velocity it said the dislocation velocity is the function of the
if you can see here of the applied stress has and the length of the dislocation and the temperature so where does it say the dislocation velocity goes up when the length of the dislocation goes up when the applied stress was used and it also goes up would stress because there is a reduction see you in the minus sign a reduction of the activation energy as we applied stress it we think so the you this location velocities is controlled by the piles mechanism no and there's so much of it a double kink formation mechanisms will depend on the plight of stress and the temperature and then the length of the dislocations longer this way is that because longer dislocation moves faster because it has more nuclear sites for kinks and so this is what we found in can hello L and then this factor here where you see that the activation energy is reduced by by the application of this this shear stress right so but the strain rates is maintained because of dislocations which have the right to velocity so so if we have a certain dislocation density of mobile dislocation density the people to read the role here the rate is given by indeed times dislocation and seek times this the dislocation philosophy which is stressed dependence so an increase in strain rate that call for constant dislocation it you can only achieve this when you apply a higher stress yes and what does this higher stress due yes it increases the number of double kinks on the dislocations it's related to double kink nuclear fission right and in the collision rate of kings is the controlling factor because the propagation of the king's takes no time no energy In comparison To this plenty of thermal energy around 2 look to
this focus so let's let's close now and will meet on the on Thursday morning would go to an example where we calculate some values based on this series so thank you for your attention so Alan
idea if it's a little bit theoretical don't worry about it that's what it is it's not an easy subject but I have tried to simplify things were at work possible and will extend will go into the some more detailed and and show you that that actually you can derive equations based on this approach which directly useful in practice look at shelters
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Metadaten

Formale Metadaten

Titel Mechanical properties of steel 15: single to polycrystal
Serientitel Mechanical properties of steel
Teil 15
Anzahl der Teile 24
Autor Cooman, Bruno C. de
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 10.5446/18320
Herausgeber University of Cambridge
Erscheinungsjahr 2013
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Technik
Abstract The 15th in a series of lectures given by Professor Bruno de Cooman of the Graduate Institute of Ferrous Technology, POSTECH, South Korea. Deals with the treatment of deformation on transiting from a single crystal to a polycrystal of iron and dislocation dynamics.
Schlagwörter The Graduate Institute of Ferrous Technology (GIFT)

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