Mechanical properties of steel 7: evolution of plastic strain

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Mechanical properties of steel 7: evolution of plastic strain
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The seventh in a series of lectures given by Professor Bruno de Cooman of the Graduate Institute of Ferrous Technology, POSTECH, South Korea. This particular lecture develops further the concepts of plasticity with a focus on the formability of steels, particularly those for automotive applications.
Keywords The Graduate Institute of Ferrous Technology (GIFT)
Steel Volkswagen Golf Rutschung Mint-made errors Material Material Fighter aircraft
Coating Steel Nut (hardware) Hot working Key (engineering) Cluster munition Distribution board Eisengießerei Machine Punch (tool) Punching Roll forming Locher Spring (device) Spare part Forging Shredder Semi-trailer truck Firearm Material Cylinder block Sheet metal Cut (gems) Steel Printing press Railroad car Hot isostatic pressing Hobbing Blanking and piercing Sheet metal Cartridge (firearms) Spare part Screw
Steel Machine Printing press Machine Spaceflight Punch (tool) Sheet metal Roll forming Screw Spare part Material Punching Sheet metal Backpack
Steel Bottle Printing press Brake shoe Kopfstütze Scouting Überschallstaustrahltriebwerk Volumetric flow rate Roll forming Volkswagen Golf Volumetric flow rate Roll forming Plane (tool) Spare part Forging Plane (tool) Material Mode of transport Wind wave Hose coupling Material Flatcar
Textile Punch (tool) Flap (aircraft) Separation process Deep drawing Roll forming Volkswagen Golf Screw cap Commodore MAX Machine Spare part Mode of transport Kümpeln Hose coupling Material Diamond Typesetting Air compressor Bending (metalworking) Train Hot isostatic pressing Blanking and piercing Finger protocol Sizing Tire balance Plane (tool) Remotely operated underwater vehicle Wind wave Ship of the line Stock (firearms) Workshop Punching
Typesetting Train Hovercraft Sheet metal Seeschiff Pattern (sewing) Roll forming Volkswagen Golf Cartridge (firearms) Continuous track Plane (tool) Food storage Ship of the line Kümpeln Material Flatcar Sheet metal
Depth sounding Ship breaking Typesetting Train Kopfstütze Wire Sizing Volkswagen Golf Cartridge (firearms) Alcohol proof Mode of transport Ship of the line Miner Material Punching Gun
Steel Canoe Train Mixing (process engineering) Blanking and piercing Ammunition Turning Volkswagen Golf Volumetric flow rate Cartridge (firearms) Continuous track Rutschung Plane (tool) Forging Negation Plane (tool) Spaceport Surface mining Remotely operated underwater vehicle Miner Screen printing Material Punching
Volkswagen Golf Canoe
so well 1 religious person there together about strategy of answering the quizzes so we have a quiz every week there about their each time 10 questions that means that over this semester will answer no close to under 50 questions about so which basically do it every time you answer a question correctly you accumulate points rights and that's how you have to look at this but you know if you absent in only don't accumulate points right now and I don't I will not take that into account because I can and will normalize your great yes but the idea is not that you make 1 very successful test and then don't ever show up for the quizzes right if you're not there to take 2 quarters you know you miss out Morgan wanted to questions you know we will have a serious talk because you're supposed to be here and then when you answer please write your name you want that you don't have to write very much right you have to write your name and then and and and 10 letters fighter enough so you know there's there's still people who just you know when I get the someone who right that's right ignorance and if it's not well written it can be anything right so don't do this to me OK so this is a T and this is a matter of right and if you can't write these 2 letters in all and the it's going to be an error OK this very simple and I'm not asking too much and write your name nicely and you know so I can because there 2 people who have very similar name and it is the scribble their names on the conceded different I think there too Mister shipments please write your name carefully so I don't give you a very high grade too OK good so let's collect the papers and shrink them here in front and let's move on with what we were doing president best known the best way to do well in this course is just no participate to all the quizzes and I really stick to what I have said in the past has sold on if you if you if you go through the slides and the materials you've you had United should be OK and of course whatever level of difficulty we go into during the course of this so we would wish we had arrived at a 2 point on Monday and Tuesday Excuse me that and you know there's this whole body of theory of plasticity and I and you know and we're all happy about having a floral and everything like this and I know about our factories and Delta are and what the impact is on strain increments and things like that but it also leaves you with the feeling that but what we we can I do with this in practice and I will in practice of what when you go into the real practice of for
ability and plasticity you realize that actually stresses but this is not much discussion about stresses in that case in in practice very often but when I did there was discussion of form ability we it's about strains that the discussion goes so Over the because for ability is it worth of really nice subject In the In basically to 2 areas 1 of them expressed forming this really complex known as it is a lot of interest in and and and massive of forming which which is basically a but you know we you have big blocks of wood chips :colon union shape them you you shape them in a specific form so that you have a large deformations that people in the areas in these areas people are interesting and clusters and then of course there's a lot of work and plasticity which is related to fracture in which would was on before fracture severe when we will be talking about plastic fracture in this process he will pop up again and as as a subject but so they will focus on sheet for an inch sheet forming a unity of use big presses no where you you basically form objects like like these many things around us are and are made like this bye bye presses and the material you start with a sheet steel was flat sheet and that can be of course steel but you know we have also sheet or other metals and alloys are available as to make parts aluminum alloys Indonesian Alistair Itanium alloys zinc and are to name a few so you can see it here is nice picture you see these the sheet material is it's cut into blanks so you've got a stack of blanks here yes all using the oval-shaped here and it puts it in the process known as an outcome the spots yes and you know and and and how do you have to cut too deep from the edges you you may have to punch holes in this but you may have to do some surface coating that that took to get the final part yes and answer to this is a manual press not and young for automotive applications you get big huge transfer prices where we have huge presses 1 after the other and each to part of the of the defamation still too late you get the final part the or so L & L and obviously I we don't see this guy here what he does it is presses to knobs and very goes this is not doing much stress measurements for wondering about 4 nieces the yield criteria no so there is a little bit of a you know big divide between the making real life Pirates yes like led the side panels of the car and then when Europe making the material yes and trying to evaluate how how it will behave in this application right and so the people will do research they will do a quality control on on sheet products to evaluate how this material will work in this situation right and obviously Out the buildings and the use special parts in the laboratory the party that has looks very nice it's a so nice part has been designed so that it casts the material in the at all possible difficult forming situation but it's not used for anything acts no it's not a real Park and it's also part of that people use it developed for instance to see if when they do a finite element simulation whether their calculations mimic reality see how it the it's basically validating the colors of validating a code or of this new program and that's 1 thing but this is All already the domain of research but in practice you know when you want to see quickly evaluate and B the form ability of of the material you have simple tests and will talk about 3 simple tests today and 1 of them is a cup ,comma drawing cast very simple test and and we'll see how this test helps us to I define for mobility in practice and it will also will talk about 2 other tests the decibel whole expansion test and and the spring back test and the reason why I want to to to say this is because when you do a tensile test have already told you you can determine the R value him the part and that's what we already know that some measure of form abilities but there that's not the only measure of form ability in there all the things people are interested in and and so that's what we'll be talking about and that and go little bit into into details so you
get an idea of the complexities of so this particular on the
the Cup here they just showed you
on the on the right now OK that's that's made when the are a sheet forming task machines and and yet many laboratories people use this mission is built by Erickson the other one's has and which you basically there are 2 basic up parts in this machine and that is punch and adopt and what to these parts do I think that the yes
this of goes well you can have so look at the cross section on the upper right here so you you you have your diet you put it on this died a small circular blank knows you can't it's between the so-called blank that's the top right there and then you punched you use of punch to push the she'd into the the back and so they fight interrupted test on its way To making up a full cup this is I've you that this hat shaped and what happens is when you pushed up the the punch the diameter of the flat of the blank decreases as you punch down the materials right if the material is it's pulled into this is circular cylindrical hole OK and so we have the 3 parts to discover a flange part of the wall part and the bottom part of the East undergo a different what we call strained pack yes and so this is the sideways you see you have guy I yes you have blank older who keeps this pledge flat yes and you have a punch so but said 1st of
all when you do the simple task 1 of the 1st thing you see after you make the the cups is that while some cops all I have the nice flat bench no other cops have edges with waves which may be a very pronounced and not very pronounced usually for but and adult tells you already the appearance of this we call the years has tells you that this material is an isotropic yes it's got our values the change with direction OK so that we already there see things that tell us something about a B form ability to get from what
happens L during that the test here who can say 1st of all the tests is that you just don't go bad and just you know but this thing and and then going on makeup of you have specific test conditions which you have to determine what are the good test conditions and these test conditions once you have determined will also tell you something that form ability of but let's just don't look at it a little bit more detail in In the flow of the material so say we will have interrupted to test than we have this hat shaped knows what happens in the flange bottle you see the original Milan is basically a circular of the elected 12 centimeter or whatever sentence of that order of magnitude 10 centimeter of diameter she material and then you as you punch it shouldn't you make of the this edge moved toward the center so the material at TI edge here in this the radius all the outer rangers here it's squeezed into this radius now if you squeeze material into units that's this wide into something of this wide what has to happen the material gets there's so you get a thickening of the flange part of the Black to the thickness change and so you can see here which would we've done is we've taken it a couple captures credits Scott at the and it's it's about 1 .period I think 1 . 3 In thickness here you're at the bottom and if we go up we can see that it is a curious it becomes thicker yes and that's because we saw In the flat shoes squashed material and you make it this well where in the UK another thing that's really interesting here is as we cut this use is the walls those against it's girls yes what does this that tells you that the rest of the integer have very high internal stresses in your materials In your material so we won't be talking about this but this is something I want you to be aware of because it's exceed here of on the images at any time to deform facts yes and it looks perfectly flat you know perfectly straight there are very high and there may be very high internal stresses in this material students than they appear when you cut it off when you could pass out and in the cup is is no difference but at there will talk is employed more detailed so and so you have a thickening of the flinch the wall here is there is in what we call plane strain conditions Rooney told you that that's a rather scary condition because every full length the name this directly translated in the name of the wall and that at the bottom yes we have thinning of the bottom part of the blind because we have stretching conditions to have or we can receive different stress states in different parts of the cup let's see so but if if we look
at the the stress situation now in the of it during the Cup forming it's actually rather complex and it changes so and that so which witnesses is there would be the the circles of the you inform users circles life and you could actually determine what is what is distressed this situation for instance at the bottom of the cup as you and as you are as you do do the press years so and that this is shown here you have here is the change of distresses in this area and and this is the change of the stresses In the flat so in the plans you have different stress conditions different stressed state than in In the here right and indeed the Baltic and it also changes but the severity of the stresses change during the test you can see here that you have planes trains now excuse me up all the plane strength the refers to this the the Wall the wall part of not not be this the the flash part which is in in this so-called deep drawing stressed in the drawing we have compression in 1 direction and pulling in the and tension in the other perpendicular directions and you can see that as you go In the stresses that in the and this part here increase vary appreciably during the test let's go and the sea say something about the French part yes the flange or so we we know that this thing this outer rain has to go moved in here yes what happens if and when you do this if you like if you if you try to us To do this in a which a piece of cloth for instance you try to push a piece of cloth into the interior this whole for instance you'll see the piece of cloth will start developing wrinkles the same thing happens here if I don't apply a blank older force here yes to keep To keep the Fuentes flap these flags will develop wrinkles yes and your cup will not look like this but will look like this yes so these wrinkles yes that were under the blank holder where you know were basically deep drawn and when you get this obviously really that I got so .period I'm trying to make is that the blank holder the forests we use on this blank holder and Of the the blank relative to the diameter of the punch are important parameter became so we need to look at it but the ratio the blank diameter relative to the punch diameter and this ratio called drawing ratio so that's an important parameter of form ability another important parameters "quotation mark the blank holder Forbes can let's see how we work this out in we and you will already see for it
is also visible in this type of task we can all this graph but as schematic I show on the x axis the so-called drawing ratio In the drawing ratio is the ratio Of the blank diameter on the punch diameter so when the blind that the the ratio is to it means that I have it the diameter of blind them twice the diameter of the parched and all the Y axis I have the blank holder forks right so when it's 0 0 I have no black Holdorf there's no blank older yes Center so now let's imagine aid not too wide 80 blank and I have no blank older forces no black holder force and I'm just punching a cap without blindfolded forced the flags will start 4 waves we get wrinkling yes as I increase the blank holder forests yes I can suppress this frankly I can suppress the Ringling suppressed the wrinkling and I can make a nice guy yes can but How high it is can I go you know how don't strong connect press good the blind older what's imagine we continue increasing the blank older forests that make it very hard then at 1 time the forests on the blank holder that will still higher that the material will be unable to flow right in the middle of a disaster although the stock between the and the blend called and but the couple will break it'll just break yes so too there is a maximum the maximum yes where where I get fracture yes and so now what happens to this maximum if I make the blank a larger and larger than than make a larger black same larger right because I have a larger blank I will need less forest Les Blank older forests To make the cops break yes this upper relying decreases as I make the blank holder at the blanks size larger in other words when increase the the drawing ratios yes this curve hostess and eventually the the wrangling line that's pretty much horizontal yes the moves up slightly and the fracture lines meet and it means that I can only form a cop within this range yes within this range of blank older forests and drawing racial what is an important parameter all of the former ability is the maximum drawing ratio the maximum drawing ratio is the maximum Black Diamond that where I will still be able to make a cup divided by the punched him yes we can now say you know you don't know anything about plasticity but you've done this task and you have to materials and what material give 0 this maximum drawing ratio and in other material that's on a material gives you less please about to send them but which 1 would you rather using your press shop while the 1 that's it's not going to do you know that it's going to be not break Over a larger domain of stresses 10 drawing ratios because this is this is the range of a blank holder forests yes for 1 of the materials and this is the off-form ability for the other material to the other material is will be easier 2 4 them before the 1st material whether it has the power red forming right now so this parameter here the beaten B Max is a very important technical evaluation of form ability yet you can also already see that having no stronger material yes can improve your form ability because it allows you to use larger forces without the risk of fracture right Of course and and here I want to come back to the fact that you have to take it the idea of forests In the Bronx sense right In analysts because if you increase form ability as I have told you you can it has an impact on the stresses that the defamation and the eventual fracture will occur so indeed it in the bottom you have by actual the stretching indeed flan you have drawing because the materialist squashed in this direction and pulled in this direction but drawings situation appears to share if you want and then in the In the wall here we have planes straight yes the and and we know we have blamed strained because the material can get longer in this direction but it cannot it cannot change its West and the reason why it's it cannot change with it's because it's constrained by the presence of the punch .period surface is there and so it's just basically stock against that it cannot get smaller yeah or a larger units the president's plane strain and we know and this was really important that we couldn't you can have stature hardening has ended at high our values you can yielded became mixed material basically the stronger in in the important places you don't want to fracture here you don't want fracture here and you want to material to be able to flow here this and this is not the drawing part is not very dangerous yes and we'll see in a moment wider but
before we can do that we need to talk a little bit about strains yes strains in more detail so I say I have a piece of material yes and in this piece of material I have I imagine a little sphere of material and now I the form this material and in this particular case I've thought I would particularly questions I sequestered by half an answer because as squashed that I have to elongated because I know that you have to keep my volume in plastic deformation and an idea I moved it to the right and I turned it around said them moving a translation and rotation doesn't do anything right to the deformation so this original little circle will turn into an ellipse yes it will always students in and you can do this at home would like plastic for or any time you have at small of it has to be small enough right small enough volume what small enough while mm science yes I limited future Europe on this circle will turn into an ellipse and I was really nice because we automatically know all principle directions you always know you principal directions and that makes the analysis of he says he knows In sheet for instead of looking at a little volume of material we just such a little circle on the surface and if we do the defamation this little circle will turn into and ellipse and if we do for medical turned into an ellipse which may change its shape yes through its but it eventually it will I'm not the newer final elects them and so this allows us 2 look at this the defining the strains In terms of principle strains yes we you know we don't have to worry about shear stresses that its use trains etc. because we automatically have a very simple and way of analyzing our observations but what do
I mean well let's just look at the situation a situation that happens in the flesh of a contest or in any flange of a pocket you know where you did draw you circle little circle that you put on the surface changes for instance interior this ellipse so it has been squashed in 1 direction and elongated in another direction were where this type of information happy what it happens here if if if I drop a little circle here but if if if I'm on my original sample I have a little circle here at noon and nite track this little circle during deformation I will find that this original little circle that looked like this is now elongated in this direction and squashed in the other direction Nos you can do so it's a little circle at the beginning so I the diameter is L 0 note I do this type of straining which we call this particular type of straining called drawing yes and now this has now is now an ellipse and I can measure distillates I can measure the length storage I can measure the length in that direction yes so make the natural logarithm of and length In the principal direction divided by the starting line for 1 of the major direction and for the other major direction principal direction L 2 divided by L 0 and take the natural logarithm I basically have the 2 principle strengths the 2 principles to of and because it's plastic deformation that automatically have the the 3rd principal direction which is perpendicular to the ship yes we know because the volume is constant in plastic deformation that this strain In the the 2nd and the 3rd principal direction must be 0 so as soon as I measure 2 of the principal directions I have the 3rd 1 yes OK but these 2 are in the plane and this is perpendicular to the plane In the plane of the ship but of course when you when you deformed at a sheet at the circle can do other things right for instance it can just expand isotropic Lee if I pull by actually this circle as I increase the new strain I can have a perfect circle after the defamation right so that it is stretching it's called stretching or I can have a plane strain where 1 of the strains doesn't change 1 of the strange is 0 and I stretch the material only in 1 direction and the nice thing with this approach is that I need information you can give a sheet yes can be represented on the on this graph yes you don't need a 3rd dimension yes you go you will see how we can put any information about thickness on this craft in a moment yes but that's basically yeah and of course why would we do that because if I to form a material for instance in this direction eventually it'll it also fracture yes and I can indicate that at 1 point this fracture happens the obtaining that with the high-octane what is called performing limit diagram of can erupt but I'm just began to simplify things let's look at our tensile test because know cancel test this certainly of utensil test on the flat sheet as flat material that what happens in this case well if you are and you know if you had a standard tensile specimen like this for sheet and you know you would put some circles on this circle pattern but is we know that we have the length strain now we have a wit strains and we have a thickness string and so the circles would turn into ellipsis of this nature yes because there is no force that prevents the reduction of the with and I get ellipses that look like this yes so a tensile test on this diagram in this diagram that would look like this so as you would start having a circle here and then the Circlewood the because longer and longer like this weekend but it would so that the strain in this direction here is negative and the strain in this direction is positive because so you would have a strange passed along this direction this eventually you reach the uniform along nation right used unity you need to reach me the moment where the sample starts to neck right so that you can indicate as at this moment the sample starts to next year's and at this moment the sample breaks the and this will be another way of presenting did form ability as it were for your stop OK because I hope that's clear How at the end and so so what began with what we do what would we get is this two-dimensional graph where you put the major strains of the larger of the stew on the on this axis and the smaller 1 on this faxes and those of the major strain is always larger than the minor strains and that's why it's called the major strains but both of them are the principal strains but and the minor strain In sheet form it can be either positive or negative right take that the way you can see studied the behavior of the material in terms of how far can ID form
before it starts to neck and fracture by using a different type of samples and that France's year ended this uh bulge sample here yes when you are that put a punch here under the the sample you basically stretch into direction so you obviously go your Euros train pass goes in this direction both the major strain and the ministry are equal yes and positive I can change the shape of the sample yes Francis get this sample and get the material to the in such a way that they get playing strength and then look when there's this break so no let's add it the the dimension there sickness strength so it's very simple as I said as we know the sound of principal strains is 0 that's is basically the expressing mathematically that would be volume doesn't check them so that they can restrain is minus major and minor strains OK so that means that at every place here in the grass I can draw a line of constant thickness OK look for instance but this is an interesting line here and there let the yielded be very clear in a moment why that is an interesting life on the line here at 45 degree what what's special about this along this line there Major strain is equal to the miners strike yes OK so which is some the major strain is minus because this is negative right and this is posted the major strength is so is equal to minus the ministry said so the thickness train blasts the major strains plus the minor strain it's 0 right if if these 2 are equal in size and the different side it means that thickness strain is a 0 right so OK witnesses during 0 this alliance is the line of no change in thinking so if you can do a defamation with a strained back along here now your material will not affect yes as a soul but no we remember what are what now there are is the Of after the a whether strain Over the thickness strength right what can I say indeed and the line here yes this is slow if you refuses equation you can show that you have this when are is this very large arch with winning the art is infinite why is that because which strain thickness trained 0 0 yeah that means are is infinite Internet are we don't have that you in the best case you can have a party close to 2 4 steals Our slightly larger so I'm strained pass along with the best you know you'd never find that that's kind of the limit and of course when you deformations deep drawing information that's 1 of the reasons why you like to have are large yes it's because it allows you to do the defamation With strains that have a minimum thickness reduction and of course thickness reduction is what happens on the way to fracture and you want to avoid thickness so what if any and issue look at the use this again this equation here for instance you say OK well you plot you you basically plot constantly it so because the specific the divert the you so if the thickness if you say that this restraint is that is a constant and say we assume that that is Wisconsin than it also means that the sum of the minor and that the major strains is a constant or the my age strain is equal to constant minus the ministry yes and that's what they did this means that these are lines with a negative slope so these lines here Our lines of thickness strain but of negative ticketed here it's 0 yes In this case it 10 per cent or 0 . 1 thickness point to thickness mystery .period 3 stickers for this so when I moved from from here To here I do I get thinning of the material yes the material gets information it's In this diagram also there are areas where the where you will you cannot with no solutions basically that's that's what this area here against them the minor strains there can never be larger then the major strength so that this is no this white region of this plot because the major strain is always larger than life to this this evening we don't have in this area we can't usually come because of the the thickening was pulled out of which we have seen that it can talk about it it does occur Of at the Flach region writing you can have situations where the defamation path is such that that you get into this region where the material gets thicker than is of that's not impossible and see some example animal but that this region is really white region note that cannot be data points to regret right so so
you have this feeling that on this diagram I can plot for certain streamed past years I can plot combinations of strains of majors and my minor strains of wire where to fracture will occur but this is an example here I might have been saying this sample here and no pushover a punch underneath it so it's true that the the material stretched into directions as In positive amounts to I have minor Major strain our equal yes inside so I move I make this circle those my circle grades expand expand bad I start to get a crack and then it breaks right and I can mention I can say OK well that moment yes I make a point here and then I try to build this for the rest of the defamation modes yes and I can determine a range where the deformations this will be safe will not lead to necking and fracture and of course the larger I can make this range yes the better my former ability president but if so how how
would you do this because it looks like My God you know how how can I you know of different strain past the obvious you know in a would showed you here you have to know you can make screen pass or if I do by actual I can make but also very well-defined strains that I well it's in there is what's called the Nakashima approach which you basically do if you you basically take as samples there's no use the same defies this is the same the Gulch test Nos where the punch is basically the adult but when you want to do that by actual task you have the full this is the the full square around blank if you want to do the other the string passes you reduce the West the sample the becomes progressively narrower and narrower and here it's very narrow strips yes and anyway when you do this basically go from stretching to drawing or or you the tension now there just just Inc for to those were not from Europe in this test you don't make a cop yes the edges Of the sample or firmly gripped yes you really deformed the material yes it doesn't flow it doesn't float Towards the center right it's not like in the Cup when you make a performing tests you really want to material to flow and form the cops now in this case when you're doing this FLD asked you firmly keep the edge from moving going anywhere so so what you do is on all the samples you make a little circle grants put little circle grits and I a new measure you know basically measure for instance because this is an example of some measurements so let's just look at by actual strangers would be for instance the sample here the relatively small sample of 30 centimeter by 30 centimeters years she lives like this and I've put a circle great over this the sample and I measure the strain yes restraints all 4 this the divulge now and this is this is what I get this is my actual situation so that the stresses the strains accuse me in 1 direction and the proponent should be about equal continued you can see you can see this squares fall on top of the the other symbols that their descent the thickness strain it's very large and minimum because when you stretch into direction everything has to come from thickness of how much is it well you have about .period for strain for each 1 of them in each direction volume is constant sorrow the thickness strain should be the sum of this winter . 4 plus . 4 -minus know so about .period 8 and that's what you planes trains yes we're in a situation where we're in this situation here we have a positive Major training and is 0 minor stress so positive Major strains positive magistrate negative miners but that was the reason why this changes here it's because I'm measuring different positions on the sample and and this To this point here is where it it starts to break or where it starts to the word starts to fracture dancers in this case my minor strain is 0 0 yeah 0 so all the uh that lit lengthening is translated into thickness straight and this is the situation here where I'm at the other end so in this in this case this specimen here if I measure the strains
there I've find was a positive major strain a negative -minus strength and this that's where you get the smallest thickness strength and that's that's to be expected because we get closer to this life here Of the 0 take mystery but not not in this the figure here this is data this actually measurements here and you can see of these points here at this point here in particular right and this point here and that's where the fracture occurred this is the these are measurements made very close to the track yes so these are the points that I will put on my diagram it seems that this is rents were low carbon steel and for so-called you will face steel data he has sold in town for instance the port this point here corresponds to a measurement 4 major and minor strains where the daily I will have fracture get and so this allows me yes 2 the fine the region deformations and strains where it's safe to deform the material up to that amount of information I can deform the material without problems care and so obviously you want this slide to be as high as possible In its highest possible and the so the minimum in this life we're and since this is missus goal the FLC C 0 .period here this this point here is very much determined by strain hardening yes the strain hardening so the larger our strain hardening Art and value there's if you want it is the higher Our the foreman limit curved the cops I always get them the confuse with the words of this forming limit diagram forming limit curve this curve here is that limit and this .period it's very dependent on the end values of you want this point to be as high as possible because it gives me a lot of stuff but this space as it were in strange space where I can perform without having fracture which reached the the end of the lecture time so will meet on Monday and Tuesday next week and meanwhile Have a good day


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