Mechanical properties of steel 20: grain size strengthening

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Mechanical properties of steel 20: grain size strengthening
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The 20th in a series of lectures given by Professor Bruno de Cooman of the Graduate Institute of Ferrous Technology, POSTECH, South Korea. Deals with the theory and practice of grain size strengthening.
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so this afternoon will start With the strengthening
mechanism of some really very important it is not
In many skills and to the world and screen size it's
a it's a structural strengthening mechanisms on and and analysts it's very young efficient having said that it's complex To understand how it really works mineral models that's 1 thing and 2nd there are limits 2 the use fullness of X and more talk about this
In my introduction is so-so again the strengthening comes from putting obstacles in the way of dislocations very good obstacle is to just and the the blight plane on which the dislocations move and a grain boundary just dues because there is discontinuity In the lattice just does just stepped in its of I guess it's a very strong but it's a very strong obstacle very very strong very difficult for the dislocation to crossed the boundary and what it can happen but the boundaries and need to have a very specific crystals structure of themselves to allow for dislocation to actually crossed the boundary and that often involves dislocation reacted so that we will just think of the grain boundaries is a very strong obstacles it will come back toward the end of this section about the importance of the Miss orientations between boundaries also in terms of how strong the the the strengthening right and not in undergraduate and introductions to science you know that the areas this affects all of us the a grain boundary strengthening is expressed through this whole batch relations where I originally there the and 1 should use these 2 gentlemen have fallen and independently from and patch of founded that there was a relation of empirical relations years between the yield strength of proof stress of but steals and the 1 0 for the square root of the grain size and you can see the data here that this this holds for all our and pure iron and and for all steals at room temperature and it's a nice linear relation very often but so let's have a look at within 1 bounce Justice relations appeared to hold it appears to hold 4 steals of within a very wide range of grain sizes so that we can technically achieve them so if if we plot here the distressed yield stress the low-carbon steels In function of as a function of 1 over the I we see this linear relationship and so on at the end other large Grain limits but this line which seem to end where it's supposed to end close to the the just the the yield strength for a single pressed so that is but the grain is so large grains boundaries don't have an effect and basically the the yield strength you measure it is related to the single crystal properties alternatively on the other side of when we have a very tiny grains of less than 10 nanometers as very small islands the value you know if we if we continue the line would end up close to the theoretical strength of of our which we calculated somewhat earlier in the cost to be about 8 thousand make about so it seems to hold for a wide range of grain sizes will come back to to that in a moment and the kind of grain sizes we deal with it and I 4 steals art in this area he assistance scan gray zone you have steals would very large grain sizes loser electrical steels and very large grain sizes I'm sorry the grain oriented electrical steel sessions they're almost single crystal materials From the point of view of the whole batch of relations and then on the other end you have structural units that are smaller than my problems in decomposition products such as baby Night or more so these are very common and this is very low and wide range of of dimensions he said
1 of the applications where a grain size controlled it is very much used it the high-strength low alloy still and they're very often for some reason presented as precipitation hardened steel actually there are grain refined students the if you compare the contribution of precipitation hardening To the contribution of grain size hardening the grain size effect is much so where does this How do we in this case achieved very high very small grain sizes Excuse me that is by controlling the statically crystallization between 2 defamation passes during hot deformation this is that we presented here for a hot rolling mill patrolling operates at temperatures so that we deformed a material in Austin Texas state and when the material gets rolled In 1 pass it will instantaneously were crystallites instantaneously meaning within With less than a 2nd I'm so that means that we crystallization kynect ecstatic with his or very fast yes and you will actually achieve grain growth before you reach the 2nd of the day and the next formation In the next role staff when you add an element Niobe you to this you get a phenomenon that's called you to drive and this all you drag suppresses the the motion of the richest PlayStation from in the Microsoft and that it doesn't yet it suppresses it doesn't stop at 100 % it suppresses it sets a precedent long enough so that so when you deforming grain in this the 1st stand years a new Pancake Week we said the pancake the Austinite grain that's the way crystallization rate the static for crystallization it is very much slower I needed to present this myopia desk so that but the material is not very crystallized by the time you do next information so you you have what's called accumulation of strange there's or pancake Of the Austin and then when you do the transformation of the transformations from deformed Austinite and the nuclear issue rate is very high and as a consequence to get very fine grain sizes and there is also during the transformation process petition of niobium carbide and that that gives you this additional precipitation hardening but again as I said in these particular steals it is a contribution that is not as important as the contribution from the the grain size reduction so here you have the some data Florida personal for carbon manganese constructional scissors normal consumption feels you have the yield strength as a function of the reciprocal None of the grain size the square root of the grain size and you see that abuse squares you see a straight line and the pretty much Of stops here at around with less than 10 microns and that's basically all you can get you need you cannot refine the grain size much more than 10 micro if you do not do anything special the addition of niobium extends this domain too much lower values can go close to 5 microns yes the union which emaciated to extend them the whole batch a fact that to lower grain size and you can also see that there is a slight increase an additional increase in strength and that slight additional increases are comes from the presence of the press but it's become so strengthening effect back by reducing grain sizes vary ,comma and and and and and the clearest grade steel grade where this is is being dollar are now will be in alloyed steel grades and it's not only she'd material plate material many graves are and they will be added to obtain grain refining through what's called with the process of described a moment ago thermal mechanical process so so that's wonderful we have methods to control the grain size make it smaller we can go down to 5 microns so that's very good so long we're all for grain size reduction right so grain size reduction gives you strength but it doesn't give you former ability so you all when you reduce grain sizes you will always paid in terms of form ability and the best example all of this is shown is shown here to look for protect steals and false Semitic deals here on the right what you see is we plot the strain hardening coefficient as a function of 1 over the square root of the and and what we see is just the reverse and that's all we had for the for the whole batch original batch went like this yes it as a function of 1 already this is goes like this so that's that means that aren't as I reduced the grain size so you go this way I will get more strength but I will get less strain hardening Of course if I get less strain hardening it means I get less innovation uniform illumination that and you can see this on the on right here is this the In period instead of the strain hardening coefficient the elongated for Austin textiles as a function of 1 over the square root of the new reduced the grain size I paid the price In terms of plastic plasticity plastic deformation and that's very general by the way is not a it's not specific to steals any material crystallizes all across line material you reduce the grain size you reduce it you will lose classes right and just a few words about Severe plastic deformation there's been a big effort in the material science community 2 achieved tremendous strengths in materials metals and alloys but I reducing the grain size by taking the whole patch equation to its extreme that's and so on on then the Medea methods the cap you've probably heard about all accumulative role bonding is another 1 of these methods and you can buy plastic deformation reduced grain size tremendously so Francis the accumulative role bonding which you do is you you love you start with your material 18 In a
so-so nicely recruits lights the repress lawyers spheroid grains you hear all this material you you are you heated up a little bit so a new role at times so you know you get crystallized verite you consider pancake as and when you do a reduction of 50 per cent of the them at the plate is now twice as long right you were you clean it the oxides are gone and then you cut it in half yes you put this spot on top of this 1 so you basically cuts the material and stack it now the new heat heat this stack again it looks exactly the same as your starting material new role again when you repeat the process and then you always role material that's a stake as the starting material but you accumulate a huge amount of strain and on huge amounts thank you and you you can obtain a grain
sizes that are a few less than 100 nanometers but what you see is precisely what I said earlier it is and when you do grain size refinement by severe plastic deformation it leads to the collapse of plastic deformation ability materials will have huge friends but no former Belichick and it's definitely the case for single phase for Riddick steals the winter the grain size is less than 1 micron you can see here the yield strength as a function of 1 so that I should see Nice "quotation mark patch relations that's OK and I see that for the tensile strength I also have a whole batch relation but it's flatter the slope of this relations is last yes and so they need at this point when the yield strength and the tensile strength meets means there is not much deformation in between right and indeed that's what you see you see the total that the defamation decreases and the uniform village defamation is reduced to 0 so technically and we we can makes deals with 5 micron grain sizes it is possible the EIT by this method to go do not 1 micron moralists but there's not much point in going to 1 might call last unless the material you make doesn't require any form ability so so it's important differences is that the only remaining amount of defamation here this post uniforms that is after the yield of and and so you can see this is the illumination times 20 so you have here about 10 per cent or less last and best of defamation potential in your material so if you like if you are interested in having the material with some
amount of defamation possibilities in the application of going a very small grain sizes and single phase deals is not an option having said that there are methods to we 2 1 2 2 Have ultrafine materials but union multi-phase materials multiphase materials and wait the little specially designed to regain the power to give you back there the plasticity so let's now and have a closer look at this whole batch equation so the original equations is based on experimental observations rights of this people just rejected and not it look like a straight line so that's and it was originally designed for the yield strength because of steel it it turned out that later wrong 1 day we noticed that there was also a Hall patch equations where is similar to the I hope that equation for Utrecht flow stressed so they need to any amount of strain but was also some related to no 1 over the square root of the the grains now you are so used to this yes From your undergraduate studies and talking about it that and many people repeated all the time yes this inverse square root dependence is widely accepted but in there many alternatives I there yes and owner there are people who don't believe this is actually a correct rest and and as urged by no means conclusively and nicely theoretically established then in and you know you can find in the literature that when you plop flow stressed In general yes you can it's 1 over D to some power but that all you know you can have this and value between one-third of . 3 to 1 so it's not it's maybe not necessarily 1 over the square root of deep yes because if you play around and you try other than you know did you try the of . 3 0 you you trial .period sex what the difference is not that so we have to be careful
about this also important is the if you look at the I hope that equation 4 the flow stressed yesterday so what what does that mean that the whole batch equation for the most which which is basically do it is you knew you have flow stressed for a certain grain size D 1 yes we have a flock of stress-strain press strength and the same material now you have refined the grain and you have another the scientists as the yield .period I'm students now we get to finer grained you get the and the 3 that and so as I said the original you want to US Sprint 3 as the original hold that equation was about these values the flow stress equation says that if you plot for any strain specific strain New Paltz the flow stress for this grain size the flow stressful events grain size monsters visit you will also find hold batch like equation and so this is important because yes you find at home a similar relations between the flow stress and the the grain size for different strains but the slope changes as you can see this steeper at think for the yield at it reduces In the coming of the curve now becomes flatter as might increase distract yes the impact Of the grain refinement is the largest at lower strings and you can see that Sigma zeros to the 2 columns 2 Constance varies but very often called Constance Sigma 0 and the whole batch slope came after yes they're actually not Constance they are string dependent promise and in general and you can varies cedars from here of Sigma 0 will increase with the defamation whereas the considers that the cost would become flatter as the case value decreases so important message here these parameters are not constants when you use them you have to do strength calculations the very careful what you using this is your by you using this equation to calculate the effect of the grain size on the yield strength has or on the
that 2 these are just a few words of caution however but this something more profound to this equation and that is when we were 1st exposed to a whole batch equation we With said you know we talk about the grain stocks the material has a grain size I'm not but when you know if we think very a little but not even deeply about brain size like actually difficult to say what is it that people say is the grain size of a material so and so let's let's just have a look at a center for the experimental difficulties of theoretical difficulties because we don't we would like to assign a grain size to material In a single grain size yeah the 1st of all there's no single grains you take any material those who take any material and you can but when will see some of these methods you can measured the grain size of individual grains you will never find 1 single value you will find a distribution and this distribution maybe I a brawl at all shop but it's always going to be a distribution in France and this is for the the irony of ironies Neal that's 650 with 25 minutes In 625 minutes of distribution of this frequency of certain grain sizes in this system presented in such a way that that it's it's normalized to the mean diameter of 2 grains that you can see there is a distribution endit isn't this distribution the peak of the distribution here is lower that's a 55 calculate if I look at mean value right that's number 1 here you can see that the the peak is not equal to the peak value after this is not the same as I mean value of the grains all right but obviously it there's a problem here just about but when we use the grain size we automatically assume that this distribution can be described by 1 single number whereas it's district of 2nd all grains are three-dimensional things not two-dimensional soul we when we analyze grain sizes of materials of Steele's we make assumptions about the three-dimensional shapes of teens great so when we do thank you know that if you've ever done this if you you do a standard level of graphic technique you will need you can have the distribution and use of our the size of the grains In two-dimensional two-dimensional section so if you want to have but true the feeling for what is the right size at 3 the size of the grain in you you have to make assumptions about the grain trade or you baseball you have to you go into a full 3 D analysis of of you microscope you can soak up
well let's have a look at the number of possibilities that are being used by 1 of the I know most commonly used method to determine grain sizes would call the linear intercept method so and what you do is is you you make an assumption 1st of all you make assumption that the grain size is related to the AP & L is the intercept distance across the grain measured on the micrograph Of the mike Estrada taken at a certain magnification and so we measured the number of intercepts in between a straight line of length L right and wrong on this micrograph and this so the intersection between this this line and the grain boundaries and the average linear intercept light is then given by the the length of that line as defined by the magnification divided by the number of Anderson all this society do it basically I just make line through this micrograph you measure the intersects with the grains when you count the number of grains you have encounter yes so here I have encountered 10 grains and have also encountered a grain partially and on both ends like counties for half In total I have 11 grains and I know that With taking my magnification into account of this length is 1 millimeter so the grain size is 91 migrants if you mean linear intercept for this particular line is 91 micro 10 right and and so that some would be best served steel grain sizes typical constructional steals grain sizes go from as said around 10 microns to 20 migrants that's a pretty coarse grain and I can tell you why that is a pretty cuisine in its 8 hot-rolled material that was annealed and it's a frantic stainless steel so it didn't go through phase transformation so you can be grants regrets that and so on but but now this this is not really a grain size linear intercept linear intercepts of 91 it's not really grain size it's is linear intercept so now I'm going to make 80 Stat yes I'm going to assume that the grains are made they don't look anything like spherical but I'm just going to do this so but if spherical yet and then there is a simple 1 the reason why we do this is because there is a simple story a logical relation between this this length this average length and the grain diameter yes it takes into account the stereo logic that if I make a a random cut through these grains and some cuts may be very may be close to the pole of this great others may be through the equator of that grain there's so this equation takes care of this and it says the relation between the mean intercept length and an equivalent three-dimensional spherical grains is the so grain diameter is 1 . 5 times the mean intercept and so if I measure it 91 91 value 91 Micron for mean intercept length the grain size is larger actually 100 and 37 like that's a method that's very often use however 0 you can ask yourself whether the choosing the circle are in spherical grains is such a good idea no are in particular because you you feel unions will not difficult to understand every spherical grains there's going to be lots of spaces In the end the solid yes that will be empty and I am so so you can use on the grains that are not that are all the same in shape but they're not spherical and 1 of the ways that a we like to do this in material science but is by using a 14 cited Polly he no which goes by this the word that tidy Baker had saying yes I and it shown here have to have the staff policy dropped next to each other day of there will you can fill space with that there would be no end to volume yes I end up so you have the flat interfaces and on top of that the amount of interface we have is a minimal yes because you could have used instead of these all the heater you could have used shields right yes but then the amount of grains surface boundaries would not have been minimal because this is 1 of the reasons why we kind of like this this while he drove yes it fails space and it also minimizes the amount of interface right In this case there is a relation between the 2 you identify and if I would make a cut two-dimensional the random cut through this structure that looks like this has and I would find that it to be the equivalent diameter if I replaced of Polly heater which with the spherical Volume I would find 1 . 6 8 times the but mean intercept like so not the 1 . 5 foot 1 . 6 8 so I would have a grain size it would be slightly larger than the 1 I would get with by applying the standard a linear
into something that could arise but there's nothing that prevents us from doing all the facts yes so why do we measure I'm linear intercepts why don't we measure surfaces instead yes we couldn't made measure surfaces and so and so is the dearer alternative methods where we use surfaces so he is a circular lying to compute a growing area that's another approach to grain size measurements where you say what is the number of grain for area has and will will in the moment will see how we do this in engineering and and that's actually in the standard AST and methods of measuring grain size exactly what we measure we don't measure a great side we measured the number of grains for surface area but we can also from this approach making assumptions about the shape of degrading that Tweedy shape of the grain get in get value for the grain size Kansas at St. for instance here you have a circle with a diameter of about 8 centimeters US 5 thousand mm an area in there is drawn on a micrograph but taken at certain magnification these numbers are at numbers here and and that it has to it's just the example here for this formula I and and and have a microscope truth taken at the magnification of this and so an account a number of grains inside this fear has this is why this has to 3 4 5 6 years and I also count the number of grains which intersect the circle so this grain here which is like a little bit inside the circle I count also but not as 1 grain as a half agree just like it did for the linear into some of that but and I saw that the idea the account number of grains per square the surface squaring is square root of the magnification divide by 5 thousand at this area at times and 1 place and 2 divided by 2 and 1 is to the number of grains inside and to use a number of things we can just so I can compute the average grain area then In drain area there for 1 square millimeter right so I have Grain area In square millimeters 1 over and so have an 8 1 over an 8 but is that the the area of the grain no and then I can compute something that is called the equivalent circle diameter so there I miss and basically as soon that the the area it this this area and determined this is equal to pipe times the equivalent circle diameter divide by 2 2 square With a base sight the surface by Medford it may not be circular but also its circle has and I will determine the equivalent diameter so this equivalent diameter is equal to the square root for times a this divided by Park right now so I assume that these grains are spherical and then I have that is assistant simple stereo logical relation between the intercept area and the grain diameter yes and so if you could assume you combine these 2 equations between I know that we have here we find that the is 1 . 2 to 4 times the equivalent circled there so it's it's it's it's not 1 . 5 is not 1 . 6 its 1 . 2 2 for right so depending what I want to illustrate his depending on which way you've decided To determine whether Diaz in your all patch equations you may get a different slightly different answers note if I might information is right this is the way the UBS the programs calculate grain sizes using the equivalent circle diameter 10 as I said in the standards in engineering grain sizes are computed all the time because it's a for production purposes it's very important to have an idea Of the grain size and steals for and to track the grain size because if you suddenly have the way In grain size is controlled in steals having precipitates In the MicroStrategy use precipitates 10 the grains and prevent grain growth yes during annealing for instance if the precipitation is incorrect yes and you get bring growth locally or an over large areas yes but it basically means that Europe mechanical properties will collapse yes locally or on big areas yes and you may find itself with major troubles because of the soul for certain grades of steals and certain applications the grain sizes are constantly monitored yes by automatic it was systems and automated system and I have been in the steel industry and we use what's called a grain size number we we actually do not use grain diameters we good news grain size number and it's a little bit confusing because
it's it's not a grain size as it is it measure Of the number of grains for surface area yes so number of grains per surface area so if I have a surface area of and have many grains yeah yes or I have a surface area with only for grain the grain size here will be high yes and here the grain size will be small but if I'm talking about the number of grains for surface area GE where will she be large you will be large here yes and you will be small here so it's the opposite of grain size so when people give you a large GE number for or grain size number yes it means that the grain size is small and and you don't give you a small number of it means the grain size is large so it's a little bit confusing the but again it's another approach of measuring the grains and it's a quality that tool it's not it's you don't measure grain size in necessary to check if the whole batch equation applies we just want to make sure that nothing is happening to your grandson and because it impacts history so so we have a scale its originally as STM scale I need some more ideas uh used and it's calculated on basis and which is the number of of grains per square inch on the micrograph taken at magnification 102 slow lets on was very specific it is also a little bit bothersome because it's in square inch that the the number of grains is measure we have in international Standard Organization caught corresponding grain size numbers which called G I and there it's but we use the number of grains per square millimeters on the micrograph of magnification want you so other than that there isn't the simple relation between the AST M uh the ISO which is and this relationship here so it's it's not a big difference actually but there's so AST M so if you if you have measured the aid the dissident number of grains per square binge at the magnification of 100 you can compute the G value GST and screens number according to AST and have just simply using this form so have to you get basically a table AST I'm going from 1 the 10 and beyond you can go beyond here of course the grain area yes is of course that's the small numbers small numbers means large grains you have this is the year of the size here this seems to be long grind grain like this if you have the slightest changes into mm mm and so and and the grain area at 10 is the 100 and the say mm I want to correct this is my crops because this is my prom square and this is my crops of mm of course OK so this is 205 my microns very bothersome from Microsoft and always 1 to correct things like this have you can so large grains load values small grains lodging values the sea of how we play with this was saying we have the average grain diameter in Niobe you it's azules steel and we're told that the yes grain size number is 10 years it was would stick with the grain size if I want to changes into grain size the grain size number is converted to grain density 4 square inch yes we we 1st changed the 10 into 512 grains per square inch as we're seeing at the magnification of hunger the brain did so this for magnification of 100 right so if I correct and bring it back to the real magnification and as 1 by 1 1 1 time magnification no magnification of worth grain density the square inch is the 5 and 12 times 100 times 100 the forest and I by using the relation between inches and mm I can calculate that I have close to 8 thousand grains per square millimeter surface area of the grain can be computed in demeans surface grain diameter can be computed as if I have to surface area of the the graying and I find 7 . 14 it is the Sox but if I assume a spherical grains yes the mean three-dimensional grain size is too I have to multiply this 1 . 4 him because this this value is the two-dimensional two-dimensional measurement of 10 so anything I get into dimensions I will have to correct for what it would be if it was me dimension that's that's why we do this last step here and so we find that 11 micro candidates nicely what it should be clear don't should be left it is the level right that's we
are the wondering how come we have this relations as a whole batch relations and there is a in which we can theoretically the Rifaat I welded to the 2 main much models if you want or types of models so many many people I've known bin very creative as to why generating theories for the the whole batch equation and in general which it sees that you have theories said are based on what we call this location Puyallup models and then we have this look the series that are based on work hardening models the dislocation pile-up model that's the 1 it's you commonly presented to us and works like this when you foreign dislocation pilots at grain boundaries and you know this results in a local stress concentration which makes it possible for plastic deformation to propagate through the grain boundary Sunday pilots will make it possible do you have the grain boundary crossed by the slept with without having actual dislocations crossed the the boundary and and their different mechanisms and of some people say Well the pilots can just burst through the grain boundary somewhere on of all the people say Well the and the pile-ups generate stress raises points where this distress is raised and that will forests this location sources to be activated in adjacent boundary agreed on a grain 6 me and said that well that's the the good thing is that all the series and find the same answer was all proportional to 1 over the square root of the grain size for the yield strength and and the flow stress so the the debate controlling factor here is busy distress required to generate dislocations or to activate Frank sources and so it's it's distressed required to generate dislocation it is generated by the dislocation pilots at the boundaries of the slept with me just illustrate what I said with the drawings here the schematic the Selena center here we have for instance Frank rate soars that generates dislocations In my the dislocation loops in my a variety dress for instance years and this is locations they're all the same this look is all that the same Burgers vector and they're all run on the same glide plane into this grain boundary so this pile up years this this location well has the will push this location number 2 and this location number and back so you will generate 8 Back stressed on your resources From the dislocation and so you have to things is that 1st of all the presence of this dislocation pilot stopped the source from creating more mortgage this dislocations and the other thing is that because you have this pile-up you get a magnifying of the but stress case and so on 2 things can happen according to some people this dislocation pilot can births the brain boundary according to others the increased the magnified which stresses the caused by this pile and well in Jason drain generator had cost the Frank Reed source to generate dislocations for instance by the mechanism of double-cross that's we know but that's lipstick justified minute break here Bond


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