Modern Steel Products (2014) - Twinning & Dislocations: lecture 17

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Modern Steel Products (2014) - Twinning & Dislocations: lecture 17
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17 (2014)
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Professor de Cooman talks about strengthening mechanisms, in particular, mechanical twinning, dislocation interactions and more complex phenomena. This is a part of a course of lectures given at the Graduate Institute of Ferrous Technology, POSTECH, Republic of Korea.
Keywords The Graduate Institute of Ferrous Technology (GIFT)
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Tin can Steel Suspension (vehicle) Air compressor Reel Angle of attack Mechanical watch Cartridge (firearms) Plane (tool) Musical ensemble Scooter (motorcycle) Musical ensemble Ship of the line Van
Steel Typesetting Schubvektorsteuerung Spaceflight Angle of attack Überschallstaustrahltriebwerk Roll forming Mechanical watch Screw Canadair CL-44 Alcohol proof Locher Rutschung Plane (tool) Spare part Forging Material Engine displacement Van Typesetting Schubvektorsteuerung Air compressor Printing press Car seat Machine Texturizing Ammunition Rail transport operations Cartridge (firearms) Work hardening Matrix (printing) Screw Plane (tool) Single-cylinder engine Ship of the line Glider (sailplane)
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Cartridge (firearms) Mechanismus <Maschinendynamik> Rutschung Kümpeln Material Texturizing
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Ammunition Überschallstaustrahltriebwerk Tin can Mechanic Mechanismus <Maschinendynamik> Gentleman Remotely operated underwater vehicle Gas turbine Engine displacement
Widerstandsschweißen Mechanismus <Maschinendynamik> Schubvektorsteuerung Firearm
Typesetting Überschallstaustrahltriebwerk Pattern (sewing) Hot working Cartridge (firearms) Mechanismus <Maschinendynamik> Air compressor Suitcase Car dealership
Unterseeboot Roots-type supercharger Gentleman Mechanismus <Maschinendynamik> Gemstone Plane (tool) Kümpeln
Tin can Mat Cougar Roots-type supercharger Sizing Cartridge (firearms) Stagecoach Mechanismus <Maschinendynamik> Gemstone Negation Engine Model building
Mat European Train Control System Mechanismus <Maschinendynamik> Negation Last Van
Aerial work platform Roots-type supercharger Mechanismus <Maschinendynamik> Gemstone Mail (armour) Lumber
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she so that's go through our own review of some
mechanical properties here steals quickly the EU
is a of material on on the
E-Class site and this is just so we we we will not
all of you won't go through this all this material on to I just
want to highlight a few
essential points bandits and maybe some of you will not take the class I teach in default on mechanical properties of steels and and in that case it may be interesting to have this this and this status as background data so somewhat what's there that but I do want the number of things a slice of what would be to discuss because the important 1 of them is related to the you the fact that as I stressed during the last lecture the Senate and with whatever you you know about for learn about verite off Riddick excuse does not necessarily apply to Austin and 1 of them is the fact that our new you can assume that Austin will In general be softer than forensic skills when it comes to yielding yes but not when it comes strain hardening the strain hard much faster yes but then attic sales so and as a consequence you get out of more along the Asian higher strengths at rupture this also therefore ability is usually perceived as being better because of this work harder and it and again as I said did the key for this behavior is related to the fact that the dislocations In Boston are characterized by playing the gloss was not playing a delight in general doesn't have doesn't necessarily have to be but June to no stacking fault energies but in this particular case for Austin that extremists deals which tend to have low the perspective all energies that's the main reason the low stacking fault energies forces the dislocations to stay on the slip planes did loose-lipped plans they cannot cross slip easily and that gives you the and the need to have higher stresses acqui-hire stresses for the dislocations to cut through all pass these obstacles and so you get string harder in the case of the 1st excuse which have all of them have very high extremely high stack energies you don't problem and dislocations and counter obstacles soldiers happily moved to another slip planes by cross slip and so you won't get this strain hardening effect the intent of difference here between BCC and SEC OK tho and so the question is is it possible to turn a BCC Mattel into behavior of FCC metal please NOTE but you can engineer Mike rastructure yes to improve thanks and and so general that's the reason why people develop a multi-phase Mike rastructure right selling this stable here just the table that can help you as a reference to compare FCC NBC C from the sled that is 1 thing here that right I do want to mentioned and forget about the crystallography here but this is the fact that of of 20 yes is I remember that when we the task Viridian Riddick steals at temperatures are lower and lower the in sub-zero temperature which we see is a very strong pronounced increase in the stress strenghtened flow strengthened yield strength tensile strength that I and this effect is a function of the strain rate that will apply to all if you have a low strain rate part you have something like this if you have very high strain rate thousands per 2nd it's very high string of you can't do this with a conventional tensile testing machine no sooner did increases but the effects it remains stepped there is a strong temperature difference and I told you that that the all of the the cleavage this is flow stress could increase and go beyond the cleavage stressed and material become brighter days are now very good closely associated with this is 20 but at low temperatures the frantic steals will display 20 so and and that is a different defamation laws and its belief that the cleavage is very often preceded by 20 1 2 twins and tract which each other will create a very microscopic cracks which will lead to the cleavage of your steel but the 2 winning again is characteristic of low temperatures deformation or very high strain rates the formation infrared so I usually if you do normal room temperature stress strain measurements are not you never gonna see however if you take a a Sharpie tested samples the low temperature low temperatures you will see that in these low temperatures samples you will see twins in bcc you so you the observation of twins usually tells you but that the material has been performed at low temperatures Orangerie highs during it's OK even if you don't know anything about this material has and you have to do a failure analysis and you observe twins in these in this microscope tour of the young you know that you know it's either been tested or subjected to high strain rates or deformations at very low temperatures the twinning is not rare In so it's relatively rare to see 2 wins in bcc offer Riddick steel but it's not rare to see twinning Inc In SEC and it's closely related to the fact that the but the partial dislocations that that forms but this associated dislocation are actually partials that that are responsible for the 20 of which again with that's more detailed stuff I don't want to go into detail this is just
an example of the use of these are twins the endemic violence it or in this actually not demands of the stainless steel and you can see that these 2 twins are deformed used is very straight bonds here is another deformation of user we crystallization what's theirs and so if you get a sample you don't know what it is that which is CDs grains with all these parallel lines you know it cannot be a aphoristic extinct for antics seals also that they have 2 wins and the twins Aree special there always extremely thin then yes they're never read crystallization twins there never request was there always but there always defamation this an example here of a twin of twins many twins in the for attic steel that's been tested at low temperature during impact load them and some people will call them you know I'm honor-bound bands after the personal 1st observed good
so I important to know that uh dislocations that we introduced in the microscopic are surrounded by 8 by deformation plastic deformation of the lattice and also by stresses yes so at the end of the a profile of the stresses that are relatively simple if I have a pure edge dislocation here suspense dislocations in the variety of the you have an area where we have such called compression area and tension area delectation area in the case of the scooters which can be very cut much more complex where the compression and the power of tension areas are our change changes so this isn't compression this and the litigation compression litigation and so on so that means that because of this elastic energy that strain energy in the lattice dislocations carry energy increase the energy of the crystal end but that also means that the dislocations will interact with each other they were Dayton the tracked each analysis of the when
dislocations get close to each other these military Shenon compression areas can interact which each other in this location pushing each other apart or attract each other France's even too
simple the edge dislocations here france In this geometry the if you if you plotted the ratio of X over why you're there will be regions here where you'll have attraction so this region
here where this is 45 degrees so if the dislocation is on this side of this line you will tend to have attract attractive interaction there on the on the other side instance in this location is here yes they will you will have repulsion and so this interaction is important for instance because it gives rise to the recovery structures when you we crystallize a material before you re crystallizes the dislocations will rearrange themselves in low-energy configurations which is basically the dislocations under the influence of this the role stress and strain field will rearrange themselves to low-energy configurations so that's when you leave them to their own let let them do what they want you and then you don't apply any of this stress external stress however when you apply stresses this occasional move around us and they will interact and this interaction can be very different depending on the situation Yukon say there is 1 thing interaction has happened but in general so what we do what we say is that this dislocations can I will act as obstacles to other dislocations and this it it doesn't necessarily mean that the dislocations well 1 like hang onto each other sometimes it's something different have so says this is an important part of interactions in BCC irony that's that's what we call the formation of Cecile jocks all right so the deities the following week instead when dislocation cut each other they can pass each other but when they passed yes they change the structure of the dislocation and they can make a little piece of the dislocation prevented from moving yes and so that's that's what is a called Cecile John little piece of dislocation but cannot move anymore so it's it's basically becoming a pending .period it's become a pending court and that the actual obstacles it's not beyond the dislocation it's the fact that this although this locations made a job on the distinctive soak up so this is the idea so I have to say you have here a dislocation here is an edge dislocations and here we have another dislocation on another blind playing tennis and uh this dislocation the moves for instance this way and then it it will cut this dislocation so in this particular case then when concept I for a job here you see because the winner dislocation passes there is a little shares so this part of the crystal is shared so there is new form a job and this is very tiny the strongest of the magnitude of it is OK but this isn't and another situation here this is dislocation and now it is this location on this plane that moves yes so the seats in the other direction is in this direction and it cuts the same dislocation but in this case both dislocations and up with the change yes and deserves Scrooge or what we call the screw jogs and user edged job and the edgy arcs have as if we fight magnified this they look this this burgers factor here disparate prospective isn't it it's it's an edge job type the it's a scenario can this interaction this jobs for that information so when you have to screw dislocations that interact you will form to edge job like this this year and the burger factor yes he said that the bird this factor you can see is Burgers vector of this plane but not of this play now the problem is that this little job lies in this plane so it cannot go wide anymore so this John here In suspension of acts as a very strong pending .period coiled Cecile job no 1 of the things you will notice is in order to have this type of job formation I have to have dislocations on different Goliath play that's why this interaction is called Forest dislocation interaction it's as if a dislocation moves through a forest of dislocation on all the light .period and forests this location interaction is the the reason 1 of the main reason for strain hardening is 1 of the main strain hardening 10 when Lancelot dislocations moved yes I get I can Strange but because of this terrain yes is in very specific directions on very specific claims if I look at a single crystal and I do have a lot of dislocations passing on glider planes years there will be the displacement sideways displacement that in general for instance if you test a single crystal the force that you apply it will always be determinants by the machine yes the machine doesn't like mission states like that and if this crystal is embedded in the matrix same thing if even W crystal moves this way the surroundings prevent this from happening again so but so this displacement does not occur so when the way the crystal Will makeup for this is by rotations and it is this rotation of course not and this rotation is made possible by others slip systems yes but this rotation yes I the results in texture formation the picture for so I'm not going to go into this house so this part of the the slides just have a look at it's issue background information on texture yes but what is important for you to know is that texture is can be due to defamation yet but it also due to the transformation so because when you have you transform Austinite to far-right theirs if you're Austinite is structured in a certain way that will carry it through To the Charite they so there's lots of information about
Rick crystallization of suicide and and and how treacherous measures to just have a look at
it and certainly if you're not familiar with DEC shares
and both figures that there are
very few very simple pictograms that allow you to do I understand what in
principle ODS are such that and again
that's not the point of the
year the course here this so that the the reason why there is the texture when you do transformation that's because there are orientation relationships between the far-right and also and that the 1 that's the most important and chicken use in practice In most cases is called it the so-called S orientation relationships between far-right and Boston area so in that sense that the close-packed planes will be parallel and that the close-packed directions will be so that means that if you have single verite already assured of a single Austinite grain single Austinite orientation then you have 25 24 possible equivalent far-right orientations yes so in general if this turns into the far-right units and so this would be a variant 1 variant to variant 3 or 4 variant so in general transformation decrease texture yes because you have when you go through the transformation the Crystal has 24 choices yes so that's 1 of the reasons why when you do Re crystallization and link yes you never go into transformation region this because you don't want to this effect of randomization friends of friends you have offered Dick Steele I used cold-rolled it heavily to get the right 1 1 1 texture yes you do Re crystallization annealing but not you don't transform the steel you want we crystallization and grain growth so you get the 1 1 1 oriented great but you don't transform the MicroStrategy gamma even though it might be crystallize faster than all the views the softer material that you cannot do this because you will lose your texture so in general transformations lead to randomization of the orientation and so agenda agendas of some of the interesting data here that
I did not there will not go into well and they were did
so on Thursday's that
the texture but you don't have to we believe that there will be there won't be any questions on the on the texture of the case OK so don't
don't go and learn that segment of this material right but so the it's optional the texture crystallographic texture but there's quite a lot of slides I don't want you to go and study them it's just for your information and in particular for the people who may not take 6 6 9 you know they have something up their forever they needed they can look up but again and also
with this part of the the material we're just going to focus on the essential beds and a lot of additional information that you may want to look up and you know if you're interested in the theories etc. that will be discussed in in fall In the end of course I teach but again we just need to know the essential that's and I'm so this about strengthening strengthening and of the common ways we strengthen steel grades yes I don't know start strengthening it's basically dislocation accumulation that's basically what you do what you do have and when there the strength mechanisms that work are the ones that are you you make a lot of dislocations you make sure they get stuck at obstacles yes and and you prevent us from being annihilated now this may sound like a very strange concept what happened you annihilate dislocation but while 1 of the ways you annihilate dislocations is good through their interaction with other dislocation within a simple example for instance if I have say this is a dislocation and this is the same dislocation loop the band and they have the same Burgos vector last December respected here here the basis in this look at their on the same glide plane was the next to each other and I'm applying stressed that and so they become larger and at 1 time they will meet each other yes they meet each other here so what happens here what I would like to have in terms of strengthening its while that you know I get dozens more dislocations as possible however in this case but if I were to look at the at this location core here I would see that 1 of the dislocation it's a dislocation looks like this in the core and the other 1 is a dislocation that looks like this OK I'm not going to prove this going say so you have an extra half playing here next have played here and they moved toward the sun when they meet In the dislocations got this just but until the end of a perfect crystals that and the this location is up to this piece of this look is suddenly put it's got so it's a it's dislocation annihilation by Joseph here I had 4 times and here 4 times out in terms of and when they when they means you know I lose this this part and did so on so will allow will just going to how this is how this is done the strengthening them but and
lets us see I think in terms of steals what are typical mechanisms that we use 2 To strengthen Steel's shares and give some examples of of steel examples because is this an important table because so it it shows you how how these mechanisms are actually use that 1 of the things you can do this solitude actor this basically alloy Yang yes and the solutes evidence can be immobile they can work as a mobile obstacles and those are usually for 4 steals are substitution all elements but they can also be mobile sposób you and undeserved interstitial elements but we can see the strength crystals by dislocations 1 of the important mechanism was just job formation that I explained so the mechanism is just other dislocations interacting With just look at grain boundaries act as very effective obstacles to disappear because there's been interrupts the the blight play at the boundaries so and hear the important thing we will work with his the grain size With precipitation hardening I've basically introduced particles in the matrix very important particles in the matrix particles at grain boundaries don't do anything more .period but grain boundary already did this so very important if you doing of precipitation hardening they should be aimed they what us know these particles there can be soft particles that means they can be cut biden dislocations or they can be hard particles the work is very strong obstacles to dislocation blind Italy's cannot pass we can Hardin by the use of multiphase MicroStrategy we have add additional phases and we can have a structure strengthening I don't and that's where the basically we use transformation or to winning mechanical swimming mechanical transformation mechanically induced transformation to get strengthening the Ugandan Martin citic transfer can occur in a single phase steal it can occur in multiphase steals what we can do defamation 20 also in single phase multi-phase deal for some examples from the 1st whistle you'd times we can add phosphorus silicon or manganese to steal mobile obstacles are used when we make big hardening states make hardening steel for automotive applications this locations are used as strengthening mechanisms strain hardening all all the steals U.S. grain boundaries of course occurring false steals because there polycrystalline aggregates and also In the Micro allergies because in the Micro Alicea silly we can engineer a grain size so that it's it's it's much smaller than usual precipitation hardening soft particles 4 steals well Copper Copper steals well contain soft Copper precipitates that compact give you prospectus and strengthening or you can have a very hard microbiologist deals on Ma aging steals yes which contained Carbide nitrites or some intermetallics yes To hardened steel multi-phase Mike rastructure are very common nowadays in certain applications you have the standard fare perlite steals which strengthened basically by the presence of semen tight In the perlite due face steels are strengthened by the presence of Martin site fades into my prescription and you have duplex structure and 1 of the most famous ones duplex stainless steels where you have a mixed verite plus Austinite might restrict In the unstable which we call unstable Austin antics stainless steel that means that when you deformed and part of the MicroStrategy
turns into Martin's side we have strain induced Martin site formation In trips steel we also get strain induced transformation but only in the retained Austinite face and to whip steals also structure strengthening I have strained induced 20 I will give you the the strengthening mechanism for so what's the picture from which to watch the picture it is 1 of the year the interaction of dislocation with .period like obstacles In the gelatinous what a deep pants all the interaction of strong interaction and so the and depending on the situation you can have unknown local or what we call the diffuse interaction between the obstacles he did his job security obstacles and the dislocations in this case did the dislocation kinds of know wiggled its way between the obstacles yes some obstacles attract some obstacle repelled the dislocation yes and so on but the wavelength here of this the dislocation can be a very much larger then the the distance between the obstacles and the obstacle can be weak like in this case and I have a long way like or the obstacles can be very strongly interaction be strong stand then the focus much more curvy it is it's got much more stronger influence from each obstacle so this is for diffuse situation dislocation kind of wiggles its way between the obstacles in the case of the .period like the interaction I have a very strong attractive interaction between the point defect the solutes the obstacle what have you and the dislocation and is and this is a very localized interaction you can see the dislocation is really at the obstacles and this can be a week obstacle that means that the dislocation bedrooms as an increased stress the radius year increases and then when I reach a maximum Florida on the dislocation it just jumps to the next obstacles basically and this can be a weakness is a case of the week obstacle with this radius doesn't become a stays very large or this ridges can be very small but smaller units of the order of half the the spacing here will and then before it will be released and then you also have situations the obstacle move To the dislocation so there we have mobile obstacles and the end dislocations are immobilized 1 does this happen well for instance during aging you helped you can have carbon atoms move into dislocations in the pen has but if you do that you take a frantic steel that contains some carbon solution and you do attested height at 100 degrees then the carbon is mobile enough to catch up with the dislocations it's mobile enough because when dislocations move they move this stop at obstacles which are always in the lattice In the name of an Indian break free of the sort but during the time when their stocks yes sir yes we call that waiting time they wait the force has to be increased before they get released yesterday but during that waiting times carbon atoms can hop To the dislocation and pendant the fact that phenomenon is this it's also aging but we call a dynamic ages 5 and dynamic strain aging because it's related to dislocation so what's the you obstacles do not necessarily have to be immobile that you can have more mobile obstacles and stationary dislocation and that's that's
again so I the strengthening of mechanisms at various essential because the yield strength of pure irony 30 to 40 megabytes so it's it's not you know and of debts
not enough so we have the let's look at some fundamentals here I'm not going go into too much detail but basically and if you have a localized obstacle you can use this basically that's a potential around this obstacle and so the forest only the dislocation is the derivative of this potential so goes up and down hills so that means that as the dislocation approaches .period the fact it's attracted to it so here it's that attracted to it and then once a it's at the obstacle if I want to move it further then I have to going the other way I have to pull it away by so it's stuck at the obstacles so in other words you have this forced displacement currency yes that characterizes this obstacle so if I have a very strong interaction it's like this the Red curve means I will have a much stronger in obstacle to overcome because the depending force has is much higher so the optical attracts and then when you want to move it we would beyond the obstacle you have to give VAT increase mixes with the applied force them that you can that there is a very simple relations which I will not derive here today is that between the forests and underlying tension of the dislocation of the forest is related to the wine tension and this is the sign of this article here and
so skipped this so the way this this
is what I want to show you the way that you have to think about it is this this obstacle here exerts a retaining force staff here and on the this location like .period force here has and and as I applied stress on my dislocation the forests is stressed times Burgers vector you will need to get out I get along forests From the the this location To be yes from the dislocation of counteracts this the force of the obstacles which is due to the effect of these 2 why intention vector so if I make some of the East on in this direction at every time but every time I have equilibrium between this factor and this factor here that's basically what this equation said but
let's now there and have a look at typical in interactions and difficult the interactions that our .period life are wits solid solutions have solid solutions and so I can have a substitution of solid solution yes it gives me strengthening for instance silicon and phosphorus manganese tightening enabled him etc I yeah so that means that when you add these elements they will replace Byron in the Microsoft rupture in the lattice and then I have interstitial the following elements such as carbon and nitrogen and they will sit at opted he drove positions so what happens is that as you when you add this element it does to the goal these elements locally I had the modulus change this the latter's becomes softer order lattice becomes stronger yes that's 1 thing the other thing that happens is the lattice parameter yes doesn't equal to the lattice parameter of pure yes In the case of silicon and phosphorus it decreases In the case of the other elements it increases but With the amounts the different from pattern to act so it's in these 2 facts which we call a modulus and the whole lattice distortion has ordered to remain the reasons why solutes act as obstacles for dislocation motion look at that it's important for you to realize that did this the lattice distortion then is also specific for instance With these
elements silicon phosphorus manganese fighting units address I get a dealer tational distortion of the left so the lattice is you can basically think of them of these items as spherical impurities and they will either expand the lattice locally and 4 Frankart locally interstitial atoms yes or very small at yes the way they distort the lattice by sitting in interest optic he drove into social locations and when they do this they give them a symmetric distortion of the leftist yes so the what is his work ,comma is extended in 1 direction and compressed in the other direction and so I considered having a spherical the debilitation I get this elliptical distortion of the latter's that's why we we we we talk about In the last indictable yes and this firm actually this particular type of distortion makes it so that these interstitial interact very strongly with this location In fact much more strongly the most the substitution of elements and that is the reason why carbon and nitrogen have such a huge solid solutions strengthening effect on on the on the lattice not because they like to go to location it's because of this the Stickler distortion lattice distortion that they give now it if you if if if the atom scientists say we have molybdenum in the C C R has that atom is oversized ears it creates a debilitation pure delectation of field that's so the atom is in compression this but and it compresses the lattice around it and so I have to stress the hydrostatic stress has to be the molybdenum abdomens isn't fully in compression inside the items because do stresses constant and outside yes I also have a hydrostatic stress but its it doesn't carry on forever it has it decreases in radially but as it is has won all 4 are to get the best the the the that will therefore have a limited the range of influence at the time but because we have a regularly decreasing compressive stress around an actor whose you have to imagine friends and this is a large molybdenum atoms which is oversize and give you this but it's the
SSI when so went an edge dislocation is put in the lattice you have stresses and around it yes but a very different years and the solutes atoms will interact With this and this dislocation Vidor for the the lattice distortion and violent the the change in the modulus that you have here locally now
and you can show that From a theoretical point of view yes Indian when I have answer the atoms In solution the strengthening effect from these atoms usually go is is usually proportional to the square root of the their concentration this square root of the total concentration no it is when
you go into actual data well 1st of all this square root relations this is 1 of the theories are all that their results show you want to I think in a moment but L what you find is that the at times as when you alloy don't they don't have a very simple behavior as following sums of for instance it was 1 of the things that you have is the size of these atoms you the interstitial deliveries the small yes but as I said they have a very pronounced hardening effect because of the way to distort the latter's most of the allying elements that we use for solid solution hardening are within the band of plus or minus 15 15 per cent away from the lattice parameter of Byron this year so from a point 21 to .period 29 nanometers and the elements niobium and molybdenum are not generally the largest patents In this and the elements phosphorus and silicon are the on the Yoder scale sold most of these elements here give me a lot this expansion it in the silicon and the phosphorus given at local lattice contraction the case and in general you you know and that the misfits that you get this is larger look the larger the atom is that as you expect and you can see here that it is a phosphorus it's negative silicon it's negative information these it's it's positive 10 but
so so you you can determine a misfit parameter on the basis of the size of the actors or more accurately on the basis of the measurements of lattice parameters you can add enough silicon or not molybdenum to steal and measured the loudest from you see in 1 case last forever will be reduced and the other 1 it'll increase that allows you to determine dismissed parameter yes and you see it's it's a very small parameter rioted you you have to think of this Delta as as a strange as to what we were talking about variant small amounts of strain in the lattice parameters now Over the weekend many of them is also show that if if you know this parameter this isn't known the number of simplification hold and surprisingly it's it's very often the case that you can apply them but if you know this misfit parameter the do the strength of the interaction will be proportional this dismissed and it's multiplied by cheese Delta is not very large tend to the minors for which she is very hot very hot yet so together this product comes out to be quite impressive so so what we have here is a again you know 1 really glossed over the theory here is that the solid solution hardening it is proportional to this misspent has and is proportional to the square root of the density or concentration all of my that's all you want is basically what series that give him the so and so did this Delta just is this is basically if you if you want to correct theoretical the correct way of defining and is 1 over a D C 5 were a is the lattice parameter of variety for instance and DCI is the concentrate CI is the concentration of an following this and so we have a size effect and as I said solutes all also have a modulus effects so you you can measure the modulus and the change of the modulus With the concentration of your yellowing elements in these 2 parameters are the most important ones but in general you this size effect will be the most on so that this formula here is actually quite a handy way do a back-of-the-envelope calculation of what at the time hardening will be solid solution warning will be for a certain element of instead of opened in here by the way it is an alternative formula 4 the strengthening effect from solid you and you can see I don't have 1 half and I'd and here have also not 1 but 4 thirds and that's a little bit of a problem With the theory of solid solution strengthening in 4 steals his the theory is based are not advanced enough at this stage for us to really be able to use them in practice very easily and the different theories France and we don't know which 1 applies to which element such so what we can say is well there's good concentration effect and there is a effect due to the lack distortion Maude lattice distortion hired a strengthening the higher my concentration at the higher the strength now so I if you assuming if you're an engineer you do need to know you know what is the impact of the strengthening so what people do in general yes it is you know you just say Well you know if I don't have a good theory all justice I I have a linear relation and I'll just use experimental data to make the relation between the concentration and salute solutions solid solutions strengthening for specific element so so you just say stringing from solid solution in a tensile test is equal to the
concentration of a certain element times the solid solution in fact and you do you just some for old the elements of a new stew composition so for instance on if that 1st element is phosphorus than salute solution is 680 mega Pascal's horror last person and facilitate an 83 make Pascal for masters and for manganese 32 major Pascal so that's at 1st on view seems to be a very simple way and convenient way and quick way to do things there is a problem however instead many people do the experiments and they don't come out the same data has so far there is a everybody agrees that this is a very high strengthening and that this is number 2 and this is number 3 but the variations can be very important and again you have to that the problem is that a lot of these solid solutions strengthening measurements are not done in a scientific way so you the people don't make nice single crystals and don't make pure very pure binary alloys has led issues states and then of course you have I know you don't be some carbon don't be so oxygen all kinds of elements that may influence the outcome of this experiment gets so and so it's a challenge also 2 of how you can do this in practice but just for your information this was the these are very good values yes of course on the solution strength for substitution and this is a huge value was very very large value so obviously that's 1 of the reasons why and you will see USA phosphorus that's because it's got a very large strengthening effect at low concentrations that's also why often silicon and manganese are added to for instance constructional steals because they give you a lot of strengthening for a lower amount of Halloween edition however was can you add 1 per cent of manganese for phosphorus to steal nowhere to be very bad idea because it may get become very strong but other properties assessed toughness etc. will just go down the drain so you cannot do this at best maybe all of them like 700 500 ppm 800 ppm that's about the most you can add up to be on the safe side for um terms of toughness Samart silicon silicon about it's much less than the phosphorus but you know it's still close to 100 megabytes Culpepper for with percentages that so but that is here again if you add up the mat 1 must Percent of silica you will see a very bad impact of toughness and so the most you can add for strengthening purposes about half a per cent half a person is safe and and and not have any negative impact on toughness manganese it is the ideal because if you added you get strengthening and it doesn't have any negative effect on the moon in negative effect on on toughness it it doesn't have any the negative effect on the actually it improves the toughness the important thing again that I want to say this is for fairer yes for Austin may take the alloys and steal it's the situation is even worse very little data available and and and the strengthening effects do not hold for Austin it's OK conference for all Semitic steals this is close to 0 or even negative yes so this is not the strength the in Boston and 1 In scientific silicon however is a very strong strengthened in Austin to also In general the solutes solution strengthening Of the following elements In Austinite is much lower than in fair there's have these large effects regulatory
scheme of this is important figure here because it's less you you can see what factors off in practice has 4 the differences you have a lower concentration and here yield strength and then you have a mail selling themselves tracked and you can see that Silicon manganese nickel-titanium are in the same range as are are strong strengthen theirs the reason we're taking him isn't also nice strengthen we don't use it because it's kind of expensive following element and the cost considerations are always very important for us for erratic steals Of course if you have data like this yes you could say Wall it's very simple to check series because if you have a theory that tells you the strengthening From solid solution is proportional to the square root of he has then if you do the natural log plot then data this data overseas this data should have a slow love perhaps right and and aerials see directly on so this is this is actually Don here this is not what this is slow for 3rd sold half is somewhere in between as you can see that basically you have all kinds of slopes yes and and it's actually very difficult to the side with theories applied because within the ranges where we can do the alloy Ewing theirs that there's very little difference between a slope of two-thirds 3 has won have and that's a big deal with the challenges that the data that we need to check theories for steel when it comes to steals it is not there yet OK so that's that's 1 of the the the challenges this is some
data here but this is an example here will boost inferences yield strength of In Martin said take this structure the seat as a function of the nickel content if you use the data that's directly quenched data there is a lot of the substructure effect from the Martin if you re crystallized a model IGC you see a nice linear lying as that Nicole to the one-half this is solid solution strengthening of the BCC irony like carbon In this particular case you get a nice square root of carbon dependency same here for In the FCC this for FCC alloy it this is a data for nitrogen and this is for the BCC yes 4 the carbon so you can see that you moralists have a linear relations has 4 the nitrogen and and ,comma at and and this is
an example here of the solid solution strengthening of differences of phosphorus I have values that give you 12 thousand 50 make Pascal and and the lowest is around 500 years and you see the same thing he would silicon very high values extremely high values and and much lower values etc. But that's very very common to see this summer you vary widely so what the on again I'll discuss this in more detail in the costs in the fall but that the best thing to do is to take what to leave out there the values that are not and no way to which the research was not solid enough us in terms of information on the on the steel knowledge about steel composition and then take on the median value the median value Of not to mean value but the median value and that gives us a pretty good pretty good approach there are people today who were trying to work things out from 1st principles No using our molecular-dynamics things like this but did you and there are lots of physics is involved very fundamental physics that's not solved yet so we cannot at this stage we on on this kind of research to begin to build to design alloys and but you know and I'm pretty confident one-dayer it'll be possible I rights but this is a tensile strength increase the other people with solid solution hardening just to finish here to wrap up on for the interstitials is very large yes so you you have values that go into the 5 thousand years nitrogen here 5 thousand 500 boron very very hot and I so the obvious thing to do is to alloy with these elements the trouble is what's the problem with carbon in variety while you cannot dissolve it in it has no at room temperature basically has no solubility so the 1st thing it tries to do is to go to dislocations all a ghost of grain boundaries for its forms Carbide's and so yes it's a fabulous effect but you can't really use it very often somewhat lesser problems with the use of nitrogen has but it's very difficult to Aloia nitrogen so that's a challenge and death and the number of issues with boron that I am not going to go into the main 1 being related to the the abilities but the again I want to stress the fact that the a solid solution mining from indecision is very very proud of it will continue this on on Thursday thank you for your attention


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