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Mechanical properties of steel 21: grain size strengthening

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it it so let's get going so when you basically have to imagine here you have a little frantic steel for instance are in the middle of the grain we have a piece of screw dislocation that has double-cross and that's it generating this location of 1 after the other they expand and then there reach the by the grain boundaries so you've got a set of dislocations which repel each other and and so they exert a back stress on the dislocations that are generated by the French we'd sold and these are generated by the externally applied for us obviously the this this back stress the size of these back his back stress will be determining will be determined Excuse me by the number of dislocations in the pilot was so as is as it nears a the different resources will stop producing dislocations when this back stress is large enough To prevent further emissions of this location from this source and the number of dislocations in the pile-up but is determined that the by the back stress so we'll end we will
use what we know of dislocation Teri to try to get some quantitative values here so we assume we have then
again so we have been applied
stress which recalled how acting on the slip planes where at work where you have to the source and where you have the pilot case that the pile-up yeah works yeah works as magnifying the magnifier also this stress you apply and you I'm not proving that spread just take my word for it that's it's 1 of the things I get from my dislocation theory is that the this is distressed that is this is the grain boundary and this is distressed and I'm wondering what is the stress on this 1st dislocation if it's if you have endit this location locations the same dislocations piled up again well this location theory that tells me that this is the effect of this pile is to magnify indeed stress and shear stress acting on this dislocation the talk normally it would be applied for stems from respect now it's end-times new platforms and services sector and the length of the dislocation and which is part of the Gadabout Lane and dropped the Burgers vector and so we say the incident was the stress on leading dislocation of this pile is and times the applies shoes but so now the question right so I can I can no what this stress cheers trust units now this final and right so again here I use as a result from this location theory about these these pilots so and it is equal to the number of Constance pie GB & K 1 constants in this if 2 brothers when is the applied applied the shear stress and l the length of my I look at itself the have and so smitten that's the situation what would we calculated as did the moment aware you have and and dislocations forming a pile-up of length L over distances and the distance at the time that they will prevents the sources from creating more dislocations and and that equilibrium state yes so but say I have applied last fall I don't the plight has worsened and the small right because so if applied on big forests yes I I will Bush a lot of the dislocations against the barrier at the the back stress balances the applied shear stress this my applied choose a very small the number of dislocations here will be small too the because you won't need to have this much back stress to stop the source from generating this and look at so but so so To some the number of dislocations per unit length of the the pile up and over Elvis is a function of the applied force should right and if you if look at it as is as if this equivalent to stating that if you have a pilot and dislocations it you can pretty much think of it as a single this location with a very large Burgers vector so because this is equivalent to the dislocation with a burger sector being that affect the time spent the cannot make sense in the dislocation of very close to each other you have all these extra have planes that and so it kind of magnifies the the Burgers vector parts and is the length L is the length of the slip planes with these wild of dislocations the Is the applied stress the 1 is constantly here in this parameter itself and then you know coming from the smoking seriously want is 1 4 screw dislocations and is 1 minus the all ratio for edge dislocations it's very simple parameter so this stress I'm at the grain boundary on this on this people in this location it is now so this was my equation here n times the applied stress so I just take this this year and multiplied with it by simply these 2 equations together give me not surprisingly Taiwan is the party won by GB L times tell me square In the end no
obviously this solves everything and this assumption is made but multiple in multiple theories are you make this step and you say the length of the pile-up is isn't related to the grain Greenbaum the grain diameter if I have small grains I will necessarily have smaller smaller grain sizes it is if if I smoke rings with me I will have a smaller pilots it's so it's kind of reasonable the so and then very often in the series in the theory of peoples as well as public close to 2 half a grain size so Ellis half of grain size all their bounce you don't have to assume it's half I think in the end and then you find Taiwan is equal to those OK that's the same equation yourself on the last slice cake but now would you say if this the shares stressed that that's pushing this dislocation but into the boundary here so I end times tau applied against and so which which is equal to the squared times fell president and all the other parameters which are constant stance on if that shear stress is high enough 1 set of theory 1 theories as if that's the case if you reach if you if this reaches a critical value then you will have breaks this this slip will somehow generate dislocation of the grain boundary and you have the breakthrough burst through the the grain boundaries of the pilot dislocations can burst through the grain boundary when you reach a critical stress analysis so but if Taiwan which is in turn a is larger of equal there is critical straight shear stress then you will have you and your movement of the the slip through the propagation of the slip through your so that a new resource rearranged as you are you in 1st get to tell in square and then you tell and you find all surprisingly won all 4 square root of the grain size that's a reasonable think that's unreasonable about this model is of course yet we know dislocations will very rarely crossed boundaries yes so wiped out other theories although another theory says and that's to control theory you may have heard of yes and say well this large share stress you have here this is actually not used burst through the grain boundary but to activate but sorry that's into the adjacent grain yes so alternatively that the piled up dislocations caused Frank Reed dislocation source to generate circuit as it is and the way the original series build up is that they the look at the this pile-up as the sheer crack and aid determined on the basis of the geometry here the maximum shear stressed at a distance are from this crack as you can show that this is shares stress is equal to the applied stress times the square root of the grain size divided by 4 times are lobbying the distance between the grain boundary and the Frank Reed source in the grain and so now again it this shear stress is larger than a critical stressed to activate the Frank reach stores by then I have the the propagation of slaves and so simply by rearranging this equation you can see that the applied stress His again proportional to 1 over the square root of tea in this case or so this is sound
but in general how people trying to make sense of the word 1 over square root deep relation that we observed in the whole patch equation 4 steals but it's been when you're going to do some details it turns out that these models will miss a lot of the also features all of the process In and we'll talk about 2 features of 1st feature is the fact that grain boundaries have properties to yes In fact grain boundaries can emit dislocations them set can be sources of location it's 1 thing and 2nd the grain boundaries are places where you have what we call the strain incompatibilities the grains to form and 2 adjacent grains to form and where they meet there is what we call strain incompatibility and that gives rise to we talk about this in a moment geometrically necessary dislocations and rabies In all the theories about the source of strengthening grain size strength so so what's the problem with 1 of the problems with the dislocation pilot models but does not explain why for instance interstitial carbon and nitrogen are affecting the whole package slope differently so carbon and nitrogen have an effect on the distress needed to unlock dislocations of this from their atmospheres but carbon has a very noticeable influence on the hall patch parameter I OK so what would people basically that's that's what you see here for instance if you have you have the whole batch relation for and I are still doesn't contain any yeah carbon you get a very slow the value the White House you add some carbon yes in solutions to mold low amounts of carbon of course and you see that the more you I'd carbon the higher take becomes the way you can understand OK if you want like a physical explanation for K Kate tells you how difficult is it for defamation to pass through the boundary the to the higher octane value the higher the and the more difficult it is to propagate slipped across the boundary so why would carbon-have that influence yes there's no mechanisms indeed in these pile-up theories that can account for this you see nitrogen very low effects Of the nitrogen on the case value in the hope that equation the but In Boston epic deals you see the same also for nitrogen you see that as we add nitrogen 2 are Austin Semitic steals dictate value increases dramatically yes so it is he tells you that suddenly all you grain size fact is improved just because you have some nitrogen so obviously there's something more than just the size of the grain that plays a role and that is that the properties of the grain boundaries are also important in the whole batch relations Lieutenant so and write to the promise effect of carbon and nitrogen decision so we we have to think of the fact that the role of grain boundaries is also important and there are some models which takes that into consideration and so the the grain boundaries are assigned a more active role and in fact that's being done by just saying Well the grain boundaries in Metz dislocations that act as sources of dislocation so you have to go and there are ways to show that if you have lectures on grain boundaries steps since it is possible this form of purely geometrical point of view too to have these ledgers dislocations in the dislocations sources and as I'm in this case will not go into that all the details but in this case you you make use of do you the question we we no which relates flow stress on the floor she had stressed to the dislocation density square root of the dislocation density location this being dislocation answers and we make use of this blast an experimental observation at this location densities are proportional to 1 over Degrange sites and so when we do this when we combine these 2 type of equations we find that shares of flow stress is proportional 2 1 over of the square root of the grain size again so but
that's this alternative matters a little bit more and worked out here detects but that's basically the same Let's listen to read through the Dexia hope patch could trail approach was criticized on the basis of experimental observations may the carbon and nitrogen effect and there is another effect that the reason why the people do you have objections against the Puyallup model is because if you take steals yes I knew deform steals and you look into the grain boundary region you don't see pilots yes you don't see burst truce either but you certainly don't see pile the the reason areas that far-right yes once you have this location which feels a pretty high Forest building it is crossed slips which is not says Forget it I'm not I'm not standing in this role of the dislocations that it's compressed just crossed so that the but but there are no the pile-ups in in Feira basically so and you cannot explain the carbon and nitrogen effect right and so you can this is the relation that between the dislocation density and the of the size of the grain here now and this is a more muscle experimental observation strong experimental observations there and then you out you you plug this into the the relation between the shear stress and the square root of the dislocation density that's what we just this year so I'm so that the properties of that the grain boundary are important and so the question is no can we explain perhaps what the effect is of the carbon unit will the I'd be the thing is we know that when we have carbon in the infotech steals a carbon well the solid carbon will very likely the segregated in grain boundaries yes and there it will strengthened the grain boundaries and 1 of the things that it's believed to do is make it harder for this locations to be generated at the boundary and that's the reason why you get a steeper slope it becomes harder to generate dislocation at the boundary and more carbon you have the steeper the slope becomes why don't we see it for nitrogen because nitrogen doesn't do this nitrogen in contrast to Carbone doesn't particularly favor grain boundaries for some reason it will stay pretty much homogeneously distributed yes so I needed that is probably the reason why there is this compositional effects right up
so because you can read this but when you look at the slight but
there is also this on this idea that is very important where people have said that look found it when you when you did you know when you deforming a crystal uniform another person with another orientation and so however the crystal here and I letter deformed and say dispersal doesn't care about each other brains around yes then dislocations would arrive at the end of this 1 of their I'll miss plane and don't move out of the crystal yes making steps steps at the summit the boundary will have steps and the other grain will do the same thing yes so soon enough if you let all the grains to that but you will find that necessarily there will be grains grain boundaries that are holes have become holes and other grain boundaries where I don't know how they fix that yes but you know there is material extra material yes so obviously that cannot happen right so what happens In order to avoid this happening yes but the person's name was associated acts at the Abbey said well In order to avoid this these volumes that are too much or not enough they're missing material or too much material that's just dislocations special chips dislocation geometrically necessary dislocations yes that they're being introduced in the model for geometrical reasons if we don't introduce them their urea crystals Pollack Crystal will contain overlapping material or holds and that kind of happened so might introduce these geometrically necessary dislocations on top on top of the normal dislocation yes and so we have to groups of dislocations statistically necessary this is statistically store dislocations article for or these geometrically necessary dislocation what will talk more about them and how you can derive their density later on another stage of the course because they pop up any time you have a problem with strain the 1 thing 1 part of the solid deforms the other party forms also but that's not compatible at TV interface 1 of the ways to resolve the issue is by introducing geometrically necessary dislocation right but you get small grains you've got you know you'll need more geometrically necessary dislocations and that stimulation now between why is it that I need I have more flow stressed His because if the grain size smaller anymore distant images it is necessary dislocation and we know the flow stress is proportional to the square root of the dislocation density that's basically at this location model and so on so with smaller grain sizes we get a higher rate of dislocation accumulation and because power it is proportional the square root of this location since then and so this becomes increases as the grain size decreases because that's that's the way that becomes the the connection as it were so there is no and so in this model there's no need to I had to make to have been the pilots at all you will need 4 points the 1st Earl suited the the 2 reasons are you have the at the strain incompatibility in Europe due to difference in crystal Crestline orientation leads to the formation of these extra dislocations was there just like you need these extra dislocations here and in addition to the statistically accumulated distributors the wanted to give you a regular swept and so the total dislocation density is increased by these this density and the 2nd lose Why do I have more dislocation accumulation with small grains is that we get a reduction of the average distance of locations in smaller grains so I will need an increase in the dislocation density to achieve a specific strain Justice remember strain is a product of the dislocation density times the distance that the dislocation will right so if I make the distance the disappears Comeau smaller but I still have to get the defamation right that's the only thing I can do is increase the dislocation density this would happen all right
so the picture that emerges it a very different picture from the original pile-up model yes or dislocation of Puyallup breakthrough model is you have grain interiors where you have single slept serving at the beginning of the defamation the accumulation of geometrically necessary dislocations at the at the boundary OK so ended in
note you will see In some equations theories Puyallup theories on grain boundary dislocations that sources for geometrically necessary dislocation theories of some equations that are derived from this series you can have a look at the time and so so
How do we effect of all this In truth what we have I had the right to there previously so now if you sigh you know I have a steel grain size but and I want to know you know what kind of way put it in my grain size In my equations for calculates the strength of the material so what you do the strength of the just function of strain will be pursued which should 1st write equations in terms of sheer stressed here's history I'm so 1st do the lattice structure that's that's too critical result shear stress on you do a calculation at room temperature that is 19 major Pascola 20 then you add His solid solution strengthening effects and then you add your if the fact of the grain size on the yield strength write to this KY divided by the square root yes you have to address and then you have this universe .period foreign terror yes where you compute as I showed you last Will this week earlier this week where you compute the evolution of the dislocation density would stress and you remember there we had a term the I mean free path Of the dislocations and that's where you put the at the term ends you have 1 source so here if you remember so if there is a union numerically integrate this equation so here there is constant and trying to make sure I don't care this wrong this this is the grandson yes that's how you take you do the numerical integration of this equation here you have the grain size as the strong boundaries and that's that's in there because this is not something you can put that take into account the the grain size in the series of strain hardening yet the that but you should not forget to have to add the the strengthening effect on for the yield strength because because the mystery here is just takes into account of the effect the grain size will have on dislocation accumulation of and if you do that you can actually checked the you know if the whole batch equations should hold yes but it is another .period it's interesting to look at because the 2 now what we've discussed are we've talked about constructional steals about fair I basically and in relation to the I hope that equation but we have in many situations where we don't have you know we're not even talking about whether the grains are circular not you know don't I look at this market what's what's the grain size you know there's no this this this this is there an equation for and grain size Martin side awful Bain I'd be nights just looks very much like to know can we talk about Mike rastructure refinement and it's important because marked site is a very you know very hard material and so on and it's what vary widely used in In that engineering applications so originally to make this markets like you can work with this variety and perlite a constructional steel and to thermal treatment and you get this very homogeneous Mike rastructure Nos L and the question is now is there's no can we look at Mike rastructure refinement In the
structures like mine the Martin side and an hour equations that resemble a whole batch of relations for this type of my question and the answer is yes actual there the Yukon and refined Martin site and uh and change of property don't so the might restrictive will to say something about Martin side particularly after Martin cited consist of packets yes OK so you have packets which were formed within the or regional lost Austinite grades so you know Martin site as you get that when you quench Austin so you have your original P g these so prior Austinite grain boundaries an inside you have the aura of the consists of packets and induce packets you have parallel blocks can and these packets are typically 100 to 150 insights so that it can be a big enough for a prior Austinite grain size of Anderson's again thanks to Microsoft this is Micron please and these packets are subdivided into many parallel blocks using Spurlock's here which contain groups of narrow lacks and when we talk about this might restructure here being
laugh Martin side that's the last we talk about these
narrow last so the blocks are 1 to 15 micron that yes and the Lance are typically less than half last month yes again all of them the should corrected when posted on the class tonight but less than a half a mile from thick black size is independent of the right post my brain and what's important here is that the last is very elongated let's have the same habit .period so although they look like very small units there actually highly oriented yes and they don't really work as grain boundaries even the From a forest a few of them it it would look like that in fact if you want if you put this in a TM and diffraction patterns from these last groups of last usually see a single crystal diffraction pattern and despite the fact that you have all these dislocations and interfaces lap interfaces and that's because the enormous orientation is very small the misery and tension between Latins very worrisome and then also within In these blocks here we have the close-packed crystallographic planes of the lattes within a packet are also nearly parallel and so the crystallographic differences within blocks are small because I'd also want to stress dislocation and the lots as but because that Chris graphic differences here or very small we never have very high on old boundaries and slept can easily propagate between the lapse the packets are
meaningful the structural units yes that you can were called in to get refinement effect for Martin site the the packet size rather than land with or block size all are the main grain size strengthening contribution in last March and you can see that if you plot and at control below the the packet lovers simply by having a smaller prior Austin migraines as you can see here if I have a very small prior Austinite grain size I will also have a smaller packets side so it is meaningful to refine the Martins I just as much as you can refine far-right predicts sales of constructional steals to get a whole batch the structural unit of importance is the packets so
the whole patches we actually applies to the new carbon Martin side in but it did the year is the packet size this is the is controlled by the or regional Austinite grandson and the reason is because you have high orientation of angles between packets and the back and it's the Packard boundaries that act as very efficient but barriers to dislocation motion and it's works very well because this is a fresh markets either .period to carbon you can see very nice but hope that relations and you have a high value of KY of of the of the whole batch the parameter doses to transfer of slipped across packet boundaries is difficult and I again here just as in the case of regular steals this very high resistance is believed to be related to Of course the Miss orientation but also the presence of carbon atoms at this boundary In the Martins and the reason why we know that that's the case is because this if you
tempered the inside this is before tampering this is after tempering what happened to the slope the whole batch equation instead survey they have a nice high Katie value we have almost flat so suddenly the microscopic hasn't changed by the way but it is still laugh markings to suddenly something has happened has to make the Packard boundary much less of an obstacle to the propagation of defamation and the reason as well as the carbon carbon that used to be In the packets boundaries is now not in the Packard boundaries anymore it's foreign car yes it's 1 ,comma so but suits which we get is the tempering of democracy side has in effect on the package size strengthening it reduces the packet size dependence of the yield strength and because of the smoke here and reduces the work hardening rate of the Martin site as a constant supposed effects are due to Carbide formation all right so this
pretty much ends the department wants to discuss about the grain boundary strength and just to close this afternoon session so what's what's important for you to to realize is that you may have thought of that who Hall patch equations of know operating was settled it's actually not against others still things we don't understand and know he has been particularly well everything that's related to the grain boundary properties and that our won over square root deep relation is no may not actually hold them in principle if we have them if we ever find the right theory having said this you not working on reducing the grain size is very efficient from an engineering point of view in the industry and the metals industries steel industry aluminum industry working on refining the grain is very high always very high priority but because you get very high strength before having said this I also illustrate the fact that I'm pushing this to the limits by having a very tiny grains doesn't really make sense because you kill the plaster suggest that you make totally brother and finally with the Martins side very important also you can also we find it shows that you can also refined Mike rastructure is that look very tiny already on their side in particular for steals Martin and a nite but if you are able to refine the starting Austinite Michael structure you will also refine the of the structural units in March inside and a knight and and get an equivalent of the fact but don't forget and again as I said I didn't use the theoretical basis fought for the strengthening is a little bit weak swipe at this stage the best thing to do I used to to use your whole patch equation yes but be very careful when you you know what KY value-use because as I've shown it's very very sensitive the defamation prior defamation and it's very sensitive to composition common no ,comma tempered not tempered so the very careful when you select a KY value for your calculations OK thank you very much and I have a very pleasant with
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Formale Metadaten

Titel Mechanical properties of steel 21: grain size strengthening
Serientitel Mechanical properties of steel
Teil 21
Anzahl der Teile 24
Autor Cooman, Bruno C. de
Lizenz CC-Namensnennung 3.0 Unported:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/18307
Herausgeber University of Cambridge
Erscheinungsjahr 2013
Sprache Englisch

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Fachgebiet Technik
Abstract The 21st 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.
Schlagwörter The Graduate Institute of Ferrous Technology (GIFT)

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