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# Mechanical properties of steel 23: precipitation hardening

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right now I'm so 1st of all summer organizational points Everybody hadn't yet so far that's next week I think this week of December 2nd round will be the last teaching week for this course because the week after that I have to do and teaching in India Support we be teaching next week and also will try to finish the course next week so I will all know by Monday whether we need an extra class without probable probably would come by Monday and so next week will also be the last question was usually on on Thursday right and as as we have said and there will be no final exam just use your quizzes the 2 In but the final results right OK so a few things that get I haven't put up the the final of the slides a version of the the slides more the precipitation strengthening our on class but I'm anyway and some slides I amended 1 of the slides diamond is the relation between the remember
this very interesting relational here that we
found which would which
connects the the spacing between the particles of suspended their radios and the volume fraction right this very useful relation to
to use in practice right assistant example here if if if you use it if you have a volume fraction of 10 to minus 2 dance I hope this is a book by witnesses volume fraction rights of maximum values 1 not 100 OK this this is 1 per cent f 0 . 4 1 is 1 that's so if that means you have a L will be 14 times the particle rages for instance I don't know but this is the basic equation you can use it as I said if you have a little volume fractions of spied on and of course and there are lots of simplifying assumptions in uh when we computed and so on and there are more correct the equations 1 of them is shown here which this is a better approximation so again if you apply this formula here you can see that before you get 16 times there radius of the precipitate for the if you have a volume fraction of 1 per cent I and I will and I
also give you the equation it's similar it's not it gives very similar results than the previous ones but this is actually the correct 1 you know if you want to be absolutely correctly and not make cuts this is the 1 you should use it as an end I have taken the I'm notation where the where we use the diameter instead of the registers used the here and now so so you out by GM measurements for instance you are able to determine the particle sizes yes you can calculate the mean value of the particle size the news color particles in diameter and then make a column with the squares of these yes of the measurements and then the few of these measurements and then you measure the mean value of these 3 columns yes and that gives you the mean value of the diameter mean value of the square of about a mean value of the a few of the particles and then you substitute this and this and that will give you 8 need to nearly absolute correct uh steering logically correct value because if you don't want to know whether new Ph.D. for instance by Dexter formula I would use of course the the problem is In order to get this be able to use its value you need to have you know to to have measurements of D now and if you don't have that right then used a simple formula which will give you the values of close enough to warrant so everything depends on your particular situation which formally you want used by you're going to find the difference is not yet but is it going to matter a lot with the type of data you'll be able to get probably not but it's nice to know if you have that you know measurements of actual particle diameter that you get for instance from extraction replicas with 2 younger listeners way to measure of course How many should you measure nowadays you can do automated measurements so you can measure hundreds of particles so you get good statistics but if you can include samples of course and over the but that's basically what I want to say about this this form of so
we will discuss this don't have anything the different in front of
so but we have said that you know if we introduced particles in the matrix that's important here we're talking about particles in the matrix this is a grave the particles should be in the matrix and and 2 things can happen either the particles but it cannot pass the the particles Nelson and we have a bypassing or the dislocations can go through the particles pretended we had we would talk about the would discussing so that the particle gets shared by the dislocation .period and of course there will be a force that obstacle the particle will have exerted on the distribution will depend on the shearing process and so we had discussed modulus hardening and in some that there all alone on refuted but there other a possible hardening mechanism stacking fault hardening Warda hardening chemical hardening and coherency heartening that the possible so will go people of will 1st review would we found for model it's heartening to see that look at the system where words being used and it's that we've already introduced copper and iron and that and will discuss a bit more quickly the other part of the other hardening might just just repeating here modulus hardening is when you have the precipitate has a difference the modulus than the at this location at us and we will theory the other as I've added this year in the back
insist it's going theoretical background and was kind of interesting to know because of the equations you'll get so you know not supposed to on we learned this in our by hard to in any way but and it's a derivation the that basically shows you right and it's it's headed here but that in the declared situation that we encounter the office now as it is that the the hardening effect that you will get from the cutting here there will be proportional to the the maximum that the obstacle exerts on the dislocation to the power of the Habs and so that's show how you can get specific power in this life here so remember that because of adjusting case you're wondering why when we go through different formulas why there's always this powered through to rehouse there you can find it back here is it's basically simple math and that is related to this simple model of which is called Fidel model Fidel statistics model that's with when you when this revision has through 8 an array of obstacles you get some kind of steady state that each time when that dislocation advanced by passing 1 obstacle in getting called on and the the next optical so the dislocations moved in like that and I am so that allows you to do some simple geometrical calculations which we call Fidel statistic right and then if you apply this you find that you find the cradle here stressed which is 1 of which is the maximum of retaining forces that the obstacle has on to the power of 3 have spoken and yes if that's so that son go on I so we we we been talking about the the copper precipitation right as an example of modular strengthening and and had reminded you of the fact that the strengthening effect is related to the reciprocal of the distance and that's really important parameter the smaller and make it the larger I get strengthening and the coastline of the breakaway uncle has took the breakaway on goal tells me something about f max basically yes and at its maximum value is for the breakaway angle 0 yes is 1 of them and so we had gone through the
theory and and the result yes and this is this is how you have to imagine the the dislocation going through this particle when there is a difference in In modulus what it means is that I have a difference in eye In the at this location tension has this devalue here has and finally
we get How can we get
this equation here right this equation here right and it tells me that the strengthening is proportional to 1 over L the distance between the Earth the copper precipitates and then this factor here square root of 1 minus the ratio of the model of particle and the nature and but if again but some of you I don't
know maybe 40 researchers all you world and all you're going to literature and then use the wall on the radio I can't find this equation or is this obviously this equation is simplification has and 1 of the things that is simplified here is and
you need to take off the solid solution hardened by copper we also discussed how last year the Monday how but you make this precipitation by supercenter in this this kind of a
I will use copper To strengthen its it that it doesn't have negative of the have a negative impact on other mechanical properties for instance in terms of toughness it's it's the toughness is not of influenced negatively by the addition of copper the only problem areas is when you make this team at high temperature the copper tends to 4 liquid films along grain boundaries against ensued materials can literally break when you trying to process process so so actually steelmakers hate cops and we try to make sure that we don't put copper in any over steel yes unless but that the method is used to you you have copper and steals but usually forestry products of and all that many other people high-volume products you don't you stay you generally stay away from confrontation it for precipitation strength because of the steelmaker of so now and let's let's have a look at this and other data here so In this case we do have the distance strengthening effect in a major Pascal from a tensile test and so and I've already converted the data is a function of precipitation precipitate ranges but in this direction could also have aging times in which a seen I reached the maximum the US and then a decrease materials over to what is how can I use this data yes you can use a state actually cleverly you can say OK in this case it's only the strengthening rights so we took away all the others strengthening contributions solid solutions Of of the Pyros illustrating the effect of the grain size etc. there so we have a pure precipitate strengthening and nicely the we find the peaks of hardening is indeed around 300 my capacity like we calculated for the heartlessness just what can we do here we measure this Delta Sigma just about 300 make a Pascal and you know I can always converge tensile data into sheer data by using my the of Taylor factor so did so for it by measuring this I can calculate the the increase in the sheer strength from but the a due to precipitation hardening again now yeah I know how much copper I added so I can calculate the volume fraction of copper in my because copper I remember my news not really soluble the most of it will for a precipitate so I can calculate the volume fractions and I can measure the radius of the precipitates was simply known as I said you Richard samples to put them in the Tiananmen you just measure and so you can calculate the the critical goal for for the breakaway so you can do this and indeed and which a fight if if the parties a very small the article is 180 degrees what it this article to 2 times this on the list is 180 degrees yes and and then as the particle the increases in size it goes it decreases but because the bottle and I think that's right yes it's pizza the appearance of soft particles and then it increases the uncle the decreases as the particle becomes more and than and I can calculate that the maximum force also so as the article decreases the force has to increase the ad when this was remember copper so b The on all the critical on should be about 80 degrees has so let's see if we reached 80 degrees no we never reach 80 degrees we reach into degrees this is 90 degrees right so we're we're still above so that means the dislocation can continue to cut 2 particles even the way beyond the peak aging what else can I sell yet so it's also important is yeah where do we get the peak aging and why do we get the peace aging well you see apparently it's related to the structural change in the park the new Member I said when the particles that form a very small classes a B C C and admitted the new change into the all the types of crystallography before becoming the FCC will you can see that we reached a peak in Beijing when we have tiny clusters of copper and the irony that particles in the air which are body centrifuge few that's that's appears to be the of the reason why we have this the for the
rights so it just to so if you more things the BCC copper is modulus effect sued it's soft particles so we get so attractive the obstacle In the TEM analysis people have reported that they don't see the Oops around the particles so when I when the the breakaway bungalows are so that the fly-on-the-wall here is very very small close to 0 but the the saying should give me particles which loops around the nose and for every dislocation another new units that's how you can tell experimentally in and if you have cutting or bypassing of the person so that TM show that there is no bypassing if the precipitate is less than 35 microns and the peak is at 5 Microsoft's way beyond and do the maximum a the peak aging that you get the standard that the bypassing process starts at this location passing a very low on those here takes place when the particle Regis is larger than 35 millimetres but the fire Michaels and there is also no work hardening in the overreach condition is basically means the same thing you know you don't accumulate dislocations right and then then so be it serves only to go back here and at the way this this this
diagram is on this little bit confusing which on it's because of the there it should go from here right now it's it's cruel it should go from prior to
right so so what would you basically have is as the particle becomes costs b the critical all is this is not to fight the fire itself has decreases and I go from particle cutting eventually 2 the particle bypassing but only after 35 centimeters on long after the the peak strength began right so let's let's quickly over few now that strengthening of the strengthening mechanisms and we have another mechanism is coherency strengthening the differences in volume between particle and matrix matrix volume that it replaces will give us elastic stresses acting on the matrix and so 1 of the reasons why that happened is because of the different lattice parameter it's actually difference in lattice that the atomic radio I and we can change this into or we can connect this with lattice parameters and and then in the final of parameter Delta which controls this coherency hardening and that's basically laughter strength that we do this Delta is the lattice parameters of the particle mines like spread matrix divided by the letters from and until we usually and then we for the theory we need to have some of the Corian see strengthening we have to use a misfit parameter epsilon has and if you look up in the literature of you find pretty complex equations for this parameter it's legal to Delta times for instance this parameter here where Jesus share modulus and and this is what some mothers and the thing is very if you if you go through this you see that there was a modulus is typically about a . 3 services and one-liners .period threes .period 7 times to is 1 . 4 yes and this is 1 plus the modulus is 1 . 3 so this is best the busily you can just forget this parameter here it's a very it quickly simple to relate soon this goes away and and this goes away so you can relate this Epsilon too estimated difficult for others to 2 Delta yes so easily you can simplify this 1 plus 1 right
so so the maximum interaction force by theory that I did I don't arrive at here is related to they this is the strength of the mismatch lots mismatch is increases the amount interaction force and then but if you go through theory most of the theories and with the strengthening effect which is proportional 2 this coherency affected the power 3 thirds the rehousing we have and the square root of at times don't mean particle diameter has kept and so this is what we know to be the case for for some of the it's heartening and and this is what I told you that being the case of transposition hardening we get the maximum interaction the power of the soaked in practice but for instance yes this would be a former which is derived from this 1 that you would use in practice where the reason why look so different it's not very complicated it's because we have changed replaced the the outlying tensions with the appropriate performance but at the end of the day In practice so we don't have epsilon would we have dealt out to the power 3 hats and the important factor the square root of volume fraction Times particle dimensions and you can using this theory also determine what will be the maximum the big stressed there's an aunt watch radius you have this expressed if you go through the ever go through analysis of this coherency hardening mechanism yes but you will you will see that there different theories None of the series is more correct than the other 1 they just use different approaches to solve the problem because of geometry how they average the because this is a macroscopic value ESS which you measure would in tensile test for instance I'm so you need to go to average out the effects of a distribution of particles on the distribution of this location so you don't get parameters that may differ instance here in although was serious and agreed with this part of the formula this factor here this numerical factor may vary slightly less than 2 to 3 years so that will impact the results these formulas give him but again the ideas
as a our you can use a formalist guide you yes I to what's important to do yes but in practice you used you work in the reverse right you you do measurements and then use what is the hardening mechanism yes what is the Harding what's the operating hardening recognized then you apply these formulas to your data to see which 1 fits situation the chemical hardening effect this is basically due to the following you have dislocation passes the particle it was shared the particle yes and when it's tennis sharing a particle you can see here and here I've I've created new interfaces new interfaces and these interfaces have I have energy right so the creation of this interface is what causes the the effect of the a restraining effect the obstacle the effect of the particle on the dislocation just and so well if this the particles has a special audit structure this is sharing calls the formation of an and face pottery and then we have to take care of that but in this case we assume that the particle is not order yes it basically shared a particle and you form the eastern surfaces in effect so if you if you do the theory the maximum force interaction force is proportional 2 the energy of these interfaces makes sense right and the head the chemical hardening effect can be calculated and the theory gives chemical hardening effect is again the maximum interaction forces To the power the rehabs units still as the maximum interaction forces proportional to this surface energy you that's what you find here it's proportional to the square root of S and oddly enough it's 1 is proportional 1 over the particle radius of 10 so so the theory predicts then what so if you have fixed after the strengthening will decrease With precipitates and this is not just not observed in age hardening so that part and then the impact of this process all the hardening it's probably minimal because we never observed this they this the fact that the particle gets larger and we it's the stuff gets soft just so I so that mechanism is probably unlikely to to be of any importance the forensic for
instance you could have thought that when you share these copper particles the creation of these interfaces might cause the strengthening will obviously that's not the case because we don't observed a decrease the the strengthening with the Rangers of the part of the game another strengthening effect is it takes into account the fact that in certain alloys systems we have no stacking fault energies so we have dissociated dislocations yes and the 2nd false training is in fact due to the difference in the 2nd fault energy between precipitate and make that maximum interaction force is proportional to this difference there's so as a consequence the strengthening effect is proportional 2 the stacking fault energy difference the power we have and as expected for age hardening is an aura of precipitation hardening it's also proportional to volume fraction and the radius of the particle the square root of the so write to that's that's that's a possible situation that kit that can occur an important however in practice right and in it is for precipitation hardened alloys has order hardening often of curse so that that's when dislocations glide and it cut through particles which are awarded particles you will create 8 all lattice disorder and the formation of an face boundaries and there is a very important growth of SEC metals and alloys which are and so on I Byron based on nickel base of so-called bald based which are based on this precipitation hardening models of so this is good for instance the 8 to structure forms of BCC Byron instance so if I look along the 1 1 0 the directions years and I shared the lattice on the 1 1 2 playing tennis I share it over burgers Factor 8 upon too 1 1 1 this is before this is after shares in the woods what's to say nothing right after this location has passed I still have a perfect perfect lattice that now is is now I look at the cesium chloride a B 2 structure of nickel of iron aluminum for instance and I share this lattice then I do not get the same structure but of course and I had the same structure here in here but where the sheer happens it does not look the same for instance there are no In the .period captaincy a large dark at that so close to each other normally in the lattice yes so I created what's called an and phase boundary it's not a stacking faults as it's it's and I face boundary so and that's
a said so in the same situation as would I showed 4 chemical hardening the dislocation passed to the particle and at the interface we create an interface boundary and that has a certain energy so that would be for instance I have glide here on FCC on this plane yes and it means that after the passage Of the dislocation so princess and Mikael 3 aluminum particle yes on this plane I created and that high energy and faced boundary it's similar to the stacking fault but it's not a 2nd
because of stacking fault across the stacking fault is still have normal stacking and the atoms across this technicals our you know where they're supposed to be if you look at any 2 1 1 1 planes In the letter writer sister stacking is it's all in this case you have at the boundary there's just at the wrong atoms across the boundary so high energies much higher energies and efforts by much higher energies than stacking I am so probably is Inc the maximum force that we get is proportional to this and I face I think boundary energy and and of course if I compute these the strengthening effect I find again the and they faced boundary energy to the power we have at times are well-known square root F times poppy relations so and this is an example you where this theoretical equation is used in practice but you you get the same basically the same behavior was so very important here and that were well known system is the so-called Gamma Gamma prime the system In Ireland-based support dialog that's and it's it's very similar to the nickel based super alloys with diversity right so then so
let's talk a little bit about these um how we make these this type of precipitates in half in super alloys of 1st of all it really important here In Indiana FCC the structure we do precipitation hardening with nickel 3 aluminum yes legal thriller that precipitate is formed in the matrix and you can see it requires nickel wrinkle-free Titaniums in which you could form for instance by adding 2 impulse domestic steel of Tania is a similar precipitated but it's it doesn't forming the matrix it forms and bring about this is not he is you have to have the right precipitous has to form the otherwise I don't presentation it's the same thing in bcc alloys in BCL is we don't really use much precipitation hardening In the BCC himself but in Martin said steals we do use that and here we use SEL yes because it forms and the military there although you can fall on precipitates the suggests a nickel and of molybdenum to these alloys conform molybdenum these offers are in the grain boundary now this this mean that we always avoid these these particles that are in the grain boundaries no because sometimes for instance if we have applications at high temperatures we want to have particles in the matrix which give me precipitation hardening and we won't have particles in the grain boundaries which will prevent grain growth remember grain sizes also a strengthening mechanism rights of particles in agreement and not necessarily bad right from the start in high-temperature applications but it so well so let's look at what how we work with this pressurization strengthening it is not very common In forensics steals yes we don't use page hardening in for a text of the Chinese very common in aluminum that's because of the because that's a very efficient way to harden the Microsoft truck but in steals and data for it Texas we don't use age hardening so much but in stainless steel is a different story so we have differences Martin said thinks steals and so it is a well-known 17 4 recipe pH precipitation hardened steel is very common precipitation hardened steel he has an MS temperature had 132 the degree C so I can Austin enticed this deal which contains 17 per cent but was 70 per cent of the chrome four-percent Nicole yes and if I call it down quickly enough I 4 Martin's democracy 60 Morton's which I can then forget quench Martin by which may be softened generally because it doesn't have much carbon and then I reheated yes 2 of 500 to 600 deg C and there can be no precipitation hardening of my Martin yeah With Austin mythic steals it's a bit different yes let's 1st before it talk about 70 Ulsterman takes this look at this the also
effective precipitation horns it was a very stable Boston so there are always Austin at yes so but you have to do the precipitation in the Austin so you reviewed this material and cool down to room temperature nothing happens right it's also nite before and after just meal to material that and white white there's nothing happened because EMS temperatures far below room temperature so I do then aging precipitation hardening or Morrow time because everything is very slow and Austinite I this and I precipitate things like Michael 3 aluminum guests in the microscope but the structure remains fully Austin taken against no precipitation of for instance nickel 3 of them in the also phase diagram here
which which tells you typically In the end In terms of the of the processing of these videos of people of very clever engineering of the this is the structure of these intermetallic compounds and which would be good for instance at 25 nickel 15 per cent chromium super alloys we use the gunman pure we used we actually use Titaniums and aluminum tubes to have a mixture of nickel 3 tightening and incomplete aluminum titan have to get the right properties so if it again this is an example here which again with these alloys they're ordered alloys right so they this L 1 2 structure on and on and and you see the strengthening it the effect here precipitations might think so at 1st as the particles growth I reach their peak strengthening and after that yes when the particles get larger again bypassing and I can't you consider bypassing here this is a TM picture frames and look at this particle here you can see the dislocation loops around the particles when using seat that that these on large particles like never before larger than the 5 nanometers and give me the peak aging value this is this is the
same here and also and the super alloys this is a very common along a 218 6 so high nickel I called him and you see here again and peak aging you need a long time for a change and and the the size of the particles at peak aging is again as you can see the respected religious about 5 nanometers the very very signing particles and let me go back now 2 this year we
also have suddenly Boston at that the precipitation hardened stainless steel is a little bit more complex has in terms of their own the way you the aging so I'm the normally the MS temperature is is below the room temperature so you can you can anneal this material and shape yes it's important in shape and then you can press in it and then you can change the location of the MST temperature the by the but the choice of the annealing temperature so if you do a high annealing temperature you don't precipitate much carbon when you do that yes so annealing at high temperature the you know the amass temperature is a function of the carbon content of Austin so if I have a lot of carbon have very little and OK so if I precipitate a little bit of carbon temperature in the case of 1 will increase a little bit In the case of 2 yes where by 4 precipitates the MSM Britcher can go up to and beyond room temperature so that after the heat treating too this I will form a fully Martin citic Mike rastructure In the case of 1 if I want to form a fully Mark Pacific Micro structure I have to do cryogenic cooling yes cooling below but which is which ,comma like liquid nitrogen or death and then I can do the steals and usually get an actual aging treatment after that 2 to 4 the prospective that's it precipitation
hardening is complex heat treatment OK so these are examples of the showed on right and you could have forensic age Hardenville steals this is an example here for uh the 2 Titaniums silicone precipitation hardened there's still some data again the maximum the big aging is always for particles that are very very tiny and dimensions
and we have some more fearful BCC steals and some of whom you can just have a look at it and I just wanted to get to this life and that is what what you do when you have a combination of both hardening mechanism in the same precipitation hardening princess you have a gamma prime precipitate in Boston to you we know any cuts this I form and I phase boundaries so that death is memories effects will impact but that particle itself it also has coherency strengths as there is also the coherency strengthening effect so if you want to have an idea what's the contribution of 1 hardening effect and the other 1 was if both of How do I add them together you for instance have only 1 mechanism want yes which give me their contribution that Taiwan and another mechanism is the contribution town to the why some little or what while I'm there are theoretical reasons why the best way of ending the the fact is using the Tabarez average so you take the square of the first one hardening contributions square of this 2nd 1 thing the square root of those that it gives you a value that's close to what you can expect an end an example and that holds for this ,comma prime precipitated the mechanism 1 would be coherence restraints and mechanism to would-be orders strains for instance due to order hardening due to and I faced became livid over time I'm so that all stop here and will allow continue Monday morning Tuesday morning and it's all about the the precipitation of nitrites and Carbide's and then will will start probably already on Monday the the last chapter which is about Mike rastructure or hardly have helped you strengthens the steals by using multi-phase Mike restructure OK see you on Tuesday morning
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