 static and dynamic and don't expect to have a presentation because he will use chalk. The tribology at work. Yeah, you can take away the... Brilliant, thank you. Okay, there's a slight change of gear in this talk because I'm not going to talk atoms at all, which in a nanotribology conference is a crime, of course. But what I'm trying to do is to actually bridge the gap, which has been mentioned many times between our engineering materials people who do tribology and what happens with this community. And to do that, I want to talk about the phenomenon of plasticity and how it is relevant to tribology. And so what I really want to talk about is how you contrast macro and nano friction. And this brings in all these questions like roughness, wear, lubrication, and so forth, which are all there. But in addition, how do you control plasticity? And there's a kind of little note I've made for myself there, which is about 25 years ago, David Tabor said to me, this 1D stuff you're doing in nano, it's great, but it's useless because you can't do anything two-dimensional. And so he said, you better do something about that. Well, I'm sorry, it's taken 25 years, David, but there you go. So what I'm going to discuss is the illiteral stages of lateral deformation, static friction, which we'll see, energy dissipation, and the tip-safe of material properties. When you have a system where you know you have some plastic deformation, so this is different from these systems where you just have purely elastic or no deformation change, which is typically the case for atomic force microscopy work. This is going to be an entirely experimental report, which means, of course, you can't publish it in physics journals because I don't have lots of models attached to it, so it gets published in other kinds of places, despite what Feynman said then is lectures to introduction to physics. So let's go. Here we go. Press the right button, hopefully. Yeah. Okay, just a quick instant review of the old stuff, which you know all about from these two gentlemen here. And of course, the history of this is basically the realization, the real area of contact is smaller than the general. So you know all this. All I want to do here is point out why this is useful and why engineers are still attracted to it. There's five things it does. It explains the fact that friction is independent. It's simple. Everybody knows that. It gives good typical values, 0.2 for metal, something like that. It gives you a quantitative mechanism for energy dissipation. Indeed, in the old debates about Coulomb, the question was always why did the energy come back? Okay, atomistically we know about that in phonons, but in the old days that was a problem, whereas plastic deformation gave you a get out of jail clause there. It's plasticity and so therefore it dissipates energy. Okay, then of course, if you reduce the shear strength at the interface, that explains how you reduce the friction, that's lubrication. But perhaps the last one I wanted to mention here, where is likely to be proportional to the area of true contact, which means it's inversely proportional to the hardness, which is one of those empirical things that engineers are very keen on and we shouldn't lose sight of it. Okay, so that was the only reason we're mentioning this. There are of course problems with this, as we know well, like why is it supposed to be strong contacts, but the decision is weak, what's going on here. And of course that's essentially because the simple picture of plasticity does not allow for elastic strains in the system and that is going to break the contacts when they're re-released, this has been known for a long time. There's the whole story of adhesion which we all know about at JKR, DMT and and and. There's this index here which is for some reason it's quite so often mentioned, which is the fuller table or index which came just after JKR. A little story here by the way, David of course should have been on the paper with JKR, but he wasn't entirely sure about the business of elastic relaxation of stresses because this is his big thing, so it should be in JKRT, but anyway whatever. Shortly afterwards with Keith Fuller, he produced this other thing which essentially says if you look at that index, it's basically a relationship, a ratio of the adhesive forces, r delta gamma or something related to it, over the size of the roughness times the elastic modules. So it says essentially if you've got systems with high roughness and high elasticity, forget it, you're not going to see adhesion, which is what gave them the get out of jail clause for adhesion. However, the most serious problem with all this, which is why we're all here, is that essentially it shoves the problem of lubrication interface slip to somewhere else, a number comes in. And that of course is why nanotribology, the area we're working in, is so important because it exactly asks precisely that question what is going on in this area. So that's the importance of the subject area. I just want to do two other reminder things. When you're in continuum mechanics, of course there's this great classic book by Ken Johnson and we know there's all sorts of interesting stuff in this, which we may or may not use some of it, but you all know if you take an elastic contact hurts in contact, you shear it, there's going to be singularities at the edge and therefore you're going to partial slip, all this stuff is well known. But I just want to make this cautionary note, that's great if it's purely elastic, but if you have plasticity, right, you get blunting of those crack tips and in fact for indents, you don't see this process at all, right. So plastic indents don't actually have that process. So the process of sliding when you've got plasticity is not the same as you would expect from all those elastic classical calculations. Then on top of that, of course, if you should go be so bold and I'll use chalk here, we can find where I put it, we're going to stress strain curves and all that stuff. And if you're working the old days of analytical systems, of course you either have ideal plasticity which goes like that, plasticity at all, or you have perfect elastic systems which go like that. Reality of course is something that goes up here. That, okay. So analytically those two are great. This one's a pain in the neck until the world of finite element came. As we'll see later on, even then it's still a pain in the neck. But that's reality. So this is the thing that David Table produced. Essentially any system where you have a contact, where you've got some surface pressure and you add an additional shear stress on top of that, of course you're going to have to maintain the same plastic yield strain, which means the sum of those two is going to be some value of P naught. You unscramble that a little bit using the errors and you get this equation here, which essentially says the area increases, the area contact area increases as you increase the shear stress. Okay. We'll come back to that later on because we've managed for the first time to actually demonstrate it. Okay. So the key question is this, how do you link this plastic stuff which engineers use with what we're doing in this community here? Well AFM and surface force apparatus, the classic for this, great stuff. You've got an interface slip. Most of these surfaces are fairly smooth. You can invest to get what's happening locally. I think you can do molecular dynamics. It's wonderful because you can add chemistry in in some reliable way. And of course, you've got some sensible way of characterizing the local and mix them. So we can all feel pretty cheerful about that. Okay. Or modeling. But some problems with this or some limitations. It's actually quite hard to represent many disparities, especially those that are deforming plastically, as we will see. Okay. And of course, you can't do that primarily because it's actually very hard to generate plasticity and system for essentially operating with soft springs. What we really want, if we're sitting there with a spy scales, what we really, really want is something which has these characteristics here, which is you want enough dynamic range, like about 10 to the six or something like that in force. That'd be nice, wouldn't it? Because then you could bridge the whole gap, measure the sensitivity and so forth. And you can do nanoscale stuff and you can do large scale stuff. And you can do the transition between them. Well, we've been working on that for about 20 odd years. It's a complete pain where we are getting there and I want to explain why this is actually quite difficult. 1D, it's not a serious problem. Okay. This is, sorry, let's start with the AFM side of it. Why is this difficult in the AFM? And there are numerous papers on this subject. It's essentially because you're using a spring driven device. Okay. So to access displacements and stiffness, which is a very far away from the stiffness you happen to have for your spring, whether it be torsional, vertical, or how you configure it, is actually very difficult because the accuracy of the measurement falls away. Sensitivity declines completely. So that's a bit of a problem. Then there's all these other questions. The more dimensions you introduce something, the number of degrees of freedom goes up to the factorial number of dimensions. Thank God there's only 3D in the world. So already for a 3D system, you've got all these rotations coming in as well, which means that coupling between those things in the spring system becomes very important. And this is particularly serious if you're looking at energy participations. So it's actually quite hard. If I'm honest here, if I look at the work we're producing in AFM, and I try and convince my materials engineering colleagues that we really know about elastic modular and so forth, they kind of take this skeptical look and say, really, how quantitative is that? Is it really calibrated? Can I put this into my materials and my finite element analysis when you're going to fly the plane? I've calculated on that. Well, we have to be honest about that. What we're looking at is qualitative characteristics, not so much quantitative ones. So as I said, this has been done in 1D, this is what nano-identation is about, and I'm sure this is all familiar to you. So you've got force and some kind of displacement along here, and you load the thing up and you unload and it comes back. That's for some spherical like this. Of course, we all know that you get an initial elastic region back down there. But after a certain point, you get some elasticity in the area under this. It tells you something about the shot. And of course, you've got elastic relaxation here. There's a famous formula there for the stiffness at the indent, and you can either work out what the elastic modulus is, if you know what the tip shape is, and if you know what the elastic modulus is, you can calculate the tip shape. So this combination is used very widely. In fact, the modeling done for this, which was summarized by Oliver and Farr, has some actually astonishing number of citations. I think about 25 or 30,000 or something like that using this. The depressing thing is if you go and read a sample of these papers, and you decide how they're using it properly, we'll ask some tough questions there. Okay, so let's get onto the meat and potatoes here. We have produced a device which does do this. There's a lot of detail in here, which I'm not going to describe. But essentially it takes two systems, which are a plier force, and measure the resulting displacement. Okay, so with this coil magnet system in the previous slide, that allows you to apply a wide range of forces, which are independent of position, apart from the springs in the system, which you know about. And then you can do this in 2D in this particular case. It's done by coupling with some glass blades, which give you flexibility in one dimension and rigidity in another direction. And that gives you reasonable minimizing of the coupling across the axes. I'm not going to say this is perfect, but we're talking about very large numbers here for these coupling things. So it's not a real problem in what I'm going to describe for you. We're going to use two, three different kinds of samples, two metals, and one, a few silica there. This all appeared in this paper recently with George Farr and Owen Brazil, who did all the great measurements himself. Right, let's get stuck straight in. This is rather a lot in this, but what I'm going to describe is the machine at the top there, essentially using vertical and lateral. So you're doing all this stuff in two different dimensions, independently and decoupled. I'll go into these, but the basic picture is what we're doing, starting off with here, is actually quite a large radius tip there. It's about one micron, and what we're going to do before anything happens is stick it in the surface about 200 nanometers, and thereby making a dent in the surface. So you've got some plasticity sitting in there. This is way beyond what happens in normal AFM measurements. This is two details, so I'll go into it in piecemeal. Essentially what happens, you can do an equivalent of this thing, but laterally. Okay, so instead now of doing this perfectly, we're doing exactly the same thing laterally, and you can do precisely the same measurement. And essentially what you find is something not too different from that. That's to say as I apply a lateral force to this system, I get a curve, well you can see it up there, which essentially says, there's a shape which tells me that I'm actually deforming this thing, and it has to be irreversible of plastic because it's not coming back to the same position. I'm glossing at it very briefly, the question which may be asked by some people, what happens when you get right down to the bottom of there? I'll come back to that. But essentially in both these metal materials and in the fused silica, you can see roughly the same behaviour. You've got some defamation process in the lateral case. If we look a little more however beyond this, when we take the defamation much further, of course this isn't going to be the same as this, at some point it's going to start to move through a large distance, and this is what you see. Okay, you can see for the three materials here, this is the friction coefficient plotted here, and on below here is plotted, whoops, the vertical defamation. That's to say what's happening here, the tip is being indented to the surface, you apply additional load, it actually sinks in further. And what you can see in the case of the fused silica, it basically moves on a steady curve there, you increase the friction, it reaches some steady value, and then in the case of the indent depth, it goes in a little bit but not much. What happens to the metals is much more striking, that's to say, first of all they sink in quite a lot at the beginning, then they rise out depending as we'll see later on material properties, but you also see a maximum of friction. This is static friction, so essentially what you've got here is an increase in static friction, purely because of the fact you deform the surfaces, you've generated a little cut for the thing, and then to get out of that requires some force which is higher, and once you actually start making continuous groove. It's kind of useful to know if you're worried whether your car tires are going to slip, as was mentioned. So actually this is a mechanism which doesn't have anything to do with asking hard questions about the chemistry of the surface of the registry, I think it's something rather simple about the geometry of the system, if you arrange for these deformations you'll get this for these metallic systems. So there you can see the two key features, there's a vertical movement and in addition there's a static friction rather obviously present in that case. Okay we can follow this a little bit further just looking at the, this is the single crystal nickel, and we're going to follow this out as we go out to the point where essentially you're getting steady grooving or sliding or scratching or what do you want to call it, of the surface, and you can see initial parts of these two bits where you get the relaxation. Two things done here, one these are AFM profiles of the initial state there, you can see the indent it gets deeper with a little wall starting to appear on the pink right hand side there, sorry another pointer, but you can see what's happening in the pink curve there, there's a wall starting to appear on the right and as you go to this sort of orangy brown color state of course it gets even higher and it's sunken even further as you're following this curve, if you push all the way across the blue curve on the top and you look at a profile you get something like that and interestingly the depth of this thing matched pretty well with what you see in the machine itself, this is an AFM cross section and you can see the images there in those three cases. So essentially that tells you that's okay, you've got the combined stresses, it gives you this increase in depth and then as you come out of it that is also the point at which you move from static friction to the kinetic or dynamic or what you call it, basically moving continuously on the surface. Okay so what I want to do now is come back to this equation because of course all this says is the ratio of the forces, the square of them because it's plasticity, to the ratio of the area change, a naught over the initial area divided by that. Now nice thing about having stiffness measurement continuously in both axes, in this case we're only going to use the vertical one, is you can measure those stiffnesses instead of the areas, you get a fourth power thing and you've got all those parameters, you can just plot it and measure it, done that and there they are, it actually works quite well. So in fact what this tells you that for these systems, the certain metallic system but it actually works also for the few silica, when you deform the surface plastically like this and then you move it laterally you do actually get exactly what you'd expect from standard plasticity theory, that's to say the area increases, depth goes down to some extent. Now of course this doesn't go on forever, as you can see they all at some point have the value of the strain here, the lateral strain, the ratio of the lateral strain and vertical, lateral stress and vertical stress at some point it stops of course and then it slides off. So what you're looking at here is the initial part of a deformation of a plastic joint which is then moved laterally by a small amount and then when you increase that eventually this obviously breaks down. It also changes a little bit with the initial depth that you make or the area in the case A here and of course if you make shallow and shallow and dense you can see what's going to happen, it's going to fall off earlier and you won't see this process so easily, we'll come back to that later on. Okay so broadly speaking what you see is this behavior but I've jumped over something here without confessing what's happening. First thing we did remember was a round tip like that, we made a crater like that. Okay carefully cheated here, this is actually very small, it's a 10 nanometer or that sort of order so this is actually a oh right okay. But this works basically because in something like that which is very sharp you're always going to get some plastic behavior at the tip okay. With something which is round there's a risk you're going to move more towards this kind of thing we're familiar with certainly weak plasticity and even elasticity, it approaches more towards as we'll see at the end of the talk approaches more to what's familiar in this community. Here you definitely get plasticity it's even better than that you see all the curves sit almost on top of each other irrespective of the size of the hole you make that's what you'd expect with a self-similar system which is what you've got with it. So this all seems to work quite nicely. Now at this point I'll be saying hey great sorted but one of the troubles in making a new piece of apparatus is that you push it a little bit further and you just go oh dear it doesn't seem to quite work as you expected and of course if you look at that you can't really expect it to work perfectly because we know reality contains elasticity so if you do this now instead of a sharp tip but instead of that something which is round where we know the elastic terms matter, matter here but they're not they're not very scale here they're even more important and what we find is actually you don't get this nice behavior once you what you find is that in fact depending on the material here and this is another story which I'm not going to elaborate on essentially what happens I'll summarize this very briefly it's easiest to see in these two sketches on the bottom right there if you have a system which you've now pushed sideways right and it's got very significant elastic stresses pushing back plastic then what's going to happen is there going to be some pushing that way okay which if it's a system which has a high elastic that's a low okay that's right right a low value of the modulus of a hardness which is the same thing is essentially saying something which is highly elastic with not so much plastic energy put into when you deform it a significant fraction is elastic which is not true here but is true here right depending on that slope then you're going to get some process which pushes it back and in fact what you see here as I say depending on low e over h that's to say high yield strain what you find is the back follows the front okay and when you're then measuring the vertical contact area you find you don't get the behavior had before what you find is it follows on there whereas in the materials which are high e over h that's low yield strain you find in fact the back seems to break away and this changes the way in which it moves into the surface and which in which you get contact area real contact area in a system this is quite a complicated story and I'm not going to say much more about it because the large tracks that we still don't understand okay and there's some issues with it not in the experiments by the way it's more in our understanding and we know that the yield strain has some effect there but it's actually quite difficult to model that um if I think there may be yes we did do one finite moment simulation for this which broadly shows the described behavior you've seen there is you change the e over h ratio you can change these curves you get behavior which shows that initial rise there but I'm not going to stress this because in fact there's quite a lot of things in what we're seeing experimentally which this simply simply cannot capture right we're going to need more information about what's happening not least about the very thing nanotribiology is good at when you do these things you're making various model assumptions about what the interface um interface shear strength is okay you either use zero or you use something or use some model or other and we find it's horribly sensitive to that when you're doing a finite element analysis and this thing we're not in a position yet to have a definitive answer maybe some folks here will take this experiment later and figure out what's happening in this case and I want to stress that because the what's happening the interface here really does matter as we'll see in the few remaining slides that got okay so let's move on so this is a kind of a semi summary of where we are what we've seen is you make a hole right you apply some lateral stress the thing goes into the surface a little bit for that this is actually from Ken Johnson's book that's work in the 90s on ideal plasticity the slip line field theory I don't think anybody does that anymore that's kind of stuff and essentially what you can see happens is that you generate on one side a wedge a material in fact there's a whole engineering industry in this because if you get the angles right this thing doesn't turn into a blob it turns into a chip okay which comes away which is what's happening in metal cutting okay the whole raft of things that you can talk about there for shaping materials and so on but the person I want to make here is that that modeling slip line plastic modeling has its own serious limits despite the fact you've got these quantitative things like the angle of the cutting edge and so forth there's never any friction drop in the whole thing and you don't see a lot of the dynamics that we see in the plots I've shown you and in fact this has been known for a long time and David Tabor suggested what's actually happening in this case is the reason you get a transition is because the edge previous slide probably loses it here the trailing edge here or rather the front edge this part down on the blue right hand side there is actually starting to slide at the interface see what's happened here is his frictionless okay got to do some more we've got to insert some nanotribology into this macroscale friction this is a good moment also to mention of course Mark Robbins and my colleague who of course was very active in this whole business and particularly his observation that the interface layer presence of a carbonaceous interface layer actually matters quite a lot and this is something that David suspected long ago and it's of course interesting to see that of course Mark's married to Paddy McGuigan who you all know as a colleague of Jacob Azaralkvili with whom I remember sitting in David Tabor's office discussing many things together with both students that was an interesting experience too with Jacob but essentially you can see the threads connecting here it's good that all this communication is going on as we all have here so it's excellent to see that happening question is is there some evidence which you can add from this experiment to say well is there actually some slip occurring the interface at this point and of course this is the point at which it took some more recent data measuring at the same time the phase angle between the oscillatory force for applying and their displacement response and of course as that increases it's an obvious signal of dissipative energy you see what's happening here in the case of the case of the single crystal nickel you've got that falling in and then it starts rising out again look at that phase angle rapidly rises very rapidly by a large amount exactly at the moment when you'd expect the thing to start to slip okay and as you carry on slipping there it is steadily giving you a steady signal in the whole thing okay this applies actually for all materials if you once you start that constant sliding essentially you see a rapid increase in the dissipation energy observed from the phase angle of the applied load okay so this is clear signal you've got interface sliding and you've got a way of measuring that so that localized interface we've been talking about is of course critical in this case you can see evidence for this related notice how when you get initial sink in initial static friction there isn't any right that force is generated essentially by geometry that you've made with the plastic deformation it only comes about when the interface starts sliding okay so that's that's one point now i'd want to finish yeah i'm getting off okay here um with a one more piece of data because of course there's a little summary for you what we said so far tip rises out of the surface once you start transition to this plowing or scratching what do you want to call it and at that point the energy dissipation observed from modulation rapidly increases very significantly there's other implications of this by the way it implies that even in systems which are deforming plastically like scratch process it's that interfacial energy sliding which is actually the dominant process which from the point of a nanotribologist should be mightily encouraging because it means even in stuff where you're causing grooves in surfaces right what you're measuring at that single atom and molecular scale really matters despite the fact that it appears to be a purely plastic process that's very encouraging question is can we scale a thing down down here or rather with the radius um and see what's seen in kind of typical fm sfa experiments and of course i wouldn't be standing here if we hadn't done that okay so there's three examples here taken from a small radius tip a burkovich tip which of course would mean smaller radius and we deliberately chose a much larger radius tip and you can see what happens here as you increase the radius or you decrease the applied load on the thing essentially what happens is these curves which show you for example you've got a sinking in or you've got an increase in friction or whatever turn into something which is much more familiar which is to say you have an initial slope and it turns over to a steady friction which is what you see in typical fm type of experiment there's a whole map of these things here um i see whatever um that pretty much says what you need the one on the bottom right there for example is essentially the sort of thing you'd see you can see there's a region which is bigger you're going to kind of plateau of some kind due to the fact you've got a deeper hole or a larger load and it takes longer to reach that steady state process but essentially in the case of the large radius which is essentially one where you're getting minimal plasticity in fact zero plasticity you get something which much more closely resembles what we see in fm i should say by the way that um there's i've in the previous few graph there it is this one i've casually said that there's plastic or non-plastic you can justify this exactly if you do these measurements in normal indentation and for all the ones which we know are purely elastic this is exactly what you get they come up they come exactly back down the same line okay but independent evidence that there is no significant plasticity in those cases that show that behavior so that's essentially you can bridge the gap i would be dishonest if i were to tell you this problem is entirely solved right um there's some rather strange things happening when you get a very small loads here which again what you'd expect in nanoscale stuff uh one of which is that and i'll tell you this right one of which is that actually when you use small very small shifts the process is actually elastic too if you're a person into plasticity this is bad news didn't happen right but it does okay that's one of the reasons why the finite element is actually a problem because you put in a constitutive relationship which governs the material but doesn't govern the whole story so something's going on there which tells you when you make very small lateral displacements with a plastic hole remember we're talking about the equivalent of afm that's a region we get elasticity it's even worse than that you can look at the lateral stiffens the vertical sniffers and it gives you a really nice Poisson's ratio number which works really well so clearly it is elastic i don't have a good explanation for that in terms of constitutive relationships but it tells you the kind of complications so if i go back to that summary here okay essentially with these plastic dents you can quite easily get static friction hands kinetic friction which is useful and it's essentially associated with the fact you've made a plastic indentation you don't require any special magic chemistry or time evolution of anything like to do that you can just get it straight it's probably why they have hard additives into cartiles i don't know i'm not sure about that but you know there's that sort of thing for initial lateral loading you get this simple plastic junction growth that i described for basically essentially metallic materials for materials which have a significant last day recovery at the trailing edge you get a more complicated picture but essentially you can deal with it and the important thing here at the end is that the transition from static sink into kinetic sliding is affected by directly about interface friction you can see that in terms of the energy dissipation it's also affected by the shape of the tip that angle actually matters so the geometry of these particles i'm sorry to say sorry to have to say this but they do actually matter the shape of the tip matters and of course this year the h ratio so there's a kind of quick run through plastic deformation which is a nasty subject but it does actually rate quite nicely to what we're doing here and so i want to finish with a couple of slides one some of you may have been to that famous meeting in the view the view from the terrace this is partly a memoriam of another colleague who left us a while ago Sanjay Biswas who essentially the meeting was organized because of their partly because it was a nice place and it's of course that's why it's nice to be here in interested too but also because there's an old there's an old in the 1930s apparently Bowdoin did kind of public science and publicity was done quite a lot even then and he was on the radio trying to explain why it is that their new theory of friction involving multiple disparities was relevant and he said basically you take austria and you turn it upside down and put it on top of switzerland the area of true contact is going to be rather small i think he was referring to physical contact rather than political but i'll leave that question to you thank you nobody likes plasticity okay everybody agrees on this problem although for the happy word the graphene this becomes less important fortunately yes okay there is a question so i believe you said the well what was the smallest size curvature radius of the various tests i guess was it the berkovich yes like and that's about a hundred nanometers or something like that maybe less than that even in the clean clear ones i'm wondering if any of these experiments would be affected by the fact that it's around that length scale or below you start getting these scale effects in plasticity because of dislocation starvation and yeah and then also more importantly as we realized recently strained rate the matters for those and of course that was the point originally that the interface region is of course not typical of the bulk and that's again another reason we described earlier on i think it's it's broadly true that the sharpest of these tips will just about explore that region but the problem is it as we've discovered in recent times it isn't just you know the so-called yield strength change due to dislocation interaction the strain rate matters a great deal at that point and i think this is one of the things we should take into account when we're thinking about simulations the fact there's a time scale difference between what's happening in experiments and the modulation simulation is actually still pretty serious and there's a very strong strain rate effect in all of these things especially metal and one other follow-up if i may is since you can have the two-dimensional capability could you apply this to say an anisotropic material like graphite or some layered material so that you and in particular it would be nice i think to use this to really show what the elastic just the elastic properties are because i think people often don't use the contact mechanics properly for the anisotropic case but but the solutions exist and you could probably show what the right way is to do absolutely right i mean this is essentially a new machine we just haven't got around to doing it so all suggestions really welcome if you've got a problem you've got burning a hole in your theoretical pocket why don't you do an experiment on this please let us know back at ten to five