Okay, let's talk a little about plastic deformation. Now that we have some crystal structure under our belts. So we know that atoms will move to new positions when you're plasticity deformates. So in fact, we're in my paper cup, well there it is. I think there's a little paper clip and I put it on too many of these in the paper and it deforms permanently. Well, there's some elastic spring back like that, right? There's some elastic spring back. See if better on this camera. But then obviously some permanent deformation. And what's happened is at the atomic level inside, we've got planes of atoms starting to move past each other. So what I wanted to do is I like to cycle back and look again at our stress strain curve for a typical metal. We know look something like this. Okay, let's see if we can define a few things a little bit more carefully. So, you know, we certainly know that we've got the young to modulus here. What I'd like to look at is when the deformation becomes permanent. And what we said originally, we first looked at the tensile test as well, probably somewhere close to the end of the straight line. Okay, so you remember here, in this straight line region here, we said that stress is directly proportional to strain. It's directly proportional through this constant of proportionality, the young's modulus. So when the line ceases to be straight, we could just call that the proportional limit. End of the straight line, but that's actually a very little practical use to us because, sure, if you know, you're professor of drowsy-big-orange dot on the line, well, it's clear where the end of the straight line is. But if you remember from the tensile test that we did, the end of the straight line is very difficult to determine exactly where it is. So it's not really very practical as a definition of plastic deformation. In fact, it's not entirely correct either because there's a little region here which I've identified. And I've actually exaggerated this. Okay, I should make a note of that. This is really not to scale. I've amplified it a little bit or considerably, but there is going to be some region after the proportional limit where you have what we would call nonlinear, but still elastic. So nonlinear elastic deformation. Okay, this region here, driven by Hooke's law, was both linear and elastic. So most materials, well, on materials, we'll have a little bit of nonlinear elasticity. Metal's not very much, but a bit. And so if you want a thorough understanding of this plastic deformation, we need to appreciate that. So elastic. And then the other thing I want to discuss is what about the peak of the curve here? Well, the peak of the curve. If you go ahead and I'll give you the name for it, it's called the ultimate tensile strength. It goes by a few other names. Sigma UTS, or sometimes just UTS, or sometimes Sigma TS. So that's the peak of the curve. I want to explore that actually in a little bit more detail. What happens right there? So to do that, I've drawn in a little tensile specimen. Okay, one of those specimens we put into the tensile test machine, we've been stretched it out. Now, if I say identify this as the initial unloaded sample, what's going to happen when we, when we, when we put it under load, what I'm going to try to do here, if this cooperates, is okay, we all copied it out. And what I'm going to do is I'm going to just stretch it out a bit. Okay, so we can describe a certain type of behavior here. This is through this reduced section here. The elongation is distributed across that reduced section. So we call that uniform deformation. And say if we aren't be careful, we can say an issue, this is uniform elastic. So if I identify that as region one, well on this curve over here, region one would span from the start of this curve all the way to the end of the non-linear elastic region, where it starts to accumulate plastic deformation. Alright, so that's fine. What if I continue to load beyond that, so what I'm going to do is I'm going to put another sample over there. Okay, and I'm going to stretch that, and I'm going to stretch it even more. So now what I'm trying to describe is what's happening in this region here. It's starting to plastically deform. It's permanently forming. It's permanently changing the fracture that wasn't supposed to happen. The sample is permanently getting longer. But it is still uniform. So I'll call that two. I'll identify that over here as two. So then the big question is still is, well what's happening there at the peak of the curve? And so what happens at the peak of the curve is this. Okay, so I'm going to copy one of these samples there. And I'm going to give myself a little extra space here to work with. So I'm going to actually copy that sample over here. And then I'll try to replicate what we had done up to the UTS. So this sample has gotten significantly longer. Right, we'll appreciate that. So this is, you know, at the UTS. But why does the engineering stress decrease after the UTS? And that's what I want to show you here by adding something to this. So somewhere inside the, inside this specimen in the reduced section, you get a little localized deformation. That plastic deformation is no longer evenly distributed. Suddenly in a small place gets smaller. Okay, that might look a little bit like a neck. You know, neck of an animal or something like that or a human. No, it doesn't really. But it's called a neck. That's actually what we described. So at the UTS, we could say that we have the onset or the beginning of necking. And it's because of this sudden decrease in cross sectional area. The area gets very small. That we see the engineering stress decreasing. So the engineering stress decreases. And it decreases because the area gets so small here. But remember, this equation is sigma is equal to force over a knot. It's a constant. So really what we're observing is the force decreasing. The force decreases because the cross sectional area gets so small. If I were to plot for you the so-called true stress, that is the stress that the material is actually experiencing. It would look something like this. But we're not going to explore that actually in this course. But that would be the stress that the sand material is actually experiencing in through there. And in fact, it's interesting to note that the metal actually continues to get stronger or to strengthen. Even though we see this engineering stress decrease, that's only because the cross sectional area has gotten so small there. So this to finally just give you the last little bit of terminology. This type of deformation here, the necking is referred to as localized plastic deformation. Localized plastic. Okay, great. Thanks a lot.