[SOUND] Hi, this is Module 9 of Mechanics of Materials Part I. Today's learning outcome is to define and discuss something we're gonna call stress-strain diagrams. So as a review, we looked at axial centric loading where we applied an external force to a member. It stretched out and became long in length. We did a transverse cut. If we did a transverse cut, we found out that the normal force was equal to the external force. And we talked about concepts of stress, or force per unit area perpendicular to the cut surface. And strain, which was elongation per unit length. To examine material properties we can perform tension tests. In graphing the results, we will plot stress strain instead of force and change in length. This allows for the removal of geometry from the problem and allows the results to be used for different geometrical shapes of the same material. We will look at this diagram in more detail later in the module, but as an overview, here's what a typical tension test looks like. There is a linear elastic region where stress and strain are directly proportional to each other. And then the materials starts to yield until fracture occurs. So here's a video of typical tension test. The video starts of with a test specimen in a tension test apparatus. Notice that there is a gauge attached to the specimen to measure strain. As the load is increased, I've included the creation of what we will call the stress strain diagram. As the specimen is continually loaded, you'll notice that it starts to neck down or become smaller in diameter, until it finally fractures. The specimen used in this test is one quarter inch diameter steel. It's classified as 1018 hot rolled steel. This type of metal is typically used for things like machine parts or shafts like the driveshaft in cars. And steel is a ductile material, and we'll talk more about ductility in a minute. So let's go ahead and draw a normal stress-strain diagram for a typical tension test. I'll draw it for a typical ductile material like steel, which we just saw the test of. Remember, these diagrams are material dependent, you can find different diagrams for different materials just by searching stress-strain diagram on the Internet. Okay, we start by drawing strain on the x axis, and we'll plot stress on the y-axis. Now this is stress up here, sigma. And this is strain down here, which is epsilon. And we start off at 0 stress strain, and then we start to load our specimen. And this is gonna be an example of my specimen. Now, this is not a solid specimen, this is actually a spring. But I can't stretch a solid specimen to show the results I want to show. And so, this acts exactly the same way. There's a range in the spring, where if I load it, it snaps back. It's the elastic range, okay? So I put a load on, it stretches, and then it goes back. And we call this the linear elastic range because there's a direct proportionality between stress and strain. So, this is called the linear elastic region and it's directly proportional. Okay, so this is linear region. So the linear region ends at what we call the stress at the proportion limit. That's where stress is no longer beyond on that going to be directly related to strain. And the slope of this linear elastic region is E, or what's gonna be called Young's modulus, or the modulus of elasticity. And we'll talk more about that later on. >> Beyond the proportional range, we go into a small nonlinear range, where there's no longer direct proportionality. But we're still in an elastic region where we start, where we continue to recover all of the displacement that takes place. And so, this again, this is the, end of what we call the elastic region. So we call this the elastic region. And the end of the elastic region is called the yield stress. This is where any stress beyond this point is gonna produce permanent yield, or permanent set, permanent deformation. The body is not going to return back to its original position. And so, let me do an example here, with a smaller spring. Here I have the linear elastic region. I keep pulling it, and at some point If I pull it hard enough, it's not going to return to its original shape. And you can see here that it's not fully reformed, so it's starting to yield. After the yielding, we start to get a lot of strain for little or no increase in stress. And so, we go along, and this can be a very very long section, so I'm gonna put some marks here indicating that it could go on quite a ways, and we continue out. And this is called the perfectly plastic region cuz it's plastically deforming. And in fact if I go back to my spring here, okay? Once I get beyond the yield stress and I continue to get strain with very little additional force, you can see that I just start to plastic out. And so it just becomes perfectly plastic. And so, let's draw that. So this is the Perfectly plastic yielding. And then we get to a point where we start to get what's called strain hardening. And the strain or the stress goes up again. And so it starts to go up until we get to something called the ultimate stress. That's the highest amount of stress the material can take. So this is the ultimate stress At the end of the strain hardening. And so this section is strain hardening. And Then the specimen starts to neck down, or the diameter becomes smaller. And it continues to become smaller as you saw in the video clip, until it actually fractures. So we go along here until we get fracture. So, this section is called necking. Until we get to a point where the specimen fractures. So what I've drawn is the engineering or what we call the nominal stress. Remember, stress is equal to the force over the cross sectional area. And for engineering a normal stress, the area we say stays the same, but we know in this case that it doesn't. It necks down and so the n force becomes less and less and so this goes down until it fractures. Now if I wanted to plot true stress, it would actually continue to go up until it fractures. And that's because as it necks down for we're talking about the actual area which gets smaller and smaller. And so, the stress continues to get higher and higher. And so that's a good stress strain diagram for a ductile material. Here is another picture of it. And so we'll use this in the future. It's a little bit better diagram than what I've drawn. But this is a typical stress strain diagram. [SOUND]