[MUSIC] Hi and welcome back. Today, we're going to go through Module 4, which is in the Unit 1 Material Properties and Design. So in Module 4, we're going to examine the modulus of elasticity of materials. Before you watch this module, I ask that you complete a knowledge check, and go ahead and work through Worksheet 1, and then check all of your answers. And if you have trouble with Worksheet 1 and you feel like you're really struggling to understand these concepts. It's probably a good idea to go back and review Dr. Whiteman's Mechanics of Materials 1, Fundamentals of Stress and Strain in Axial Loading modules. Specifically modules 9 and 10 will cover the stress-strain diagram. So the learning outcomes for this module is first to understand the quantitative and qualitative meanings of the modulus of elasticity. And then also to become familiar with common engineering material's values of the modulus of elasticity. Some assumptions that we're going to make in this module and also throughout this course is first that we're dealing with a isotopic material. So isotopic means non-directional. For example, steel is an isotopic material and its density, its strength and its modular to elasticity don't don't vary depending on the direction that you're loading it in. Where bone and certain composites tend to be very anisotropic materials and can have very different material properties, depending on the direction and type of loading you're applying. We're also going to assume that we're dealing with homogenous materials that have a uniform composition. So again, steel is a great example of this, it's iron that's been alloyed with carbon atoms and it's uniform throughout the steel. Unless otherwise specified in this course, you can assume that the design is occurring at room temperature. And primarily, in this course, we'll be looking at analysis that is valid for the elastic range. Which means that it's conforming to Hooke's law where stress is equal to your modulus of elasticity times strain. So, a quick review for a Stress-Strain diagram. So on the x-axis here, we have strain, and then on the y-axis, we have stress. And then you can see the loading curve occur throughout the diagram. So we also have the yield strength of the material and past the yield strength in this region right here. This is the plastic region where you'll get plastic deformation or permanent set when you remove the load. So when you removed the load from the object, the object will be permanently deformed in someway. Where in here we have the linear elastic region where you can remove the load and the object will go right back to the configuration it was in the beginning. So it's not permanently deforming or experiencing any permanent set, and this is typically the area we'll be running our analysis in. This linear elastic region. And then you remember the slope of the linear elastic regions is the modulus of elasticity. And that gives us the relationship that's Hooke's law, which is that stress is equal to the modulus of elasticity times the strain. And this is often the first thing students tell me when I asked them what is the modulus of elasticity? They'll say it's the stress divided by your strain. But as a mechanical engineer dealing with design, it's important to understand these material properties on a qualitative side as well. Which brings me to my next question, so how would you explain the elastic modulus to a third grader? So you can't use equations for a third grader, how would you explain this qualitatively to a third grader? Okay, so if we are trying to explain the Modulus of Elasticity to a third grader, a good way to do that is to think of it in terms of stiffness. So you can think of it as the stiffness of the material. Now this is not the geometric stiffness. Clearly, if you have a thick steel bar and then a bar that's made of the same exact steel that's thinner, the thick steel bar is going to be much thicker. But if we look at it just from a material perspective, taking geometry out of the equation, you can think of the modulus of elasticity as a stiffness. It's how easily does a material deform due to an applied load? And so let's think about this a little more, which would have a higher modulus of elasticity? Steel or rubber? So, we can actually run a really simple experiment. When I pull on steel, this is a paperclip that I've bent to be straight and I'm pulling on it, and you can see I really can't deform it at all, right? I can cause very little deformation in this x direction. But when I pull on rubber, it's very, very easy to cause deformation. So the modulus of elasticity for steel is much higher than that of rubber. Steel is much stiffer than rubber. And so some key takeaways from the lecture, the modulus of elasticity and this class will be the notation for it will be a capital E. The slope of the linear elastic region of the stress-strain curve is the modulus of elasticity. So stress is equal to your strain times your modulus. And then a measure of stiffness, the modulus of elasticity is really, can be thought of as a measure of stiffness. So for rubber we saw, which is very easy to deform, it's about 0.1 GPa. But steel, much, much, much harder to deform, so it's 200 GPa for steels. And this is a material property that's again intrinsic to the material. All right, so I'll see you guys next time. [SOUND]