Hello, this is Professor Cummings and I wanted to continue this series on stress and strain, you know, strength of materials. Today I wanted to go a little bit further, take those concepts and run with them a little bit. So start off with a little bit of review. What we started off last time, or in the last part of the series, was a definition of stress, which was just the load over an area, in this case the load that you're designing for, and a cross-sectional area of the point of interest.
We also went over a little bit of what strain was, which was simply a change in load. length over its original length you know so whatever the length was that you got to change to minus the original length all over the original length so it's a more of a percent it also strain doesn't have any dimensions or any units to it we also went over different types of load a compressive load you think of that as something being squeezed uh tensile load something being pulled apart and then shear load you know this would be what happens at a lot of joints a lot of bolts, a lot of fasteners, they end up with a load pulling it crossways, kind of scissored across the area. In all of these there's a load and there's a cross sectional area and they all have their own version of stress. Stress and strain, how much they're distorting.
Now there's one more concept I want to bring up, one more idea of stress and strain and how you actually look at stress and strain, how they work together and what a material goes through. as you have a increasing strain or increasing amount of stress and strain on that material. A tool that is often times used for this is a stress-strain curve. So what we have is a stress-strain curve.
Every material can have this, particularly ductal materials have a stress-strain curve and they typically follow a similar profile of a stress-strain curve. So it's something that a stress-strain curve looks at how much it reacts. under load it has different stages to it and each stage gives you some idea as to what's going on with that material and some ideas to where you are in terms of how your your part is being designed or whatever it is you're trying to accomplish you know all the way from design performance all up to failure Now you could take this stress-strain curve and think of it as four primary sections. You know, the first section is this. Let me use this pen here.
The first section would be in this section here. You know, we can call this... the elastic section and actually it's a difference between two sides of the curve. One is the elastic region over here the first section and the other rest of this is a plastic section and that's very significant especially in terms of design but just looking at this from the first section of the stress-derain curve that first section is the elastic region and it's also known as the hooks region or the proportional limit the significance of that is a material that's under load while so long as in this strain or in excuse me in this in this limit it should recover and come back to its original shape and you can see this portion is also a very linear portion you know so it's it's very proportional hence the name proportional limit and you can see also why it is called the hooks limit if you understand hooks law because it does react just like a spring so it's the that's the elastic portion the second portion of it is known as the yield so it's just the yield limit and materials you know this area might be a little different depending on the material sometimes it's a little longer sometimes a little shorter and all that means is that it's a portion of the material where you have permanently deformed it you've permanently deformed the material it's not going to snap back you know however much it's been stretched it's going to stay in this region The next section would be called strain hardening.
You can see it's already laid out here. This whole third section is known as strain hardening. This strain hardening section is a very unique section because you're changing the crystal structure of the material. You're putting enough strain on the material that it actually changes the crystal structure of the material.
actually is changing the crystal structure in this section you're actually making the material harder and tougher and that actually is can have a very useful there's actually something very useful of having that and i'll go into it a little bit later because that does you know that is a section of it and it's you know it's not necessarily a bad thing and then the last section over here is what's known as necking. Now once you've gone to this section you know you have the material is doing nothing but getting weaker. It's moving towards failure.
Here right between strain hardening and necking is what's known as the ultimate strain. The ultimate strength means that the material has gotten the strongest it's going to get. You know you've strained it to the point where it's stronger than it's going to ever be because you know the strain hardening.
stronger than it's ever going to be strong strongest that it's ever going to be and from that point it goes down to the snaking stage where it's just getting the more strain the less stress it's able to handle and it literally will start to neck down which you kind of kind of goes back to this original equation you know the smaller the area the greater the strain or the greater the stress until finally you get a rupture so what does this look like so you've got these four stages elastic, yield, strain, harden and necking so what do these look like in real life in real life when you're going through these different stages you can start with the elastic stage this is where you want to do your design work if you're designing a product you're designing in this case leafs springs for a vehicle you want to be within this elastic region this is where you know you're safe you know your parts are going to always be the same size you know that you're not going to have any type of distortion any kind of potential rupture you know you're going to recover from whatever amount of load you're in now when you do this in terms of a design you need to know the capacity you need to know all your geometry so you can actually state here is the limits that you can put on this particular component and again that's where you do most of your design work most of your engineering design takes place in the elastic region now when you're looking at something such as yielding so you have a material you've actually gone beyond the you put enough strain on it to where you're beyond this elastic stage you're out of the proportional limit you're out of the hooks limit and you have yielded the material you have permanently deformed it you've permanently deformed it and this you end up with with a you know usually this is the material is either dented or stretched or somehow it's been distorted or just one point i want to bring back here of young's modulus you know young's modulus all that is when talking about this elastic limit it's just the ratio of stress to strain if you look at any handbook on materials when giving you a material to give you a design limit to work within they'll give you this slope and since this is a proportional limit you know that slope is going to change or isn't going to change all throughout the process throughout since it is linear and you know it's a good tool when you do any type of design work based on a material because it is very material specific okay so as far as the next limit so that's what happens in the yield you've actually distorted it changed it permanently uh change the way it's going to be shaped and the material has been yielded it's not going to come back from that now strain hardening i'd mentioned that that was a unique section strain hardening hardening, you know it's not necessarily bad. All materials go through this when you apply enough strain to them. And like I said you're changing the crystal structure. And this is what you're doing when you're cold forming or cold drawing material.
You're actually going through a strain hardening stage. You're actually going through a strain hardening stage, changing the material and making it harder, making it stronger and usually that's going to be for some other manufacturing process or something you're going to do just before uh... just as the product is released this is good in terms of things such as a lot of tooling a lot of knives get strain hardened or cold worked you know because you want them to be stronger and closer to that ultimate tensile strength or ultimate yield strength ultimate tensile strength excuse me before it actually can potentially uh... fracture and the final stage again that's necking and you can see here we have a an axle on a vehicle that has fractured. A little easier to see.
So this material has been under a load or enough load, or maybe it's been damaged to where it just couldn't handle enough load, but it was brought to this stage where it actually fractured. You know, so that is... when it went through a necking station if you do some sort of failure analysis and you were to actually look at this section and see what you could see in terms of what that fracture looks like what some of the properties are you will see that it has been geometrically changed change, it's been molecularly changed down to the crystal level because it's gone through the strain hardening and you would be able to see some of the yielding that took place before it actually went through this fracture. So this is just a little bit more on stress and strain and strength of materials.
a little bit on the stress-strain curve and what each one of the four stages means. Again, this is Professor Cummings, and thanks for watching.