 Hello. So in this video, I'm going to talk about the stress strain curve. The stress strain curve is a common tool that we would use to better understand material properties for a variety of materials, primarily in the in the metal family. But it's a useful tool in that it allows us to, you know, take experimental data and visualize it and kind of understand what's going on. So a stress strain curve would be developed typically using a tensile test machine by measuring the load that we apply to a test specimen and then the deflection that it undergoes. So this this process then produces load deflection data which we can then turn into to turn into other data like stress and strain if we know the initial condition. So if we know the area, cross-sectional area of the test specimen and the initial gauge length, we can, you know, use that to get more information about the curve or about the stress in the strain. So I'm going to go ahead and bring up my notes. And I have already pasted in here an image of a of us example curve probably for a ductile material just based on on what it looks like. So typically, or some of the typical features that we would expect to find are this you know linear elastic region where the the stress increases at a constant rate as strain increases, a yielding phase so where we see the yield behavior happening, some strain hardening where the stress continues to increase, some peak, and then we have necking and this is you know if you're testing a ductile material you you see that necking behavior where the material starts to thin down until it eventually breaks. So there's a lot of useful things that we can get from here as we we find you know the information that we need for our analysis. So typically we might pull from this you know point this max point the ultimate stress of course we might find another common property that we want is the yield stress which we can pull off of there and that's all great. Also as I'm sure you're familiar with the the elastic modulus or the Young's modulus or the modulus of elasticity whichever word you want to use we can pull from the slope of this linear elastic region of the curve and we take you know the rise over run of that in order to give us stress over strain and we typically call that E for that elastic modulus and again that's that's a useful tool for us. So again this this material is is just kind of an or this excuse me curve is just kind of an example curve for you know a ductile material. Of course they don't all look exactly like this sometimes we might see we might see curves that if I can get a different color up here we might see curves that you know after this linear elastic region they kind of instead of having this you know steep bend they might just kind of curve over like this until there's a fracture you know that might be be more common of like an aluminum alloy or something like that compared to a steel or like a low carbon steel and you know it's not always easy to see where that that yield point begins to occur of course you know looking at this curve we can see okay it's straight straight straight and then eventually it it begins to to curve over and that might give us some information. One thing that we might use and one kind of standard for finding the yield in that in that situation we might use what's called the the 0.2 percent offset so basically what that means is if we come down here to this bottom corner we find where the strain is 0.2 percent so you know I've probably exaggerated here it's probably much closer to to our line but if we take this and we we go up from there well well I can't draw a straight line to save myself but if we go up from there and find where that crosses then we might say okay that's the yield stress based on based on this 0.2 percent offset method where the slope of this offset line has the same slope as our linear elastic region just offset by that 0.2 percent of strain so that's that's a way that we might find that and then again we call this region the linear elastic region basically up until we start to see yielding that's what we look for there ductile failures and the reason we see necking like this generally due to dislocation of the molecule so if I have my you know tensile specimen and I'm applying a load to it what I'm really seeing is some dislocation plane typically pretty close to a 45 degree angle and I might see slippage of my molecules along that plane so if I you know kind of zoomed in I'm going to draw some some molecules on here shade one of them to highlight it that's why it doesn't like um do something like this I have these molecules and if I get a dislocation basically what's happening is say this top row moves over until those two dark ones uh do two shaded ones are aligned and eventually until that molecule slipped past the other one and it's it's a dislocation of the molecule so they slip relative to each other move over a jump and and that eventually causes that necking and that you know tend to be that um conical shaped failure so when you have a ductile material and you pull it in tension it fails along that 45 degree angle and we can see that when we you know closely inspect the tensile specimen now if I compare that all of this to to what I might expect for a brittle material for a brittle material I'm going to get much more of a much more of a sharper line gosh a sharper line and maybe it fails like that with very little in in the way of strain much less strain than we might see with stress and actually if I was drawing this accurately I'd probably go much higher on the stress because brittle materials tend to have a um higher stress capacity while having a much lower strain capacity and so typically this this ultimate strength of a brittle material is is kind of the the main thing that we need to consider and when I'm looking at a brittle material loading it under stress I'm not going to get that 45 degree slip I'm going to get more of a fracture which is right across the middle um parallel I guess or excuse me perpendicular to the direction of the load being applied and in that case my molecules that I'm that I'm looking at instead of slipping along that 45 degree they're really just separating and kind of you know cracking across that so it's it's a it's a higher stress because the force is required to separate those molecules would be higher than than just to cause them to slip from one to the other you have to break those molecular forces in order to get that that failure to occur now if I look at another chart which I'll put up here in a second we can get some interesting information from these these charts too so again I've just got a slightly different version of this here much simpler version which shows a brittle versus a ductile material and the key point I want to make here is that this area under the curve equals absorbed energy so that's something we call toughness it's the ability of the material to absorb energy so as I deform it as I you know take a hammer to it whatever I'm doing I'm you know causing all sorts of strain and dislocations within the molecules which is basically energy that gets stored in the material and ductile materials are much tougher which you know we might expect we can smash things that are ductile like steel things with a hammer and not expect them to break much more readily than we would you know smash a brittle material like glass and you know expect it to be able to absorb that so we can see that when we look at this the strain energy or this this area under the curve and it's the energy that the material is willing to to accept before it eventually fails and mostly the things that we want to consider are or keep in mind are all of these different quantities that we can pull off from here I do want to just while I have this picture up mentioned again you know we have what we consider the elastic region which is everything to the right and then we have the plastic region which is everything to the left and basically what we're seeing is which deformations can be recovered versus which ones can't so I'm talking specifically about ductile materials here when we say something has elastic deformation basically what we're saying is we expect that that deformation can be recovered so if I release the load it'll go back to its original shape once I've plastically deformed something then we say that that that deformation isn't going to be recovered right if I release my the load that I've applied to it some of the the shape will be recovered but not all of it right and we can actually kind of see that like if I am traveling along this curve as I apply greater and greater load to my part we could actually say let's stop here and go back on a line that's you know if I could draw parallel would be parallel to this linear elastic region and this this area here is basically the the elastic recovery so that's deformation that gets recovered when the load is removed but all of this this deformation down here that isn't recovered that's that's the plastic deformation so that's the the deformation that isn't going to be recovered now when we're designing something you know we can take both of these things into account and it really depends on the application in terms of what matters right sometimes or many times our applications require that nothing yields right so we don't observe any plastic deformation and that's you know critical for a lot of things right things we don't want to permanently deform and not go back to their original shape however there are also applications where plastic deformation is okay as long as it doesn't break right you know you could think of like safety features you know if I have a one-time use you know pin on a on a roller coaster and it's intended to take a certain amount of load and you know not you know not fail it's like a last-ditch safety effort or something like that maybe an emergency break it's perfectly fine if it gets plastically deformed because as soon as it's used it's going to be thrown out and replaced but we don't want it to break obviously you know because uh say it's you know this emergency break if it fails then then we have bigger problems so we might you know consider all those different things and of course deformation in in and of itself might be a failure we might not even be all that concerned about stress we might be concerned about how much something deforms so if I have two gears that are meshing and they're mounted on a shaft and or on shafts and one of those shafts deforms too much and it brings the gears out of mesh well that might be a problem right for my application so sometimes deformation is the thing that we have to worry about and all of these things you know are some things things that we might want to consider so that kind of gives my my broad overview of you know what we're looking at when we look at a stress strain curve we're going to get into stress here shortly in the next video and then we're going to start talking about you know once we know a stress what what is what is it that causes failure how do we know when that stress causes failure um so yeah I think that covers what I wanted to cover today all right thank you very much