 Hey everyone. So up until this point in fatigue, we've basically been talking about how to determine what the limit for our stress is under fatigue, under a fatigue situation. So anytime that we have cyclic loading, loading that's applied on and off or positive negative kind of any sort of fluctuating loading. And that's great. That's the first step. We need to figure out what the limit is. The next step then is to be able to take the stress that is actually applied to our part and compare it against that limit so that we can know if we're predicting failure or not. And there's another basic graphical tool that we'll use for that called the constant life fatigue diagram or sometimes called the Goodman diagram, which helps us kind of visualize what's going on and all the things we need to consider. So first I just want to talk about this idea that there is alternating loads. And the easiest example is probably the paperclip being bent back and forth. If I take my paperclip, don't have one, but if I take my paperclip, which we'll pretend is this pen, and I bend it back and forth, if I look at a spot on the top of the pen, it's going to be in compression and then tension and then compression and then tension and then compression and then tension until it in theory fails. And in that case, I probably as long as I'm going, you know, the same amount of force up and down, I probably am going to have a cyclic loading centered on zero, right? And that may be the case for a lot of problems or it may not be the case. There's nothing that says that the the average of my cyclic load has to be zero. So in this this plot that's on the screen, that's kind of what we're seeing is that, you know, I might have a mean stress or whatever that mean stress might be, it might be zero or it might be something else. And then I have an alternating stress. And, you know, in a standard sine wave, you know, we're probably familiar with amplitude and all of these sorts of things. The stress can go up and down. And it may or may not cross zero, depending on the relationship between the mean and the alternating stress. So those two things need to be known in order to kind of fully understand what's happening. And in the plot on the right, we can see that the mean stress is greater than the alternating stress, such that the stress never crosses zero, right? It's always, in this case, positive or intention. And this could be an example where we have, you know, more than one loading at the same time. So I might have a part that's being pulled, while also being cycled this way, in which case I may never cross below zero, even as I compress the top by bending it this way. If I'm also pulling, I may never actually drop below zero and put it in compression. So those two things kind of have to work together to help us understand what's going on. So once we know our mean and alternating stress for a situation, then we can employ this constant life fatigue diagram to kind of understand our situation. So this is an example of what that constant life fatigue diagram might look like. And basically all we do is we're pulling information from our SN curve, such as that 10 to the third cycle that I talked about, or limit that I talked about, and our endurance limit, which we usually say is, you know, 10 to the six. So anything there and above would be our endurance limit. And I've plotted those here and said that anything, those values slope down towards the ultimate strength on this tension side of the mean stress. And that gives me kind of this converging plot of blue lines that all meet at the ultimate strength, because nothing's going to exceed the ultimate strength. We're not going to exceed that and still have our part survive. So that is important to consider. And then we have a dashed line here plotted, I guess, dash dotted line, which has limits at the yield strength on both axes, and then connecting those lines. And the reason for that is that we can't exceed the yield strength, right? Yield generally comes from static loading, but if we exceed the yield strength, we're still going to yield, even if we have this cyclic dynamic loading. So we still have to kind of keep that in the back of our mind. So as you might imagine, we can, for any situation, as long as we know the mean and alternating stress, say I have a data point here that represents how I'm loading my part, I can say, okay, well, that's safe, right? It doesn't exceed any of these lines that represent my limits. This is safe, you know, for an infinite number of cycles. Now, and kind of interesting thing is I can, if I would were to dash in a line through that point from the origin, I could actually use this line as sort of a calculation of my safety factor. My safety factor is really a metric that says, you know, how close am I to failure? So if this is where the first failure would occur, if I'm interested in infinite life, then my safety factor is going to be the ratio of how far I've gone or how close I am to that dot over that total distance. Now, if infinite life isn't my interest, maybe I only need my part to last 1,000 cycles, then my failure point is out here. And I have a whole new scenario, right? I have a much higher safety factor if I'm not not very close to that part. So great. That gives me a good understanding of, or at least visually, graphically of what I'm looking at. And I can do that comparison. And this slope of this line is, you know, just the relationship between so rise is the alternating stress, run is the mean. And it gives me that relationship between what this looks like graphically, and then, you know, the mathematical equation. So if I know that slope, I can go ahead and write equations of these lines if I wanted to, and set them equal to each other and find where their intersection point is. And that would tell me, you know, what I'm looking at in terms of what I would expect for failure under these criteria. So just to kind of reiterate what this chart does for us, it allows us to take our limits, which are, you know, SN prime for, or SN for the, you know, long life endurance limit, you know, basically infinite cycles, or anything in between, you know, down to like 10 to the third or anywhere in between there. What that limit is, that's the limit on my stress. And then I look at my mean and my alternating stresses and plot them on the chart alongside my limit and do that comparison point. So am I exceeding my limit? Or am I not? So I kind of have the two sides that I have to figure out, what is my stress? What is my fatigue limit? And once I do that, I can, I can calculate what's happening for my part. All right, thank you.