[SOUND] Hi and welcome back. In today's module, we're going to start looking at fluctuating stresses. Fluctuating stresses are different than fully reversible, so we're going to need to learn how to quantify them. And at the end of this module, I would like for you to be able to calculate the alternating and midrange stresses in fluctuating stresses. So let's get started. So far in Failure Theories, we've taken a look at static failure theories, which we completed in unit one and now in unit three we're looking at fatigue. And we're focused on the stress life method of fatigue analysis. And we've completed how to study fully reversible stresses. But life is rarely that simple, so now we're going to get into more complex loading by looking at fluctuating stresses. And then at the end of this course, we'll look at varying stresses. So, let's take a look at the differences between fully reversed stresses and fluctuating stresses. For fully reversed stresses, over here at the top, what happens is you go from, say, 20 ksi down to negative 20 ksi and then back to 20 ksi, right? So your stress amplitudes are always equal and your mean stress, so if I were to average these stresses it's always 0. So I'm always going from 40 to negative 40, or 80 to negative 80, or 50 to negative 50, and that's a great place to start. And the analysis is relatively straightforward and we can approximate the SN Curve for fully reversible stresses using these equations. However, there are a lot of situations where your loading is more complex so it's not this fully reversible. And the next level of loading, the next level in terms of complexity is fluctuating loading or fluctuating stresses. And that's where maybe I start out and I cycle up to 40 ksi, but maybe I only cycle down to -20 ksi and then I go back to 40 ksi and so forth and so on. This pattern is going to repeat, so we don't have varying stresses, but they're no longer fully reversible. So the question is now here we had this sigma reversible to plug into these equations. And here, we don't really have a sigma reversible, so how do we quantify this type of stresses or this type of loading? And so let's look at the answer. So here we have our fluctuating stresses and what we can do is we can quantify these stresses by looking at the maximum stresses and the minimum stresses. So our minimum stresses in this case are -20 ksi and our max stress in this case is 40 ksi. We see those right here and right here. And using those maxs and mins we can start to quantify the stresses a little more. So, we can look and we can fully characterize this type of fluctuating loads or fluctuating stresses using something called the mid range stress. So that's essentially the average stress. It's the maximum stress plus the minimum stress divided by two. So in this case, 40 + -20 divided by 2 is going to be 10 and that's my mid range stress right here. We can see 10. Now the other component to this is we're going to quantify an alternating stress. And so the alternating stress can be thought of as the amplitude of this stress curve. And an alternating stress is the maximum stress minus the minimum stress divided by 2, which gives you the amplitude of this curve. So in this case, it would be 40- -20 divided by 2, and in this case our amplitude is 30. Our alternating stress, rather, is 30 ksi, right? So 40 minus 10, that gives us 30, 10 minus -20 gives us 30. And so, using the midrange stress and the alternating stress, we can fully quantify a fluctuating stress. Now, in the next lesson, we're going to learn something called the Modified Goodman equation. And that's going to help us use these midrange and alternating stresses to determine how much life is remaining in the part and if it's in an infinite life or a finite life range. Some things to keep in mind where students often get confused in midrange and alternating stresses, is if you have any of type of discontinuity where you're changing diameters near the fillet radius or you have a hole or maybe you have a key in a shaft. You're going to need to use a fatigue stress concentration factor. And so students get it confused. Should I apply the stress concentration factor to just the midrange stress or just the alternating stress? And in this class, we're going to simplify life a little bit and we're going to assume that there's no plastic strain at the notch. And in that case, you can apply the stress concentration factor to both the alternating and the mid-range stresses. Now, if you're designing in a way where the plastic strain at the notch can't be avoided, so you're going to get some sort of plastic deformation at that stress concentration factor. Then you can go ahead, if you're going to act conservatively, you can assume that you just apply the stress concentration factor to the alternating stress and not to the midrange stress because the midrange stress is kind of a static component. But there's some other methodologies that you can also utilize in this case that can be found in Shigley's machine design textbook. However, here in this course, we're going to simplify life and we're going to assume that there's no plastic strain at the notch and so you apply the stress concentration factor to both the alternating and the mid range stresses. Now ideally, again, what we're doing with these equations is we're modeling a material and we're trying to predict its behavior using models, right? The golden standard or best practice is always to test and to test with your actual geometry configuration. So here in Mil-Handbook 5J you can see they've run fatigue cycle tests and it says right here that the Kt, so their stress concentration factor is 2. And then they give you the actual geometry of that stress concentration factor up here and so this is really nice because your stress concentration factor is already built into the load. If you can test with a fluctuating load, that's even better, so if you're testing with your actual loading and the actual number of cycles. And here the stress ratio of -1.00 means it's fully reversed, but they also have a stress ratio of 0.54, which would be more of a fluctuating situation. And you can see for this material, this is 4340 steel, they've tested both a KT of 2 and 3. So, sometimes you can go and find test data with your actual stress concentration factors, built into the test and if you can find it and use it, that's the best way to go. A lot of times you won't be able to find that data, or maybe you're trying to run analysis to see if your part is going to survive the testing, which will come later. In which case you can calculate with the stress concentration factor. So, that's it for today's module. Next module, we're going to take the alternating stresses and the midrange stresses and look at the Goodman diagram and the modified Goodman Equation and figure out how to determine if you're in an infinite life region or a finite life region, and how much life is remaining. I'll see you next time. [SOUND]