 Hi everyone. So continuing my discussion of fatigue failure in parts, I mentioned previously that we gather our information about when we can predict a fatigue failure based on these repeated experiments that generate a whole bunch of data that we can then analyze to determine whether or not something will fail and how we can predict whether the part that we're designing will fail based on that information. So I pulled up a few figures here from the textbook to talk about where we can get this information. And of course the data presented in the textbook is just one source of information. We could find other sources of data and likely would when we're trying to pick the criteria for a specific thing that we're actually working on. But it's a good example set. So this is what a fatigue strength versus number of cycles plot might look like if we collect a bunch of data. So what we can see here is that on the left hand side we have a bunch of these data points, right? And they're all clustered here under or at a low number of cycles. And then there's a few out here at a very high number of cycles. And basically what this data then tells us is that, now obviously there's only three data points out here in a real set of data that we'd be using for this, we obviously rely on much more than three tests to determine that. But what this tells us is that the strength as we continue to increase the number of cycles, the strength that our part will survive until goes down very quickly. And then at some point the part seemed to last a really long time. And note here it's not 100 cycles, it's 100 times 10 to the sixth cycles. So that's what like 100 million cycles, right? Quite a bit. And it gets easier to visualize this data if we change the axes a little bit. So this is another view of this data. But now using a log scale on the x-axis. So all that data that was initially to the squeezed over in the left hand side is now here kind of in the middle. And we can see there's a curve passing through many of the data points that we could plot. And then again we have these data points out to the right, which look like they lasted quite a long time. Now if I scroll down again, I can change my axes again to say, well what if we have a log-log curve? And that means putting a log on the y-axis in addition to the x-axis. And again we plot this same data. And what we now find is that, okay, we get kind of this linear line. And then eventually it becomes a horizontal flat line out at what we are calling the endurance limit. And the nice thing about this version of the chart is that it gives us kind of a clear transition point, right? A clear number of cycles transition point. And we can see, you know, the data a little bit more clearly. Really what we're interested in here is this SN prime, which is under these ideal test conditions. What is the the long life endurance limit? So if I wanted to put this part into into a service life effectively forever, or at least high enough number of cycles that we'd never never observe the failure, then I want to stay above this endurance limit. Or excuse me, below this endurance limit for the stress that I apply. This would be the limit on the stress or the limit imposed on the load that I apply to my part. And that's all good information. So once we know that, we can do something with it. Now of course, when we're actually designing a part, we're not likely to design something for infinite life, right? That's typically expensive. We might design something for a predictable amount of life. And again that's another situation that we'll talk about later. So this is another plot of some data. And this is specifically for rot steel. So it's a specific material set of material conditions. And it gives us a data set for that. And it's something that we can use then in that they took all these data points. And of course, as we would expect with anything that's, you know, a little bit unpredictable, there's a wide range, right? It's not just, you know, everything falls on a nice line and plots cleanly. There's a range of values at each life cycle for when these parts failed and what sort of stress they're under when they failed. So what this line represents then is information about, you know, I think in this data set, it's 90 percent reliability. So we can expect roughly 90 percent of our parts to survive, not fail, under these conditions, if we stay below this line. Because all of these dots represent failures during the experiment. And the dots below the line represent ones that didn't fail. So, or I think I said that backwards, but yeah, so the ones above that, well, I can scratch that, take that back. All of the dots represent failures, right? The ones above the line are ones that lasted longer than what this, you know, data is suggesting for that limit, that endurance limit. The ones below the line didn't even make it to that point that this data is providing. But again, it's because we're using this 90 percent reliability idea to get that information. So there's kind of two key things that we would often, two bits of information that we would often use when working with this kind of data. One is over here on the left hand side, we have the 10 to the third life. So down here on the x-axis, this is 10 to the third cycles. So that's 1000 cycles. And we get some information, they're saying that the endurance limit at 10 to the third would be 0.9 SU, or, you know, these other measures, depending on what we know, for example, Brinell hardness or something like that. And then we have this data out here, which is for anything greater than 10 to the sixth cycles. So a million cycles, we have SN prime and SN prime is going to be 0.5 times the ultimate strength of our material, or again, in hardness values or in relation to the hardness. And the nice thing about these two data points is we really only need these two data points to define the whole chart, right? Because these are straight lines, if we can plot this point, and we can plot this point here at 10 to the sixth, then we can define this whole chart, the line connecting these two data points, and then it's a horizontal line over from there. So that gives us a lot of information. And we can read off of this style of chart the bits that we need, the SN prime value in terms of ultimate strength and the 10 to the third life, again, in terms of the ultimate strength, and we can use those to do calculations. All right, thank you.