 Hello everyone. In this video I want to talk about fatigue. And fatigue is another form of dynamic loading failure that is probably the most common form of failure that we would find in a lot of machine parts. So fatigue is basically failure of a part due to repeated cyclical style loading. So usually the failure will start at some sort of micro crack and that crack slowly over time propagates until it it results in a catastrophic failure. And you know you've you've all experienced this most likely if you take a paper clip and you sit there and repeatedly bend it back and forth so that we're cyclically loading it eventually it'll break doing that right. So we've experienced fatigue and that is a fatigue failure when we do that. And that's kind of what makes fatigue interesting is that it's hard to predict. We don't always know exactly where the failure will occur. Oftentimes it'll occur at any place there's any sort of imperfect imperfection. So like a defect in the material an inclusion or something that was you know due to the the casting of the metal or or anything like that surface flaws you know sometimes just surface roughness you know it's a sand cast part so it's got a pretty rough surface that gives a lot of opportunities for kind of microscopic problems. Holes anywhere there's a hole or a cut that's made threads have been tapped in the material. All of those kind of defects can lead to the initiation of a fatigue failure. So if we were to kind of visualize what a fatigue failure might look like you know say we have a round shaft we can often if we you know have one that's broken we can often tell if there was fatigue and a fatigue failure because we'll see a pattern like a striate striation I don't know if I'm using that word right kind of pattern where it'll propagate out from some initial starting point and it'll continue to do that and basically this is just the growth of the crack over time and this could take hours it could take years you know whatever depending on what the load is and and how fast it's cycling that could take a while and basically what's happening is this crack is reducing the cross sectional area of the part and therefore reducing its strength by increasing the stress right if the area gets smaller than the stress gets larger for the same applied load and then eventually it fractures and so we can see this a lot of times when we look at parts we can see this kind of slow growth it might be smooth because it's you know been moving while these two parts were actually had a crack between them there's been moving and and kind of small you know rubbing between the two which would smooth out that surface until eventually that crack was large enough that it caused a catastrophic fracture and this is a problem right because usually if it's when it fatigues to failure it fails at a point below its yield stress so while static loading analysis may predict that this part would be perfectly fine under a fatigue analysis it actually fails right so like I said it's it's pretty difficult to to actually predict when this is going to happen you know just analytically we can't just apply standard mechanical engineering theory to a part because we don't know where the where the imperfections are so instead what's been done is they do standard testing standardized testing in order to generate a bunch of data that they can apply statistics to and give us a an opportunity for a best guess at when a part is going to fail so this is just a on the screen this is a an image from the textbook on what a fatigue test might look like and you can see there's a motor for rotating that shaft and then we have a test specimen and in the middle of our diagram there's this machined area which gives a you know very precisely known failure location so it's it's smaller diameter right which is often what we do with our test specimens you know to make sure that they fail where we think they'll fail or where we want them to fail and then it's got these loads that are applied or a load that's applied to to provide a stress at that location so it's going to introduce a bending stress at that location so then as you can imagine with bending stress just as an example there's tensile stress on one side compressive stress on the other side and neutral axis is of course in the middle so as this sample rotates any one particular spot on the surface of that shaft as it goes around passes through tensile loading compressive loading and zero loading as it travels around so we can spin this at you know however many rpm we want to and subject it to that many cycles of loading so we do that run it for you know hundreds of thousands millions of cycles with different varying amounts of load through the application of weight until it fails and then you know that gets a little data data point check mark on on our you know spreadsheet I guess and then we do it again and then we do it again and then we do it again and you generate this data until you have enough that you can you know with some level of statistical accuracy can predict when an unknown part is going to fail so great that's the general process and then what we end up getting from that and I'm just going to put this here but I'm going to talk about it in in later videos as well what we end up getting from that is what we call an endurance limit and the endurance limit actually the first endurance limit I'll call sn prime but doesn't really matter they're both kind of the same thing uh this endurance limit tells us you know what we can expect under these these particular ideal conditions right so sn prime is kind of under test conditions that's what we predict statistically and then we can correct that because again we're using statistics and most of the time we're not designing and installing parts in perfectly ideal test style conditions so we introduce all these correction factors so we have c sub l which is a load factor this corrects for the type of load some typing types of load are more susceptible to imperfections in the material just based on how the stress is distributed we have a gradient factor which is kind of dependent primarily on the size of the part so again you know a larger part has greater chance of having material imperfections and things we have a surface factor I mentioned that many times fatigue like a micro crack um in fatigue might start at a surface imperfection so depending on how our part was made we might have a higher susceptibility to surface imperfections we have a temperature correction um primarily because higher temperature materials uh cause a decrease in the strength or higher temperatures because a decrease in the material strength um so this can correct for that over you know certain temperatures and then we have a reliability factor so really what this is taking into account is that the the the specification for sn prime which is the endurance limit from our experiment is based on a a certain set reliability so we kind of limit what we you know what we say by saying oh you know 90 percent of parts will survive by default right or not by default but by statistical prediction based on our experiment and the number that we put out there however maybe you're doing an application where you need greater reliability you know a lot of lives are at stake um that sort of thing very expensive so you can increase that reliability by reducing your endurance limit your corrected endurance limit which is this sn so that gets factored into this to this c sub r and i'll talk about kind of a little bit more about all of these but each one of these factors is trying to account for different things and build in um a statistical analysis or statistical understanding of whether or not we would predict part failure all right thanks everyone