And now we're going to go to a video lecture and introduce the definition of fatigue in a formal way, and see how that has an interesting relationship to the concept of fracture toughness that we introduced earlier. So now let's look at another type of test, which is a variation on our traditional tensile test. And that's involved in the definition of fatigue. Just like ourselves, late in the day, we'll feel tired. Materials get tired, too. They fatigue in the following and specific way. So it's simply saying that after several cycles of use, that a material that we would expect it to bear that load application under normal circumstances, under a single stress application. After many, many cycles, suddenly, shall we say, gets tired and fails. And this can happen well below the tinsel stress which we tend to associate with the maximum stress that engineering material can withstand under the definition of the traditional parameters associated with the tinsel test. So of those big four parameters, the tensile stress is again that maximum or ultimate tensile stress that is maintained over the course of the stress application. So let's again do as we did before. Remind ourselves again we now know this by heart, but let's just draw again a stress-strain curve. The elastic portion, the plastic portion and ultimate failure. So now let's just colorize this. And now, consider what happens if we do this experiment, but stop well below the tinsel stress, again remember out tinsel stress was up here. Let's say that we now simply load the material way below the tensile stress, maybe halfway up to the yield stress. So we're very safely unambiguously within the elastic portion of the material. We'll also draw in the yield strength here. So tensile strength yield strength, we're going to stop the load application right there about half way up to the yield strength so it should be absolutely no problem. The only thing different now is that as we learned in the earliest discussion of the tensile the test and the nature of elastic deformation, which is temporary deformation. Plastic deformation is permanent deformation. Elastic deformation is temporary deformation. So if we do this loading up to this very benign level, In which expect no damage at all. We've just disturbed the material with a very, very small amount of elastic extension and then we take the load off and we just go right back to the origin again. So again, no harm whatsoever. But let's say we wait a few minutes and we decide to do that test again and for whatever reason, we decide again to stop at the midpoint. And we only have, again, loss of destination, we remove the load and it goes back to the origin again. Again, pretty boring stuff. But now, let's do the following. We'll add another color here just to round this out. Lets now consider the origin and if we're gonna keep track of this, lets consider now a time access that comes out of the board. And so now let's look at the stress-time axis. And that's basically what the sketch is here, originally on the screen. So what we have is the stress, relative to the tensile strength of the material, over a long period of time. And so our point is, just as we looked at a fresh way at the stress-strain curve when we're talking about creep deformation back in our discussion about mechanical properties, now we're looking at the stress-stain curve in a novel way, in this case by looking at a third axis, at a time axis coming out of the plane of the stress-stain curve. So now we have plane of the, again the stress versus time plane, that curve. Well, again as I had suggested if we took a few seconds to stress the material up to, now our suggestion about half the yield strength. Release the stress, again the strain on the material would have gone back to zero and then just do this sawtooth effort all along and perhaps a few million times we do this. All of a sudden we have something that reminds us of this bad story. The catastrophic failure that we talked about in the discussion of fracture toughness. Now we have a catastrophic brittle fracture of this material that we thought was pretty ductile and would have had a very benign general yielding type of behavior that would have been desirable.