And finally, let's look at the practical application of the fracture toughness in distinguishing between what I call good fracture and bad fracture, a play of good and evil. And now we can appreciate exactly what's going on overall, and why we see a dashed line up here and we see a dashed line over here because those are mechanical responses that will not happen because the other possibility is occurring. And what's the other possibility? Well for very small flaw sizes. The experiment is going to, if this surface crack is small enough, and the fracture toughness value is large enough, then the experiment will really look like our conventional one. For all practical purposes, the flaw is subcritical, it's below the critical size, so as a result, it's as if it's not there. And if you stop and think about it, even in the most perfectly machined samples, no matter how smooth, and I'll go back and kind of colorize our original test here, just to suggest that if we were to look at those, that outer surface of a machine cylindrical sample that we're doing tensile testing on. And under a very high powered microscope, we'll see some variations, some machining grooves that are cut into the material that's not absolutely atomically smooth on the surface. It's a little bit of machining roughness, and those discontinuities, those surface defects and notches if you will, microscopic-scale notches, are not causing a problem. Again, it's as if it's a flaw-free sample. So only when that flaw becomes some significant size we begin to worry about it. And again, until it's a critical size, it's as if the flaw is not there. So it is essentially, effectively, a flaw-free surface. But once we're beyond the critical flaw side, then we see the solid line indicating that the fracture toughness equation is dominating. And so as we load the sample, as we did over here, as we increase the stress up to some point, we're going to reach a stress. For a given flaw size where the material's gonna break. And again, the insidious part is this is flaw-induced fracture. It's gonna happen very rapidly. In fact, the better term for this is fast fracture, catastrophic fast fracture. So again, we wanna really put some intense language on this. We want to emphasize and cannot over-emphasize, and we'll get right down to the nitty gritty here, this is bad. Can we be more explicit than that? And this is good. So, we suddenly are dealing with a play of good and evil, here. We now have, for this case, over here, as long as the flaw is sub-critical, we're going to make it. To the yield stress. We're going to make it to the yield stress so the material is going to continue to deform and it's going to start to show observable amounts of plastic deformation. And again that's what we mean by general yielding. Again, the reason that's good is that it's not ideal, that we probably don't want to distort the dimensions of this part. But as long as it doesn't catastrophically fail, it gives us a kind of practical early warning. So in other words, if we're using some steel structure and say some small bridge and we drive a truck across that and we see the bridge is starting to buckle a little bit under that weight, that's an early warning that we have to go back to the drawing board and make that bridge stronger. What we don't want, if there's some critical flaw, is for the truck to drive across that bridge, and suddenly, the whole thing collapses, as if it's made out of glass at a very fast fracture.