And so let's continue the lecture now. And see how the Arrhenius relationship, introduced earlier in our discussion of diffusion, also plays a very important role in this very important mechanical property. And gives us a quantitative description of how creep deformation increases exponentially with increasing temperature. First of all, so called primary stage involves a kind of rapid increase in deformation and then as some of that, so we talked about cold working, this is sort of warm working. We now have additional thermally activated processes happening. We'll talk about what those processes might be in a moment. But we now are finding that as we are straining the material by these sup par undisclosed mechanisms, we're making it a little bit more difficult for more deformation to take place. So the strain rate drops off a bit and it reaches kind of a steady stage, so called secondary stage. Sometimes the material will actually fail at the end of this more or less linear region. But very often we'll see another, as the material starts to approach failure, various deformation processes are starting to kick in, and sometimes it'll uptick in the rate of strain, and then failure occurs. So, again, this is called creep deformation defined in a formal way as deformation occurring under a constant load that dead load over a long period of time. So again the is creeping along, creeping along in its deformation history. Well as we said it is thermally activated, so again as we had said early on when we introduced Svante Arrhenius and his extremely important contribution to science and technology, the realization that chemical reaction rates increase at an exponential rate by an equation of this sort. We said we would see many examples in the material sciences, and of course, we dwelt on the diffusion coefficient being our first. An excellent example of that, here we see the same thing again. If we think of that strain rate that's occurring in the fairly linear portion, obviously an easy slope to measure, that it follows the Arrhenius form. A pre-exponential constant and then the exponential term with the activation energy for this mechanism, Q over RT, just as we've seen a number of times before in that lesson on diffusion and related phenomenon. So the question now is what is the mechanism associated with the activation energy? We should also appreciate that, again, the power of the Arrhenius relationship is that it in some ways isn't essential, that we sort out what the mechanism is. That's the job of the material scientists to determine specifically what atomic scale, mechanism, or microscopic scale mechanism might be contributing to this phenomenon. The important thing is we have an empirical relationship here that tells us how this particular strain rate is gonna change with different temperatures of service for this particular material. So again the power of the Arrhenius plot is it allows us to plot the data, and then determine what that particular activation energy is, what that Q value is, from the slope, just as we talked about before. This is an especially good example, that we were hinting at when we introduced the Arrhenius relationship, as how this can be used as a predictive device. So the situation is that when we do have a material, it's gonna be used at a high temperature, say a boiler material. It's gonna be operated at a constant boiler pressure for a long period of time. And under that essentially constant load the hydrostatic pressure on the walls of the boiler would be unchanging over a long period of time. It's gonna be comparable to that dead load in our elevated temperature tensile test. And we may be concerned about some plastic deformation that we now realize can come into play at the high temperature this boiler's operating at. But we of course don't want that high temperature defamation to occur over too short of a period of time where the plastic defamation will distort the material until that boiler goes out of the dimensional specifications that we would allow for that system when it's too much plastic deformation too much. So one way to determine that of course is simply put it in service, and see how many years it lasts before it has distorted too much. Well, obviously that is not a very desirable way because if that time is too short, and the expense of making the boiler from that particular structural material has been money wasted. Again, if it doesn't last for the 5, or 10, or 50 years that we might want this boiler to be in operation. So what we can then simply do is take advantage of our Arrhenius nature and do a number of high temperature measurements and get our regression line through there, and see it's a nice, straight line. And it tells us what that activation energy is, and again, even if you don't determine what the exact mechanism is that's responsible for the activation energy. We know empirically that there is that value. Then, we can extend it to lower and lower temperatures. Of course, 1 over T is going up. That means that the temperature is decreasing to the right. So, temperature is increasing to the left, decreasing to the right. So the service temperature where we might want to hold this, maybe a few hundred degrees Centigrade. Looks like I'm looking at about seven hundred degrees there. If that is gonna be my service temperature, then by having done a few laboratory experiments up above 1,000 degrees, I can make an accurate prediction of just how rapidly that material might have gone to failure because of this extra crepe deprivation or plastic deprivation at elevated temperatures. So you're in a very powerful technique, and it allows us to make design calculations well in advance of the actual service. One note of caution, this is assuming of course that this straight line extension that I've done here is physically accurate. And it is possible sometimes that there are different mechanisms that can come into play in different temperature ranges. So in this low service temperature range, if there were some other mechanism that would've involved a different activation energy, this projection could be inaccurate. But as long as the same mechanisms were taking place over a wide temperature range and that is physically valid, as you extrapolate into your service temperature range then, it is a very accurate way to make those long-term predictions.
