The Physics Philes, lesson 69: Hooke’s Law, Line, and Sinker
The past couple of weeks we’ve discussed the different types of stresses and strains that can act on an object. In that discussion I brought up a concept called Hooke’s law. Remember? If the stress is small enough, the stress and strain will be proportional. Well, I’m finally going to answer the question that I bet has plagued you these past two weeks:
What the heck does that even mean?
The whole discussion around Hooke’s law so far has brought flashbacks of first-year law school discussions about what, exactly, a “reasonable person” is. (Spoiler alert: Nobody knows.) Luckily, this isn’t law. It’s physics, and we have an answer. So let’s get started. It wouldn’t be The Physics Philes without a crappy drawing from yours truly, and this week is no different.
So…this is obviously a graph of some kind. It’s illustrative only. It’s not actually a graph of anything. Please don’t use it on your homework or anything.
What are we looking at here? It’s a graph of the stress as a function of strain (the y-axis is the stress and the x-axis is the strain). As you can see, between the origin and point (a), it’s a straight line. On a real graph of this type, the slope would be Young’s modulus. That straight line indicates where the stress and strain are proportional. As you can see, it’s a relatively small part of the graph. Where that straight line ends (at point (a)) is called the proportional limit.
That’s the area where Hooke’s law applies. But what happens to the object as the stress applied causes the object to surpass the proportional limit? Lots, it turns out.
Take a look at the graph again. There is a small area when the material isn’t permanently deformed (between points (a) and (b)). Between those points, as stress is removed the object will return to it’s original shape. This is called elastic behavior, and at the end of this region of the graph is called the yield point and the stress at the yield point is called the elastic limit.
Moving beyond the yield point, the material will not pop back into place. We say that the object has undergone irreversible deformation and has acquired a permanent set. On the graph, you can see this happen at point (c). The bigger the load gets beyond this point produces a large amount of strain for a relatively low increase in stress. Eventually, the stress and strain get to be too much and the material fractures. The behavior of the material between the yield point and the fracture point is called the plastic flow or plastic deformation and it’s irreversible.
You probably know from everyday experience that some materials break more easily than others. If there is a large amount of plastic deformation between the elastic limit and the fracture point, we say that this material is ductile. If a fracture occurs soon after the elastic limit is passed, then that material is brittle. The stress it takes to fracture a certain material is called the breaking stress (or ultimate strength, or for tensile stress, tensile strength).
Sometimes something weird can happen when material is stretched and allowed to relax. Some material follows a different curve for increasing and decreasing stress. This is called elastic hysteresis, and it means that the work done by the material when it returns to it’s original shape is less than the work it took to deform the material in the first place. This has something to do with non-conservative forces associated with internal friction. Or something. I’m not sure. But it happens.
That’s it for stress and strain! Try not to be too sad. Next week we start a discussion on gravity, which will include Newton’s law of gravitation and Kepler’s laws. I’m so excited!
Featured image credit: Martin