 Have you ever wondered why some rivers flow smoothly and calmly while others are rough and turbulent? A calm river is good for lazily floating downstream, while choppy waters make for great whitewater rafting. Even though it's not aerospace related, I was curious and did a bit of research. At first I suspected that the speed of a river would be a major influencer of turbulent behavior. But then I learned that the are a tributary of the Rhine and Switzerland flows very quickly but isn't choppy at all. Instead, I learned that the water flowing over any kind of disturbance, such as sharp rocks, can cause large speed variations. This water then mixes with the surrounding unaffected water causing turbulence. By contrast, a calm river probably has a smoother riverbed, thus fewer local velocity changes. Knowing what we know about rivers and rocks, I'm now wondering if this idea is applicable to solid materials as well. We already learned that stress can flow in a material by way of load paths, and that it's not unlike the flow of a liquid in a channel. Even though a solid material doesn't ripple or foam in the same way a liquid would, there is a possible analogy here. Maybe we could think of turbulence in a river as water failing to hold itself together, which is similar to a solid material failing under an applied load. I don't know about you, but I think there's a possible hypothesis to be found in this. Let's see what we can come up with. Two pieces of knowledge will inform our hypothesis. First, that water flowing over sharp rocks is more likely to cause turbulence than smooth rocks. And second, turbulence in water could possibly be analogous to a solid material failing under load. Therefore, I will make the following hypothesis. A sharp edge in a material will cause a part to fail more quickly than a smooth one. By now you know that before we jump into testing, we'll need to find an experimental design that will prove or disprove our hypothesis. Though we can't really see stress flowing in a material, we can use something that will easily deform and allow us to more easily observe how loads affect it. Paper is a good option. To test our hypothesis, we'll cut out squares and circles from the paper, giving us sharp corners and rounded edges. Now if we just pull the paper apart by hand, we have two issues. One, the paper isn't strong enough on its own to take much load, and two, there's no quantitative measurement. To address these issues, we have some basic wooden frames that can be loaded with weights using a hanging weight stand, and the paper can be attached to the frame using double-sided tape. The frame provides rigidity, but the paper will still be the weakest element of the setup, which is perfect. And now we can also have quantitative results. Seems easy enough, so let's get to experimenting. We'll start with the square cutouts. As we add the weights, you can start to see some diagonal lines form in the paper, which try to flow around the cutout. You might also see some of the wrinkles pop in or out. Both effects are the result of the paper trying to deform in the most efficient way under the load. Now look really closely at the upper right corner of the left-most square. Some of the diagonal lines seem to be moving upwards, and a small tear is forming at that corner. On the opposite corner, there's also another tear forming. Even though we've now stopped adding weight, the tears continue to grow until they reach the frame edges, the final failure point, with a load of 5.5 kilograms. Now let's try the circular cutouts. Like we saw with the squares, there appear to be diagonal lines forming in the paper as we increase the load. Let's pause for a second and observe what's happening when we get to a load of 5.5 kilograms. What do we see? Is there any evidence that tears are starting to form? Let's keep going. Now the diagonal lines are starting to deform more dramatically, and the holes start to look less circular. Finally, just as a weight is being put onto the stack, the paper fails catastrophically, and we were able to put on 7.5 kilograms. So what can we learn from this? We hypothesized that the shape of a cutout affects its load carrying capability, and we observed that the circular cutouts were able to withstand a higher load than the square cutouts, 2 kilograms more to be exact. Thus, our hypothesis was proving correct. What we saw in the experiment was that in the square cutouts, the sharp corners produce a concentration of stress, a stress concentration, if you will. Like the sharp rocks in a riverbed, stresses in the paper flowed to a point where disturbances could converge. At a certain critical load, the paper failed completely, similar to the loss of smooth flow in a river. The circular cutouts were able to withstand more load, even though they don't have sharp corners, there are still stress concentrations present. The key difference is that the load can redistribute more evenly and efficiently in the circle, where a sharp corner doesn't allow for that. And the fact that the circular cutout has a stress concentration still makes sense in our rock analogy. Even a smooth rock will produce turbulence if the water flowing over it has a high enough velocity. It just takes a bit more load to produce the same result. In aerospace engineering, stress concentrations are an important aspect of design for safety. Aircraft windows, for example, are rounded to prevent high stress concentrations from forming under the high pressurization loads. Stress concentrations are also important to consider when machining or joining parts, since sharp corners of junctions could lead to early failure compared to rounded edges. Maybe one day you'll use your knowledge on stress concentrations to design a new and safer structure.