#30 - Composites in Plain English Pt. 5
Another Evil Genius, Another Composites-Related Riddle
I’m back, baby! I’ve been busy moving up to Oakland and restarting my projects. I brought the Saab with me on a trailer. Even though I drove it for a total of 20 feet, it still found an opportunity to show its “character”. The door refused to unlock in front of the new place and the usual jiggle of the key didn’t work. So my brother and I resorted to breaking into our own car by taking out the back window.
That’s it for the life update -- now back to your irregularly scheduled programming.
Previous parts: Part 1, Part 2, Part 3, Part 4
For the second time in this newsletter’s history, I will (potentially) save your life. Last time in “Composites in Plain English”, we discussed what to do if you’re captured by Mr. Evil -- an evil genius who gives you a life or death riddle about which is stiffer under tension: carbon fiber composite (with glue) or carbon fiber without glue. Let’s take a trip back into that hypothetical world.
After your ordeal, you wake up staring at the ceiling of your living room. You remember surviving Mr. Evil’s riddle but can’t remember how you got back to your place. You puzzle over it for a few minutes, but shrugging your shoulders, decide that it must be an evil genius thing. For a few weeks, life plods along as usual, though you do stress-eat more mac ’n’ cheese than usual. And then -- bam! -- it happens again. You find yourself in another evil lair but, instead of Mr. Evil, a woman stands beside you. She introduces herself as Mrs. Evil, the wife of Mr. Evil. (They’re apparently going through a rocky part of their marriage and are living in their own separate lairs for now.)
As you look around, you realize that you are again in front of an alligator-infested pond that has two ropes hanging above it. As you start to tell Mrs. Evil that you’ve been through this already with Mr. Evil, she angrily interrupts you. These are crocodiles not alligators. (You have no idea what the difference is.) And the riddle is different.
Mr. Evil’s ropes were long enough that your body weight would stretch one of the ropes and lower you to the alligators. Mrs. Evil’s ropes, on the other hand, are shorter. They won’t stretch enough to put you in danger. Instead, Mrs. Evil plans to suspend you from your chosen rope with a weighted vest. The riddle is designed so that one of the rope options will break, dropping you into the crocodile pond, while the other will stay intact. Your two choices are: a rope of carbon fiber composite (with glue) and a rope of plain carbon fiber (without glue). The ropes are the exact same weight. Which rope do you choose?
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Thinking Space
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If you chose the unglued rope, congratulations! You’re safe. If you chose the glued rope, well…
So what’s the explanation? How does adding glue make the rope weaker? In the riddle, both the unglued and glued ropes weigh the same. If we’re looking at ingredients, the unglued rope only has one: fibers. The glued rope has two: fibers and glue. Since the ropes weigh the same amount and the glue is not weightless, the glued rope has less fibers than the unglued rope. In other words, glue takes the place of some fibers.
If you remember, that proportion of fibers was the key in Mr. Evil’s lair. The fibers were stiffer than the glue. The unglued rope had more fibers than the glued rope. So the unglued rope was stiffer than the glued rope.
In Mrs. Evil’s lair, we are interested in strength, not stiffness, but the same idea applies. The missing piece is whether the fiber or the glue is stronger in tension. Knowing what we know about the structure of fibers from part 1, it’s not too surprising to find that the fiber is stronger. In the case of our carbon fiber composite, the carbon fiber is at least an order of magnitude stronger than the epoxy glue. That means -- the fibers are stronger than the glue. The unglued rope has more fibers than the glued rope. So the unglued rope is stronger than the glued rope.
That’s all there is to it. But am I going to stop talking? No.
There are two other ways to look at the same thing. Either I’ll help you to a more complete understanding or I’ll more completely confuse you. But before I get into the other two explanations, I need to introduce a graph.
Image taken from this otherwise unrelated paper, which I did not read.
It’s called a stress-strain curve and it can reveal fantastic insights into a material’s properties. The vertical axis is the stress (how much force the material is experiencing) and the horizontal is the strain (how much the material stretches). There are some extra lines on this particular graph but just pay attention to the three diagonal lines.
Each line corresponds to a material. The line ends when the material breaks. With just those few keys, we can figure some stuff out. The higher a line gets before it stops, the more force is required to break the material. In the graph above, the fiber is the strongest material (takes the most force to break). The further to the right a line gets before it stops, the more stretch is required to break the material. In the graph above, the matrix (fancy name for glue) is the stretchiest material.
Let’s revisit our strength-based explanation and make sure that the graph agrees with us. We said that the fiber is stronger than the glue. On the graph, the fiber’s line reaches higher than the matrix’s, so that checks out. Then we compared the composite/glued rope to the unglued rope. The composite has fewer fibers, but adds glue. So we expect the composite to be somewhere in the middle for strength. Again, the graph agrees.
Now let’s look at things from a stretch-based point of view. Typically we think about how hard you need to pull on something to break it, but it’s equally valid to think about how far you need to stretch something to break it. So let’s do that now. From the graph, you can see that you’d have to pull the glue a lot further than the fiber. But why do the fiber and the composite break at the same level of stretch? Remember that the composite is just a mixture of fibers and glue. The glue doesn’t change the fibers themselves. The fibers have a hard limit on how much they’re willing to be stretched before they tap out. In the composite, they tap out at that same limit. The only difference is that there are less of them. So, like we learned in Mr. Evil’s lair, the composite is less stiff. In other words, it takes less force to stretch the composite to that breaking limit.
If you’re especially clever, you might be wondering -- what happens to the glue? Clearly we haven’t stretched it to its breaking limit so it should still be intact, right? You might be expecting something like a bunch of broken fibers embedded in glue. That’s a very good thought, but unfortunately -- even though the glue can take the stretch -- it can no longer take the stress. All of that force that was being shared by the fiber and the glue is now the sole responsibility of the glue. And that responsibility proves to be too much. To tie it back into the graph, the point at which the composite breaks is to the left of and above the breaking point of the matrix. It still has capacity to stretch, but it’s run out of strength.
We’ve looked at Mrs. Evil’s riddle from two perspectives: strength and stretch. There’s one more angle that I want to cover: energy. But I’ve rambled long enough for this post so I’ll leave you there -- safely hanging above the crocodiles.
Corrections? Questions? Comments? I’d love to have your input. Leave a comment, email me at surjan@substack.com, or find me on LinkedIn.
Drawing exercise #19. If you missed it, here’s why I’m learning to draw.
Welcome to Oakland; it's an amazing place! Check out Graffiti Pizza, Swan's Market, and Hot Boys (if you eat meat). Go get groceries at Market Hall and ramen at Ramen Shop. Hope you're close to Lake Merritt -- it's wonderful.
Oh, and great post, as usual.