#21 - Composites in Plain English Pt. 2
How did I end up reading a book on yarn?
In this series, I’ve been trying to deepen my understanding of carbon fiber and other modern composites. Back in Part 1, I learned what it is that makes fibers so strong. Here in Part 2, I fully expected to write about the glue and maybe even wrap things up. But that didn’t happen. The more I write, the more I find things that I don’t fully understand, and the longer this series gets. In this post, I followed the thread of my curiosity to the subject of yarn.
Where we left off last, we had established that fiber is a fantastic building block. But the very thing that contributes to the fiber’s strength, its thinness, presents a challenge. A single fiber is extremely thin -- about a quarter of the thickness of an average human hair. While a fiber is supremely strong for its thickness, it’s not all that strong in absolute terms.
[Some quick, skippable math: From numbers on the internet, we know that it takes ~500,000 psi to break carbon fiber in tension. We can also look up that a fiber has a diameter of about .0004 inches. So the area of that circle is .00000013 in2. Multiply that times the strength and you get .065 lbs.]
Roughly speaking, you could hang a double A battery from a single carbon fiber before it breaks. If you’re making anything other than gallows for batteries, you’ll probably need more than one fiber. As it turns out, the manufacturing processes for glass and carbon fibers do take this into account. The vast majority of fibers get processed in a way that allows multiple fibers to work together.
There are two ways to make this happen. The first is to twist the fibers together into a yarn. The second is to gather the fibers together, leaving them untwisted, and binding them with a glue. This second solution - the group of straight fibers - is called roving when talking about fiberglass or tow when talking about carbon fiber. I’ll just refer to it as tow.
Why would you choose one over the other? I couldn’t find the answer to this in any of the books about composites, so I had to turn to a field of engineering that I didn’t even know existed: textile engineering. More specifically, yarn engineering. (If there happen to be any yarn engineers reading this, please jump in if I misrepresent any of your work.)
The answer depends on length of the fiber you’re starting with. Fibers come in one of two flavors: short or long. The short fibers, called staple fibers, are typically an inch to a few inches long. Wool, for example, is a staple fiber, because sheep hair can only get so long -- even if the sheep evades shearing for six years.
On the other hand, the long fibers, called continuous fibers or filament, are basically longer than anything you could make from them. Silk is a natural example of a continuous fiber, because a silkworm produces about a mile of filament to make its cocoon.
The continuous fibers, then, are long enough to be used as is. They’re lightly glued together into untwisted tows to make them easier to handle and process. (Remember just how thin the individual fibers are.) The short staple fibers, on the other hand, need some help to get to a more usable length. The staple fibers are twisted together into a yarn.
What exactly does the twisting add? When twisted, the fibers are compressed together. Picture wringing out a wet cloth. When you twist, you can see the cloth getting squeezed inward and forcing the water out. Similarly, the fibers in a yarn are squeezed tightly inward. This increases the friction between the fibers, making it harder to pull the fibers apart. So essentially, the twisting adds an invisible hand, which tightly grasps the bundle of fibers.
So we twist the staple fibers as tight as we can and get a yarn that never breaks, right? Well, not quite. There’s a conflicting factor at work. The tighter you twist the yarn, the further the individual fibers get out of alignment with the yarn. In other words, let’s say you start with a bundle of fibers oriented vertically. The more you twist, the closer those fibers get to horizontal. Why exactly is that a bad thing?
Think back to the last time you took your pet rock for a walk. For most of the walk, you were able to pull on the leash forward, in the direction you wanted to travel. When you did that, 100% of your pull propelled Rocky forward. However, when you had to go around a puddle, you changed course. Meaning that you pulled on the leash at an angle compared to where you wanted to go. At that angle, only a fraction of your pulling moved Rocky forward. The rest of it was wasted going sideways. In the case of the diagram below, for example, only 3/5th of the pulling force was directed forward.
If you wanted to match the forward pull of the straight leash, you would have to pull 5/3 times harder on the angled leash. The more angled the leash, the harder you have to pull to match the straight one. To bring it back to the fibers in the yarn, the more the angled a fiber is, the harder it has to work to match a straight fiber. And the greater the twist, the more angled the fibers. So the more twisted the yarn, the harder the fibers work to support the same amount of weight.
Now we know the two conflicting factors at work on the yarn. If we twist the yarn too little, there’s not enough friction holding the fibers together. The yarn will break by the fibers pulling apart from each other (cohesion curve below). If we twist the yarn too much, the fibers will have to work extremely hard to support the same weight. The yarn will break by the fibers themselves breaking (obliquity curve below). Yarn engineers have to find a balance between the two.
Figure from Peter Lord’s Handbook of Yarn Production. I can’t believe I read it either.
Learning about twisted yarn also gives us insight into the advantage of untwisted tow. In tow, the fibers are all aligned in the pulling direction (like when you pulled Rocky straight forward). So we’re able to utilize more of the fiber’s strength in the direction we want. This is one of the reasons that continuous fibers, like silk, are so strong.
One more way to think about it is with the concept of load paths. Pinch a sheet of paper on two opposite corners, and pull apart. You’ll notice that only the material in a straight line between your fingers gets taught, while the rest stays floppy. This is called a load path, the most direct route between where the load enters and exits. When pulling on a continuous fiber, the load has a straight, continuous path that it can travel on. When pulling on a yarn, the load not only has to spiral, but jump from fiber to fiber. The straighter and more direct the load path in your structure, the more efficient it is, because there’s less material required to do the same job. It’s the difference between a fire station equipped with a fireman’s pole and one equipped with a spiral staircase.
Knowing all this, it makes sense why carbon fibers are found largely as continuous fibers and bundled together as tows. (For anyone who has shopped for carbon fiber, the 3K, 6K, etc., is the number of continuous fibers in a tow. 3K = 3,000.) In the case of both tow and yarn, we now have a better understanding of how fibers can be packaged into a more usable form.
Corrections? Questions? Comments? I’d love to have your input. If you want to get a hold of me individually, you can respond to this email or find me on LinkedIn.
Drawing exercise #11. If you missed it, here’s why I’m learning to draw.