or: in which the tensile strength of my brain is tested
Honestly, this is in part just a continuation of this post about coming to terms with not finding answers. As much as I'd love to tie up all these loose ends (and believe me, I would -- I might literally collapse of happiness), find a nice equation that will give me solid theoretical values to work with... the real world is not a place of fairytales, where everything magically works out, if only you work hard enough. (That's why we write fictional ones.)
Maybe there is an answer, somewhere out there. It's not one that's been found, though, as far as I can tell -- and 5 trials by an annoyed, sick, impatient, stubborn, generally incompetent high-schooler is not going to change that. (Even for things like frictional coefficient -- something that is definitely actively used -- we have to determine values experimentally.) So -- perhaps that's the real interest in this project. It is the acknowledgement that few things can be wrapped up in neat little bows, and whenever you make a choice to try, you open yourself up to the possibility of failure.
I dunno. I'll stop trying to justify myself now.
(As always, other research progress posts -- which are formatted much more like my normal research notes -- can be found under the Secondary Research tag. This one is kind of blog-y, because I didn't find any sources that really contained a lot of good information, so formatting it that way would largely just be a waste of space.)
pt i: layman's reading
Here is the fun thing about my research: it is a generally accepted fact that number of plies increases strength. This is pretty much just something that the layman could tell you, and a vaguely scientifically inclined individual might even be able to tell you why. It's not particularly complicated -- you can find agreeing comments on this from various casual sources like many textile arts blogs and even Reddit threads. Wikipedia did not even deign to give a citation for why ropes are twisted. It's something a lot of people know from experience (e.g. breaking single-ply yarns by hand), if not simply just from instinct: things made out of single plies are weaker.
However.
Here is the 'fun' thing about my research: that doesn't mean it's simple, or even something that can really be calculated. Because making a single-ply into a 2-ply does not just mean doubling the strength -- you are not simply adding a 'number' of plies, you are changing the entire structure of the yarn. You are adding more twist, creating more torsional balance, diminishing the size of the plies, decreasing the amount of exposed surface area, and adding friction between the fibres -- among other things. Depending on the material, this can mean different things -- maybe there are too few fibers in each ply, maybe the material felts together, maybe something else happens.
So, no. According to my research -- and I have done hours, if not straight up days of it -- there is no universal formula for how number of plies impacts tensile strength, because it's just not that simple. (This is a conclusion drawn from the lack of evidence, though, so there's always a possibility that my mind is simply not there. And this is a definite possibility, because I spent over an hour this morning incapable of dividing two numbers with a calculator.) Different materials will react differently, and it's something that needs to be determined experimentally. Over the course of this project, I've come across a lot of graphs, a lot of numbers and statistics -- but what I haven't come across is a way to mathematically relate them all to each other. I have seen manufacturers sharing the tensile strengths of their products, sure, and I'm entirely sick of articles about how 4-plies are stronger than 3-plies. Coats give a solid argument for why 3-plies are stronger than single-plies. The (free) scientific literature community, though? Nothing.
pt ii: twisted research
This is incredibly bloody ridiculous, but after a rather lengthy conversation with my dad lamenting my lack of answers, I came back to my research with a fresh (but still annoyed) mindset, having finally concluded that no, I was not going to find some sort of beautiful all-encompassing formula that would solve all my problems. I wound up just deciding to Google 'why are steel cables twisted', and -- naturally -- that got a lot more results.
(This is when I curse my textile niche, because seriously? For the record, when I searched up 'impact of number of plies on strength', I got information on ballet pliés -- which I've got nothing against because I am a classical dancer, but it was decidedly not what I was looking for.)
It's kind of crazy, honestly, all the different ways that physics can impact so many things -- and in so many different ways. There aren't universal laws that can dictate everything (because let's be real: even things like the 'universal' gravitation equation are not quite truly universal, for they ignore a boatload of other factors) -- how can there be, when the world is merely a cacophony of living things, a mosaic of beautiful chaos?
Anyways, existential crisis aside -- it always amazes me how important twist is to keeping rope together... but then also how unwanted twist can decrease strength. This is something we tend to see with things like braided rope; whereas torsion helps balance the distribution of tension in twisted ropes, when a braided rope is twisted, it causes a force imbalance.
I suppose that part of this is likely because any imbalance can throw a material out of whack. I have even talked about this before, in reference to single-ply yarns -- because part of the importance of plying (for hand-spinning, at least) is creating torsional balance by adding twist in the opposite direction (e.g. if you spin singles with an S-twist, you ply with a Z-twist). Based on what little I've been able to read, it seems like multi-strandedness in steel cables allows it to better resist twisting; this implies that plying adds stability (which is corroborated by my experiences, but still does not help with the theoretical physics).
Unfortunately, I have absolutely no experience in metallurgy, and the Internet was not quite so useful as I'd hoped. I am rather well-aware that StackExchange is not a reliable source, but even just reading this thread suggested to me that finding answers regarding plying would still be difficult here. It did, however, again bring up the idea of strain hardening -- something that I'm fairly certain does apply to my work.
When hand-spinning, it is quite evident that the thinner a material is, the more accepting it is of twist. This can be seen throughout the drafting process, or when smoothing out lumps in the yarn; one notices that slubs do not typically have a lot of twist, but when drafted out, the twist evens out. For tensile strength, what this means is that as that thick section of the yarn reaches a necking point, the balance of force will actually be improved, rather than destroyed. Of course, this is another interesting aspect of how a single-ply yarn will behave differently from a plied one; as proponents of multi-ply products are wont to note, when one ply reaches ultimate tensile stress and breaks, there is still another ply (or other plies) left to support the force. (I think this is more important for short-staple fibres than with something such as steel cable -- because twist is what keeps short-staple fibres together, whereas the steel is bonded to itself chemically. Although, once again, I am not a metallurgist, and might be sorely mistaken here.)
It seems, however, as if helically-constructed ropes experience additional strain due to their plies pushing against each other. This, I should think, is actually something of a benefit for yarns/ropes, since they are comprised of many short fibres, thus necessitating that some forces acts upon them. Honestly, it was quite difficult getting through some of this content -- while my dad might have been a CS/EEE major, I must admit that engineering is not a field I'm particularly comfortable in. I may be a textile artist, but the moment DIY extends into more wood-work type stuff, I am completely and utterly hopeless. All that to say, I might not have gleaned all the actionable information possible from this paper. It contains a lot of discussion about tendency to twist, and while it was interesting, it wasn't super relevant to my work, since my yarns were held doubled (i.e. their ends were secured, thus preventing additional twist from entering the system).
However, one point of note -- for while I haven't been doing direct quotes much, I feel that this one bears repeating -- was this:
"In the case of multi-layer wire ropes, the calculation of the moment cannot be carried
out with satisfactory accuracy, because our knowledge of the load distribution as a
function of the load is insufficient. Consequently, the moments as functions of the
loads have to be determined by experiment. [...]"
Furthermore, this graph, showing torque constants for various styles of cables, was included:
Although this is not directly related to the ultimate tensile strength of yarns, I find it worth noting that these values do not seem to follow a predictable trend. Consequently, it can be concluded that finding theoretical values for items related to load strength, especially as it relates to rope structure, is nigh impossible.
pt. iii: fabric physics
After my brief 'eureka!' moment with the twisted steel cable research (which, unfortunately, really did fall flat), I decided to return to textile research. As a textile artist -- a prolific knitter, amongst other crafts -- I have a lot of empirical knowledge of basic textile physics. I understand the structural difference between different types of yarns and fibres (e.g. staple length, microns, etc.), as well as how different kinds of fabric can be engineered to have different properties (e.g. stretch, stability, recovery, etc.). This can encompass things like gauge (how tight/loose the fabric is) or the craft (knit, crochet, woven, felted, etc. fabrics all behave differently) or even just the stitch (within knitting, stockinette vs. garter vs. ribbed vs. cabled vs. lace vs. whatever-else). Perhaps this is why I've been so disappointed in my secondary research -- as an inquisitive person who has been knitting for about a decade, I feel as if I haven't learned much. Given that I can be quite stubbornly independent -- and my knowledge is therefore based largely around only my own experiences -- I think I'd hoped that I'd come across some more theoretical knowledge to supplement my existing empirical knowledge. Instead, I mostly found more anecdotal accounts.
Which is fair, because as I've said before, this is quite a niche project, despite the potential for various applications.
Anyways, as I returned to looking specifically at yarn, I stumbled across some work regarding the engineering of knit fabrics. Honestly... this tangent was no more helpful than any of the other readings I dredged up during this midnight oil arson session. It wasn't really any less helpful though, either. In any case, this is an interesting read if that's something you're into, but I'm not going to delve into it here since I wasn't able to glean any helpful/relevant information.
pt. iv: (k)not a problem
cw // discussion of sutures, because apparently the tensile strength of knots is only relevant to the internet in terms of a) rock climbing, and b) sutures. obviously, the scientific journalling community tends to focus on the stitches.
Sorry about the pun. I am tired and snarky and cannot resist anything right now.
Since my research on twist and plies was clearly going nowhere, I decided to look into how knitting impacts tensile strength, as I felt that there might be a correlation between plies and knotting (i.e. they are both physical manipulations that impact strength). During my research, I came across this gem of a quote from a publication on rigging:
Nearly all rope systems use a knot or knots in their construction, so understanding the
strength and behavior of knots in a variety of materials is important for understanding system tolerances. This also means that the strength of knots is a heated topic, one that can cause stern conversations between professional and volunteer riggers alike. However, when pressed to provide data, rarely can riggers trace their strong opinions to publically available testing data. As a result, there is quite a bit of rigging lore associated with knots, knot tying, and knot usage that may or may not be consistent with reality
That is 100% how I feel right now. Sure, there's this empirical knowledge that permeates everyone's minds, but there's little to no data. In any case, the data presented by this work showed quite clearly that the residual strength after tying a knot was less than the initial strength of the material (as is implied by the fact that it is called 'residual' strength). This study cites that in 710 out of 720 cases, sutures broke off at the knot. I could not access the entire work, but it seems as if the strength of the knot depends on the material it is tied in; this corroborates my hypothesis that where the material breaks might be related not just to the knot but also to the material itself. (The rock climbing study, on the other hand, seemed to suggest that knot strength is unrelated to the material, but I am inclined to believe that the materials tested there were of more similar composition. That's purely conjecture, though.) This one says that the impact of material on knot strength is greatest with simpler knots -- which makes sense with my experiment, since I was just tying overhead knots. With that said, this research plot bunny can be laid to rest... and we can go back to the theoretical physics of why knots weaken string.
(I would also, however, like to note for the record that knot strength is also something that has to be determined experimentally. More points for the 'nope-I-can't-give-a-proper-theoretical-value' team. Also, this study shows that knot strength can definitely depend on technique, which reaffirms the possibility of my brain fog causing a margin of error in my results. It also shows a tensiometer as a tool for measuring tensile strength, which is cool and obviously not something I have on hand but definitely a better option for this kind of experiment.)
This (short) article says that knots weaken a rope because the bend causes there to be an uneven distribution of tension. Recalling the article about rotation in steel ropes, helical construction is something that can help to reduce this imbalance; this might be another contributing factor to how my results came about. In fact, during testing, I mentioned that my single-ply yarns had a tendency to break off near the knot, whereas the plied yarns often broke off in other places. One might conclude that this occurred because in a single-ply yarn, the knot was able to place much more strain on the fibres than would occur in a plied yarn. (My results regarding the single-ply yarns are also corroborated by the fact that medical studies support monofilament sutures as being weakest near the knot, but I can't find much evidence regarding plied sutures.) Unfortunately, none of this information is particularly helpful in determining how plies might impact tensile strength in the absence of knots.
(diagram was sourced from this article)
pt. v: ...problems
cw // discussion of toilet paper. links associated with toilet paper occasionally include content that might be considered nsfw simply in that they... discuss... toilet paper...
Last night, while messing around with my data, I also noticed that when treating all the yarns as if they had the same cross section, the order of strength (least to greatest) was single-ply, 3-ply, 2-ply, 4-ply (based on averages). When measured based on actual cross section, the order was single-ply, 2-ply, 3-ply, 4-ply. This is another interesting idea that might have an impact -- as I've touched on before (if not on the blog, at least in one of the videos, although I'm too tired to recall which one at this point), greater plies tends to mean smaller cross-sectional area. This occurs because plying creates denser yarn (although I've seen some posts that counter this idea, saying that 3-plies tend to bloom and become larger -- this was not my experience, but who knows?).
So... do plies just increase strength by increasing density, because a given cross section actually has more fibers? This is clearly not the case with the 2-ply or 4-ply -- with them, plying seems to quite clearly add strength -- so what makes the 3-ply different?
Even outside the realm of yarn/rope/cable, the difference between 2- and 3-ply is something of a disaster. Here's an... interesting Reddit thread commenting on the merits of toilet paper plies. I guess this is actually part of why I wanted to explore this for my project -- I was really curious about whether having more plies was what was truly beneficial, or the contents of those plies that was relevant. (Or is it just because more plies is often associated with more thickness?) This Quora thread expounds on people's experiences with how quality and ply are not interchangeable terms.
(Look... don't make the same mistakes as me. Searching things up about number of plies without context will just get you a lot of talk about wiping one's nether regions. You have been warned.)
Perhaps one of the most relatable examples of this (other than toilet paper, apparently) at the moment is face mask structure. The video we watched in class exploring N-95 face masks pointed out that with a filtration system like a sieve, additional layers do not really help. However, if we think about a different example of filtration, such as water purification, we might note that one important aspect of those systems is that the water is sent through various layers -- not just more than one layer, but more than one type of layer. Even going back to face masks, when we consider disposable (or even handmade reusable) ones, more layers tend to be important, because some of those layers consist of different types of fabrics. The article linked suggests that 3-ply masks are important not because they have an extra ply, but because that extra ply is a filter.
This thread newsletter on the other hand suggests that 3-ply is just intrinsically stronger than 2-ply. Which was, of course, not necessarily my experience.
At this point, we blow out an exasperated breath, look at the time, and realize that the Internet is well and truly committed to not answering these questions.
conclusions
So.
I think the main thing I've been taking away from my research is that... an experimental makeover (that is definitely not the technical term) is in order. When I started this project, I guess I was just really hyped up on the idea of specifically getting to test yarns of the same cross-section. That was my main fascination, so I stubbornly insisted on focusing on that when I designed my experiment, much to the detriment of the science that I can study.
At various points in time, across various posts and videos, I've discussed a vast number of ways that this experiment could be adjusted for accuracy -- as well as reasons why I might've seen so much deviation in my results. I'm not going over all that again, because frankly, I am currently incredibly pressed for time and energy (and besides, it's entirely fruitless to continue dwelling on it). However, I will say that I'd be quite interested in redoing this experiment with different parameters -- perhaps exploring something like degree of twist would be interesting.
(Then again... I'm also pretty sure there's not much literature about that, either. I think there's probably at least some, though.)
Anyways, that's all for now, since I really need to get on to doing the final compilation posts (and finish editing videos). I know that I am literally a 16-year-old girl, and this is typically a sentiment reserved for older people, but my body is not what it used to be, and I can no longer push myself so hard without facing actual consequences. So, well, this is it. I might do some more research about this over the summer, but right now, I've gotta put a stop to trying to find more information, because there's a lot of housekeeping work that needs to be done over the next 3-ish days, and I'm already not feeling 100%.
As much as I love you, dear lofty expectations, I'm afraid we need to take a break.
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