in which I play the hand I dealt myself the only way I know how
Did I say I was going to stop researching? Yes.
... have I had a tiny bit of spare time while my videos export that has been used for research? Also yes.
This was all sort of a Hail Mary attempt at getting some extra information, not that that's particularly helpful given that I already have, like, an hour of video content uploaded to YouTube. I guess I'm just hoping that in the final hours before this is due, I can try to get something done -- and if that means going through all the Google search results, then that's what it means.
(To be fair -- 'throw things at the wall until they stick' is not much of an ace in the hole anymore given that my energy levels are not what they were.)
pressure-sensitive fibers (Delbert, 2020)
color-changing fibers are used to understand why some knots are stronger
shows which parts of the knot are working hardest
believe that twist fluctuations increase how securely a knot holds
a knotty problem (Greenfield-Boyce, 2020)
scientists struggle to explain why knots do what they do
knowledge is experiential rather than theoretical
twist is a key feature
twists going in opposite directions lock it
twists going in the same direction can cause knots to roll out
also impacted by friction and overall complexity
spun yarn strength as a function (Ghosh, 2004)
strength of spun yarn depends on the gauge length and rate of extension
standard measurement of yarn strength is executed at 500 mm gauge length and 20+/-3 sec
experimentally determined strength behaviour of yarn at short gauge length is more appropriate to simulate the mechanical behaviour of fabric
it is not realistic to measure yarn strength at all possible lengths
the presence of flaws in the yarn leads to the localization of stress in excess of theoretical strength, initiating the rupture process
fall in strength with increasing test length is due to the increased probability of encountering a fatal flaw
(lots of interesting reading here, and some fun math, but not really relevant to number of plies and time crunch dictates I move on)
studying the tensile strength of a two-ply (Olsen, 2020)
the overall tensile strength of ply yarns is greater than the sum of the tensile strength of the composing single ply yarns
one study found their 2-ply cotton yarn to be about 2.73 times stronger than the single cotton yarn
total strength is the sum of the tensile force and the interaction force
tensile force
T=AeE (tensile force = cross sectional area * fracture strain * tensile modulus)
e = delta(L_break) / L_original (fracture strain = change in length of string when it breaks / original length)
E = stress / strain = (F/A) / (delta(L)/L_original)
based on Hooke's law, F/delta(L)=k, so E=kA/L_original
interaction force
T = f = aN (interaction force = frictional resistance = cohesion coefficient * radial pressure)
there is an ideal degree of twist for a yarn that gives the greatest tensile strength
mechanical properties of cotton yarns (Schiefer, 1935)
β = angle of twist
D = diameter
T = turns of twist per inch
M = twist multiplier
C = count
formulas are derived from the assumption that exposed fibers are arranged as helices on a circular cylinder and that yarns of different counts have the same density where angles of twist are equal
β = (pi)(DT)
T = (M)(sqrtC)
found experimentally that angles of twist were consistently greater theoretically than observed
β = [(arctan)(pi)(DT)] / [1 - (0.4)(sqrtC)], T=(M)(sqrtC) was found to work empirically
yarn is a heterogenenous material
fibers of various length, cross-section, and strength are held together by twist
yarn strength is related to fiber strength
fiber length (longer is stronger), preparation (combed is stronger than carded)
adding twists decreases the diameter by bringing the fibers in closer contact by a radial pressure
increases frictional forces between fibers and resistance of fiber slippage
also introduces torsional forces or shearing stresses which reduces individual breaking strengths of fibers
(again -- lots of data, not really relevant, might come back to this once the project is done)
relationship between tensile strength of yarn and woven (Malik, 2015)
not much relevant info here -- just a note that there's not really been much work done for how to predict the relationship between tensile strength of yarn and fabric, either; we don't have a nice equation for that, similarly to how one is not popping up for plying
fiber slippage and breakage varies with yarn structure (i.e. rotor, ring, friction) based on spinning system
evaluation of the quality characteristics of ply yarns (Uster, 2013)
coefficient of variation is less in a plied yarn based on the doubling law
knots, hitches, bends, and anchors (chapter 5)
effect of single yarn twist and ply (Palaniswamy, 2006)
hairiness of ply yarn decreases with increased twist
protruding fibers are inevitable as yarn is made of staples of finite lengths
easily peeled off in single yarns
surface fibers are trapped by each other in ply yarn, which improves abrasion resistance
an investigation on the effects of ply and single twists (Ömeroğlu, 2013)
ply improves strength, elongation, evenness, hairiness, abrasion resistance, bulkiness, twist liveliness, etc.
strength of a spun yarn depends on fiber orientation and fiber to fiber adhesion
twist decreases fiber orientation but increases fiber to fiber adhesion
ply twisting (Science Direct)
plied yarn (Science Direct)
TL;DR -- basically, still have not found answers in scientific literature.
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