secondary research
There is really not very much literature on the topic of how plies impact various traits of yarns -- either that or I am just being picky. Even odds, really.
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I am not going to go over all my research here. If you want to read my research notes -- which, be warned, tend to involve a lot of snark and even more terrible formatting -- check out the Secondary Research tag on the blog.
STRESS-STRAIN
When placed under stress, materials follow a stress-strain curve. This looks different for different materials, and different people use different terms to describe the regions. However, it can be largely divided into 3 sections: the elastic (linear) region, the plastic region, and the necking region. In the elastic region, the yarn is not pulled enough to permanently deform it. Once we reach the yield point, we reach the plastic region, where deformation becomes permanent. This leads to the point of maximum strength, after which the yarn breaks.
PLIES + EVENNESS
When yarns are plied, some of their inconsistencies are worked out since they are balanced with other parts of the yarn. This is a fairly simple mathematical concept: imagine you have a single-ply yarn with a spot that is half the diameter than the rest. Now ply it with a yarn of the normal diameter; you'll get a yarn that is 75% the goal. If you ply it with two other yarns, you'll get to 83%. Four plies will give you 88%. In this way, the more plies you have, the more even the yarn will be.
EVENNESS + STRENGTH
Yarn tends to experience necking -- that is, the stretching out of the material when subjected to sufficient stress -- at a localized point. Intuitively, one might deduce that yarn will fracture at its weakest point. This leads to the conclusion that evenness of yarn is important to maximizing strength.
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Resultantly, the mathematical relationship for the coefficient of variation of yarn can be defined as CV_ply = CV_single / sqrt(number of plies).
PLIES + HAIRINESS
Hairiness is a property that is inversely proportional to the number of plies. As yarn is composed of short staples of fibers, there will be some that protrude on the surface. In a singles yarn, this phenomenon is more prevalent. However, when a yarn is plied, the axial friction reduces the protruding fibers. The surface fibers are ths trapped by each other. Resultantly, the hairiness is minimized by plying.
HAIRINESS + STRENGTH
Decreased hairiness provides increased abrasion resistance, since the fibers are better locked in place by the twist. This means that the yarn can better hold up in the face of friction -- a trait that is beneficial when testing tensile strength.
TORSIONAL BALANCE
Another important aspect of yarn is torsional balance. A yarn that is balanced will hang straight, rather than wanting to kink back on itself. This is important to ensuring that the distribution of force across the fibers is even -- that is, making sure that none of the fibers or parts of the yarn experience more stress than others. Single-ply yarns are not torsionally balanced, since they are only spun in one direction. On the other hand, plied yarns can be torsionally balanced.
INTERACTION FORCE
A 2-ply yarn is stronger than just the sum of the strength of its plies. This is why it is stronger than a single-ply yarn of the same cross-sectional area.
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The tensile strength of a plied yarn is equal to the tensile strength of its plies plus the interaction force between them. This provides additional tensile strength.