Textile Structure
how cloth is put together
Concept

Breaking extension — where it appears

The strain at which a fibre fails, measured and reported as a range. It is carried apart from the tenacity and modulus on purpose, because dividing those two gives the strain a linear fibre would break at and the two figures disagree by a factor of six for some fibres.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

The tightest fold a 20 tex cotton yarn can be given. A cloth folded as sharply as it can be folded. The two yarn crowns on the inside of the fold cannot pass through one another, so the fold's radius is the yarn's own — 0.084 mm for a 20 tex cotton yarn — and there is no measurement of an iron anywhere in the argument. At that radius a fibre free to slide is strained 7.14%, which is √(packing × fibre tex ÷ yarn tex), and the whole yarn bending as a rod would be strained exactly one hundred per cent. Cotton's measured breaking extension is 6.0% to 10.0%, so the free bound does not survive and the locked one cannot. What the drawing cannot show is the fibres inside the yarn, which is exactly what the argument is about — the picture is the same either way and the strain is fourteen times different.

A crease is a fold the crimp cannot supply

A fold needs its outer face longer than its inner, and a woven cloth's way of supplying a length is to move crimp. That runs out at a radius of millimetres, and a pressed crease is tenths of one — so the fold is handed to the fibres. How hard it strains them turns on a question this collection has been unable to settle for two fields, and a crease settles it by refusing.

finishing · Crease Elastic recovery against strain, for seven fibres. The elastic recovery of seven fibres at the strains it is reported at: extend to a stated strain, unload, read the strain returned immediately. Each fibre's points are joined and the line stops where the measurements stop, which is the point of the figure — a fibre strained past the last point on its own line is a fibre this collection declines to answer for. Nothing here is measured below one per cent of strain, and a woven cloth just past its own interchange budget is at a thread strain of a few hundredths, so the region that matters most for a fabric is the region nobody has reported. Recovery falls monotonically for every fibre, which is what lets the unmeasured region be bracketed between the lowest measured value and one rather than extrapolated. What the plot cannot show is the delayed recovery, which is excluded by the convention and is largest for the fibre with the best reputation for recovering.

Recovery is measured and nothing predicts it

A fibre's stiffness is a bracket this collection can compute the ends of. What fraction of a strain it gives back is not: it has to be looked up, the tables are thin, they stop exactly where a fabric needs them, and the most attractive explanation for the ordering they show turns out to have no signal in it at all.

mechanics · Yarn stiffness The strain at a fold against the strain each fibre breaks at. For each fibre, the surface strain at the sharpest fold a 20 tex yarn of it can make — which is √(packing × fibre tex ÷ yarn tex), with no measurement of a crease in it — beside its own measured breaking extension. cotton and flax are strained past the low end of their breaking range, so some of their fibres break at the fold, and that is what a linen crease is. The rest survive, and among them viscose and wool return less than three fifths of what they were given, which is the other way a cloth creases. Both columns are needed: viscose survives with a factor of two to spare and is among the three worst by measurement. What the bars cannot show is wool, which the census puts in the wrong column because the recovery figures are the immediate ones and wool's is the most delayed of any fibre here.

Which fibres crease, and why there are two answers

Run the sharpest fold a yarn can make against every fibre's breaking extension and its recovery, and the ranking that falls out is the trade's own — linen worst, cotton next, wool and the melt-spun filaments best. It falls out of two columns rather than one, because two fibres in the bottom three get there by different mechanisms, and a treatment that fixes one does nothing for the other.

finishing · Crease A bundle is weaker than the threads it is made of. Threads pulled in parallel do not break together. The weakest goes first and hands its load to the rest, which are now carrying more than they were, so the bundle's peak load is reached before every thread is at its own strength. With a load per surviving thread of x carried by the fraction that has not yet broken, the bundle's strength per thread is the largest value of x(1 − F(x)) — Daniels' maximum, which for a lognormal at CV 15% is 0.7380 of the mean thread, reached with 93% of the threads still unbroken. A simulated bundle that knows none of that arithmetic sits above the limit at every finite size — its strength is a maximum over the sample it happens to have drawn — and closes on it as the bundle grows: 0.753, 0.744, 0.741 at the last three sizes. The scatter falls the other way, from 14.5% at one thread to 0.7% at 1600.

A bundle is weaker than its threads

Threads pulled together do not break together. The weakest goes first and hands its load to the rest, so a bundle carries its maximum well before every thread is at its own limit — and the shortfall is a quarter, decided by the spread and by nothing else.

mechanics · Tensile A cotton yarn at a fold, at both ends of its bending bracket. The same 20 tex cotton yarn bent to a radius of 0.084 mm under the two assumptions this site's bending bracket is drawn between. If the fibres slide freely past one another each bends about its own middle and the surface strain is 7.14%; if they are locked the bundle bends as a rod and the outermost fibre is strained 100%. The ratio is 14.0, which is the ratio of the two diameters and therefore the square root of the fibre count over the packing — so the bracket of 327 this site carries in a stiffness is a bracket of 14.0 in a strain. What the drawing cannot show is which of the two a real yarn does, and the answer is settled by a refusal: at the tightest fold a cloth can make, the locked bound asks for a strain of one, and a creased cloth does not fall apart.

A wrinkle cannot settle what a crease settles

The first rung of this ladder found that a pressed crease decides a question this collection had been unable to settle for two fields — whether a bent yarn's fibres slide or bend as one body — and it decides it by refusing: the coherent branch would strain the fibres by eighty-four per cent and cotton breaks at six. A wrinkle is the same fold at twenty times the radius, and there both branches are survivable. So the bracket that a crease collapses stays fourteen times wide at every radius anybody actually creases a cloth at accidentally.

finishing · Crease

Named alongside it

The objects these essays reach for when they reach for this one.

Elastic recoveryFibre finenessBending bracketFold radiusPacking factorYarn diameterBending rigidityInterchange budgetPermanent setTenacityBundle strengthCloth thickness

All concepts