Textile Structure
how cloth is put together
Concept

Fold radius — where it appears

The radius a cloth or a yarn is bent to at a fold, which decides the strain in the fibres on the outside of it. It cannot be smaller than the yarn's own radius, because two crowns on the inside of the fold cannot pass through one another.

Named by 6 essays across 3 fields — each of them below, with the objects they name alongside it.

A 5.0 mm cotton pile standing and crushed. A pile tuft standing 5.0 mm proud and the same tuft pressed flat, which turns it through a right angle over its own length and so bends it to a radius of 3.18 mm. Its fibres are strained 0.187% — an order of magnitude below the smallest strain anybody has measured a recovery at, so this file declines to say what fraction comes back. The consequence is that a crushed carpet is not held down by its fibres: what keeps a pile flat is the tufts leaning on one another and the friction where they touch. Below 0.469 mm the fibre does enter its measured range, which is the difference between a carpet and a velvet and has nothing to do with what either is made of. What the drawing cannot show is the neighbouring tufts, which are the mechanism.

A crushed pile is not held down by its fibres

A carpet flattened under a foot has bent its tufts through a right angle, which sounds severe and is not: the fibres in a five-millimetre pile are strained under two tenths of a per cent, an order of magnitude below the smallest strain anybody has measured a recovery at. What holds a pile down is the tufts leaning on one another.

fancy · Pile 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 A 3-pick fold across a 8-end satin, move 3. A 8-end satin, move 3 on point paper with a fold 3 picks wide drawn across it at pick 3. A warp end's crimp is made where it turns from over to under, and the dots mark the turns that fall inside the fold. Averaged over the ends there are 0.75 of them, and 4 of the 8 ends in the repeat have none at all — those ends are marked with a line, and each of them crosses the fold dead straight with no crimp to give up. Over every fold position, 50.0% of end-and-place pairs are like that. What the drawing cannot show is what happens to those ends instead, which is that the whole of the fold's length difference goes into their fibres.

How sharply a weave lets a cloth fold

A fold's length difference is paid for out of crimp, and crimp is not spread evenly along a thread — it is made at the interlacings and nowhere else. So what a fold has to spend is not the weave's average crimp but whatever is inside the few picks the fold crosses, and in an eight-end satin half the warp ends have nothing there at all.

weaves · Float 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 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 A 4-layer stack round a 180° fold. 4 layers of 260 µm cloth taken round a 180 degree fold, drawn as concentric arcs at their own separation. The outer layer runs round a larger radius than the inner one, so it must be longer — by the angle times the separation, which is 2.45 mm here and 0.82 mm at every interface. In a loose stack that length is found by the layers sliding over one another at the fold. In a stitched seam they cannot: the stitches pin them every 3 mm, so the slip a fold needs is 82 per cent of the distance between two stitches and has nowhere to come from. What the arcs cannot show is what happens instead, which is that the fold opens out to a radius the stack can manage.

A crease cannot cross a seam

The outer layer of a folded stack has further to go than the inner, by the fold's angle times the stack's own thickness. A four-layer seam of quarter-millimetre cloth taken through a half turn needs its outer layer to be 2.45 millimetres longer than its inner — and a stitch line every three millimetres has pinned them. So the fold opens out where it crosses the seam, which is what a trouser crease visibly does, and the arithmetic gives the radius it opens to.

finishing · Crease

Named alongside it

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

Elastic recoveryFibre finenessBending bracketBreaking extensionBending rigidityCloth thicknessCreaseInterchange budgetPacking factorPermanent setYarn diameterAnchorage

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