Textile Structure
how cloth is put together
Concept

Weakest-link — where it appears

The principle that an assembly fails where its weakest member does, so its strength is an extreme rather than a mean. It is why a yarn's thinnest place and not its count decides what it breaks at, and why a designed variation with a floor is kinder than an accidental one of the same coefficient of variation.

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

A coating over the hole it has to bridge. Four warp ends of 40 tex seen end-on at 20 per centimetre, with a 120 micrometre PVC film over them. The film is supported everywhere it lies on a thread and unsupported over the 252 micrometre clear span between them, which is the same span at every hole in the repeat. The film's thickness is drawn to scale against that span; the bulge is exaggerated. At 20 MPa the film will hold at most 381 bar, which is a bound and not a prediction.

A coated cloth fails at its holes

Spread a film over a fabric and it is supported everywhere it lies on a thread and unsupported over every hole. A woven cloth's holes are all the same size — exactly, because a repeat is a repeat — so the film has one span to bridge and the fabric has a burst pressure rather than a distribution. A nonwoven gives it a distribution, and a membrane fails at the largest hole it meets.

applied · Coating A designed thin place does not get worse and an accidental one does. The thinnest place a yarn reaches, against how many gauge lengths of it are tested, for a slub yarn and for a randomly uneven yarn of the same 36.3% coefficient of variation. The slub's floor is its base count — 89% of its mean — and it is a horizontal line, because a designed variation has a stated minimum and never goes below it. The random yarn's minimum is an order statistic and falls without limit: 56% over 10 lengths and 22% over 30000. So the advantage is not a number but a function of how much yarn is being asked about, running from 1.6× to 4.0×. What the curve cannot show is the break itself: a yarn's strength at a thin place is not proportional to its linear density there, and the conversion needs a fibre model.

A designed thin place is kinder than an accidental one

A slub yarn and a badly spun one can carry exactly the same coefficient of variation, and the number tells a mill nothing about which it has. The designed variation has a floor — its base count, and it never goes below it — while the accidental one has a tail that falls further the more yarn is tested. At 36% CV the slub bottoms at 89% of its mean and the random yarn reaches 24%, and the gap widens from 1.6 to 3.7 times as the test grows from ten gauge lengths to ten thousand.

fancy · Fancy yarn

Named alongside it

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

Burst pressureCoatingCoefficient of variationCoverFancy yarnFilmMembraneNonwovenOpeningPopulationPore distributionSett

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