Textile Structure
how cloth is put together
Concept

Crimp interchange — where it appears

Crimp moving from one thread system to the other as a cloth is pulled, so one direction lengthens as the other contracts. It is why a woven cloth has a Poisson ratio at all, and why that ratio is a property of the construction rather than of the fibre.

Named by 22 essays across 7 fields — each of them below, with the objects they name alongside it.

Pull it lengthways and it narrows. The same cloth before and after a small extension along the warp. No thread has stretched: the extension came out of the warp crimp, that crimp went into the weft, and the fabric is narrower for it.

Crimp, and why cloth narrows when it is pulled

A thread in cloth is longer than the cloth it crosses. Pull the fabric one way and that extra length is taken out of one direction and put into the other, so the cloth gets narrower without a single fibre stretching.

setting · Crimp Four ways a fabric gets longer without stretching. Extension available from each mechanism, computed from the geometry that provides it. None of these numbers involves a yarn changing length; every one of them is a shape changing, and they differ by an order of magnitude.

Why a knit recovers and a woven does not

Four fabrics get longer without a single yarn stretching, and the four mechanisms are worth wildly different amounts. Three of them are recoverable and one is very nearly not, and which is which follows from where the extension came from.

knits · Knit What a balanced cloth wastes under pressure. The fraction of a balanced fabric's fibre that is along for the ride, in a stress field of each ratio. A closed cylinder is exactly two to one — the ratio of the two areas the pressure acts on — so a balanced cloth reaches its limit around the circumference with the axial system at half its capacity, and a quarter of the fibre is doing nothing.

An inflated cylinder wants an unbalanced cloth

Balance is a virtue in almost every other cloth. Under pressure it is a defect with a size — a closed cylinder carries exactly twice the stress around its circumference as along its axis, so a balanced fabric reaches its limit in one direction with a quarter of its fibre doing nothing at all.

applied · Membrane Everywhere a sheeting can go. Every state a sheeting of 28 × 26 threads per centimetre in 25 and 25 tex can reach without a yarn changing length, solved from Peirce's plain-weave geometry. The set is a curve and not a region: 4.03 per cent of extension is available along the warp, and reaching it costs 6.98 per cent of the width.

A cloth extends by moving its crimp

Everybody says the extension available along the warp is the warp's own crimp. On six of eight ordinary cloths it is not — a close sheeting has 14.61 per cent of warp crimp and reaches 4.03 per cent, because the limit lives in the weft.

mechanics · Tensile A membrane is cut smaller than it is. Warp and fill compensation against how far the crossings flatten under prestress. With the thread lengths and the cloth's thickness both fixed there is no strain available at all — the closure condition determines the state — so the whole of the compensation is the crossings squeezing and the crimp coming out. The direction that arrives with less crimp gives back less, which is why a warp compensates less than a fill.

A membrane is cut smaller than it is

A tensioned fabric roof is cut to a pattern smaller than the shape it will take, because stressing it makes it grow. At a fixed cloth thickness a prestress can only interchange crimp — one direction grows and the other shrinks — so everything that makes both directions grow is the crossings flattening, which is the one quantity here this site cannot compute.

applied · Crimp Pull it lengthways and it narrows. The same cloth before and after a small extension along the warp. No thread has stretched: the extension came out of the warp crimp, that crimp went into the weft, and the fabric is narrower for it.

What crimp interchange actually conserves

Pull a cloth lengthways and it narrows, because the crimp moves from one system to the other. Inextensibility says that much and no more — it is one equation short of an answer, and the second equation everybody uses is an assumption with a name.

setting · Crimp Everywhere a muslin can go. Every state a muslin of 24 × 22 threads per centimetre in 20 and 20 tex can reach without a yarn changing length, solved from Peirce's plain-weave geometry. The set is a curve and not a region: 6.59 per cent of extension is available along the warp, and reaching it costs 21.82 per cent of the width.

Pulled both ways, only one can give

A cloth at constant thread length has one degree of freedom, so its reachable states are a curve rather than a region. Equal extension in both directions meets that curve at exactly one point — the state the cloth is already in — so the amount available is nought.

mechanics · Tensile A ratio that will not hold still. The exchange rate between the two directions for 4 cloths, against how far each has been extended along the warp. Every curve is above one half everywhere it is drawn, and every curve rises — so a single number for a cloth's ratio has to name the state it was read at, which a material's ratio does not.

A cloth's Poisson ratio is not a material's

The ratio of a cloth's contraction to its extension has a name everywhere else in mechanics, and it breaks every rule the name comes with — above one half on all eight cloths measured, doubling across a four per cent span, and not reciprocal between the two directions.

mechanics · Tensile The two routes a poplin has to a strain. A poplin drawn in section at three places: as woven, at the end of what its crimp can supply, and past that. Between the first two the warp's crimp falls from 8.97% to 4.85% and the weft takes on what it gave up, and the thread length is 0.4953 mm in both — nothing has stretched, and the cloth is 3.93% longer. Between the second and the third the geometry cannot move because the weft's straight run has vanished, so the cloth's extra 2.0% is the thread's extra 2.0%. What the drawing cannot show is which of the two a piece of cloth has had: the first two states look different and the last two look the same, and it is the last two that differ in whether the cloth comes back.

A cloth gives back less than it took

Everything this collection computes about a deforming fabric is reversible, and no fabric is. The repair is not a new material property: a woven cloth has two routes to a strain, one of them costs its threads nothing and comes back in full, and where the first route runs out is a number about the sett with no fibre in it at all.

cloth · Memory The energy well, and where the cloth sits in it. The bending energy of a sheeting at every state on its own constant-thread-length locus, plotted against how the crimp divides between the two systems. The minimum is at 1.22 and the value every Peirce solution here is drawn at is 1.00, marked. The well's depth decides how firmly the ratio is settled, which is why an open scrim's measured crimp scatters and a close sheeting's does not. What the plot cannot show is the friction that stops a cloth reaching the bottom, which turns the minimum into a band.

The crimp ratio is not a measurement

Peirce's geometry is two thread systems, four unknowns and three equations. It cannot say how the crimp divides between warp and weft, so every cloth solved so far has been drawn at a ratio somebody chose. Give the threads a stiffness and the missing equation arrives — and for six of the eight cloths in the table it arrives with no material constant in it at all.

setting · Crimp The load–extension curve, computed from a stiffness. The tension in one end of a sheeting against how far the cloth has been extended, computed as the slope of its bending energy along its own constant-thread-length locus. The curve passes through zero at the state of least energy, which is where an unloaded cloth sits, and rises either side of it. What the curve cannot show is what happens after the crimp runs out: past the end of the locus the load is carried by stretching yarn rather than by straightening it, and that is a modulus three orders of magnitude higher and a different figure.

The locus gets a force

This site has drawn the set of states a cloth can reach without stretching any yarn, and has never been able to say which of them it is in or what it would cost to move. Both questions are one derivative of a bending energy — and the answer explains the flat start every fabric's load–extension curve has, which is not slack yarn but a symmetry.

mechanics · Tensile A front on a thread with 8 per cent crimp. Three rows at one scale. The top row is the warp end laid out straight, with the wetted front marked at four equal quarters of its own length — which is where Washburn's law puts it at four times whose square roots are evenly spaced. The middle row is the same thread crimped at 8 per cent, so it covers 92.6 per cent of the paper the straight one did. The bottom row is the cloth, and the four fronts on it are the four above pulled back by 1.08. A coefficient is a length squared over a time, so it comes down by 1.1664 — exactly (1 + c)², with no property of the liquid or the fibre in it. The thread's thickness is not drawn and neither is the liquid: a meniscus in a 2.33 µm pore is finer than any line on this canvas.

Wicking is slower along a crimped thread

A front travelling up a warp end travels the thread's path, which is longer than the cloth by exactly the crimp. So the wicking coefficient measured on the fabric is the yarn's own divided by (1 + c)² — 14.3 per cent lost at eight per cent crimp, whatever the liquid.

applied · Wicking The resting band, not the resting point. The bending energy of a sheeting along its own constant-thread-length locus, with the band in which friction can hold it shaded. The minimum is a single state; the band is 10.9 per cent of length wide, because the cloth stops sliding as soon as the energy it can release falls below the 0.0756 N friction takes to move a crossing. What the drawing cannot show is which end of the band a given piece of cloth stops at, which depends on the direction it arrived from and is what makes relaxation hysteretic.

A cloth relaxes until its threads stop pushing

The finishing field treats the relaxed state as a place a cloth arrives at. With an energy along its own locus and a friction at its crossings it is not a place but a band — and which point of the band a piece of cloth stops at depends on which side it came from, which is why washing it twice gives two answers.

finishing · State The poplin's two budgets as it is held stretched. What is left of a poplin's interchange in each direction as it is held at more and more warp strain. The warp's budget falls to nothing at 3.93%, which is the point of the curve; the weft's rises, because the crimp the warp gives up is crimp the weft takes on. There is one locus and one position on it, so the two are not two quantities that happen to be related — they are the two distances from one point to the two ends of one curve. The consequence is that a pre-tensioned cloth has almost no warp recovery left and more weft recovery than it started with. What the plot cannot show is that the exchange rate between them is not constant: the curve is not a straight line, and its slope is the Poisson ratio this site computes elsewhere.

A cloth has one budget for two directions

A woven cloth looks as though it carries two independent reserves of free extension, one along the warp and one across the weft. It carries one. There is a single curve of states and a single position on it, so every hundredth spent one way is refunded the other — which means a pre-tensioned cloth has not used its recovery up, it has moved it.

mechanics · Tensile Wash-by-wash shrinkage, reported and modelled. The shrinkage an unfinished cotton cloth shows in each of five laundering cycles, beside what a model with no rate in it predicts. The model says a wash lets every crossing whose frictional barrier is below the cloth's current excess slip to the edge of its own band, and that is a distribution rather than a rate. Two numbers are fitted — the excess the cloth came off the loom with, 7.13%, and the spread of the barriers, 37.2× — against the first two washes. Washes three, four and five are predictions with nothing left to adjust and come out at 0.506%, 0.284%, 0.179% against reported 0.50%, 0.30%, 0.20%. What the bars cannot show is the finding underneath: the reported yarn-on-yarn friction range gives a spread of only 1.34×, which would have the tail over by the third wash.

A cloth shrinks most the first time

A laundering test reports five numbers and they fall away like a geometric series. Nothing in a wash is slow — a cloth is agitated tens of thousands of times in half an hour — so a second wash that shrinks it again is direct evidence that its frictional barriers are spread, and the ratio between successive washes measures how far.

finishing · Shrinkage Shrinkage from wetting, cloth by cloth. The change in each cloth's relaxed construction when its threads swell by 20% across and 1.2% along. Both states are least-energy states of their own constant-thread-length locus, which is the only comparison the locus admits: its minimum is a state at its own sett, so it may be compared with another minimum and not with a quoted construction. Positive is smaller. Every cloth that has a wet state closes up except the cheesecloth, which opens by half a per cent because the fibre's extra hundredth of length outruns the extra crimp a thicker partner costs. What the bars cannot show is the three cloths that are missing, which have no wet state at all.

Wetting moves a cloth to another locus

A cloth's constant-thread-length locus is built at a fixed thickness. Swelling changes the thickness, so a wetted cloth is not somewhere else on its own locus — it is on a different one, and the distance between the two least-energy states is the shrinkage. Five of the eight cloths here have a wet state, and one of them gets bigger.

setting · Crimp How far each cloth's sett moves between the loom and the finished state. A cloth on the loom is held: the warp is under beam tension and the picks are driven up at whatever density the take-up says. Let it go and it relaxes to the least-energy state of its own locus, which is a state at a different sett. The bars are how far each sett moves, and they always move in opposite directions because there is one locus: warp ends per centimetre fall as the cloth widens and picks per centimetre rise as it shortens. Seven of the eight move a little over one per cent; the poplin, whose two counts and two setts are the only unbalanced pair in the table, moves six and ten. What the bars cannot show is what a designer does with them, which is that the two numbers a specification quotes are not two free numbers — the finished construction is a point on a one-dimensional curve.

The construction a loom must be set to

A specification quotes ends and picks per centimetre in the finished cloth, and a loom is set to neither of them. The cloth relaxes to the least-energy state of its own locus, which is a state at a different sett — and because the locus is one curve, the two numbers a specification quotes are not two free numbers.

setting · Take-up What a tensioned sheeting has left of its load. A sheeting pulled to a strain, clamped at that length and left. Its length does not change, and its load does: crossings rearrange locally until the load has fallen to what friction alone can hold, which is 0.0756 N per end and is the same number whatever the cloth was pulled to. So the fraction retained is that floor over the load applied, and it falls — a cloth tensioned to 4.94 per cent keeps 29 per cent of what it was given. Below the resting band's own edge nothing is lost at all, because the cloth was never outside what friction could hold. What the plot cannot show is time: nothing here says how long the rearrangement takes, only where it stops.

A tensioned cloth loses its load

Clamp a fabric at a fixed length and its tension falls overnight. Nothing crept and nothing flowed: the crossings rearranged locally until the load had dropped to what friction alone can hold, and that level is the same number whatever the cloth was pulled to — so the harder it was tensioned, the smaller the share it keeps.

mechanics · Set The locus a warp knit's underlaps put it on. Width against length for each shog, at 28 needles an inch and 14 courses a centimetre. An underlap keeps its own length, so the two spacings lie on a circle and every fabric moves along an arc of it. A tricot can be pulled 27.3 per cent wider and 62 per cent longer; a cord 7.5 and 173. The shog decides which.

The shog is the anisotropy

An underlap is a straight run from one needle to another on the next course, so it is a hypotenuse — and its length is fixed while the two spacings are not. Pulling the fabric wider turns it towards the horizontal and pulls the courses together, on a circle. Every state a warp knit's underlaps allow lies on that circle, its as-knitted point sits where the shog puts it, and the ratio of the length it can give to the width it can give runs from 2.3 at a tricot to 218 at four needle spaces.

knits · Warp knit Which end of its interval a construction falls to. For a balanced 20 tex, 24-thread reference with its weft count and weft sett scaled, the share of the crossing height the warp takes at the least-energy state. 25 of the 28 solvable constructions land at an end of their own feasible interval — nought, with the warp dead straight, or one, with the weft dead straight — and the few between them are the frontier where the two regions meet.

The energy has no crimp ratio to give

The account left a gap at its top: a construction whose preferred crimp ratio lies outside the interval its geometry admits sits at a boundary, and boundary states had not been studied. Profiling the whole energy rather than its minimum says there are two regions and a frontier — six of the eight cloths in the table of cloths here fall to an end of their own interval with the weft dead straight, and the two that do not have wells 3.27 and 0.52 per cent deep, against a rigidity known to within a factor of 408.

setting · Crimp What a figured warp pays in tension to share one beam. For six pairings of figure and ground, the difference in warp tension that lets their ends share one beam: the force per end that takes the take-up difference out of the ground's crimp, along that region's own constant-length locus, with the yarn's rigidity at both ends of the band two tests place it in. a damask: satin on its own complement, 0.00% apart: none needed; an eight-end satin figure on a five-end satin ground, 0.31% apart: 0.006 to 0.020 N; a five-end satin figure on a 3/1 twill ground, 0.90% apart: 0.021 to 0.069 N; an eight-end satin figure on a 2/2 twill ground, 3.02% apart: 0.304 to 0.995 N; an eight-end satin figure on a plain ground, 14.15% apart: past what the ground's crimp can give; a 2/2 twill figure on a plain ground, 11.14% apart: past what the ground's crimp can give. The loom's front shaft holds 0.52 N an end. What the chart cannot show is how uneven a warp's tension may be before it shows in the cloth.

A figured warp pays in tension before it needs a beam

Figure and ground take up warp at different rates, and counted against a fixed slack, any difference at all — a third of a per cent — made a round figure need four beams. A real let-off holds tension, not length. Ends that consume more pull harder, and an end pulled harder gives up crimp, until every end consumes alike. For an eight-end satin figure on a five-end satin ground that costs a hundredth of a newton an end, and one beam serves. For a satin on plain it costs more crimp than the ground has, and no tension will do.

fancy · Jacquard The crimp split of a muslin against the warp's tension. The warp's crimp and the weft's at the least-energy state of a muslin at its own sett, with the warp held at tensions from 0.0001 to 1.0 newtons, and the yarn's rigidity 4.0 times the free bound. With no pull the warp holds 28.5 per cent and the weft 0.0; they are equal at 0.019 N, and by the front shaft's 0.52 N the warp holds 0.00 per cent. What the plot cannot show is friction: a real cloth is held wherever its crossings stop it, not at the least state.

The loom hands the crimp to the weft

Bending alone gave the fixed-sett energy nothing to say: six of eight cloths fell to the end of their interval with the weft dead straight. Put the warp's tension in and the answer is not a well but a switch. The crimp changes hands across a factor of two or three in tension, at a few hundredths of a newton — and the loom holds its warp at half a newton, so on the loom every cloth's warp is as straight as its geometry allows.

setting · Crimp

Named alongside it

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

CrimpTensile locusPeirce's geometrySettJammingBending rigidityExtensionThread lengthInextensibleSpecificationAnisotropyInterchange budget

All concepts