A crepe is a yarn that will not lie still

A crepe cloth has a surface like fine gravel. It is not a weave effect — a crepe weave produces a related texture by a different route — and it is not a finish. It is the yarn.

A crepe yarn is spun at twice or more the twist anybody would use for an ordinary cloth, woven under tension, and then released: wetted, relaxed, and allowed to do whatever it wants. What it wants is to unwind, and a cloth is not strong enough to stop it.

The mechanism #

A twisted thread under tension stays straight while its torque is below twice the square root of its bending rigidity times its tension. Below that tension the straight state stops being a minimum and the thread coils on itself.

A yarn in a cloth is not free to coil — it is held at every crossing — but it is free to buckle out of the cloth’s plane between crossings, and that is the same instability with a different boundary condition.

So a crepe cloth’s surface is a field of small buckles, one wherever the yarn had enough free length between constraints to reach its threshold. The cloth is not smooth because its threads are not straight, and its threads are not straight because their torque is above what the cloth’s tension can suppress.

The size #

The instability picks a wavelength, and the wavelength sets a radius: two over the stiffness ratio times the twist rate.

Every term in that is known. The stiffness ratio is a quarter for cotton, a sixth for polyester, four fifths for wool. The twist rate is what the spinner set.

At fourteen hundred turns a metre — an ordinary crepe twist — a cotton coils at 0.91 millimetres, so the buckle is under two millimetres across.

A crepe’s pebble is about one to two millimetres. That is the prediction and the observation, and the prediction contains no fitted constant.

The number does not know about the yarn #

The reason to trust it is what it does not depend on.

The radius is two over the ratio times the twist rate. The bending rigidity cancels — it appears in the numerator through the wavelength and in the denominator through the torque — so it does not matter that this collection cannot pin the rigidity down to better than a factor of three hundred.

The count cancels too. A crepe spun at ten tex and one at forty coil at the same radius, at the same twist, and the pebble should be the same size.

So the pebble’s size is a function of the twist and the fibre, and of nothing else about the yarn.

What a spinner is choosing #

The arithmetic turns the trade’s own variables into a design rule.

More twist means a smaller pebble, inversely: doubling the twist halves the radius. So a fine crepe with a tight granular surface is spun harder than a coarse one with a bolder texture, which is exactly the practice.

A different fibre means a different pebble at the same twist. A wool crepe should have a pebble a third the size of a cotton one at the same twist, because wool’s stiffness ratio is three times cotton’s. A silk crepe — silk’s ratio is 0.375 — should sit between them.

That last is a real prediction and it lines up with something the trade knows without a reason: crepe de Chine and wool crepe do not look alike, at similar twists, and the difference is usually attributed to the fibre’s handle.

Why a crepe has to be woven under tension #

A consequence that explains the whole of how the cloth is made.

The instability is suppressed by tension. On the loom, the warp is under tension and the weft is beaten up against a tensioned fell, so the yarn is above its threshold everywhere and lies straight. The cloth comes off the loom flat and featureless.

Take the tension away — wet it, relax it, let it go — and every thread is below its threshold at once. The buckling happens everywhere simultaneously, and the pebble appears.

The crepe effect is created by removing a constraint rather than by adding a treatment, which is why a crepe cloth is finished by doing nothing to it very carefully.

Which direction the pebble runs #

The instability is chiral: a Z-twisted yarn buckles in one sense and an S-twisted one in the other.

So a crepe woven from all-Z weft has a directional texture, and the cloth pulls to one side as it relaxes. That is a known and unwanted effect, and the trade’s answer is to alternate: two picks S, two picks Z — the same balancing a stripe of two twists exploits rather than cancels, so the two senses cancel and the cloth relaxes square.

That practice is universal in crepe weaving and is usually explained as balancing the twist. The mechanism here says what is actually being balanced — the handedness of a buckling — and predicts what would happen without it, which is a cloth that skews.

It also predicts that alternating in pairs gives a slightly different texture from alternating singly, because the buckles of like-handed neighbours reinforce. That is a fine distinction and it is one crepe weavers make.

What separates this from the weave effect #

The distinction is worth drawing because the word crepe names two different things and this collection has already written about the other one.

A crepe weave produces a broken, non-directional surface by scattering its interlacings so that no twill line or repeat is visible. That is a pattern effect: it is in the matrix, it can be enumerated, and this collection has counted the weaves that achieve it.

A crepe yarn produces a granular surface by buckling. That is a mechanical effect: it is in the yarn, it depends on twist and tension, and no matrix contains it.

The two are used together and separately. A true crepe de Chine is a plain weave of crepe yarn — the weave contributes nothing to the texture. A crepe weave in ordinary yarn gives a matt broken surface with no relief. The two together give the deepest texture of all.

So the word names a look rather than a mechanism, and two entirely different pieces of machinery produce it. Knowing which is which decides what to change when the cloth is wrong: a weave problem is fixed at the draft and a yarn problem at the spinning frame.

What was counted, and how #

The criterion is Greenhill’s, unchanged, and is not derived here.

The radius is two over the stiffness ratio times the twist rate in radians per millimetre, which follows from the criterion in one substitution and is checked by computing it from the bending rigidity and the torque separately and finding the two agree at both ends of the stiffness bracket.

The stiffness ratios come from this collection’s own fibre tables, where they are twice the shear modulus over the tensile one.

The comparison against a crepe’s pebble is an observation about cloth rather than a measurement made here, and it is stated as such: one to two millimetres is what a crepe looks like, and 0.91 millimetres of radius is what the arithmetic gives.

Why a crepe shrinks #

A consequence the mechanism explains and the usual account does not.

A crepe cloth shrinks a great deal on relaxation — ten per cent or more, far beyond what an ordinary cloth of the same construction does — and the shrinkage is what produces the texture rather than accompanying it.

The reason is geometric. A thread that has buckled out of the cloth’s plane takes up more length than a straight one covering the same distance, so the cloth’s dimensions fall by however much length the buckling absorbs. The pebble and the shrinkage are the same event.

That gives a relation the arithmetic supports: the deeper the pebble, the greater the shrinkage, and both go with the twist. A cloth that has crept only a little has shrunk only a little, and a fully developed crepe has shrunk a lot.

It also explains why crepe cloths are woven much wider and longer than they finish, and why the finished width of a crepe is a process outcome rather than a loom setting. That is unusual: for almost every other cloth the finished width is set at the reed.

Why a crepe is unstable in wear #

The last consequence, and it is the reason crepe garments have a reputation.

The buckling is held by nothing. There is no set, no bond and no interlacing preventing a buckled thread from straightening again if it is given tension — which is what happens when a crepe garment is worn, pulled, or pressed.

So a crepe cloth loses its texture where it is stretched and gets it back where it is released, and the result is a fabric that changes appearance with wear and recovers unevenly after washing.

The trade’s remedy is to set the cloth after the crepe has developed, which fixes the buckles in place at the cost of some of their liveliness. That is the same trade-off setting always presents, and here it is being made on the fabric rather than on the yarn.

Where the model stops #

The boundary condition is wrong. The criterion is for a free thread under uniform tension, and a thread in a cloth is held at every crossing. The correct problem is a buckling between supports, which has the same wavelength scale and a different threshold — the supports raise the tension needed, so a cloth suppresses buckling better than a free thread.

That means the criterion under-predicts the twist needed to crepe a given cloth, and the direction is right: crepe twists are higher than the free-thread threshold would suggest.

The pebble is a surface and the criterion gives a wavelength. How high the buckle stands out of the cloth is a question about the cloth’s own resistance to being deformed out of plane, and nothing here computes it.

And the yarn is treated as unset. A crepe yarn that has been steamed does not crepe, which is the whole reason crepe yarns are handled wet and never set — and it is a reminder that every torque on this ladder is a property of a fresh yarn.

Why crepe is spun and not woven #

The rung explains a division of labour in the trade that is otherwise a matter of convention.

Almost every fabric effect this collection has studied is produced at the loom: a weave, a colour arrangement, a sett, a float. The draft decides and the cloth follows.

A crepe cannot be. Its effect is a property of the yarn’s twist, so it is decided at the spinning frame, hours or days before anybody chooses a weave — and no draft can produce it in an ordinary yarn.

That makes crepe one of a small class of cloths where the spinner rather than the designer owns the appearance, and it is why crepe is bought as a yarn specification rather than as a weave.

The other members of that class are worth naming because they are the same shape: a fancy yarn’s slubs and loops, a chenille’s pile, a mélange’s colour, a high-lustre yarn’s shine. In each, something was decided before the loom that the loom cannot change.

The generalisation #

The rung is an instance of a move that this work has made repeatedly and that is worth naming.

Take an instability nobody wants and find the product that is made of it.

Snarling is a nuisance in every part of the trade except one, where it is the entire point. The same criterion that tells a spinner how much tension to keep on a yarn tells a crepe weaver how much twist to put in it, and the two are the same arithmetic read in opposite directions.

This collection has one other pair of that shape. Felting is a fault in every wool fabric except the ones where it is the finish, and the site’s own ratchet that makes wool felt is the mechanism read as a process rather than as a defect.

Wherever this collection has a mechanism for a fault, it is worth asking what is made of it deliberately — because the deliberate version is usually where the mechanism has been characterised best.

The measurement that would settle it #

The prediction is unusually easy to test and the test needs a ruler and a magnifier.

Take three crepe cloths of the same fibre at three different twist levels, and measure the pebble spacing on each. The arithmetic says the spacing should go as one over the twist, exactly.

Then take two crepe cloths of different fibres at the same twist — a silk and a wool, say — and measure again. The arithmetic says the ratio of their pebble sizes should be the inverse ratio of their stiffness ratios: a wool’s pebble should be about a third of a silk’s.

Both are comparisons rather than absolute measurements, which is the right shape for a prediction whose absolute value depends on a shear modulus with a factor of two on it.

And the second is the sharper of the two, because a factor of three between two fibres is far outside anything a measurement of a pebble could get wrong.

What would break it #

Two outcomes would say the mechanism is not this one.

A pebble that depends on the count. The radius contains no count, so a fine and a coarse crepe of the same fibre at the same twist should have the same pebble spacing and different depths. A spacing that moved with the count would mean the buckling is being set by the cloth’s geometry rather than by the yarn’s instability.

Or a pebble that depends on the sett. Likewise: the sett decides how much free length a thread has between constraints, which affects the threshold and not the wavelength. A spacing that tracked the sett would say the buckling is a between-supports problem rather than a free-thread one, which is the more likely of the two failures and would be worth knowing.

The second is the one to expect, and it would not overturn the account so much as refine it: the wavelength would then be set by the constraint spacing where that is shorter than the natural one, and by the natural one otherwise.

Who found it, and when #

Crepe yarns and crepe cloths are old, and the account of the effect as the yarn’s residual torque acting on a relaxed cloth is standard in every weaving text.

Greenhill’s stability criterion is from 1883 and has, as far as this collection can find, never been applied to it — which is a little surprising, since the effect is manifestly a buckling and the criterion is the standard one for a twisted rod.

What is this collection’s own is the pairing, and specifically the observation that the wavelength is bracket-free: the pebble’s size can be predicted without knowing either of a yarn’s two rigidities, because it depends only on their ratio.

What a crepe costs, briefly #

The effect is bought and it is worth naming the price, since a crepe yarn is not a free choice.

Strength. A yarn twisted past its optimum is weaker than one at it, because the fibres are running at too steep a helix angle to contribute along the yarn’s axis. A crepe twist is well past the optimum, so a crepe cloth is weaker than a cloth of the same count at ordinary twist.

Handling. A crepe yarn cannot be handled slack at any stage. Warping, weaving and every transfer has to be under tension, and any slack loop snarls irrecoverably.

Dimensional stability. The cloth shrinks enormously on relaxation and continues to move afterwards, so a crepe garment’s dimensions are less reliable than almost anything else.

And cost. All three of the above mean lower machine speeds, more stoppages and more waste.

Against that is a surface no other route produces, which is why crepe survives despite every one of those and why it has always been a more expensive cloth than its construction alone would suggest.

Where the ladder goes next #

A crepe is one thing a high twist does to a cloth and it is not the only one. Twist changes the cloth’s cover, its handle, its strength and its shrinkage, and the trade’s twist limits are a compromise among all of them.

What a high-twist yarn costs a cloth puts the costs beside the effect they buy.