Which fibres crease, and why there are two answers

Linen creases and the crease does not come out. Cotton creases and can be pressed back. Wool hangs out overnight. Polyester does not crease at all, which is the whole of why it exists as a shirting.

Those four sentences are the accumulated experience of everyone who has worn clothes, and they are usually explained by pointing at each fibre’s chemistry in turn. This rung explains them with two numbers per fibre, neither of which is a chemistry — a breaking extension and an elastic recovery — and finds that the four sentences are covering two different mechanisms that happen to end in the same complaint.

The claim #

Two different things end in a crease, and both are needed to order the fibres.

The first is that the fibres at the fold break. Their fraction of the fold’s strain never comes back because the fibre carrying it is no longer continuous, and no amount of pressing, hanging or steaming restores it. That is flax, decisively, and cotton, marginally.

The second is that the fibres survive the fold and return very little of it. The fibre is intact and it has taken a set. That is viscose, and it is why a viscose garment creases badly while being made of a fibre with three times the breaking extension of the cotton beside it in the same wardrobe.

Ordering the fibres by either column alone gets one of them wrong, and the two failures are not repaired by the same intervention.

Where the strain comes from #

The whole of the input geometry is one expression. A cloth’s sharpest possible fold has the radius of the yarn it is made of, because two crowns on the inside cannot pass through one another; at that radius a fibre free to slide is strained by the ratio of the two diameters; and the ratio of the two diameters is

$$\varepsilon = \sqrt{\frac{\text{packing} \times \text{tex}_{\text{fibre}}}{\text{tex}_{\text{yarn}}}}$$

with no measurement of a crease, an iron or a pressing force anywhere in it. For a 20 tex yarn at a packing of 0.6 it gives 7.14 per cent for cotton, viscose and nylon, whose fibres are all about 1.7 decitex; 12.25 for wool, whose fibres are 5.0 and therefore much coarser; 6.00 for silk at 1.2; 6.71 for polyester at 1.5; and 9.49 for flax at 3.0.

Those numbers are the whole geometric input. Everything else in this rung is two measured columns.

The first column: which fibres break #

Compare the fold’s strain with the low end of each fibre’s measured breaking extension, which is the conservative comparison — some fibres in any real yarn break at the bottom of the range.

Flax is strained 9.49 per cent against a breaking extension of 1.5 to 3. The margin is 0.16, which is to say the fold is six times what the weakest fibres will take and three times what the strongest will. A linen crease is a line of broken fibres, and the reason it does not come out is that there is nothing left to pull it out.

Cotton is strained 7.14 against 6 to 10. It straddles: the fold is past the low end and inside the high one, so a fraction of the fibres at a sharp fold are broken and the rest are at a strain where cotton’s recovery has fallen to about half. Cotton creases for both reasons at once, weakly on each.

Everything else clears its own breaking extension with a factor of 1.8 to 2.8 to spare.

The high-modulus fibres are worth a line even though nobody creases them. Glass, carbon and aramid are all strained past breaking at their own tightest fold — glass by a factor of two, carbon by two and a half — which is the arithmetic behind a familiar practical rule: a woven reinforcement must not be folded sharply, and a crease in a carbon fabric is damage rather than an appearance defect.

The second column: which fibres do not return #

The second column is elastic recovery, and it runs into the gap the fibre ladder records: four of the seven common fibres have no recovery figure at the strain their own tightest fold imposes, because the tables stop at five per cent and the fold asks for seven.

What is quoted instead is the recovery at the top of each fibre’s own measured range, with the strain it was measured at attached. Since recovery falls with strain, that is an upper bound on the recovery at the fold, which is the safe direction for an argument about what a fibre fails to give back.

Viscose returns 0.32 at five per cent — the lowest figure in the table by a wide margin, below cotton’s 0.45 and half of silk’s 0.65, and it is the second time water separates viscose from the cotton this site’s geometry cannot distinguish it from. It survives the fold with room to spare and gives back a third of it.

The census, and the one fibre it puts in the wrong place #

Sorting on both columns gives three verdicts: fibres break, survives and does not return, survives and returns.

The check is that the sorting agrees with a measurement this arithmetic has never seen — the crease recovery angle, which is a fabric test: fold a specimen through 180°, load it, release it, and read the angle it opens to. Cotton reports 85 to 115 degrees, viscose 70 to 95, flax 70 to 85, silk 120 to 140, polyester 120 to 140, nylon and wool 130 to 150.

Both fibres that break are in the bottom three by that test. A fibre that does not break is in there too, so breaking alone does not order the table. And every fibre that neither breaks nor returns badly is above 120 degrees, without exception.

One fibre is in the wrong column, and it is wool.

Wool’s fibres are coarse — five decitex against cotton’s 1.7 — so its own tightest fold strains them 12.25 per cent, the largest strain in the table, and it returns 47 per cent of that. By the census’s rule that is “survives and does not return”, and wool has the best crease recovery of any fibre in it.

The reason is the convention at the head of the recovery table rather than anything in the argument. Those figures are immediate recovery, read at once on unloading, and wool’s recovery is the most delayed of any fibre here and the most helped by moisture. Hanging a suit in a steamy bathroom is not folklore: it is the one input this ladder cannot compute, changing.

That the census has exactly one exception, and that the exception is the fibre whose measurement convention is least suited to it, is asserted rather than noticed — a second misplacement would mean the two columns were not doing the work claimed for them.

A prediction with no fabric in it #

The two columns say which fibres crease. It is worth asking whether the recovery figure is even the right size, and there is one independent test available.

A specimen creased through 180° has a curvature imposed on its fibres. A fibre returns a measured fraction of a strain. Curvature is proportional to strain at a fixed radius. So the angle recovered should be 180 degrees times that fraction, with no sett, no weave and no friction anywhere in it — the crease recovery angle a fibre would have.

The errors have both signs, and that is the finding rather than a disappointment. The two mechanisms left out push in opposite directions. Friction between the yarns holds a fold in after the fibres have finished pulling on it, which makes the real angle smaller than the prediction. Delayed recovery lets the fold out over the hours after the test ends, which makes it larger. Neither dominates, so a fibre-only estimate is an estimate.

What it does establish is that the recovery table is the right size. A table wrong by a factor of two would show up here as a systematic error of a factor of two, and it does not.

What the two columns imply for a treatment #

The practical value of separating the mechanisms is that they respond to different things, and the difference is not a matter of degree.

A fibre whose fibres break at the fold cannot be helped by anything that changes its recovery. Recovery is what an intact fibre does with a strain it survived, and a broken one has no opinion. The only routes available for flax are to make the fold gentler — a coarser yarn, a lower packing, or a weave that keeps crimp where the fold falls so that the cloth-level route lasts longer — or to accept the crease as part of the material’s character, which is what the linen trade has done for several thousand years.

A fibre that survives and does not return can be helped by a treatment, and cotton needs both. Cotton straddles: some of its fibres at a sharp fold are broken and the rest are past the strain at which its recovery has halved. A cross-linking finish addresses the second half and leaves the first, which is consistent with such finishes improving cotton’s crease recovery substantially without ever making it behave like polyester.

There is a third route that this collection can point at and not price, and it is the one the weave offers. Nothing in this rung has a sett in it: the fold’s strain depends on the two counts and the packing and on nothing else about the cloth. But whether a given warp end has any crimp to spend at the fold’s own position is a question about the matrix, and a construction that guarantees every end a turn inside the fold is a construction that spends less of the fold on its fibres. That is a lever a finisher does not have and a designer does.

What was counted, and how #

Three assertions carry the census and the second is a refutation of the first taken alone.

Every fibre whose fibres break at the tightest fold must be among the three worst by the crease-recovery test. Some fibre that does not break must also be in there, so that breaking alone is shown not to order the table. And every fibre that neither breaks nor returns badly must be above 120 degrees.

The recovery lookup refuses a strain past a fibre’s measured range rather than extrapolating, and the census uses a separate function with a flag on its answer for the capped case, so that no essay can quote a recovery at the fold’s own strain for a fibre that has none. Four of the seven are capped and the figure says which.

The strain expression is checked against the direct computation of the two diameters, to a relative tolerance, because the closed form is the thing every number here is quoted from.

Where the model stops #

Twenty tex is a choice. The fold’s strain scales as the inverse square root of the yarn count, so a coarser yarn strains its fibres less at its own tightest fold — a 60 tex cotton reaches 4.12 per cent rather than 7.14, and clears its breaking extension comfortably. That is the arithmetic behind heavy cottons creasing less sharply than fine ones, and it means the census’s verdicts are verdicts at a stated count.

The packing factor is 0.6 throughout. It enters under a square root, so the sensitivity is mild, and a highly twisted yarn at 0.7 strains its fibres eight per cent more than the figures here.

No treatment is modelled. Durable-press finishes work by cross-linking, which changes a fibre’s recovery and its breaking extension together, and this collection carries neither the chemistry nor the modified numbers. What it can say is that such a finish must move the first column as well as the second for cotton and cannot help flax at all, because flax’s fibres are broken and no chemistry unbreaks them.

And moisture is absent. Every figure is at standard conditions. Wool at high humidity is a different fibre in exactly the respect this rung measures, and the census’s one exception is the standing reminder.

The count at which each fibre stops breaking #

The limits section notes that twenty tex is a choice and that the strain falls as the inverse square root of the count. Inverting that gives the count at which each fibre clears its own breaking extension, which is a more useful number than the verdict at one count.

Setting the fold’s strain equal to the breaking extension,

tex_yarn = packing × tex_fibre ÷ ε².

Flax, at 3.0 decitex and a breaking extension of 1.5 to 3 per cent, clears at between 200 and 800 tex. That is rope. No linen cloth is woven anywhere near it — a heavy furnishing linen is fifty or sixty tex — so flax breaks its fibres at its own tightest fold at every count anybody weaves, and the verdict is not a verdict at twenty tex but a verdict everywhere.

Cotton, at 1.7 decitex and 6 to 10 per cent, clears at between 10 and 28 tex. Commercial shirtings run from ten to twenty, which is inside the bracket at both ends — so a cotton shirting really does straddle, in the exact sense that the coarser it is the fewer of its fibres break.

That gives the trade’s own experience a shape. A coarse cotton creases softly and a fine one creases sharply, and the boundary is near thirty tex: a denim, a drill or a canvas is above it and has no broken fibres at any fold, while a voile or a lawn is well below it and has many. Which is exactly how those cloths behave, and it has never been attributed to a count before.

And the fibre’s own fineness is the other lever #

The same expression carries the fibre’s decitex, and it carries it upstairs — so a finer fibre at the same yarn count strains less at the fold.

Cotton at 1.7 decitex reaches 7.14 per cent at twenty tex. A long-staple cotton at 1.2 decitex reaches 7.14 × √(1.2/1.7) = 6.00 per cent, which is exactly the low end of cotton’s breaking range rather than above it.

So spinning a finer cotton moves the fibre out of the straddle and into the clear, without changing the yarn count, the weave or anything else. That is a genuine prediction and it is a known reputation: Egyptian and Sea Island cottons are said to crease less than ordinary upland cotton at the same count, and the reason usually offered is the staple length.

The staple length is not in this arithmetic at all. The fineness is, and the fine cottons are fine as well as long — so the reputation may be attached to the wrong one of the two properties that always travel together.

That is a testable separation. Two cottons of the same fineness and different staple should crease alike; two of the same staple and different fineness should not. The prediction is that fineness decides it and staple does nothing, which is a comparison the trade has never had a reason to run because the two are bought together.

Which orders the levers for a fabric that must not crease #

Three of them now have exponents, and they are not equal.

The fibre’s fineness enters as a square root and is a purchasing decision. The yarn count enters as an inverse square root and is a construction decision. And the fibre’s breaking extension enters as a square in the count — so a fibre a tenth more extensible clears at a count a fifth finer.

The last is the largest and it is the one nobody can change without changing fibres. Which is, in the end, the answer the trade reached: the cloth that does not crease is made of a different fibre, and the two levers available inside a fibre are both square roots.

The generalisation #

When two mechanisms produce the same symptom, an ordering built on one of them will be right about most cases and confidently wrong about a few — and the few are where the interventions differ. Fixing viscose’s crease is a recovery problem and fixing flax’s is a strength problem, and any treatment aimed at the wrong one is money spent on the wrong column.

The diagnostic is available in general and is worth stating as a habit. If a ranking is nearly right and has a stubborn outlier, look for a second mechanism that the outlier is the pure case of, rather than for a correction to the first.

The second lesson is about measurement conventions. A convention that suits the instrument can misclassify exactly the case the subject cares about most. Immediate elastic recovery is a sensible thing to measure and it is the wrong thing for wool, whose whole commercial value in this respect is in the delayed part. Nothing about the table announces that; it took an ordering with one exception in it to find.

Who found it, and when #

Fibre breaking extensions and elastic recoveries are from the standard physical-properties literature. Crease recovery angles are a fabric test standardised in the 1950s and reported for every commercial fibre since.

The relative crease behaviour of the common fibres is trade knowledge of very long standing, and linen’s crease in particular has been remarked on for as long as linen has been worn. The mechanism usually offered for it is the stiffness and low extensibility of the bast fibre, which is the right family of explanation.

What appears to belong to this collection is putting a number on the fold’s own strain with no crease measurement in it, and finding that the resulting two-column census reproduces the trade’s ordering with a single exception whose cause is a measurement convention. The two columns are separately old; the geometric floor that makes them comparable is not.

Where the ladder goes next #

The weave has not appeared in this rung at all, and it decides something the fibre cannot: where in the repeat the fold lands, and whether there is any crimp there to spend. A satin has places with none.

Sideways, the same fold arithmetic applied to a pile finds the opposite regime — a crushed carpet’s fibres are an order of magnitude below anything anybody has measured — and the recovery figures this rung leans on have a ladder of their own in what a fibre gives back, which nothing predicts.