Abrasion takes the hairs first

A cloth loses its strength before its mass is one of this collection’s sharper results about wear. Material comes off the whole surface and it comes off every thread at the same place, and a thread breaks at its thinnest place — so at one per cent of a cloth’s solid volume removed the section of every thread is already eight per cent smaller on a plain weave and under three on a satin. A mass loss understates the damage by three to eight times, and the ordering is the ordering of the crown line.

That essay assumed the mass being lost was cloth. For the first several thousand cycles of any abrasion test, it is not.

The cloth #

An abrasion test rubs a specimen against a standard abradant under a standard load for a counted number of cycles, and reports either the cycles to a stated end point — a broken thread, a hole — or the mass lost at a fixed cycle count. The second is the quantitative version and it is the one used to compare fabrics.

Everybody who has run one knows that the specimen goes fuzzy before it goes anywhere else, and that the fuzz then comes off. That observation is treated as a nuisance in the early cycles rather than as the first stage of the measurement.

It is a stage of the measurement, and on some fabrics it is the whole of it.

The claim #

The first material off a fabric is its hair layer. That layer is a tenth of a per cent of a bare cotton cloth’s mass and seven per cent of a napped one’s, so a bare cloth is through it in a few thousand cycles and a napped cloth is not through it in twenty thousand. Two fabrics taken to the same reported mass loss have therefore not lost the same thing, and the more heavily napped one may not have been damaged at all.

There is a second half that follows from the balance one rung down: the hair layer regenerates, so it does not come off once. It comes off continuously, at a rate set by how fast rubbing frees new ends, and that rate is part of what a steady-state mass loss is measuring.

The arithmetic, which is one division #

The hair layer’s mass is a length of protruding fibre per unit area times a fibre’s cross-section times a density, and the population supplies the length. For the long population on a sheeting it is a tenth of a per cent of the cloth’s areal mass; grossed up by the split it is under one per cent, which is what a singeing takes off and is the model’s cheapest check.

Raising multiplies the population, so a cloth raised sixty-fourfold carries nearly seven per cent of its mass in hair.

An abrasion test removes some fraction of the cloth’s mass per thousand cycles. Dividing the hair’s share by that rate gives the cycles spent in the hair stage, and the two answers are five thousand and three hundred and forty thousand.

Twenty thousand cycles is a long abrasion test. So one of those numbers is inside the test and the other is not, and the difference between them is a finishing operation.

Why it is not once but continuously #

The stock is not the whole story, because the layer is a balance rather than a stock.

Rubbing frees fibre ends that spinning left buried, from a reservoir more than twice the size of the population spinning released. So while the test is removing hairs it is also making them, and the population goes to a fixed point rather than to zero.

A steady-state abrasion mass loss is therefore partly a measurement of the generation rate. The material leaving the specimen is a mixture: some of it is crown material worn off the threads and some of it is fibre that was pulled out of the yarn body, entangled, and rubbed away. The second is damage of a sort — the yarn has lost a fibre — but it is damage of a completely different kind from a worn crown, and it is not distributed where a worn crown is distributed.

That distinction is what the strength argument turns on. A worn crown thins every thread at its thinnest place, which is why a mass loss understates the damage. A pulled fibre thins the yarn everywhere at once, which is a much gentler kind of loss, and it is the kind a napped fabric’s whole test consists of.

What this does to a comparison #

The consequence is that the standard comparison is unsound in one specific and correctable way.

Two fabrics identical in weave, yarn and sett, one singed and one raised, will report wildly different mass losses at twenty thousand cycles — and the raised one will report the larger loss while being the less damaged, because most of what it lost was standing in the air.

That is the wrong way round from what the number is used for. A larger mass loss is read as worse wear resistance, and here it is a measure of how much loose fibre the specimen had.

The correctable part: run the specimen to a fixed loss and then measure its strength, which is what the strength-before-mass essay argued for on entirely different grounds. A strength measurement cannot be fooled by material that was not carrying anything, because material that was not carrying anything does not appear in a strength.

Where the layer sits relative to the load #

There is a mechanical reason the hair stage is not merely first but necessarily first, and it is the crossover from the contact ladder.

An abradant pressed onto a fabric at the standard load is at a pressure of a few kilopascals. On a bare cloth that is above the crossover — about a fifth of a kilopascal — so the abradant is riding on the crowns and the hairs are being caught by whatever passes them rather than being the load-bearing surface.

On a raised cloth the crossover is fifteen kilopascals, which is above the abradant’s pressure. So on a napped fabric the abradant never touches the fabric at all: it rides on the nap for the whole test, and every milligram it removes is nap.

That is a much stronger statement than the mass arithmetic makes. The mass argument says a napped cloth would take three hundred thousand cycles to consume its hair; the pressure argument says the abradant is not in contact with anything else in the first place. The two agree and the second does not depend on the assumed loss rate.

The end-point tests are better and for a reason worth naming #

The other family of abrasion tests reports cycles to an end point — two broken threads, or a hole — and it is usually treated as the cruder of the two because its output is a threshold rather than a quantity.

It is the sounder one here, and precisely because it is a threshold. A broken thread is a fact about the cloth, and no amount of hair coming off brings one closer. So an end-point test on a napped fabric spends its first three hundred thousand cycles achieving nothing and then measures the fabric, which is slow and correct; a mass-loss test on the same fabric measures the nap and reports a number, which is fast and wrong.

The trade’s preference for end-point tests on pile and napped fabrics is therefore not conservatism. It is the right instrument, chosen for a reason that has not been written down.

Where the crown argument resumes #

None of this touches the crown result once the hair stage is over, and the boundary is clean.

Past the hair stage, the material leaving the specimen is crown material and the abrasion arithmetic applies exactly: the wear is where the crowns are, the crowns are where the draft puts them, and a satin’s shallow wide crowns lose section more slowly than a plain weave’s points for the same mass.

So an abrasion test on a bare cloth is two measurements in sequence and the second one is the good one. The fix is to discard the first few thousand cycles, which is a standard technique in other kinds of wear testing — a run-in period — and which abrasion testing does not use.

The reason it does not is worth guessing at. A run-in is normal when the surface changes shape in the first cycles and then stabilises, and a fabric’s does. What is unusual here is that the material removed during the run-in is a large fraction of what will ever be removed, so discarding it feels like discarding the result.

What was counted, and how #

Three assertions, and the third is the one that makes the essay matter rather than merely being true.

That a napped cloth carries more than ten times a bare one’s mass in hair. That at the same reported loss the two have lost different things, compared at twenty thousand cycles where the model says they differ. And that a bare cloth clears its hair stage within the standard test range while a napped one does not — two inequalities against one number, which is a statement about a published test rather than about a fabric.

The mass-loss rate is assumed and it is the one input with nothing behind it. It is set to a fraction of a per cent per thousand cycles, which puts a twenty-thousand-cycle test at a few tenths of a per cent of the specimen’s mass — the right order for a Martindale — and the essay’s conclusions are ratios in which it cancels.

Where the model stops #

The generation term is not in the mass balance. The cycles-to-clear figures treat the hair layer as a stock being consumed, and it is being replenished at the same time, so both numbers are under-estimates and the napped one is under-estimated by more.

The abradant is not modelled at all. Whether a given abradant reaches into a nap or rides on top of it is a question about the abradant’s own surface, and the whole difference between a wire tooth and a woollen cloth is in there.

Nothing distinguishes fibre pulled out from fibre worn through. They leave the specimen the same way and weigh the same, and they mean completely different things about the yarn left behind.

And the loss rate is taken as constant. A real curve accelerates once threads start to break, which is the condemned-area argument and is a different regime again.

What a specification would have to say #

The essay has one actionable consequence and it is a short one.

An abrasion result needs the specimen’s surface state attached to it, in the same way a thickness needs a pressure. As woven, singed, cropped or raised are four different fabrics as far as a mass loss is concerned, and they can be the same fabric in every structural respect.

The version of the rule that survives contact with a testing house is simpler still: singe the specimen before an abrasion test, or report an end point. Singeing removes the stage that is not the measurement, and it does so without touching the cloth — under one per cent of the mass, and nothing structural changed.

That is a slightly startling recommendation, because it amounts to modifying a specimen before testing it. It is defensible for the same reason a run-in is defensible: the state being removed is one the fabric will lose within days of being worn anyway, so the test is being started from the state the fabric spends its life in rather than from the one it left the finishing works in.

The load a test would have to apply, and why it does not #

The pressure argument gives the test a number to be measured against, and putting the two side by side says the problem is not marginal.

The crossover — the pressure at which an abradant stops riding on the hairs and reaches the crowns — is about 0.2 kilopascals on a bare cloth and about fifteen on one raised sixty-fourfold. The standard abrasion loads are 9 kilopascals for apparel and 12 for upholstery.

So the bare cloth is tested at forty times its crossover, comfortably in contact with its own crowns, and the raised cloth is tested at four fifths of its crossover — below it, on the wrong side, for the whole test. Not marginally below: a fifth short, with no setting in the standard that would clear it.

And the fabrics most often napped are the ones tested at the upholstery load, which is the higher of the two and still not enough. A furnishing velour, a moleskin, a blanket cloth: every one of them is a construction whose whole selling point is the layer the abradant is standing on.

Raising the load would fix the contact and break something else. Wear rate is not linear in pressure, the standards’ loads were chosen to match service conditions rather than to clear a threshold, and a test run at fifty kilopascals is measuring a different mechanism — crushing and cutting rather than rubbing. The instrument cannot be fixed by turning it up, which is why the essay’s recommendation is to change the specimen or the end point rather than the machine.

That recommendation needs one refinement, because the balance undoes it. Singeing a specimen does not remove the hair stage; it delays it. The population regenerates under rubbing towards a fixed point set by the test itself, so a singed specimen re-fuzzes over the first thousands of cycles and the mass it then sheds is hair again. What singeing buys is a start further down the curve, not a different curve.

The version that actually works follows from the same balance: pre-abrade the specimen to its own fixed point and then start counting. At the fixed point the layer’s mass is constant, so everything leaving the specimen afterwards is being generated as fast as it is removed and the net loss is cloth. That is a run-in in the proper sense — the surface has reached the state it will stay in — and it needs no chemistry, no flame and no modification of the fabric beyond what the test itself does.

The cost is that the run-in on a napped fabric is the three hundred thousand cycles the essay computes, which is no test at all. For a bare cloth the fix is cheap and for a napped one it is impossible, and that asymmetry is the honest summary: a mass-loss abrasion test can be repaired for the fabrics it was already working on, and cannot be repaired for the ones it was failing.

The generalisation #

A cumulative measurement of a process with stages reports the stage it spent the most time in, and the stages are not comparable.

The transferable form: whenever a test integrates something over time and the mechanism changes partway through, the reported total is a weighted average of two mechanisms whose weights depend on the test’s duration rather than on the specimen. Two specimens can be ranked correctly, incorrectly, or not at all depending on where the test happened to stop.

The remedy is always the same shape and it is always available: measure the thing the test is about rather than the thing the test can count. Strength rather than mass, an end point rather than an integral, a fixed damage rather than a fixed duration.

This site has now met that remedy three times: in the strength-before-mass essay, in the fitted compression exponent, and here.

Who found it, and when #

That fabrics fuzz before they wear is universal knowledge and is the basis of every pilling test, which runs a specimen through exactly this stage on purpose and grades the result. Abrasion testing and pilling testing are the same rubbing done for two different reasons, and the fact that one of them regards the first stage as the signal and the other regards it as noise is not usually remarked on.

What is added here is the arithmetic: the layer’s mass from a hair population rather than from a weighing, the cycles to clear it, and the observation that the two families of abrasion test respond to it completely differently.

Where the ladder goes next #

To the stage this essay discards, taken as the subject rather than as the run-in. A pill is anchored, not made is the balance with a stabilising term in it — fibre that comes out and is entangled rather than removed — and the strong fibre is the one that pills is what happens when the removal term is small.

And the same rubbing, seen as a source rather than a sink, is why singeing does not stay done.