Structural Engineering & Statics
where the load goes
Concept

Autofrettage — where it appears

Pressurising a thick-walled cylinder once past yield, so that its yielded inner layers are squeezed into compression when the pressure is released. The locked-in compression offsets the hoop tension of later service pressures, raising the pressure the bore can take elastically.

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

What is left when the load comes off. Mild steel taken to a strain of 0.60% and then unloaded to zero stress, at which point the strain has not returned to zero: 0.469% of it is permanent.

What is left when the load comes off

Unload a section that has yielded and it does not return to nothing. It returns to a self-equilibrating stress field it did not have before, a permanent set, and an elastic range wider than the one it started with.

materials · Unloading Past a wall ratio of 2.22, a thicker tube gains nothing more. The most autofrettage can raise a thick cylinder's elastic pressure, as a multiple of its first-yield pressure, against its wall ratio b/a. Yielding the whole wall would buy σy ln k ÷ py (faint), which keeps rising; the release caps it at 1 + β, where β is the reverse yield strength over the forward one. With β = 1.0 the two meet at b/a = 2.22, and the gain is 2.00 for every thicker wall; with β = 0.7 the two meet at b/a = 1.80, and the gain is 1.70 for every thicker wall; with β = 0.5 the two meet at b/a = 1.55, and the gain is 1.50 for every thicker wall. Thinner walls than that can be yielded right through and gain less.

The overstrain the release gives back

A thick tube is pressurised past yield once, at the factory, so that releasing the pressure leaves its bore in compression and the working pressure must overcome that before it does any harm. The obvious rule is to overstrain as far as possible — right through the wall. For a tube whose outside is more than 2.22 times its bore that is wrong: the release itself reverses the bore past yield, and every newton of overstrain beyond twice the first-yield pressure is given back on the way down. The best overstrain stops part-way through the wall, and a steel that yields early in reverse stops it sooner.

materials · Unloading

Named alongside it

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

Bauschinger effectResidual stressUnloadingHoop tensionKinematic hardeningPermanent setPrestressSelf-equilibratingShakedownSuperpositionThick cylinderTresca

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