Concept

Unloading — where it appears

The removal of load from a material that has already yielded, which follows a path parallel to the original elastic line rather than retracing the loading curve. What is left behind is a permanent set and a residual stress field the next load case starts from.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

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

Yielding one way makes it easier to yield the other. Mild steel taken to a strain of 1.20% and then pushed back the other way. The stress falls by 550 N/mm² before it yields again, against a yield stress of 275 — the elastic range is twice the yield stress and not once it, which is the Bauschinger effect and is a consequence of the yield surface sliding rather than growing.

Yielding one way, and then the other

A material that has yielded in tension yields earlier in compression than it did the first time, and by an amount that is exactly what makes its elastic range twice its yield stress rather than once it. That is a property no monotonic test reports and every reversing structure depends on.

materials · Ductility

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 effect Residual stress Autofrettage Kinematic hardening Buckling-restrained Cyclic loading Ductility Energy dissipation Free body Hoop tension Hysteresis Low-cycle fatigue

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