Structural Engineering & Statics
where the load goes
Concept

Plastic strain — where it appears

The part of a deformation that remains when the load is removed, produced by slip rather than by stretching bonds. It is what a ductile structure spends to redistribute force, and its capacity is the property that separates a warning from a collapse.

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

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 The curve the machine drew and the curve the material was on. The same tensile test twice. Force over the ORIGINAL area against extension over the original length is the engineering curve, which peaks at 431 MPa and 24.6 per cent and then falls. Force over the ACTUAL area against the natural logarithm of the length ratio is the true curve, which passes 538 MPa at the same instant and keeps rising. Nothing softens anywhere on this figure: the descending branch is the original area still being divided by, and the material is hardening the whole way. The two separate at the very first plastic strain and the gap between them is exactly e^ε, which is 1.25 at the ultimate load. Past that instant the deformation stops being uniform, so the engineering curve is drawn dashed: the real one falls faster than this, because the extension is now happening in one short length of the bar and the strain axis is still dividing it by the whole gauge.

The curve was rising the whole time

Every tensile curve ever printed turns over and falls, and nothing about the material does. The fall is the original area still being divided by after the specimen has stopped having it — and correcting the two denominators turns a strength, a ductility and a failure into one exponent.

materials · Gauge length

Named alongside it

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

DuctilityBauschinger effectBuckling-restrainedCyclic loadingEnergy dissipationFree bodyGauge lengthHysteresisKinematic hardeningLocalisationLow-cycle fatigueNecking

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