Structural Engineering & Statics
where the load goes
Concept

Strain hardening — where it appears

The rise in a metal's flow stress as it is plastically deformed, from dislocations obstructing one another. Its rate decides when a tensile specimen necks and how much a plastic hinge can rotate, and one exponent describes it well enough to make both calculable.

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

Three materials pulled until they stop. Three stress-strain curves — mild steel, high-strength steel, aluminium alloy — plotted to a strain of 2.0%. One of them has a plateau, so the stress at which yielding starts is something the specimen does rather than something anyone chooses. The 0.2% offset construction is drawn on the high-strength steel: a line of slope E from a strain of 0.002, cutting the curve at 460 N/mm².

The stress at which nothing in particular happens

One material in six has a yield point that a specimen actually does something at. For all the others the yield stress is a construction — a line drawn at an arbitrary offset — and every calculation on this site depends on it.

materials · Proof stress 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.

DuctilityConstitutive lawElastic modulusGauge lengthIdealisationLocalisationNeckingPlastic strainProof stressStabilityStress-strainStress-strain curve

All concepts