Structural Engineering & Statics
where the load goes
Concept

Uniform elongation — where it appears

The strain a tensile specimen reaches at its greatest load, before it begins to neck. It is where hardening stops keeping pace with thinning, so it measures how far a bar stretches evenly along its length, and in a member of two materials side by side it lies between theirs.

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

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 The weakest weld is not the one straight across. The ultimate strength of a member of 6082-T6 (parent ultimate 310 N/mm², zone 185) whose heat-affected zone crosses it at every angle from along the load (0) to straight across it (90 degrees), as load over the gross section. Across the load the zone's neighbours stop it contracting, and it carries 214 N/mm², 15 per cent above its own uniaxial 185. At 54.7 degrees, the angle a free sheet necks along, they give it nothing and the member carries 185. Below 24.2 degrees the zone's own neck would need more than a section through the parent can carry, and the member reaches 278 — the strength it has with the zone, 25 per cent of the section, running along it. At 30 degrees, 237; at 70, 196.

The weld that is weakest at fifty-five degrees

A soft heat-affected zone that the load crosses fails by necking along its own line, and it can do that only if nothing along the line has to stretch. Straight across the load, the parent on either side stops the zone contracting and lends it 15 per cent. At 54.7 degrees — the angle a free sheet necks along — it lends nothing, and the member carries the zone's own strength. Below 24 degrees the zone cannot neck alone at all, and a weld running along the member costs a tenth of its strength while adding to its stretch.

materials · Heat-affected zone

Named alongside it

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

DuctilityLocalisationNeckingStrain hardeningAluminiumConstraintGauge lengthHeat-affected zonePlastic strainStabilityStress-strain curveTensile strength

All concepts