The tensile test and the stress–strain curve

A tensile test loads a specimen of measured initial area A₀ and gauge length L₀, recording force and gauge extension. Nominal stress is P/A₀ and nominal strain is δ/L₀.

Normalising by the initial dimensions allows specimens to be compared under equivalent test conditions. Temperature, loading rate, material orientation and specimen geometry can still affect the results, especially after localisation.

A typical mild-steel tensile curve begins with a linear elastic region whose slope is E. The proportional limit marks the end of linearity; the elastic limit concerns recovery after unloading.

Yielding may produce a plateau, followed by strain hardening as further plastic deformation requires higher stress. Not every steel has a distinct plateau.

At the maximum nominal stress, deformation begins to localise into a neck. The specimen then carries a decreasing load as its section reduces. Damage can develop before fracture, so neither continuing hardening nor a visible warning in a structural member should be assumed from this curve alone.

Brittle materials have limited plastic deformation before fracture. Cracking and other observations may occur, but should not be relied on to provide warning.

Materials without a distinct yield plateau can be characterised by proof stress. For 0.2% proof stress, draw a line parallel to the initial elastic slope at an offset strain of 0.002. Its intersection with the measured curve defines the value. With elastic unloading at that slope, the corresponding permanent strain is 0.002.

Ductility is measured after the test, from the broken halves fitted back together, and is reported two ways:

• Percentage elongation = (L_f − L₀)/L₀ × 100
• Percentage reduction in area = (A₀ − A_f)/A₀ × 100

Elongation depends on the gauge length used, because most of the extension is concentrated in the neck — so a quoted elongation is meaningless unless the gauge length is quoted with it. Reduction in area does not have that problem, but is harder to measure.

Ductility is not a strength. It buys you something different and arguably more valuable: warning, and the ability of a structure to redistribute load away from an overstressed region instead of tearing there.

It is worth naming the classification the tensile test implies, because it drives structural choices more than any single strength figure.

Ductile materials — structural steel, aluminium alloys, copper — have a large plastic region. They deform visibly before failing, they absorb a great deal of energy, and they redistribute load away from an overstressed region. Every method in this course that relies on redistribution assumes ductility.

Brittle materials — cast iron, glass, concrete in tension, most ceramics — have almost no plastic region. They fail at small strain with little warning and absorb little energy. Their tensile strength is also highly variable, because it is governed by the largest flaw present rather than by the bulk material.

Materials that behave differently in tension and compression. Concrete is the structural example: strong in compression, weak and unreliable in tension. That single asymmetry is the reason reinforced concrete exists, and the reason cracked-section analysis discards the concrete below the neutral axis.

Time-dependent materials — timber, polymers, and concrete over years — deform appreciably under sustained load. Their short-term test results do not describe their long-term behaviour.

The strain-hardening region seen after the yield plateau is what gives ductile materials their reserve. Dislocations become tangled and obstruct one another, so more stress is required to continue deforming. The ratio of ultimate to yield stress is a rough measure of how much reserve there is: around 1.4 for a typical mild steel, and closer to 1.1 for a high-strength steel — which is one reason very high-strength steels are treated more cautiously.