How to use this calculator

Enter the specimen’s original size and gauge length, then the readings from the test: one load and extension in the straight elastic part of the curve, the yield load (from the 0.2% offset line if there is no sharp yield point), the maximum load, and the load at fracture. Fit the broken halves back together to measure the final gauge length and the smallest diameter at the neck.

Formulas

Engineering stress and strainσ = PA₀ ε = δL₀ E = σε (elastic range)

Strengthsσ_y = P_yA₀ σ_u = P_maxA₀

Ductility%EL = L_f − L₀L₀ × 100 %RA = A₀ − A_fA₀ × 100

True values at fractureσ_T = P_fA_f ε_T = ln A₀A_f

Worked example

A 12.83 mm (0.505 in) steel specimen, 50.8 mm gauge length (the default)

A₀ = π(12.83)²/4 = 129.3 mm².
Elastic point: 20 kN at 0.040 mm gives σ = 154.7 MPa and ε = 7.87 × 10⁻⁴, so E = 196 GPa.
σ_y = 45,000/129.3 = 348 MPa and σ_u = 62,000/129.3 = 480 MPa.
%EL = (63.5 − 50.8)/50.8 = 25%; the neck shrank to 8.0 mm, so %RA = 61.1%.
True fracture stress 50,000/50.27 = 995 MPa, twice the engineering value, because the neck carries the load on a much smaller area.

Reading a stress-strain curve

The curve rises in a straight line whose slope is E, bends over at yield as the metal starts to deform permanently, climbs more slowly as it strain-hardens, peaks at the ultimate strength when the neck begins to form, and drops until fracture. The engineering curve drops because it still divides by the original area; the true stress keeps rising right to fracture.

Assumptions and limits

The modulus from one load and extension pair is only as good as the extension measurement. Grip slip and machine compliance make crosshead readings far too large: use an extensometer, or take E from a handbook.
True strain from the area ratio is the local strain in the neck, much larger than the average elongation along the gauge length.
%EL depends on gauge length, so compare results only between specimens of the same standard proportions.

Frequently asked questions

What is the 0.2% offset method?

Draw a line parallel to the elastic part of the curve, starting at a strain of 0.002. Where it crosses the curve is the yield strength. It is used for metals such as aluminum that yield gradually.

Why is my modulus much lower than the handbook value?

Usually because the extension includes slack and deformation in the grips and machine. The specimen itself is far stiffer than the test frame suggests.

How is %RA different from %EL?

Elongation averages the stretch over the whole gauge length; reduction in area measures how far the neck thinned. %RA is less sensitive to specimen length and is a good measure of local ductility.