All courses › Materials Technology › Stress–strain curve

Stress–strain curve

The stress–strain curve shows how a material responds to load. In the elastic region, stress and strain are proportional via the elastic modulus. The yield strength ( $R_e$ or $R_{p0.2}$ ) marks the start of plastic deformation, and the tensile strength $R_m$ is the highest stress the curve reaches.

\sigma = \frac{F}{A}

stress

\varepsilon = \frac{\Delta L}{L_0}

strain

E = \frac{\sigma}{\varepsilon}

elastic modulus (elastic region)

Symbols

$F$	force	N
$A$	cross-sectional area	mm²
$\Delta L$	change in length	mm
$L_0$	original length	mm

Example

Round bar $d = 16$ mm, $F = 79$ kN: $A \approx 201.1$ mm², $\sigma = F/A \approx 392.9$ MPa.

$\sigma = 40$ MPa, $\varepsilon = 0.15\%$ : $E = 40/0.0015 \approx 26.7$ GPa.

R_{p0.2}

is used when a material has no clear yield point — it is the stress giving 0.2% permanent strain.

Practise mechanical properties for free →

← Alloys and phase diagrams · Ductility and brittleness →

Part of Materials Technology: Mechanical properties.