Stress–Strain Curve

A typical stress-strain curve for a ductile material (e.g., mild steel) has several distinct regions.

1. Proportional region (linear) — stress ∝ strain; Hooke's law holds; modulus is the slope.

2. Elastic limit (just beyond proportional limit) — still recoverable, but stress and strain not strictly proportional.

3. Yield point — material begins permanent deformation; visible necking starts.

4. Plastic region — large strain for small stress increase; ductile materials stretch significantly.

5. Ultimate tensile strength — maximum stress before necking dominates.

6. Fracture point — material breaks.

Ductile materials (steel, copper) show large plastic region. Brittle materials (glass, ceramic) break almost immediately past elastic limit.

Area under the curve = energy absorbed per unit volume (toughness).