Stress–Strain Curve
Full σ–ε curve with proportional, elastic, yield, plastic, UTS and fracture zones. Watch a rod neck and snap.
Key Notes
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).
Formulas
Young's modulus from slope
Slope of linear part of stress-strain curve.
Yield strength σ_y
Above this, plastic deformation begins.
Ultimate strength σ_u
Defines material's tensile strength.
Toughness (area under curve)
Energy absorbed per unit volume until fracture.
Important Points
Hooke's law applies ONLY in the proportional region (linear part).
Ductile vs brittle: ductile has long plastic region (steel, copper); brittle has tiny or no plastic region (glass, cast iron).
Yield strength is what's reported for structural design — beyond this, deformation is permanent.
Beyond ultimate strength, the cross-section necks down — stress (engineering) decreases but true stress keeps rising.
Annealed metals are more ductile than cold-worked ones — stress-strain curve shape changes with heat treatment.
Brittle materials fail in TENSION; in COMPRESSION they can be very strong (concrete is ~10× stronger in compression than tension).
Stress–Strain Curve notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.