Pull a mild-steel specimen in a tensile testing machine and plot stress against strain, and you get one of the most informative graphs in engineering. Every mechanical property a designer needs — stiffness, strength, ductility — is read from this single curve. Here is what each part means.
The Tensile Test
A standard specimen of known gauge length and cross-section is stretched at a controlled rate while load and extension are recorded. Stress = load ÷ original area; strain = extension ÷ original gauge length. (This is engineering stress-strain; true stress-strain uses the instantaneous area.)
The Curve, Point by Point
| Point | Meaning |
|---|---|
| O → A: Proportional limit | Stress ∝ strain; Hooke's law holds; the slope is Young's modulus E. |
| A → B: Elastic limit | Still recoverable on unloading, but no longer perfectly linear. |
| B: Upper yield point | Stress at which plastic flow begins (a peak unique to mild steel). |
| C: Lower yield point | Stress drops slightly and strain increases at near-constant stress (yield plateau). |
| C → D: Strain hardening | Material regains strength; stress rises again to the peak. |
| D: Ultimate tensile strength | Maximum stress the material can carry. |
| D → E: Necking | A local waist forms; engineering stress falls until fracture at E. |
Key Mechanical Properties
- Young's modulus E — slope of OA, ≈ 200 GPa for mild steel. Stiffness.
- Yield strength fy — onset of permanent deformation, ≈ 250 MPa for mild steel (Fe 250). The basis of design.
- Ultimate tensile strength — peak stress, ≈ 410 MPa for structural mild steel.
- Ductility — % elongation (often 20–26%) and % reduction in area; the ability to deform before fracture.
- Toughness — area under the whole curve; energy absorbed before fracture.
- Resilience — area under the elastic portion; energy stored elastically.
Why the Yield Plateau Matters
The pronounced yield plateau gives mild steel its famous ductility and warning before failure — it stretches visibly before breaking. This is the foundation of plastic design and ductile (earthquake-resistant) detailing. High-strength steels lack this plateau, so their design uses 0.2% proof stress instead.
Worked Example — Finding E and Yield Load
A 12 mm diameter mild-steel rod with a 50 mm gauge length is tested. In the elastic range a load of 22.6 kN produces an extension of 0.05 mm. Find Young's modulus. If yielding starts at 28.3 kN, find the yield stress.
- Area A = πd²/4 = π × 12² / 4 = 113.1 mm²
- Stress = 22 600 / 113.1 = 199.8 ≈ 200 MPa; Strain = 0.05/50 = 0.001
- E = stress/strain = 200 / 0.001 = 200 000 MPa = 200 GPa
- Yield stress fy = 28 300 / 113.1 = 250 MPa (consistent with Fe 250 mild steel)
Ductile vs Brittle Behaviour
- Ductile (mild steel): large plastic strain, necking, warning before failure.
- Brittle (cast iron, high-carbon steel): little plastic deformation, sudden fracture, no yield plateau.
Common Mistakes
- Confusing the elastic limit with the proportional limit — they are close but not identical.
- Using ultimate strength for design instead of yield strength (with a safety factor).
- Reading proof stress without drawing the 0.2% offset line parallel to the elastic slope.