Stress-strain diagram of mild steel

The stress-strain diagram plots nominal stress $\sigma = P/A_0$ against strain $\varepsilon = \delta/L_0$ for a specimen pulled in a universal testing machine.

 stress
   |              U
   |        Y1   _.-"-._
   |         /\_/        '.
   |        /Y2             \ F
   |       /
   |      / P,E
   |     /
   |    /
   +------------------------- strain

(P = proportional limit, E = elastic limit, Y1/Y2 = upper/lower yield point, U = ultimate point, F = fracture.)

Important points

1. Proportional limit (P): the stress is proportional to strain up to here, so Hooke's law $\sigma = E\varepsilon$ holds. The slope of the straight line is the modulus of elasticity $E$ (about 200 GPa for steel).
2. Elastic limit (E): the specimen returns to its original length on unloading. It lies very close to P.
3. Yield point (Y1, Y2): the strain increases suddenly with almost no increase in stress (plastic flow). There is an upper yield point and a lower yield point; design uses the yield stress $\sigma_y$ (about 250 MPa for mild steel).
4. Strain hardening: after yielding the material regains strength and the stress rises again to the ultimate point.
5. Ultimate stress (U): the maximum nominal stress. Beyond U a local reduction in area (necking) starts.
6. Fracture (F): the specimen breaks. The nominal stress falls because it is calculated on the original area, although the true stress keeps rising.

Mild steel is ductile: the elongation at fracture is 20 to 30 percent and it shows a cup and cone fracture.

Cast iron (brittle material)

For materials with no clear yield point (aluminium, high-strength steel) the 0.2 % offset yield stress is used.