Explain the stress-strain curve of mild steel

Walk from the origin to fracture: elastic region, yielding, strain hardening, necking.

Model answer.

Moving along the curve from the origin:

1. Proportional limit. Up to this point stress is directly proportional to strain (Hooke's law). The slope is Young's modulus, about 200 GPa for steel.

1. Elastic limit. Slightly beyond the proportional limit, the material still returns to its original length when unloaded. For mild steel the two points are very close together.

1. Upper and lower yield points. Mild steel shows a distinct yield point. At the upper yield point the stress drops suddenly to the lower yield point, and the material then stretches at nearly constant stress. This yield plateau happens because dislocations break free from the carbon and nitrogen atoms pinning them. The lower yield point is used as the design yield strength.

1. Strain hardening. After yielding, the material needs more stress to deform further, because dislocations multiply and tangle. Stress rises to a peak.

1. Ultimate tensile strength (UTS). The maximum engineering stress. Up to here, deformation is uniform along the gauge length.

1. Necking and fracture. Beyond the UTS, deformation concentrates in one region, which forms a neck. The specimen fails in a cup-and-cone fracture, typical of ductile metals.

Why the curve drops after UTS. Engineering stress is load divided by the original area. After necking begins, the actual area at the neck shrinks rapidly, so the load the specimen can carry falls, and the engineering stress falls with it. The true stress (load divided by the actual instantaneous area) keeps rising until fracture.

Ductility measures. Percentage elongation and percentage reduction in area. Mild steel typically shows elongation in the range of roughly 20–30%.

Common mistake. Saying the material becomes weaker after UTS. It does not; the cross-section is shrinking.

Likely follow-up. "How do you find yield strength for aluminium, which has no clear yield point?" Use the 0.2% offset method: draw a line parallel to the elastic slope from 0.2% strain and read the stress where it meets the curve.