Q.Describe the behaviour of a wire under gradually increasing load.

A stretched wire passes through, in order: a proportional (Hooke's law) region, a slightly non-linear elastic region up to the elastic limit, a plastic region with permanent deformation after the yield point, a region up to the ultimate tensile stress (maximum stress it can bear), and finally fracture — all summarised by the stress-strain curve for the wire.

Setup. Consider a wire of a ductile material (e.g., a metal) fixed at one end, with a gradually increasing load applied at the other end. As the load (and hence the stress, force/cross-sectional area) increases, the extension (and hence the strain, extension/original length) also increases; plotting stress against strain gives the stress-strain curve, which has distinct regions.

Region 1 — Proportional limit (Hooke's law region), OA. For small loads, the extension of the wire is directly proportional to the applied load (stress ∝ strain — Hooke's law). The wire behaves as a perfectly elastic body: if the load is removed anywhere in this region, the wire returns exactly to its original length. Point A on the curve marks the proportional limit, beyond which stress is no longer proportional to strain.

Region 2 — Elastic limit, AB. Beyond A, the stress-strain curve becomes slightly non-linear/curved, but the wire is still elastic — it still returns to its original length if the load is removed, up to point B, the elastic limit.

Region 3 — Yield point and plastic deformation, BD. Just beyond the elastic limit, at the yield point (around B/C), the wire starts to undergo a large increase in strain for only a small increase in stress, and the deformation becomes permanent (plastic) — removing the load no longer restores the original length; a permanent set remains.

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