Force-Extension Graphs for Different Materials

Force-extension graphs are among the most important diagrams in the materials topic. By examining the shape of the graph, you can identify the material, determine its stiffness, find the energy stored, and understand how the material will behave under different loading conditions. In the Edexcel A-level exam, you must be able to draw, interpret, and compare these graphs for metals, rubber, and polythene.

---

Metal Wire (e.g., Copper or Steel)

Loading

The force-extension graph for a metal wire shows:

1. A straight-line region through the origin — the wire obeys Hooke's law. The gradient equals the spring constant k = F/x.
2. At the limit of proportionality, the line begins to curve upward (the wire still extends, but no longer proportionally to the force).
3. At the elastic limit, further loading causes permanent deformation.
4. Beyond the elastic limit, the wire extends significantly with smaller increases in force (plastic region).
5. The wire eventually fractures at the breaking point.

Unloading (within elastic limit)

The unloading path is the same straight line as the loading path. All elastic potential energy is recovered. No energy is dissipated.