Work Done to Break
Work Done to Break
- The work done stretching a sample is the area under its force-extension graph — the same rule as elastic PE (area = energy), now used all the way to breaking.
- For an idealised ductile metal that area splits into an elastic triangle plus a plastic rectangle.
Work done to break: triangle plus rectangle
- An idealised metal has two regions on its force-extension graph: an elastic straight line, then a flat plastic plateau.
- The elastic energy is the triangle up to the elastic limit; the plastic work is the rectangle under the plateau. Add them for the total work to break.
Worked example
Elastic energy from a straight-line graph
A wire's force-extension graph is a straight line reaching 12 N at an extension of 4.0 mm.
- The stored elastic energy is the triangle, .
- .
Answer
Worked example
Total work to break this metal
The force rises to 20 N at an extension of 5.0 mm (the elastic limit), then stays at 20 N up to 30 mm before breaking.
- Elastic energy (triangle): .
- Plastic work (rectangle): .
- Total work to break: .
Answer
Common mistake
The single most common lost mark is forgetting the in the elastic part. Also check the axes: area under force-extension is energy in joules (9702/13/M/J/25 Q21), but area under stress-strain is energy per unit volume (J m-3). Do not confuse the two.