Reading Deformation Graphs
Reading Deformation Graphs
- First read the axis labels. The gradient and area represent different quantities on force-extension and stress-strain graphs.
- Then identify the straight region, the elastic region and any plastic region before calculating.
Locate the two limits by their meanings
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- At P, proportionality ends: the line stops being straight.
- At E, elastic behaviour ends: beyond this point the sample keeps a permanent deformation after unloading.
- The region beyond E is plastic. The sample can still carry load until it reaches the breaking point.
| Graph | What to read | Meaning |
|---|---|---|
| Force against extension | gradient | spring constant k |
| Force against extension | area | work done on the sample (J) |
| Stress against strain | gradient | Young modulus E |
The drawn curve represents one ductile sample. Different materials can have different curved regions and different breaking points; the meanings of P, E and the graph axes do not change.
Estimate work from the whole force-extension area
Work done remains the area under a force-extension graph even when the line curves. Use triangles, rectangles, trapezia or square counting to estimate the whole area up to the required extension.
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Worked example
Idealised work done to break a sample
Force rises linearly to 20 N at 5.0 mm, then remains at 20 N until the sample breaks at 30 mm.
- Triangle: .
- Rectangle: .
- Add both areas.
On the paper's force-extension graph, P is at 60 mm and E is at 80 mm. State what each point means, then state the method used to estimate the work done up to breaking. (9702/23/M/J/24 Q3(b), (d))
Show worked answer
- P is the limit of proportionality, where the graph stops being straight.
- E is the elastic limit, the last point for complete recovery after unloading.
- Estimate the total area under the force-extension graph up to the breaking point.
Common mistake