Multiple choiceQuestion 1 · Recall
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By the end you can define the elastic limit, explain what happens beyond it, and distinguish it from the limit of proportionality on a force–extension graph.
Pull a spring gently and it springs back. Pull it too far, once, and it never quite returns to its original length again.
There is a largest deformation for which the object still recovers completely. Cross that line and some of the change stays for good.
That boundary has a name.
Elastic limit
The elastic limit is the maximum deformation for which an object still returns to its original shape and size when the deforming force is removed.
Below the elastic limit, deformation is elastic. Beyond it, the object is left with a permanent (plastic) extension, even after the load is removed.
You have already met the limit of proportionality. It is where the graph stops being a straight line: beyond it, force is no longer proportional to extension, so fails.
The elastic limit is where the material stops springing back: beyond it, the deformation becomes partly permanent.
For many metal wires the two points are close together, with the limit of proportionality reached first. That is why they are often mentioned in the same breath — but they answer different questions.
| Question | Limit that answers it |
|---|---|
| Is the graph still straight? | Limit of proportionality |
| Will it still return to its original length? | Elastic limit |
Between the two limits the graph curves, yet the wire still returns to its original length when unloaded. So an object can break proportionality and still be perfectly elastic.
Worked example: Worked example: finding the elastic limit from a test
A wire is loaded in steps. After each load is removed, its length is measured again.
| Load / N | Length under load / mm | Length after unloading / mm |
|---|---|---|
| 0 | 500 | 500 |
| 2 | 502 | 500 |
| 4 | 504 | 500 |
| 6 | 507 | 502 |
| 8 | 512 | 506 |
Between which two loads does the elastic limit lie?