What is the elastic limit of an object?

The elastic limit of an object is the maximum force which can be applied to an object without causing permanent deformation.

In other words, if you removed the force, the object would return to its original size and shape. If you exceed the elastic limit, the object will recover some of its deformation, but will be a slightly different size and shape to before the force was applied.

The elastic limit is usually pretty close to the limit of proportionality for most materials. The limit of proportionality is where the extension stops being proportional to the force. Below the limit of proportionality, the force-extension graph would be a straight line. Some materials can deform non-linearly (so the Force-extension graph would curve), but still recover all their deformation.

In the graphs below the orange dot P shows the limit of proportionality, and the blue dot E the elastic limit.

If you apply a Force less than E, when you remove the force, the object will recover along the grey line.

If you apply a force more than E, for example getting up to the next dot above E, when the force is removed the object will recover along a new, permanently deformed line (the yellow line)

Note these relationships are often described using stress and strain, rather than force and extension, as the stress and strain allow us to consider a material in general, rather than a particular object.