Passing limit of proportionality but not elastic limit

Question

In my textbook, the limit of proportionality and elastic limit are labelled separately, but quite close to each other. Does this mean that once a spring only just passes the limit of proportionality, but we carefully ensure it doesn't stretch anymore, then once unstretched, it would return to it's original length? Is is even possible to cross limit of proportionality but not reaching the elastic limit?

Urb · Accepted Answer

If the spring is stretched beyond the proportionality limit but still within the elastic limit, it recovers its initial length after we remove the stretching force.
However, when unloading the spring, elastic hysteresis can occur, i.e., the path taken by the spring in the load vs deformation plot is different. This means that the work done by the spring to recover its original shape is less than the work needed to stretch it.

Farcher · Answer

Beyond the limit of proportionality extension is no longer proportional to load but the spring is still elastic, ie when unloaded it will return to its original unloaded length, until the elastic limit beyond which the deformation of the spring is inelastic and so when the spring is unloaded it has a permanent deformation (is longer that it was before it was loaded).
For a lot of materials these two points are very close to one another and often indistinguishable unless great care is taken when making observations.

Passing limit of proportionality but not elastic limit

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