In all the force-extension graphs I saw, the elastic limit corresponds to a larger extension than the limit of proportionality. Is this true for all cases? If so, what are the underlying reasons?
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The "limit of proportionality" is an imaginary point where the stress–strain curve is considered to deviate from a perfect straight line. There is no such exact threshold in Nature, and there's consequently no way to precisely label the point on an experimental graph. (Put another way, the better the resolution, the lower on the curve you'll detect a measurable deviation.) Conceptually, Hooke's law describing linear elasticity ceases to apply at this point.
The "elastic limit" is the point where not all deformation is recovered upon unloading. Conceptually, we could think of it as the point where permanent deformation really starts to activate at that set of conditions (composition, processing history, temperature, etc.) Note, however, that some amount of permanent deformation—not necessarily negligible—occurs throughout the loading period through creep.
("Yield point" is also used; by convention, this is the point where the actual strain exceeds by 0.2% the value predicted by the slope of an earlier portion of the curve that is approximately straight. This can be more reliably identified and is very often used in practice as a surrogate for the initiation of permanent deformation. The elastic limit and the yield point may be conflated in practical contexts.)
Now to your question: The elastic limit is generally farther along the curve than the limit of proportionality, although the difference may be negligible. Elastic deformation can be nonlinear for a variety of reasons, including anharmonicity of the pair potential between atoms, chain unkinking in polymers, and reversible dislocation movement in crystals, for instance. Are you interested in a particular mechanism or context?
Chemomechanics
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