What is the difference between the elasticity limit and the limit of proportionality of a spring?
The change in the length of a spring, either a compression or an elongation, is proportional to the force applied. According to Hooke's law, F = -k*x, where k is the proportionality constant, F is the force applied and x is the change in length. This relation does not hold for all values of x, but is limited to values that lie within the proportionality limit. After the limit is crossed, the strain is no longer proportional to the stress applied though the spring would still return to its initial dimensions when the force is released.
The elasticity limit on the other hand is the point where a force applied on the spring deforms it to such a large extent that on the removal of the force the spring can no longer return to its initial dimensions. The deformation here becomes permanent.