Elasticity, limit of proportionality and elastic limit

     Elasticity is the ability of a material to return to its original shape and size on the removal of external forces.
     Plasticity is the property of a material of being permanently deformed by a force without breaking. Thus if a material does not return to the original shape, it is said to be plastic. Within certain load limits, mild steel, copper, polythene and rubber are examples of elastic materials; lead and plasticine are examples of plastic materials.
     If a tensile force applied to a uniform bar of mild steel is gradually increased and the corresponding extension of the bar is measured, then provided the applied force is not too large, a graph depicting these results is likely to be as shown in Figure 1.7. Since the graph is a straight line, extension is directly proportional to the applied force.

The point on the graph where extension is no longer proportional to the applied force is known as the limit of proportionality. Just beyond this point the material can behave in a non-linear elastic manner, until the elastic limit is reached. If the applied force is large, it is found that the material becomes
plastic and no longer returns to its original length when the force is removed. The material is then said to have passed its elastic limit and the resulting graph of force/extension is no longer a straight line. Stress, σ = F/A, from Section 1.5, and since, for a particular bar, area A can be considered as a constant,
then F ∝ σ.
Strain ε = x/L, from Section 1.6, and since for a particular bar L is constant, then x ∝ ε. Hence for stress applied to a material below the limit of proportionality a graph of stress strain will be as shown in Figure 1.8, and is a similar shape to the force/extension graph of Figure 1.7.