JEE Main & Advanced Physics Elasticity Stress-strain Curve

If by gradually increasing the load on a vertically suspended metal wire, a graph is plotted between stress (or load) and longitudinal strain (or elongation) we get the curve as shown in figure. From this curve it is clear that :

(1) When the strain is small (< 2%) (i.e., in region OP) stress is proportional to strain. This is the region where the so called Hooke?s law is obeyed. The point P is called limit of proportionality and slope of line OP gives the Young?s modulus Y of the material of the wire. If \[\theta \]  is the angle of OP from strain axis then \[Y=\tan \theta \] .

(2) If the strain is increased a little bit, i.e., in the region PE, the stress is not proportional to strain. However, the wire still regains its original length after the removal of stretching force. This behaviour is shown up to point E known as elastic limit or yield-point. The region OPE represents the elastic behaviour of the material of wire.

(3) If the wire is stretched beyond the elastic limit E, i.e., between EA, the strain increases much more rapidly and if the stretching force is removed the wire does not come back to its natural length. Some permanent increase in length takes place.

(4) If the stress is increased further, by a very small increase in it a very large increase in strain is produced (region AB) and after reaching point B, the strain increases even if the wire is unloaded and ruptures at C. In the region BC the wire literally flows. The maximum stress corresponding to B after which the wire begins to flow and breaks is called breaking or ultimate tensile strength. The region EABC represents the plastic behaviour of the material of wire.

(5) Stress-strain curve for different materials are as follows :