Plot a stress `to` strain curve for a metal and explain.

Explanation

A stress `to` strain curve for a metal is shown as in figure.
From the graph, we can see that in the region between 0 to A, the curve is linear. In this region Hooke.s law is obeyed.
The body regains its original dimensions when the applied force is removed. In this region the solid behaves as an elastic body.

In the region from A to B stress and strain are not proportional. The body still returns to its original dimension when the load is removed. The point B in the curve is known as yield point (also known as elastic limit) and the corresponding stress is known as yield strength `(sigma_(y))` of the material.
If the load is increased further, from point B the stress developed exceeds the yield strength and strain increases rapidly.
The portion of the curve between B and D shows this, when the load is removed say at some point C between B and D, the body does not regain its original dimension.
In this state, even when the stress is zero, the strain is not zero. The material is said to have a permanent set. The deformation is said to be plastic deformation. The point D on the curve isthe ultimate tensile strength `(sigma_(u))` of the material. Beyond this point, additional strain is produced even by a reduced applied force and fracture occurs at point E.
If the ultimate strength and fracture points D and E are close, the material is said to be brittle. If they are far apart, the material is said to be ductile.