The stress strain graph for a metal wire is shown in the fig. Up to the point E, the wire returns to its original state O along the curve EPO, when it is gradually unloaded. Point B corresponds to the fracture of the wire.

(a) Up to what point on the curve is Hooke's law obeyed? (this point some times called proportional limits).
(b) Which point on the curve corresponding to elastic limit or yield point of the wire?
(c ) Indicate the elastic and plastic regions of the stress-strain graph.
(d) Describe what happens when the wire is loaded up to a stress corresponding to the point A on the graph and then unloaded gradually. In particular explain the dotted curve.
(e) What is peculiar about the portion of the stress- strain graph from C to B? Up to what stress can the wire be subjected without causing fracture?

Explanation

(i) Hooke’s law is obeyed upto the point P, because upto this point, stress `prop` strain .
(ii) Point E corresponds to elastic limit (yield point) because the wire returns to original state O along EPO is it is gradually unloaded.
(iii) The elastic region is from O to E and the plastic region is from E to B.
(iv) Upto point P, stress is proportional to strain. Between P and E strain increases more rapidly than stress and Hooke’s law is not obeyed. When the wire is unloaded at any point A beyond E, the wire does not retrace the curve AEPO but follows the dashed curve AO’. When the stress becomes zero, a residual strain OO’ is left in the wire.
(v) Between C and B, the wire virtually flows out, i.e., the strain increases even the wire is being unloaded.