The stress strain graph for a metal wire is shown in the fig. Upto 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) Upto 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 limet or yield point of the wire?
(c ) Indicate teh elastice and plastic regions of the stree-strain graph.
(d) Describe what happens when the wire is loaded upto a stress corresponding to the point A on the graph and then unloaded gradulally. In particular explain the dotted curve.
(e) Wht is peculiar about the protion of the stree- strain graph from C to B? Upto what stress can the wire be subjected with out causing fracture?

Explanation

(a) Up to point P, Hooke's law is obeyed because the graph is a st. line from O to P.
(b) Point E. from the graph it is clear that the wire returns to its original position after being unloaded up to point E only, hence E is the elastic limit.
(c) Elastic region is form O to E and plastic region is from E to B.
(d) Strain varies directly proportional to load up to point P and after point P, strain increases by greater amount as comparted to first case (i.e., from O to P), for a given increase in load. Beyond the elestic limit E, the curve does not retrace backwards as the wire is unloaded but returns along dotted line AO' . Point O' corresponds to strain at zero load, which shows that there is a permanent strain in the wire.
(e) From the point C to B, strain increases, even when we unload the wire and at point B it fractures. This shows tant stress upto C can be applied without causing a fracture.