question_answer

The stress-strain graph for a metal wire is shown in 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 which point on the curve is Hooke's law obeyed? This point is sometimes called "Proportionality limit". (b) Which point on the curve corresponds to elastic limit and 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?

Answer:

                (a) Hooke's law is obeyed up to the point P, because up to this point, stress \[\propto \] strain. (b) Point E corresponds to elastic limit because the wire returns to original state O along EPO if it is gradually unloaded. (c) The elastic region is from O to E and the plastic region is from E to B. (d) Up to 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. (e) Between C and B, the wire virtually flows out, i.e., the strain increases even when the wire is being unloaded. Fracture takes place at point B. The stress can be applied to the value corresponding to the point C without causing fracture.