show the variation of stress with strain when a metallic wire of uniform cross section is subjected to an increasing load
Answers
Explanation:
Stress-strain curve for an elastic material:
The behaviour of the wire under increasing load can be studied by calculating the stress and strain against each load through a graph.
Suppose a metallic wire of uniform cross-section is suspended from a rigid support. When the load on the other end is gradually increased, the length of the wire goes on increasing. If graph between stress and strain is plotted, the shape of the curve will be as shown in Fig.
(a) Portion OA: The portion OA of the graph is Stress a straight showing that upto point A, strain produced in the wire is directly proportional to the stress i.e., strain a stress. In this portion, the material of the wire obeys Hooke’s law. The point A is called the limit of proportionality. The proportionality limit is the greatest stress a material can sustain without the departure from a linear stress-strain relation. If the applied force is removed at any point between O and A, the wire regains its original length.
(b) Portion AB: The portion AB of the graph is not a straight line showing that in this region, strain is not proportional to the stress. Note that the slope of the graph is decreased; this means that strain increases more rapidly with stress. Nevertheless, if load is removed at any point between O and B, the wire will return to its original length. The point B is called the elastic limit. The elastic limit is the maximum stress which a body can sustain and still regain its original size and shape once the load has been removed.
(c) Portion BC: If the stress is increased beyond the elastic limit, a point C is reached at which there is marked increase in extension. This point is called yield point. Between B and C, the material becomes plastic i.e. if the wire is unloaded at any point between B and C, the wire does not quite come back to its original length. The extension not recoverable after removing the load is known as permanent set. However, this permanent deformation is not serious enough to be important. In practice, we must keep the stress below the yield point. Here OO
′
is the permanent set.
(d) Portion CD: If the stress is increased beyond point C, the wire lengthens rapidly until we reach point D at the top of the curve. The point D is called the utlimate strength or breaking stress. Beyond point D, even a stress smaller than at C may continue to stretch the wire until it breaks.
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