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Stress-Strain Curve

The direct proportionality between stress and strain is found to be true only for small values of strain (about 0.3% of the original length). If a wire is gradually loaded and strain produced is plotted versus stress, then graph obtained is of the shape in Figure.
  1. The portion OP of the graph is a straight line showing stress directly proportional to strain. It shows that Hooke’s law is strictly obeyed up to the value of stress corresponding to point P. The point P is sometimes called Proportional limit.
  2. Beyond the point P, the graph between stress and strain is not found to be a straight line as indicated by the part PE of the graph. However, unloading the wire at point E, the graph between stress and strain is obtained in the reverse direction along EPO, then the point E is called elastic limit.
    The portion of the graph between O and E is called Elastic region. It may be pointed out that Hooke's law is not obeyed between the points P and E.
  3. If the wire is loaded beyond the point E, the strain increases much more rapidly with the stress. The slope of the graph between stress and strain after the point A becomes quite small as shown by the fig. 9.06 curve EA. If the wire is unloaded at A, the graph between stress and the strain will not be along AEPO but will be as shown by the dotted line AO . Therefore, even when the wire is completely unloaded, length increases permanently by some amount corresponding to OO . It is called permanent set.
  4. Beyond the point A, the length of the wire starts increasing virtually for no increase in stress. Thus, wire begins to flow after point A and its continues up to point C. The point A, at which the wire begins to flow, is called yield point. The increase in the length of the wire for virtually no increase in stress is called plastic behaviour of the wire.
  5. Beyond the point C, the graph indicates that the length of the wire increases, even if the wire is unloaded. In this region, the constrictions (called necks and waists) develop at few points along the length of the wire and as a result of it, the wire beaks ultimately say corresponding to the point B, called breaking point of the wire. The portion of the graph between E and B is called plastic region. The stress corresponding to the point B is called breaking stress or ultimate stress. The product of the breaking stress and the area of cross-section are equal to breaking load for the wire.
The materials of the wire, which break as soon as stress is increased beyond the elastic limit, are called brittle. Graphically, for such materials, the portion of graph between E and B is almost zero. On the other hand, the materials of the wire, which have quite a good plastic range (large portion of graph between E and B) are called ductile. Such materials can be easily changed in to different shapes and can be drawn in to thin wires.

It may be pointed out that rubber comes to its original length, even when its length is increased several times its original length. Thus, rubber has large elastic limit but it does not obey Hooke's law. Materials like rubber, which can be greatly stretched beyond certain limit.




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