Hooke's Law and Elastic Limit:

From the stress-strain curve of a material, a number of necessary mechanical properties of the material could be studied. While you look at the stress-strain curve (Figure), you can recognize segments of various natures. The initial segment of the curve is straight and steep and the strain in this range is proportional to the stress. Therefore, the terminal stage of this range is known as proportional limit. At this stage, we search some small fluctuations followed through a horizontal segment, implies in which the strain in the solid is continuously increasing without any increase within stress. Here the material yields at the end of proportional limit and exhibits plasticity (that is being strained without increase in stress) on additional pulling. This range of strain is known as plastic range, and is about 12 to 13 times the proportional range of strain. The stage whereas proportional range ends and plastic range begins is known as yield point.

While the end of plastic range is reached, additionally loading results in increase of both strain and stress. But here the stress-strain curve is not as steep as in the initial range and is also non-linear. The material having exhibited plasticity once again hardens to take further stress and therefore this range is known as strain hardening range. Straining additionally leads to ultimate failure through rupture.

To know the stress-strain relationship of the solid more clearly, additionally tests are carried out through loading, unloading and reloading of the solid at several stages and results of such an investigation are display in Figure.

Figure