Explain why stress - strain curve usually has two segments

The first segment is Elastic elongation and another one is plastic deformation.

Explanation:

The first mode is elastic elongation where once the load is removed, the piece will go back to its original position. This is shown on the curve as the linear region at the beginning.

The second mode is the plastic elongation where once the load is removed the piece will not go back to its original position. The onset of plastic region is shown on the curve when the elastic region becomes curved instead of straight.