True stress and true strain
The stress was calculated by dividing the load P by the initial cross section of the specimen. But it is clear that as the specimen elongates its diameter decreases and the decrease in cross section is apparent during necking phase. Hence, the actual stress which is obtained by dividing the load by the actual cross sectional area in the deformed specimen is different from that of the engineering stress that is obtained using undeformed cross sectional area as in equation 1.1 Though the difference between the true stress and the engineering stress is negligible for smaller loads, the former is always higher than the latter for larger loads.
Similarly, if the initial length of the specimen is used to calculate the strain, it is called engineering strain as obtained in equation 1.9
But some engineering applications like metal forming process involve large deformations and they require actual or true strains that are obtained using the successive recorded lengths to calculate the strain. True strain is also called as actual strain or natural strain and it plays an important role in theories of viscosity.