True stress and true strain

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

                                          
                                σact = P/Aact



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

True strain is also called as actual strain or natural strain and it plays an important role in
theories of viscosity.
The difference in using engineering stress-strain and the true stress-strain is noticeable
after the proportional limit is crossed