True Stress and True Strain
If we find out the stress and strain at any instant by using the cross sectional area and length of specimen at that instant then it is known as the true stress and true strain
When we plot the stressstrain curve for mild steel, the stress and strain is calculated using the initial length and the initial cross section area of the specimen. During the testing the length and the cross sectional area both change.
So, if we find out the stress and strain at any instant by using the cross sectional area and length of specimen at that instant then it is known as the true stress and true strain. The curve so obtained is known as true stress true strain curve
Nominal stress vs Nominal strain curve in tension for mild steel

The stress reduces after the ultimate stress point whereas in case of true stress vs true strain curve, the stress does not reduce up to the rupture point.

The reason for no reduction is that because the area reduces so stress keeps on increasing.
Nominal stress vs Nominal strain curve in compression for mild steel

On the compression side the true stresstrue strain curve remain below the nominal stress  nominal strain curve because the cross sectional area increases in this case.
True stressTrue strain curve remain identical in tension and compression
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