True Stress and True Strain | How to Calculate True Stress and Strain

The instantaneous stress and strain are called true stress and true strain respectively. If we find out the stress and strain at any instant by using the cross-sectional area and length of the specimen at that instant then it is known as true stress and true strain.

When we plot the stress-strain curve for mild steel, the stress and strain are 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 the specimen at that instant then it is known as true stress and true strain. The curve so obtained is known as true stress vs true strain curve.

Now, we will see how the true stress vs true strain curve varies in tension and compression.

Nominal Stress vs Nominal Strain Curve in tension for mild steel

The stress reduces after the ultimate stress point whereas, in the 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 stress-true strain curve remains below the nominal stress - nominal strain curve because the cross-sectional area increases in this case.

The true stress vs true strain curve remains identical in tension and compression.

Now we will see how to calculate true stress and true strain using formulas.

How to calculate True stress!

True stress = Load / Actual cross-sectional area of specimen at which load is applied

In the above specimen, the actual or deformed cross-sectional area of the specimen is noted after yielding has started in ductile materials like mild steel.

How to calculate True strain!

Generally, the strain is defined as the change in length(𝛿) / Original length of specimen(Lo). Instead of using total elongation 𝛿, the successive values of specimen length is noted down of specimen length L is noted down.

Then strain at each instant is taken Δ𝛿 = ΔL / L and the total strain is calculated by adding or integrating all the individual strain values which leads to the final expression given below.

True strain = ln(L/Lo), where Lo is the original length of the specimen and L is the length of the specimen at the time of observation

Now watch the below video to understand better about true stress and true strain.

Do try out this simple question to check if you have understood true stress and true strain.

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