Question

The relationship between true strain $\left({ϵ}_T\right)$ and engineering strain $\left({ϵ}_E\right)$ in a uniaxial tension test is given as

• A. ${ϵ}_E=ln(1+{ϵ}_T)$
• B. ${ϵ}_E=ln(1-{ϵ}_T)$
• C. ${ϵ}_T=ln(1+{ϵ}_E)$
• D. ${ϵ}_T=ln(1-{ϵ}_E)$

Answer 1

The correct option is C ${ϵ}_T=ln(1+{ϵ}_E)$

$\text{True strain}:d{ϵ}_T=\frac{dL}{L}$

${ϵ}_T={\int }_{L_0}^L\frac{dL}{L}=ln\frac{L}{L_0}$

As $dV=0$

$AL=$ $A_0{L}_0$

$\frac{L}{L_0}=\frac{A_0}{A}$

${ϵ}_E=\frac{L-L_0}{L_0}$

$\Rightarrow \frac{L}{L_0}=1+{ϵ}_E$

$\therefore {ϵ}_T=ln(1+{ϵ}_E)$