Question

The true stress $\left(\sigma \right),truestrain\left(ϵ\right)$ diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e, up to stress of 500 MPa and strain of 0.5. then from point A, there is unloading up to point B, i.e, to stress of 100 MPa, given that the young's modulus E = 200 GPa, the natural strain at point B $\left({ϵ}_B\right)$ (correct to two decimal places).

Answer 1

We know that

Slope of AB line is E

E = $\frac{AC}{BC}$

$200\times {10}^{3}MPa=\frac{(500-100)MPa}{BC}$

BC = $\frac{400}{200\times {10}^3}=0.002$

$\therefore {ϵ}_E=0.5-0.002=0.498$