Question

In open-die forging, a disc of diameter 200 mm and height 60 mm is compressed without any barreling effect. The final diameter of the disc is 400 mm. The true strain is

• A. 1.986
• B. 1.686
• C. 1.386
• D. 0.602

Answer 1

The correct option is C 1.386

Since, volume of disc remains constant during the process, Hence

$\frac{\pi D_1^2}{4}\times l_1=\frac{\pi D_2^2}{4}{l}_2$

$D_1^2{l}_1=D_2^2{l}_2$

${200}^2\times 60={400}^2\times l_2$

$l_2=15mm$

$\text{Change in length}=l_1-l_2$

$=60-15=45$ mm
Strain:
$\epsilon =\frac{l_1-l_2}{l_2}=\frac{45}{15}=3$

$\therefore$ True strain
${\epsilon }_T=ln(1+\epsilon )=ln(1+3)$

$=ln4=1.386$