Question

The maximum possible percentage reduction in area per pass during wire drawing of an ideal plastic material without friction is of the order of

• A. 37
• B. 50
• C. 63
• D. 75

Answer 1

The correct option is C 63

In the frictionless wire drawing process,

${\sigma }_d={\sigma }_{0}ln\left(\frac{A_f}{A_f}\right)$

where, ${\sigma }_d$ is drawing stress

${\sigma }_0$ is nominal stress

when, ${\sigma }_d={\sigma }_0$ then maximum reduction occurs

$1=ln\left(\frac{A_i}{A_f}\right)$

$\Rightarrow e=\frac{A_i}{A_f}$

$\%\text{reduction}=\frac{A_i-A_f}{A_i}\times 100\%$

$=(1-\frac{1}{e})\times 100\%=63\%$