Question

A steel wire is drawn from an initial diameter of 15 mm to a final diameter of 13.4 mm. The mean flow stress of steel is 400 MPa. The ideal force required for drawing is

• A. 15.91 kN
• B. 12.72 kN
• C. 14.28 kN
• D. 56.41 kN

Answer 1

The correct option is B 12.72 kN

Given: $D_i=15mm;D_f=13.4mm;{\sigma }_0=400MPa$

${\sigma }_0={\sigma }_{0}ln\left(\frac{A_i}{A_f}\right)=2\times {\sigma }_{0}ln\left(\frac{D_i}{D_f}\right)$

$=2\times 400\times ln\left(\frac{15}{13.4}\right)=90.23MPa$

Ideal drawing force

$={\sigma }_d\times A_f$

$=90.23\times \frac{\pi }{4}\times d_f^2=90.23\times \frac{\pi }{4}\times {\left(13.4\right)}^2=12.724kN$