Question

In a wire drawing operation, the diameter of a steel wire is reduced from 10 mm to 8 mm. The mean flow stress of the material is 400 MPa. The ideal force required for drawing (ignoring friction and redundant work) is

• A. 4.48 kN
• B. 8.97 kN
• C. 20.11 kN
• D. 31.41 kN

Answer 1

The correct option is B 8.97 kN

$Given,D_i=10mm,D_f=8mm$

${\sigma }_0=400MPa$

Ignoring friction and redundant work means

$\mu =0,\beta =0$

$Hence,{\sigma }_d=2{\sigma }_{0}ln\left(\frac{r_i}{r_f}\right)$

$=2\times 400\times ln\left(\frac{5}{4}\right)$

= 178.51 MPa

$Idealforce=178.51\times {10}^6\times \pi r_f^2$

= $178.51\times {10}^6\times 3.14\times (0.004{)}^2$

= 8968 N = 8.97 kN