Question

In a multi-pass operation, a round bar of 10mm diameter and 100 mm length is reduced in cross-section by drawing it successively through a series of seven dies of decreasing exit diameter. During each of these drawing operations, the reduction in cross-section area is 35%. The yield strength of the material is 200 MPa. Ignore strain hardening.

The Total true strain applied and the final length (in mm), respectively are

• A. 2.45 and 817
• B. 2.45 and 345
• C. 3.02 and 2043
• D. 3.02 and 33

Answer 1

The correct option is C 3.02 and 2043

$\text{Initial diameter,}{d}_i=10mm$

$\text{Initial length,}{l}_i=100mm$

$\text{Initial cross-sectional area},A_i=\frac{\pi }{4}(10{)}^2$

After seven dies reduction final cross section area

$A_f=(0.65{)}^7\times \frac{\pi }{4}(10{)}^2$

$d_f=2.21mm$

$\text{True strain},{ϵ}_T=ln{\left(\frac{d_i}{d_f}\right)}^2$

$=2ln\left(\frac{10}{2.21}\right)=3.02$

Volume after and before reduction will remain same

$l_i\times \frac{\pi }{4}{d}_i^2=l_f\times \frac{\pi }{4}{d}_f^2$

$100\times \frac{\pi }{4}(10{)}^2=l_f\times \frac{\pi }{4}\times (2.21{)}^2$

$l_f=2047.46mm$