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
1. 1.986
2. 1.686
3. 1.386
4. 0.602

Answer 1

Correct Answer - Option 3 : 1.386

Concept:

True strain:

If no friction happens between work and die surface, then homogenous deformation occurs so that radial flow is uniform throughout work part height.

The true strain, in this case, is given by:

\(\epsilon_t=\ln\left(\frac{h_{initial}}{h_{final}}\right)=2\ln\left(\frac{d_{final}}{d_{initial}}\right)\)

Calculation:

Given:

d_i = 200 mm, d_f = 400 mm, h_i = 60 mm.

\(\epsilon_t=\ln\left(\frac{h_{initial}}{h_{final}}\right)=2\ln\left(\frac{d_{final}}{d_{initial}}\right)\)

\({\rm{\epsilon_t}} = 2\ln \left( {\frac{{{d_{final}}}}{{{d_{initial}}}}} \right) =2\ln \left( {\frac{{{400}}}{{{200}}}} \right)\Rightarrow2\ln2= 1.386\)