Discussion
A solid cylinder of diameter 100 mm and height 50 mm is forged between two frictionless flat dies to a height of 25 mm. The percentage change in diameter is
Answer: D
The diameter increases by about 41.4 %.
With frictionless dies the cylinder stays cylindrical, and volume is constant in plastic deformation:
\[ \begin{aligned} d_{1}^{2}h_{1} &= d_{2}^{2}h_{2} \\ d_{2} &= 100\sqrt{\frac{50}{25}} = 141.4\ \text{mm} \end{aligned} \]
The change is 41.4 mm on 100 mm, or 41.4 %. 20.7 % is half of that and 2.07 % a tenth of that again, and 0 would mean no lateral flow, which is impossible when the height is halved at constant volume.
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