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GATE 2025 ME – Question 39

Casting, Forming and Joining Processes · Bulk forming and sheet forming, estimation of load · 2 marks · Multiple choice

Wire drawing operation is performed on a perfectly plastic metal without any strain hardening. Assuming no friction and no redundant work, the maximum possible percentage reduction in area in a single pass is closest to

  1. 51.2
  2. 63.2
  3. 75.0
  4. 93.2

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Correct answer: (B) 63.2

Explanation

For ideal drawing of a perfectly plastic metal, the drawing stress is $\sigma_d = \sigma_y\ln\frac{A_0}{A_1}$. The largest possible drawing stress is the yield stress, so $\ln\frac{A_0}{A_1} = 1$ and $\frac{A_1}{A_0} = e^{-1} = 0.368$. The reduction is $1 - 0.368 = 0.632$, which is 63.2 percent.