Discussion
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
Answer: B
The maximum reduction is about 63.2 percent.
For ideal drawing of a perfectly plastic material, the drawing stress is \(\sigma_{d} = Y\ln(A_{0}/A_{f})\). The drawn wire cannot carry more than its yield stress, so the limit is \(\sigma_{d} = Y\):
\[ \begin{aligned} \ln(A_{0}/A_{f}) &= 1 \\ A_{f}/A_{0} &= e^{-1} = 0.368 \\ r &= 1 - 0.368 = 0.632 \end{aligned} \]
That is 63.2 percent. 51.2, 75.0 and 93.2 percent correspond to true strains of 0.72, 1.39 and 2.69, which would require the wire to carry more than its yield stress or fail to use it fully.
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