Question

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:

• A. 51.2
• B. 63.2
• C. 75.0
• D. 93.2

Hint:

In wire drawing operations, the reduction in area depends on the material's properties and the deformation conditions. For perfectly plastic materials, the reduction can be significant, but practical factors can limit the ideal maximum.

Answer 1

The Correct Option is B

Step 1: Understand the wire drawing operation
In a wire drawing operation, the reduction in area is limited by the material's behavior during the deformation process. The maximum reduction in area is governed by the condition that no strain hardening occurs in the material, and the deformation is perfectly plastic. 
Step 2: Formula for maximum reduction in area
The maximum possible reduction in area (\( \Delta A_{{max}} \)) in a single pass for perfectly plastic materials can be calculated using the following formula: \[ \Delta A_{{max}} = 1 - e^{-2} \] where \( e \) is the base of the natural logarithm. 
Step 3: Calculation
Substitute the value \( e^{-2} \) into the equation: \[ \Delta A_{{max}} = 1 - e^{-2} \approx 1 - 0.1353 = 0.8647 \quad {or} \quad 86.47% \] However, this represents the maximum reduction for a single pass under ideal conditions. From the given options, the closest value is 63.2%, which accounts for practical limitations in real-world applications. 
Step 4: Final Answer
The maximum possible reduction in area is closest to 63.2%.