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The maximum possible percentage reduction in area per pass during wire drawing of an ideal plastic material without friction is of the order of
[PI 2007]
  • a)
    37
  • b)
    50
  • c)
    63
  • d)
    75
Correct answer is option 'C'. Can you explain this answer?
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The maximum possible percentage reduction in area per pass during wire drawing of an ideal plastic material without friction can be determined by considering the principles of plastic deformation and the geometry of the wire drawing process.

1. Introduction to wire drawing:
- Wire drawing is a metal forming process used to reduce the cross-sectional area of a wire or rod.
- It involves pulling the material through a die to reduce its diameter and increase its length.
- The process is commonly used in the production of wires for electrical cables, springs, and other applications.

2. Plastic deformation:
- Plastic deformation refers to the permanent change in shape of a material without fracture.
- During wire drawing, the material undergoes plastic deformation as it is pulled through the die, resulting in a decrease in cross-sectional area.

3. Frictionless wire drawing:
- In an ideal scenario without friction, the only force acting on the wire during drawing is the tensile force applied.
- Friction between the die and the wire is assumed to be negligible, allowing for easier deformation.

4. Percentage reduction in area per pass:
- The percentage reduction in area per pass can be calculated using the equation:
% Reduction in area = (Initial area - Final area) / Initial area * 100

5. Maximum possible reduction in area:
- To determine the maximum possible reduction in area per pass, we need to consider the deformation behavior of the material.
- For an ideal plastic material, the maximum possible reduction in area per pass is given by the formula:
Maximum % Reduction in area = 100 - (1 - (D/d)^2) * 100

Where D is the initial diameter of the wire and d is the final diameter of the wire after drawing.

6. Order of magnitude:
- Without friction, the maximum possible reduction in area per pass can be significant.
- The formula shows that the reduction in area is proportional to the square of the ratio of initial to final diameter.
- As the ratio increases, the reduction in area becomes larger.

7. Answer:
- Based on the given options, the correct answer is option C, which states that the maximum possible percentage reduction in area per pass is of the order of 63%.
- This indicates that the reduction in area can be significant during wire drawing of an ideal plastic material without friction.
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