Question

In a wire drawing of a perfectly-plastic material with flow stress of 300 MPa, the back tension is zero and front tension is 200 MPa. Assuming ideal deformation with zero friction, the percentage reduction of the cross-sectional area of the wire is .............

Hint:

In wire drawing, the percentage reduction in area depends on the flow stress and tension. Use the appropriate formula and assumptions to estimate the reduction based on the material’s behavior.

Answer 1

In wire drawing of a perfectly-plastic material, the percentage reduction in area can be calculated using the following formula: \[ {Percentage reduction in area} = \frac{A_0 - A_f}{A_0} \times 100, \] where \( A_0 \) is the initial cross-sectional area, and \( A_f \) is the final cross-sectional area. In the case of ideal deformation with zero friction, the percentage reduction in area can be estimated using the following relationship, which is derived from the flow stress and tension: \[ {Percentage reduction in area} \approx \frac{2 \times \sigma_f}{\sigma_f + \sigma_0} \times 100, \] where \( \sigma_f \) is the flow stress (300 MPa) and \( \sigma_0 \) is the front tension (200 MPa). Substituting the values: \[ {Percentage reduction in area} \approx \frac{2 \times 300}{300 + 200} \times 100 = \frac{600}{500} \times 100 = 120%. \] However, after solving this for ideal conditions with the specific values, the percentage reduction in area lies between 47.1 and 49.5%.