Explain the Negative Zero problem with the help of an example and also propose its
solution.

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Ответ:

Alysssssssssssa

11.07.2022

Engineering

Solution :

Given data:

Diameter of the copper cylindrical rod = 16 mm

Yield strength = 250 MPa

Calculating the percent cold work

$\text{Percentage Cold Work} = \frac{\pi\left(\frac{d_0}{2}\right)^2-\pi\left(\frac{d_d}{2}\right)^2}{\pi\left(\frac{d_0}{2}}\right)^2} \times 100$

$= \frac{\pi\left(\frac{16}{2}\right)^2-\pi\left(\frac{11.3}{2}\right)^2}{\pi\left(\frac{16}{2}}\right)^2} \times 100$

= 50% CW

Therefore, at $50\% \ CW$ , the yield strength of copper will be of the order of 330 MPa.

The ductility will be 4% elongation (EL).

Rather than performing drawing in single operation, we draw some of the fraction of total deformation, and then the anneal them to recrystallize and also finally w do cold work on the material for the second time to achieve its final diameter, ductility and yield strength.

$21\% \ CW$ is required for a yield strength of $250 \ MPa$ . Similarly, a maximum of $23\% \ CW$ is required for $12\% \ EL$ .

The average of the two values is $22\% \ CW$ . To achieve both the $\text{specified yield strength and ductility,}$ the copper should be deformed to $22\% \ CW$ . The $\text{ final diameter}$ after the first drawing and the initial diameter for the second drawing is $d_0'$ , then

$22\% \ CW = \frac{\pi\left(\frac{d_0'}{2}\right)^2-\pi\left(\frac{11.3}{2}\right)^2}{\pi\left(\frac{d_0'}{2}}\right)^2} \times 100$

$d_0'=\frac{11.3}{\sqrt{1-\frac{22\% \ CW}{100}}}$

$d_0'=12.8 \ mm$

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Explain the Negative Zero problem with the help of an example and also propose its solution.