Question

Two previously undeformed cylindrical specimens of an alloy are to be strain hardened by reducing their cross-sectional areas (while maintaining their circular cross sections). For one specimen, the initial and deformed radii are 15 mm and 12 mm, respectively. The second specimen, with an initial radius of 11 mm, must have the same deformed hardness as the first specimen.Compute the second specimen's radius after deformation.

Answer 1

Answer:

Explanation:

Two previously undeformed cylindrical specimens of an alloy are to be strain hardened by reducing their cross-sectional areas (while maintaining their circular cross sections). For one specimen, the initial and deformed radii are 15 mm and 12 mm, respectively. The second specimen, with an initial radius of 11 mm, must have the same deformed hardness as the first specimen.Compute the second specimen's radius after deformation.

The percentage of cold work to be done to deform the two cylindrical is calculated

$\% CW=\frac{A_o-A_d}{A_o} \times100\\\\=\frac{\pi r_o^2-\pi r^2_d}{r_o^2} \times100$

we input the values

$=\frac{15^2-12^2}{15^2} \times 100\\\\=\frac{225-144}{225} \times100\\\\=\frac{81}{225} \times 100\\\\=36 \%$

We can now calculate the deformed radius of the second specimen for the same deformation

$r_2=r_o\sqrt{1-\frac{\% CW}{100} }\\\\=11\sqrt{1-\frac{36}{100} } \\\\=11\sqrt{1-0.36} \\\\=11\sqrt{0.64} \\\\=11\times0.8\\\\=8.8mm$