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 17 mm and 11 mm, respectively. The second specimen, with an initial radius of 14 mm, must have the same deformed hardness as the first specimen; compute the second specimen's radius, in mm, after deformatio

Answer 1

r_d= 8.1382 mm

Step-by-step explanation:

In order for these two cylindrical specimen to have same deformed hardness They must be deformed by the same percentage cold worked. For the first specimen

percentage cold work =
`(A_0-A_d)/(A_0)*100`

`(\pi r_0^2-\pi r_d^2)/(\pi r_0^2)*100`

`(17^2-11^2)/(17^2)*100`

percentage cold work= 58.13 %

For the second specimen, the deformed radius is computed using above equation and solving for radius

r_d

`r_d= r_o\sqrt{1-(percentage cold work)/(100) }`

`r_d= 14\sqrt{1-(58.13)/(100) }`

r_d= 8.1382 mm