Answer to Question #350405 in General Chemistry for justin

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 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 deformatio

Answer 1

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

$percentage~ cold ~work= ~\cfrac {A_0-A_d}{A_0}*~100\\~\\ \cfrac {πr_0^2-πr_d^2}{πr_0^2}*100\\~\\ \cfrac {15²-11²}{15²}*100=46.2~percentage$

Percentage cold work = 46.2 %

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

$r_d=r_0\sqrt {1-\frac{percentage~cold~work}{100}}\\~\\ r_d=12\sqrt{1-\frac{46.2}{100}}\\~\\ r_d = 9.1625324~mm$

Answer: r_d ≈ 9.1625 mm