GATE 2025 MT – Question 64
A cylindrical Al-alloy billet of diameter 300 mm is hot extruded to a cylindrical rod of diameter 75 mm at constant true strain rate $\dot\epsilon=10\ \mathrm{s^{-1}}$. At the extrusion temperature its flow stress is $\sigma=10(\dot\epsilon)^{0.3}$ MPa. Assume perfectly plastic behavior and no temperature rise. The ideal plastic work per unit volume is ______ $\times10^6\ \mathrm{J\,m^{-3}}$ (rounded to one decimal place).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 53.3 to 57.3
Explanation
The area ratio is $A_i/A_f=(300/75)^2=16$, giving ideal true strain $\epsilon=\ln16$.
The constant flow stress is $\sigma=10(10)^{0.3}=19.9526\ldots$ MPa. Work per volume is $w=\int\sigma\,d\epsilon=\sigma\ln16$.
Thus $w=55.3203\ldots\times10^6\ \mathrm{J\,m^{-3}}$. The requested coefficient is **55.3**.