GATE 2022 MT – Question 60
A cylindrical aluminium-alloy specimen is cold-extruded from diameter 30 mm to 20 mm. Its true flow law is $\sigma=350\epsilon^{0.3}$ MPa. The ideal plastic work per unit volume is ______ $\times10^6$ J/m$^3$ (nearest integer). The source prints J for the scaled unit; work per unit volume requires J/m$^3$.
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Correct answer: 200 to 210
Explanation
Volume conservation gives extrusion true strain $\epsilon=\ln(A_0/A_f)=\ln(30^2/20^2)=0.81093$. Ideal work density is $\int_0^\epsilon350u^{0.3}\,du=350\epsilon^{1.3}/1.3=205.02$ MPa. Since 1 MPa = $10^6$ J/m$^3$, the coefficient is **205**.