GATE 2018 ME (ME2) – Question 56
A metal’s true stress (MPa)–true strain relation is $\sigma=1020\varepsilon^{0.4}$. Its initial cross-sectional area at zero stress and strain is 100 mm². Find its area at onset of necking (mm²), to two decimal places.
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Correct answer: 65.00 to 70.00
Explanation
Considère’s necking condition is $d\sigma/d\varepsilon=\sigma$. For $\sigma=K\varepsilon^n$, it gives $\varepsilon=n=0.4$. Plastic volume conservation gives $A=A_0e^{-\varepsilon}=100e^{-0.4}=$ **67.03 mm²**.