GATE 2023 MT – Question 63
An alloy obeys $\sigma=1100\epsilon^{0.3}$, where $\sigma,\epsilon$ are true stress and strain. It is cold-drawn to an unknown strain and then tensile-tested. At maximum tensile load, the test shows 10% reduction in area. The prior cold-work strain is ______ (two decimal places).
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Correct answer: 0.18 to 0.21
Explanation
For Hollomon’s law $\sigma=K\epsilon^n$, Considère necking occurs at total true strain $\epsilon=n=0.3$. The tensile test adds $\ln(A_i/A_{max})=\ln(1/0.9)=0.10536$. The prior strain is $0.3-0.10536=0.19464$, rounding to **0.19**.