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GATE 2019 MT – Question 61

Manufacturing Processes · Metal forming · 2 marks · Numerical answer

A metal follows the true flow curve $\sigma=1750\epsilon^{0.37}$, with σ in MPa. Find true stress at the onset of necking in MPa (nearest integer).

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Correct answer: 1160 to 1260

Explanation

The Considère criterion for uniform tensile instability is dσ/dε=σ. For a power law Kεⁿ, this gives ε=n=0.37. Substitute into the flow curve: $\sigma_n=1750(0.37)^{0.37}\simeq1211$ MPa. The relevant strain is true plastic strain in the stated power-law model.

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