The GATE Grind

GATE 2022 MT – Question 26

Mechanical Behaviour of Materials · Plasticity and yield criteria · 1 mark · Multiple choice

A strain-hardening material develops necking instability in tension when ______. Here $\sigma$ is true stress and $\epsilon$ true strain.

  1. $d\sigma/d\epsilon=0$
  2. $d\sigma/d\epsilon=\epsilon$
  3. $d\sigma/d\epsilon=\sigma$
  4. $d\sigma/d\epsilon=\infty$

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Correct answer: (C) $d\sigma/d\epsilon=\sigma$

Explanation

Force is $F=\sigma A$. Plastic incompressibility gives $dA/A=-d\epsilon$. At maximum load, $dF=A(d\sigma-\sigma\,d\epsilon)=0$, so $d\sigma/d\epsilon=\sigma$, **C**, the Considère criterion.