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GATE 2019 MT – Question 42

Mechanical Behaviour of Materials · Plasticity and yield criteria · 2 marks · Multiple choice

An aluminium single crystal is pulled along $[1\bar10]$. Which slip system is activated first?

  1. $(1\bar1\bar1)[0\bar11]$
  2. $(\bar1\bar11)[011]$
  3. $(\bar1\bar11)[1\bar10]$
  4. $(\bar1\bar11)[101]$

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Show answer and explanation

Correct answer: (A) $(1\bar1\bar1)[0\bar11]$

Explanation

Slip starts on the system with largest resolved shear $\tau=\sigma\cos\phi\cos\lambda$. For A, the tensile-axis dot product with the normalized plane normal has magnitude 2/√6 and with the slip direction 1/2, giving Schmid factor 1/√6≈0.408. For B,C,D, the plane normal (−1,−1,1) is perpendicular to (1,−1,0), giving zero Schmid factor. Therefore A.

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