The GATE Grind

GATE 2025 MT – Question 21

Mechanical Behaviour of Materials · Dislocations and strengthening · 1 mark · Multiple choice

Two randomly oriented polycrystalline copper samples with average grain sizes of 10 μm (Sample A) and 100 μm (Sample B) were tested at room temperature. $E_A$ and $E_B$ are their respective Young’s moduli; $YS_A$ and $YS_B$ are their respective yield strengths. Which statement is correct?

  1. $E_A>E_B$ and $YS_A>YS_B$
  2. $E_A=E_B$ and $YS_A<YS_B$
  3. $E_A>E_B$ and $YS_A=YS_B$
  4. $E_A=E_B$ and $YS_A>YS_B$

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Show answer and explanation

Correct answer: (D) $E_A=E_B$ and $YS_A>YS_B$

Explanation

For similarly random polycrystals, Young’s modulus is governed mainly by interatomic bonding and is approximately independent of these grain sizes. Hall–Petch strengthening gives σy=σ0+k/√d, so the 10 μm sample has higher yield strength. Hence EA=EB and YSA>YSB: **D**.