The GATE Grind

GATE 2019 MT – Question 29

Mechanical Behaviour of Materials · Fracture mechanics · 1 mark · Multiple choice

Internal cracks in two samples of the same glass have lengths c₁=0.5 mm and c₂=2 mm. Find the fracture-strength ratio σf1/σf2.

  1. 0.5
  2. 1.0
  3. 2.0
  4. 4.0

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Show answer and explanation

Correct answer: (C) 2.0

Explanation

For otherwise identical Griffith cracks, fracture strength is proportional to $c^{-1/2}$. Hence $\sigma_{f1}/\sigma_{f2}=\sqrt{c_2/c_1}=\sqrt{2/0.5}=2$. Choose C; the longer crack lowers the strength.

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