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GATE 2024 MT – Question 45

Mechanical Behaviour of Materials · Fracture mechanics · 2 marks · Multiple choice

Which graph represents Griffith’s criterion for growth of a center crack in an infinitely large, brittle isotropic plate? $\Delta SE$ is the magnitude of total strain energy released (solid curve), $\Gamma_s$ is total surface energy (dashed line), and $a_c$ is critical crack length (downward arrow). The dotted tangent to $\Delta SE$ is parallel to $\Gamma_s$.

Diagram for GATE 2024 MT question 45
  1. Graph A
  2. Graph B
  3. Graph C
  4. Graph D

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Show answer and explanation

Correct answer: (D) Graph D

Explanation

For a central crack under fixed remote stress, released strain-energy magnitude grows as a² while new surface energy grows linearly with a.

Griffith onset occurs where their slopes match, not where total energies cross.

Plot **D** marks the tangent parallel to the surface-energy line at the correct critical length.