GATE 2025 MT – Question 58
A component made from alloy A, with plane-strain fracture toughness $K_{IC}=50\ \mathrm{MPa\,m^{1/2}}$, fractures at crack length 0.4 mm under tensile service stress $\sigma$. If the same component is made from alloy B with $K_{IC}=75\ \mathrm{MPa\,m^{1/2}}$, the critical crack length for similar crack geometry under identical stress is ______ mm (rounded to one decimal place).
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Correct answer: 0.9 to 0.9
Explanation
For the same geometry, $K_{IC}=Y\sigma\sqrt{\pi a}$. Since $Y$ and $\sigma$ are unchanged, $a\propto K_{IC}^2$.
Thus $a_B=a_A(K_{IC,B}/K_{IC,A})^2=0.4(75/50)^2=\boxed{0.9\ \mathrm{mm}}$.