GATE 2024 MT – Question 63
A large rectangular component under fully reversed cyclic loading develops a dominant surface fatigue crack. Stress amplitude is $\sigma_A=100$ MPa, material toughness $K_{IC}=50$ MPa m$^{1/2}$, and geometric factor $\alpha=1.12$. The crack length causing catastrophic failure is ______ mm (one decimal place).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 62.5 to 64.5
Explanation
The maximum tensile stress equals the amplitude, 100 MPa.
At failure, $K_{IC}=\alpha\sigma_{max}\sqrt{\pi a}$.
Thus $a=[50/(1.12\times100)]^2/\pi=0.06344\ldots$ m, or **63.4 mm**.
The full stress range is used for crack-growth ranges, not this maximum-toughness condition.