GATE 2020 MT – Question 32
A tensile component is monitored periodically by NDT that can detect surface and internal cracks only when larger than 1 mm. Keeping a 10% margin of safety, find the maximum allowed tensile stress in MPa, rounded to an integer. Fracture toughness is $K_{IC}=30\ \mathrm{MPa}\sqrt{m}$ and crack geometry factor is unity.
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Correct answer: 480 to 494
Explanation
The fracture threshold for an undetected crack-size parameter a = 0.001 m is $\sigma_c=K_{IC}/\sqrt{\pi a}=30/\sqrt{\pi(0.001)}=535.24$ MPa. A 10% safety factor can be expressed as $\sigma_{allow}=\sigma_c/1.1=486.58$ MPa, rounding to 487 MPa. A direct 10% reduction gives 481.71 MPa; both conventions lie within the original 480–494 MPa interval. The allowed stress is lower than the fracture threshold.