GATE 2022 MT – Question 52
An alloy has the following high-cycle fatigue data for alternating stress $\sigma_a$:
| Stress (MPa) | Cycles to failure |
|---|---|
| 500 | 1000 |
| 400 | 10000 |
| 300 | 100000 |
| 200 | 1000000 |
The specimen experiences 5000 cycles at 400 MPa, then 25000 cycles at 300 MPa, then loading at 500 MPa. Assuming Miner’s law, the number of cycles to failure in the final stage is ______.
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Correct answer: 250 to 250
Explanation
Miner’s rule sums life fractions. The first two stages consume $5000/10000+25000/100000=0.75$. Remaining fraction is 0.25. At 500 MPa the full life is 1000 cycles, so remaining cycles are $0.25(1000)=\boxed{250}$.