GATE 2021 ME (ME2) – Question 65
The figure shows the relationship between fatigue strength ($S$) and fatigue life ($N$) of a material. The fatigue strength of the material for a life of 1000 cycles is 450 MPa, while its fatigue strength for a life of $10^6$ cycles is 150 MPa. The life of a cylindrical shaft made of this material subjected to an alternating stress of 200 MPa will then be _____ cycles (round off to the nearest integer).
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Correct answer: 163841
Explanation
For S=aNᵇ, slope is $b=\log(150/450)/\log(10^6/10^3)=\log(1/3)/\log1000$. Interpolate on logarithmic axes: $\log_{10}N=3+3\log_{10}(450/200)/\log_{10}3$.
This gives N=163840.5807 cycles, rounded to **163841 cycles**. Linear interpolation of stress against ordinary cycles would be incorrect.