Fatigue life of a material for a fully reversed loading condition is estimated from σ_a = 1100N^-0.15 , σ_a is the stress amplitude in MPa and N is the failure life in cycles. The maximum allowable stress amplitude (in MPa) for a life of 1*10⁵ cycles under the same loading condition is ________ (correct to two decimal places).

The correct answer is 195.61.

Step-by-Step Explanation:

The fatigue life relationship for the material under fully reversed loading is given by the power-law equation:

${\sigma }_a=1100N^{-0.15}$
where:
• ${\sigma }_a$ is the stress amplitude in MPa,
• $N$ is the fatigue failure life in cycles.

We are given the target fatigue life:

$N=1\times {10}^5\text{cycles}$

To find the maximum allowable stress amplitude, substitute $N$ into the fatigue life equation:

${\sigma }_a=1100\times {(1\times {10}^5)}^{-0.15}$

First, calculate the exponential term:

${\left({10}^5\right)}^{-0.15}={10}^{5\times (-0.15)}={10}^{-0.75}\approx 0.177828$

Now, multiply this by the coefficient 1100:

${\sigma }_a=1100\times 0.177828\approx 195.6108\text{MPa}$

Rounding the result to two decimal places, we get:

${\sigma }_a=195.61\text{MPa}$