Answer:
104,576 cycles
Explanation:
Step 1: identify given parameters
Ultimate strength of steel ([tex]S_{ut}[/tex])= 120 Kpsi
stress amplitude ([tex]\alpha_{a}[/tex])= 70 kpsi
life of the specimen (N) = ?
[tex]N = (\frac{\alpha_{a}}{a})^\frac{1}{b}[/tex]
where a and b are coefficient of fatigue cycle
Step 2: calculate the the endurance limit of specimen
[tex]S_{e} = 0.5*S_{ut}[/tex]
[tex]S_{e}[/tex] = 0.5*120 = 60 kpsi
Step 3: calculate coefficient 'a'
[tex]a=\frac {(0.8XS_{ut})^2}{S_{e}}[/tex]
[tex]a=\frac {(0.8X120)^2}{60}[/tex]
[tex]a= 153.6 kpsi
Step 4: calculate the coefficient 'b'
[tex]b =-\frac{1}{3}log(\frac{f*S_{ut} }{S_{e}})[/tex]
[tex]b =-\frac{1}{3}log(\frac{0.8*120}{60})[/tex]
[tex]b =-0.0680
Step 5: calculate the life of the specimen
[tex]N=(\frac{\alpha_{a}}{a})^\frac{1}{b}[/tex]
[tex]N=(\frac{70}{153.6})^\frac{1}{-0.068}[/tex]
[tex]N=104,576 cycles [/tex]
∴ the life (N) of the steel specimen is 104,576 cycles
