A rotating shaft in a power$-$generation system has been inspected by nondestructive

tests that can only reveal surface cracks larger than $2$ mm$.$ The shaft is made

of AISI $4340($T$260$C$)$ steel of KIC $=50$ MPa m$1/2.$ The loading conditions of the

shaft cause an alternating stress of $200$ MPa. Estimate the fatigue life of the shaft. Take C$=1\mathrm{.}0$ x$10-12$ and n$=3.$