Question $3$

$(40$ Marks$)$

A large crankshaft made of cast iron with fracture toughness $(K_c=50MN{m}^{-\frac{3}{2}})$ undergoes cyclic

tensile stress, $250$ MPa $,$ and compressive stress, $80$ MPa $.$ Before using the material, an

inspection with ultrasonic techniques was carried out and the largest surface crack was found to

be $3mm$ in length. For the cast iron material, the Paris law constants are

${?}^{\frac{3}{2}}$ per cycle and $n=2\mathrm{.}5.$ Calculate the number of cycles to failure $(N_f).$

Hint: This problem requires you to determine the critical crack length $(a_f).$ Take $Y=1.$