A large martensitic 4340 steel plate contains an internal linear crack of 8 mm. The crack is subjected to a cyclic fatigue loading condition such that $\sigma_{max}$ = 280 MN/m², $\sigma_{min}$ = 0 MN/m². The fatigue crack propagation rate equation for this steel at room temperature and in air environment is $da/dN = 0.66 \times 10^{-8} (\Delta K)^{2.25}$. The mechanical properties for this steel plate are:
$\sigma_u$ = 1800 MN/m², $\sigma_y$ = 1400 MN/m², and $K_{Ic}$ = 300 MN/m² $\sqrt{m}$.
Determine the number of cycles that this plate will withstand before fracture.
(20 marks)