Problem Statement:

In the below figure, a surface through crack is shown with an initial crack length of 3mm and a critical crack length of 6.57mm. If an alternating stress of 458.33 MPa is applied to the figure axially as shown and the Paris Constants are $C_{p_e} = 4.5*10^{-15}$ and n is 3; How many cycles will the member be able to withstand before the crack propagates to its critical fracture length? Use a material constant of 0.099.

Figure 13: Central Through Crack from Problem

Figure 14: Paris Equation (a is crack length; Np is Number of cycles till critical crack length; $\Delta \sigma$ is alternating stress)