2. A wide sheet of steel contains a semi-circular edge notch (K, = 3.0) with a radius of 0.5 in. Determine the transition crack length, &,, for this geometry using both the Dowling and Smith- Miller approximations. Estimate the crack propagation life, Np, of the plate at a zero-to- maximum (R = 0) nominal stress loading of 0 to 40 ksi. Compare the predicted lives found using the two estimates for transition crack length. How do these values compare to a life estimate using the approximation that the initial crack length is equal to the depth of the notch? For all calculations use a value of 1.58 in. for the final crack length, af. The Paris crack growth parameters of this steel are C = 2.96 × 109 and m = 2.385 (for these parameters, unit on da/dN is in/cycle and on AK is ksi in 1/2).

Fig: 1