#### Answer

The critical flaw is subject to detection since the value of 16.8 mm is greater than the 3.0 mm resolution limit.

#### Work Step by Step

Given:
A structural component in the form of a wide plate is to be fabricated from a steel alloy that has a plane-strain fracture toughness of$ 98.9 MPa \sqrt m (90 ksi\sqrt in.)$ and a yield strength of 860 MPa (125,000 psi). The flaw size resolution limit of the flaw detection apparatus is 3.0 mm (0.12 in.)
Required:
If the design stress is one-half the yield strength and the value of Y is 1.0, determine whether a critical flaw for this plate is subject to detection.
Solution:
Using Equation 8.7, and noting that $σ = σ_{y}/2$:
$a_{c} = \frac{1}{π} ( \frac{K_{Ic}}{Yσ})^{2} = \frac{1}{π} ( \frac{98.9 MPa \sqrt m}{(1) (\frac{860 MPa}{2})})^{2} = 0.0168 m = 16.8 mm$
The critical flaw is subject to detection since the value of 16.8 mm is greater than the 3.0 mm resolution limit.