## Q. 7.1

Design of a Nondestructive Test
A large steel plate used in a nuclear reactor has a plane strain fracture toughness of 80,000 psi $\sqrt{in.}$ and is exposed to a stress of 45,000 psi during service. Design a testing or inspection procedure capable of detecting a crack at the edge of the plate before the crack is likely to grow at a catastrophic rate.

## Verified Solution

We need to determine the minimum size of a crack that will propagate in the steel under these conditions. From Equation 7-1 assuming that f = 1.12 for a single-edge notch crack:

$K=f \sigma \sqrt{\pi a}$     (7-1)
$K_{Ic}=f \sigma \sqrt{\pi a}$
$80,000 \ psi \ \sqrt{in.}=(1.12)(45,000 \ psi) \sqrt{\pi a}$
$a= 0.8 \ in.$

A 0.8 in. deep crack on the edge should be relatively easy to detect. Often, cracks of this size can be observed visually. A variety of other tests, such as dye penetrant inspection, magnetic particle inspection, and eddy current inspection, also detect cracks much smaller than this. If the growth rate of a crack is slow and inspection is performed on a regular basis, a crack should be discovered long before reaching this critical size.