Explanation:
Formula to determine the critical crack is as follows.
[tex]K_{IC} = \gamma \sigma_{f} \sqrt{\pi \times a}[/tex]
[tex]\gamma[/tex] = 1, [tex]K_{IC}[/tex] = 24.1
[/tex]\sigma_{y}[/tex] = 570
and, [tex]\sigma_{f} = 570 \times \frac{3}{4}[/tex]
= 427.5
Hence, we will calculate the critical crack length as follows.
a = [tex]\frac{1}{\pi} \times (\frac{K_{IC}}{\sigma_{f}})^{2}[/tex]
= [tex]\frac{1}{3.14} \times (\frac{24.1}{427.5})^{2}[/tex]
= [tex]10.13 \times 10^{-4}[/tex]
Therefore, largest size is as follows.
Largest size = 2a
= [tex]2 \times 10.13 \times 10^{-4}[/tex]
= [tex]20.26 \times 10^{-4}[/tex]
Thus, we can conclude that the critical crack length for a through crack contained within the given plate is [tex]20.26 \times 10^{-4}[/tex].
