Discussion
For \( K_{IC} = 30 \) MPa root m, \( Y = 1.12 \) and an applied stress of \( 150 \) MPa, the critical crack length is nearest to
Answer: C
Correct answer: 10 mm
Rearranging \( K_{IC} = Y\sigma\sqrt{\pi a_c} \), \[ a_c = \frac{1}{\pi}\left(\frac{K_{IC}}{Y\sigma}\right)^2 = \frac{1}{\pi}\left(\frac{30}{1.12 \times 150}\right)^2 = \frac{0.0319}{\pi} = 0.0102\ \mathrm{m}, \] that is about 10 mm. Since the critical length varies as the inverse square of the stress, halving the working stress quadruples the crack the structure can tolerate.
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