A randomly oriented, short-fiber-reinforced composite plate having a central through-thickness crack of length \(2 a\) is subjected to a uniaxial stress \(\sigma\), as shown in Figure 9.1. If the composite has a fracture toughness \(K_{\text {Ic }}=50 \mathrm{MPa} \mathrm{m}^{1 / 2}\) and the applied stress \(\sigma=200 \mathrm{MPa}\), determine the critical crack size, \(a_{\mathrm{c}}\) for unstable and catastrophic crack growth.

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b 4a 2a Crack Elliptical zone assumed to be relaxed due to presence of crack FIGURE 9.1 Griffith crack: a through-thickness crack in a uniaxially stressed plate of infinite width.