The thin-walled tubular shaft shown in Figure 9.8 is made of a randomly oriented, short-fiber-reinforced metal matrix composite. The shaft has a longitudinal through-thickness crack of length \(2 a\) and is subjected to a torque \(T=1 \mathrm{KN} \mathrm{m}\). If the mode II fracture toughness of the composite is \(K_{\text {IIc }}=40 \mathrm{MPa} \mathrm{m}^{1 / 2}\), determine the critical crack size for self-sustaining crack growth.

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T 2 2a 38 mm 42 mm diameter diameter FIGURE 9.8 Thin-walled tubular composite shaft with longitudinal crack.