The \(920-\mathrm{mm}\)-diameter, \(1.6-\mathrm{mm}\)-thick spherical pressure vessel in Figure 9.27 is a filament wound quasi-isotropic composite laminate with a single 50-mm-diameter entrance hole. The vessel material has a mode I fracture toughness of \(K_{\mathrm{Ic}}=25 \mathrm{MPa} \mathrm{m}{ }^{1 / 2}\). If the vessel is to contain gas at a pressure of \(0.69 \mathrm{MPa}\), what is the critical length, \(a_{c^{\prime}}\) of a single crack emanating from the edge of the hole? The Bowie Equation 9.38 may be used for this problem, and the function \(f(a / R)\) for a biaxial stress field and a single crack of length, \(a\), at the edge of a hole of radius, \(R\), is tabulated below for several values of \(a / R\).

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R = 25 mm Mean diameter = 920 mm FIGURE 9.27 Spherical composite pressure vessel with single crack at the edge of entrance hole.