One criterion for design of a safe pressure vessel is that it should leak before it breaks:
Question:
One criterion for design of a safe pressure vessel is that it should leak before it breaks: the leak can be detected and the pressure released. This is achieved by designing the vessel to tolerate a crack of length equal to the thickness \(t\) of the pressure vessel wall, without failing by fast fracture. The safe pressure \(p\) is then
\[p \leq \frac{4}{\pi} \frac{1}{R}\left(\frac{K_{I c}^{2}}{\sigma_{f}}\right)\]
where \(\sigma_{f}\) is the elastic limit, \(K_{1 c}\) is the fracture toughness, \(R\) is the vessel radius. The pressure is maximized by choosing the material with the greatest value of
\[M=\frac{K_{1 c}^{2}}{\sigma_{\gamma}}\]
Use the \(K_{1 c}-\sigma_{f}\) chart of Fig. 3.8 to identify three alloys that have particularly high values of \(M\).
Fig. 3.8
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