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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1000 100- Fracture toughness - strength Yield before fracture Design guidelines Fracture toughness, Kc (MPa.m1/2) Ktc Kild 10 Process zone 1000 100 10 size, dy, mm Low alloy steels Metals Stainless steels Ni alloys Cu alloys W alloys Carbon Al alloys 0.1 Ti alloys Zinc alloys, Cast frons 0.01 Mg alloys Lead alloys Leather Nontechnical Ionomers Kiela, ceramics- Brick Natural Stone Silicone 0.1 materials elastomers Concrete Buty rubber Flexible polymer foams Cork 0.01 0.1 1 10 Wood PP PE GFRP PTFE PA PC ABS PMMA Phenolic Silicon Silica glass Composites CERP Diamond Technical ceramics B.C Epoxies Soda glass Polyurethane Polymers and elastomers Lower limit for Kic Isoprene Neoprene Foams Rigid polymer foams Strength, + (MPa) 100 1000 Fracture before yield MFA 15