Discussion
If the vessel is evacuated (internal pressure = 0) and subjected to external pressure, yielding according to the von Mises yield criterion (assuming elastic stability until yield)
Answer: C
Yielding occurs at about the same pressure \(p_{Y}\).
Under external pressure the membrane stresses have the same magnitude as before but are compressive: \(\sigma_{1} = \sigma_{2} = -pr/(2t)\). The von Mises criterion depends only on squares and products of the principal stresses, so reversing every sign leaves the equivalent stress unchanged, and the material has the same yield stress in compression as in tension.
So, with buckling ruled out by the assumption of elastic stability, yielding begins at the same pressure magnitude, about 20 MPa. Half or double the pressure would need a material weaker or stronger in compression, and 'never occurs' would only follow for a purely hydrostatic stress, which a thin shell does not carry.
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