How does a pressure vessel fail when the interal pressure exceeds the yield stress of the material?

When we design a pipe or pressure vessel, we look at hoop stress and longitudinal stress and then look at the material properties. We assume that the material reacts to the load as a solid. However This answer and comments claim:

Wall thickness doesn't matter if you try to contain a pressure that's greater than the yield strength. The material will permanently deform no matter how thick it is. It's like i'm trying to contain a gas bubble in a soft mud. No matter how much mud I add around it - i can't contain it.

Is this true? Do metals behave significantly different when subjected to pressures beyond their yield strength?

This could be tested experimentally: To arrive at a very thick walled pipe we could drill a hole into a block of gold (ultimate tensile strength 220 Mpa). Build the block large enough and the pipe wall thickness should withstand the immense pressure - So when we pressurize the hole to something > 220 MPa (a pressure common in water cutting, but at much other places.)

If the statement cited above is correct, we should see a different failure mode than a thin walled bursting vessel - for example creep. Or not, if material behaviour is dictated by the stress in the vessel material, not in the medium contained.

If we look at the pressures involved for even a soft metal like gold, we see that this a mostly academic question - for the vast majority of applications, the pressures encountered are well below the yield strneghts of the materials so we simply don't need to consider additional failure modes.

The above experiment is just an example, to show that such a situation could indeed be engineered. I'm sure other experiments can (and have) been done. My intution is that the material will start to flow in some way (towards the least resistance) but I'd like to know for certain.

• In practice it will be almost guaranteed to fail at the interface between the feed pipes from the pump and the lead block, which won't be very interesting. You might be able to somehow enclose some explosive material entirely within a lead block and then detonate it, or something similar. Aug 6, 2020 at 10:25
• Bomb calorimeter anyone? Aug 6, 2020 at 10:26
• cambridge.org/core/journals/journal-of-materials-research/… - an experiment with gold at pressures higher then it's yield strength. The answer to the question if additional failure modes pop up is probably in there.
– mart
Aug 7, 2020 at 5:20
• I've deleted my previous answer as I realize now it is incorrect. Having gone back and done the arithmetic, an internal pressure greater than the material yield strength will always result in a hoop stress greater than material yield strength. My apologies.
– jko
Aug 7, 2020 at 10:16
• Reminds me of a lawsuit where I was a witness; One attorney never could understand how the internal gas pressure was in psi and the steel strength was in psi , and there was NO relationship. Aug 10, 2020 at 20:25

A rupturing pressure vessel consists of an interplay between rupture of the walls, that causes a reduction in pressure via venting, while rupture of the walls also weakens the ability of the structure to sustain more pressure. Which one declines faster, and to what extent, determines what happens next.

If the rupture on the wall is small and does not propagate, or the pressure vessel has a relief valve, then excess pressure inside it is vented out in a controlled manner.

As a rupture forms on the pressure vessel, the structural integrity of the vessel decreases. For example, if the material is brittle such as glass, cracks in the pressure vessel would propagate quickly due to the low fracture toughness. Unless the internal pressure is relieved equally quickly (unlikely, because the speed of sound in solids is usually higher than gases), then rupture of the pressure vessel will accelerate, possibly leading to a mechanical explosion.

If the material from which the pressure vessel is made of is ductile, such as lead, rupture of the vessel would probably leave you with large pieces and bent metal. There are studies done on the fragmentation pattern of black powder driven bombs, and the metal pieces are usually fewer in number and larger.

Lastly, if the rise in pressure inside the pressure vessel was near instantaneous, for example due to detonating explosives, regardless of the material properties of container, you would end up with numerous, fine bits of container.

• those are the failure modes I specifically did not ask about. Unless you can somehow show that the statement I quoted is wrong, of course.
– mart
Aug 6, 2020 at 10:59

As jko points out in a comment, the hoops tress is always higher than the medium pressure, so the case as presumed in the question cannot happen and we don't see "ineresting" new failure modes.

I threw away my notes since but this can be shown using the formula for hoop stress found here - hoop stress approaches medium pressure as the inner diameter goes towards zero, so it can never be lower.