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.