Hoop Stress due to change of state
Hoop Stress due to change of state
(OP)
This is my first post so please be gentle if this is obvious. I've seen several posts regarding thermal expansion of pipes and hoop stress but mine is more related to the stress and behaviour of the material inside the pipe.
A thin walled pipe is filled with a liquid that is just above its solidification temperature (pipe at the same temperature), the temperature then drops and the liquid solidifies at which time it expands volumetrically by 1%. At the moment, I consider the pipe to be long so I can treat this as a 2D problem. I've also neglected any changes in wall thickness in the pipe to keep it simple.
If the material in the pipe is rigid on solidification, then the problem is simple, the 1% increase is related back to the change in the circumference in the pipe and the stress strain curve gives the hoop stress.
But, if the material is not rigid, and has a lower Elastic Modulus and yield strength than the pipe, what happens to this solid cylindrical plug in the pipe?
I keep thinking there has to be a closed form solution based around the hoop stress equation and strain compatibility but I seem to be missing something.
Any thoughts are much appreciated...
A thin walled pipe is filled with a liquid that is just above its solidification temperature (pipe at the same temperature), the temperature then drops and the liquid solidifies at which time it expands volumetrically by 1%. At the moment, I consider the pipe to be long so I can treat this as a 2D problem. I've also neglected any changes in wall thickness in the pipe to keep it simple.
If the material in the pipe is rigid on solidification, then the problem is simple, the 1% increase is related back to the change in the circumference in the pipe and the stress strain curve gives the hoop stress.
But, if the material is not rigid, and has a lower Elastic Modulus and yield strength than the pipe, what happens to this solid cylindrical plug in the pipe?
I keep thinking there has to be a closed form solution based around the hoop stress equation and strain compatibility but I seem to be missing something.
Any thoughts are much appreciated...





RE: Hoop Stress due to change of state
RE: Hoop Stress due to change of state
RE: Hoop Stress due to change of state
Regards,
Mike
RE: Hoop Stress due to change of state
RE: Hoop Stress due to change of state
So you assume NO deformation of the material and the hoop stress would then be be 1/3 of the 1% x the modulus for the hoop material.
RE: Hoop Stress due to change of state
RE: Hoop Stress due to change of state
The relative change in radius of the contained solid material is
ΔR/R=0.01-p(1-νs)/Es
The same for the containing pipe is (assuming a relatively thin one)
ΔR/R=pR/tEw
By equating the two it is possible to calculate the pressure p exerted by the pipe on the solid and from that the deformations of both.
All this assumes elastic behavior, of course. If the Young's modulus of the contained solid is higher than some 1/5th of that of the wall, the latter will undergo a plastic deformation.
In this case, assuming a perfect elastic-plastic behavior, the pressure will be p=Yt/R.
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RE: Hoop Stress due to change of state
RE: Hoop Stress due to change of state