Material science question about rocket fuel tanks

[Fat Rooster]

My Google Fu has failed me with regard to a fairly basic question about strength. I can find all sorts of results about uniaxial tensile strength, but nothing about whether this is applicable for more general cases. In particular, a cylindrical pressure vessel will experience both longitudinal and hoop stresses. Can we regard these as entirely independent, and just compare the required hoop strength to the uniaxial strength of our material? Obviously we can't with carbon fibre, or other directional materials. With those we use clever windings to deal with both forces, but what about with steel or aluminium? Is there some result that tells us how and why we can use the uniaxial strength as a reference? If not, why can I not find references with regards to the strength of materials with the 2-1-0 tensile forces that
crop up all the time in cylinders?

The result that spheres are better pressure vessels depends on the assumption that the most efficient way to load your material is in 2 directions equally, but I can't find anything to confirm that assumption.

[gomipile]

You should get some helpful results if you search for the keyword "anisotropy" along with the name of one potential material.

[Fat Rooster]

You should get some helpful results if you search for the keyword "anisotropy" along with the name of one potential material.

Thanks, but not really what I am looking for. Anisotropy refers to differences in strength depending on the orientation of the material, while I am asking whether load in one direction will affect the material properties in another in a fixed orientation.

For a more technical definition, is the max value in the stress tensor at the yield point dependent on the other values in the stress tensor? Shear I am pretty sure will lower it, but what about the diagonal terms?

[Rydiro]

Thanks, but not really what I am looking for. Anisotropy refers to differences in strength depending on the orientation of the material, while I am asking whether load in one direction will affect the material properties in another in a fixed orientation.

For a more technical definition, is the max value in the stress tensor at the yield point dependent on the other values in the stress tensor? Shear I am pretty sure will lower it, but what about the diagonal terms?

So you want to know if the max stress can be decomposed into (orthogonal or otherwise) components?

[monomer]

For a cylinder, from pressure loading alone hoop stress will be double that of the longitudinal stress.

Spoiler: Equations

Show

Hoop Stress: S = PD/2t
Longitudinal Stress: S = PD/4t
Where S = Stress, P = Pressure, D = Diameter, and t = Wall Thickness

That said, the total axial stress will be much higher than just the stress from the internal pressure due to thrust and weight from the rocket booster itself and the upper stages. Combining the stresses becomes very complex very fast since the loading will be changing as the velocity and altitude increase, the internal and external pressures fluctuating, and horizontal loads are applied.

For some context, there is a lot of information available for the current work on Starship as they are working on getting it able to withstand high pressure loading as well as the axial stresses and they were just able to actually get the SN5 prototype in the air for a quick test. They have had a lot of prototypes fail pressure testing, though the recent failures were due to ancillary components on SN4 (believed to be due to the fuel loading connections), and deliberately testing to failure on SN7.

ETA:

For a more technical definition, is the max value in the stress tensor at the yield point dependent on the other values in the stress tensor? Shear I am pretty sure will lower it, but what about the diagonal terms?

To get the maximum stress you have to take into account stresses in all directions. The simple answer is to determine the Von Mises stress, though for something as complex as a rocket they will be using advanced finite element analysis (FEA) modeling.

[Fat Rooster]

For a cylinder, from pressure loading alone hoop stress will be double that of the longitudinal stress.

Spoiler: Equations

Show

Hoop Stress: S = PD/2t
Longitudinal Stress: S = PD/4t
Where S = Stress, P = Pressure, D = Diameter, and t = Wall Thickness

That said, the total axial stress will be much higher than just the stress from the internal pressure due to thrust and weight from the rocket booster itself and the upper stages. Combining the stresses becomes very complex very fast since the loading will be changing as the velocity and altitude increase, the internal and external pressures fluctuating, and horizontal loads are applied.

For some context, there is a lot of information available for the current work on Starship as they are working on getting it able to withstand high pressure loading as well as the axial stresses and they were just able to actually get the SN5 prototype in the air for a quick test. They have had a lot of prototypes fail pressure testing, though the recent failures were due to ancillary components on SN4 (believed to be due to the fuel loading connections), and deliberately testing to failure on SN7.

ETA:

To get the maximum stress you have to take into account stresses in all directions. The simple answer is to determine the Von Mises stress, though for something as complex as a rocket they will be using advanced finite element analysis (FEA) modeling.

Thanks, Mises yield criterion was exactly what I was looking for! Hard to find if you don't know what it is called or where to look.

[factotum]

Just to note here: don't some rocket fuel tanks use the internal pressure as part of the structural integrity? ISTR that Falcon fuel tanks are like that and have a tendency to collapse if the internal pressure is let out.

[monomer]

Just to note here: don't some rocket fuel tanks use the internal pressure as part of the structural integrity? ISTR that Falcon fuel tanks are like that and have a tendency to collapse if the internal pressure is let out.

The Falcon 9 is generally structurally stable while unfilled, though they add in a nitrogen fill during transportation since it is weak in horizontal loading. The early stainless steel Atlas missiles which were later converted for spaceflight did require internal pressure for structural integrity as their outer skin was basically a balloon.

[Xyril]

The Falcon 9 is generally structurally stable while unfilled, though they add in a nitrogen fill during transportation since it is weak in horizontal loading. The early stainless steel Atlas missiles which were later converted for spaceflight did require internal pressure for structural integrity as their outer skin was basically a balloon.

I take it these tanks were not reusable then? I'm trying to imagine how they would restore pressure as they spend fuel, but carrying extra liquid nitrogen, or redirecting some exhaust back into the system seems inefficient. Plus, keeping the internal pressure steady during burn seems logistically challenging, since you'd be messing with the proportions of unspent fuel versus whatever inert replacement you'd use.

[monomer]

I take it these tanks were not reusable then? I'm trying to imagine how they would restore pressure as they spend fuel, but carrying extra liquid nitrogen, or redirecting some exhaust back into the system seems inefficient. Plus, keeping the internal pressure steady during burn seems logistically challenging, since you'd be messing with the proportions of unspent fuel versus whatever inert replacement you'd use.

The Falcon 9 is extremely strong axially which is what is required when completing a vertical landing, though they also keep pressures in the tanks consistent using composite overwrapped pressure vessel (COPV) tanks which release helium into the tanks as the fuel is discharged. I should also note that the body of a rocket booster that you see is the tank, and in the case of Falcon 9 it is reusable. There are no further pressure vessels (aside from the small COPVs) within the outer rocket skin, just a separator between the RP1 (refined kerosene) and liquid oxygen sections.

Think of it as basically a huge soda can (though the Falcon 9 aluminum would actually be thinner if shrunk down to a can's diameter). When full it is quite strong, and even when empty you can stand on it so long as you apply only vertical force. Poke the side of the can while applying the vertical load, though, and it will collapse.