SpudFiles

After contemplating the implications of the asymptotic behavior discussed in this thread, I began wondering how anyone could possibly contain high pressures.After all, wouldn't wrapping a tank in carbon fiber be roughly equivalent to simply making it thicker? And because the stress is greatest at the very inside of the wall, it would still yield. So now, I have a few rather deep questions:

Would a fiber-wrapped pressure vessel hold pressure greater than the yield strength of the internal metal?
Does it matter if the internal metal yields?
If not, why does it matter if the inner part of a solid metal pressure vessel yields?

How can the gaskets of diamond anvil cells survive the gigapascals of pressure they contain without failing?

A fiber-wrapped pressure vessel would probably benefit, if the fiber was wrapped very tightly, but that's going off my understanding of Young's Modulus. A material fails because it deforms too far, and it has to deform over a distance with a force applied. The fiber wrapping would decrease the deformation for any given force (in theory), and so should increase the yield strength of the overall system.

As I understand it, the diamond is in compression and some shear stress only, so the metal is in compression around the diamonds. The metal probably does deform, but the pressure value you're looking at is the pressure value between the two diamond points, NOT the pressure between the diamond surface and the steel. That pressure is probably much more manageable, because the area of the tip of a fine point is insanely small.

DYI will probably post something a lot more intelligent, but I'm just giving this my best shot, trying to be of some help.

Thanks for your help.

It's my understanding that diamond anvil cells use a (relatively) uncompressible fluid to exert a hydrostatic pressure on the sample. Regardless, it was just a convenient example.

Wouldn't more steel decrease the deformation just as the fiber does? It's my understanding that that's how "normal" pressure vessels work.

This leads me to question how the inner material can yield when it is supported by non-yielding material. Just like an insulator or capillary tube in an ETG, it has nowhere to go, so how can it fail?

Ramses wrote:This leads me to question how the inner material can yield when it is supported by non-yielding material.

Shock? Quite possible in an ETG. It's also possible that it failed because of the compression, which allowed greater tensile deformation and failure.

The additional steel will still deform at the same rate... I think. I do know that the Air Products hydrogen car uses carbon-fiber reinforced aluminium tanks to contain stored hydrogen at 10,000psi, so I assume there is some significant benefit to using something like carbon-fiber over more of the same metal.

Diamond anvil cells use P=F/A to exert large pressures from a relatively small force... or at least that's what I got from Wikipedia. They're mechanically quite simple... I think.

In high pressure high power short duration blasts heavy walls can hold together largely on the virtue of their inertia. It may not hold forever, but it's better than nothing.

This is the principle my next gun will use to "hold together". If it will work for this, it will work for anything you're doing. Well, if it holds for mach 24 shockwaves I'd sure hope it holds for whatever you're doing

I was actually thinking static pressure, but the only way to attain these pressures is with an ETC (or diamond anvil cell). I'm aware the DACs use P=F/A, but the gasket must still contain hydrostatic pressure on the order of gigapascals without the aid of a diamond. Essentially, it's a micrometer ID pipe with centimeter thick walls.

For "inertial confinement", is if fair to use the modulus of elasticity to determine reaction force, and then apply f=ma? Would that be the same equation as a (really stiff) spring?

Am I right in thinking that the maximum safe deflection for the inner wall is the deflection at the yield strength?

Also, Autodesk FEA craps itself when pressure is above yield, even if the timescale is in the milliseconds.

That's exactly how. Plus I'd guess in a DAC the same gasket won't be reused much.

Firstly, the easy answer: fiber-wrapped pressure vessels are in use because the wrapping materials tend to have tremendously high tensile strengths - carbon fiber's, for example, can be up to 800KSI (5.6 GPa). Compare to something like 40KSI for a good aluminum alloy. In this case, the aluminum forming the majority of the tank's body is simply acting like the rubber lining a braided SS hose - performing a sealing function, not a primarily structural function. As you can imagine, the strength to weight ratio for carbon fiber, when stressed in the correct direction, is tremendously higher than that of aluminum or even the best steel alloys. So, yes, a fiber wrapped vessel *could* hold pressure higher than ultimate tensile strength of the inner material... Just like a braided SS hose holds pressure higher than the ultimate tensile strength of the inner rubber lining

Now the tricky bit: I've considered this problem with the DACs before, and I must admit that their existence doesn't seem compatible with the formula we use for the yielding of high pressure vessels. I don't have an adequate response at this point. I do, however, have some idle speculation...

The formula you refer to was developed using the Von Mises yield criterion for the initiation of plastic deformation, whereas the topic of interest here is actual rupture of the material. However, it seems reasonable to presume that in this case, where the pressure vastly exceeds any yield strength which could be reached through strain hardening and the pressure does not decrease with increasing volume, the inner wall will simply continue to yield until it ruptures, cracking the inside and allowing this same process to go to work deeper into the wall. That's a very simplistic look at it, but I remain reasonably confident that an arbitrarily thick steel vessel (neglecting the case of a vessel so large that gravity becomes a concern...) could not contain pressure higher than the greatest yield strength it could reach through work hardening (especially not tens or hundreds of GPa) for an indefinite time period (i.e., inertial confinement is not a factor).

What I propose, totally without justification, is that the stresses the diamonds impose on the gasket when compressing it tend to counter the static pressure in the working volume (they tend to make the hole collapse in on itself), and that without this unique compression situation the gasket could still fail (not rupture through to the outside, but crack such that the volume increased, reducing the pressure and eventually stopping the failure).

As to inertial confinement: there's an excellent paper I found on the subject of modelling extremely high pressure launchers (mostly Voitenko implosion guns) which has a nice treatment of the basics of the inertial confinement process in such a launcher (as they tend to reach tens of GPa propellant gas pressures, they are decidely single shot).

@ DYI: My thoughts exactly. What prevents the rubber from cracking? Or is its deformation limited sufficiently by the stainless steel, or does the rubber's relative uncompressibility (which I understand is close to the highest in nature) create circumferential compression in response to radial compression? Would a metal exhibit a similar response?

I don't suppose you could link to or give the title of the paper?


At this point, I should probably be PMing DYI, D_Hall, Ragnarok, and perhaps Tech, but oh well...

I think this discussion is interesting enough to continue outside of pm, ramses.

I concur with Fnord, though I don't claim to know much about the topic, I find it fascinating and I'm certain others are interested.

I figured people would be interested. It'd also be confusing to PM 5 different people, since no-one will no what anyone else said.

What prevents the rubber from cracking?

The strain in the rubber cannot reach a high enough level to cause rupture. Granted, metals can survive nowhere near the strain that rubber can, but, sufficiently contained, the case of the fiber-wrapped tank is the same as that of the braided SS hose.

As to the paper: to make a long story short, I'm not currently on a computer which I can give you the link from (the original is only available to those with a subscription to the journal it's in, and the copy I uploaded to a storage site is not accessible from here).

The fiberglass tape is rated with some very weird number. This is mostly a sales gimmick. The tensile force on a length of tape is a number that would be slightly stronger than butter if you built up a rope of the tape 1 inch square and it broke at only 280 lbs. This is the real number that PSI for tape or anything like it is measured.

For example steel rope is measured this way.

"Plow steel wire rope is unusually tough and strong. This steel has a tensile
strength of 220000 to. 240000 psi.

With those numbers you can find the strength of a steel cable from 1/8th inch to many inches in diameter. Using Pi X R squared will give you the area of any size to calculate the strength.

When you wrap tape around a container, the strength is not what the container will hold in PSI. You need the hoop force on the tape and the cross section of the tape to find the bottle PSI strength.

What happens beyond that point is what we are discussing.

Really, I think we've already finished that discussion. Rubber lined braided SS hoses hold together just fine, and are an excellent example of just why this particular setup works - the weaker material fails at a certain level of strain, which the outer casing does not allow it to reach.

The diamond anvil cells are a much more interesting case. For that matter, inertial confinement is a much more interesting case, and a more worthy direction in which to continue this discussion.