# [Material Science] Metal foam sandwich to prevent buckling?

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1. Sep 7, 2015

### Pds3.14

Let's assume for a minute that money was of no concern. If one has a 10 MPa external environment and needs to have vacuumed-out spheres (or 1 atmosphere, close enough to call vacuum) inside of that environment.

In particular, I was thinking of a sandwiched lattice of maraging steel, with it's conveniently high 2.6 GPa yield strength as a solid sheet, but its shockingly typical 210 GPa Young's modulus, also as a solid sheet.

The problem is that the wall thickness necessary to make it survive the compressive load is very thin. A sphere a meter in radius need only have something like a 2 mm thick wall to support itself against the intense pressure, as 2.6e9 pascals * 0.002 m * 2 * pi * 1 m / (pi*(1 m)^2)=10.4 MPa. but the wall thickness necessary to prevent it from buckling, given for an (extremely optimistic) ideal spherical object by: 2.1e11 pascals * 2 * 0.002^2 / sqrt(3*(1-0.26^2)) = 1.005 MPa.

So of course, looking at the formula for stiffness, I thought "what if I could make it thicker but keep the same mass of it in order to increase the stiffness independently of the mass?" I.E. I want Pterosaur bones made of rocket-grade steel.

So I suppose my questions are:

#1. Is making a maraging steel (or similar material) foam sandwich within the current state of the art? Is it emerging technology? Is it something speculatively possible in the relatively near future? Or is it totally fanciful magitech?

#2. Would the mass-specific yield strength match that of solid steel? If not, how much weaker would it be for the foam?

#3 Would the mass-specific young's modulus match that of solid steel? If not, how much weaker would it be for the foam?

#4. If it isn't possible or it wouldn't be useful, what are some other ways of preventing a sphere or a tube from buckling without putting cross-bracings all the way through the middle? (stuff belongs in the middle).

2. Sep 7, 2015

3. Sep 7, 2015

### Baluncore

There is no requirement that there be two layers. You only need ribs cast onto the steel.

The problem is actually related to the application.

If the external pressure is 10MPa, then I guess it is effectively “underwater” and so it will have buoyancy due to the spherical volume. The best place to put the required ballast is probably in the pressure hull. In order to be neutrally buoyant with an external fluid density of 1.0 and a wall density of say 8.1 your wall thickness will need to be a significant portion of the sphere radius. For wall density = 8.1, in water, the wall thickness, if my quick maths is correct r = R * cuberoot(1 – 1/density)?, will be 4.3% of the outer radius. A 1 metre diameter sphere will need a 23 mm wall.

If you need to maintain neutral buoyancy with a thinner wall then you may need to consider a double wall sphere with a cast geodesic net of perforated ribs. Fill the spaces between the ribs with Pb (s.g.=11.3) or Hg (s.g.=13.5). Neither of those ballast elements will halve the solid wall thickness. You will have to watch out for the thermal expansion coefficients.

4. Sep 7, 2015

### Pds3.14

It would be under high pressure, but buoyancy would be largely irrelevant, as the density of the external medium would not be water-like. The stuff inside the sphere would sufficiently weigh it down.

5. Sep 7, 2015

### Baluncore

What material might that be ?

6. Sep 7, 2015

### Pds3.14

Highly compressed Carbon Dioxide

7. Sep 7, 2015

### Baluncore

Interesting, at 10MPa I would expect CO2 to be liquid with a temperature dependent density somewhere between 0.5 and 1.5, comparable to water.