Required Elastic Modulus for a Thin Walled Shell?

[dj_davo]

I'm hoping that you may be able to help? I'm a biophysicist with an engineering-type problem that is related to pressure vessels. I'm trying to work out if there is a calculation, equation or other snippet of info that may be around that calculates the required Young's modulus of a thin elastic wall subject to hoop stress under a specified internal pressure. I've performed hoop stress calculations and wall thickness calculations that can give me required thickness etc. but I'm actually interested in the modulus.

I've scaled up my biological species for calculation purposes, so here goes....

If you have a 1 m diameter sphere with a thin wall of 0.025 m (1/40th) and the internal pressure is 25 atmospheres what would the Young's modulus of the wall need to be to contain this internal pressure? In case the temperature is required for calculating, assume 37° C. If the actual sizes are useful, or better, it is for a 1 micron sphere with a 25 nm wall. The wall size is actual and this needs to be maintained in any calculation.

I can find no information on this subject, but that could be because I'm no engineer, rubbish at finding the relevant information, or that this kind of calculation hasn't been done?

Any help that you could offer would be most appreciated.

Thanks

David

 

[dhengr]

Dj_davo:
You might want to Google ‘surface tension of a bubble.’ The soap film bubble problem and the like are well studied, and are the basis for our understanding of some material and physical phenomenon. As I understand your OP, you are actually talking about a very small, very thin shelled sphere, under some internal pressure, in some surrounding environment. Don’t forget external pressures as they might affect your sphere. Temperature and temp. changes will mostly effect the pressures, although extreme temps. can also affect material strengths, viscosity, elasticity, etc., too. Also, some of our basic Mechanics of Materials and Theory of Elasticity concepts and methods might need a little adjustment in how they actually operate at micron and nano scale. With a spherical pressure vessel you actually have a three dimensional surface stress (tension or compression), similar but not exactly the same as the hoop stress that you consider when looking at a long cylindrical pressure vessel. The surface shell stress is dependant upon the pressure, the shell thickness and the radius of the sphere, the radius to the mid-thickness of the shell. The sphere radius vs. the shell thickness also plays a part; in that a very thick shell and small sphere radius must be treated differently than a thin shell of a large dia. sphere. The modulus of elasticity comes into play primarily as you consider the expansion or contraction (deflection, extension) of the sphere diameter under the pressures or shell stresses.

 

[EdStainless]

as DH said, the modulus will only have an impact on the deflection under load, the ability to carry the load will be a function of the strength.
For example you can get a steel and a Cu alloy with the same yield and tensile strengths, but the modulus of the steel is 3 times as much the Cu alloy. So the steel sphere will be stiffer, but they both will have the same strength.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube

 

[dj_davo]

Many thanks for your replies guys, it's most appreciated. I will start some reading around the surface tension of a bubble now. Regarding the modulus of the thin wall under load, I have performed nanoindentation using atomic force microscopy and typically obtain a Young's modulus of around 300 kPa at half of the depth of the wall. This is always performed at 37° C. The biological species lives on and around us and is subject to standard atmospheric pressures and temperatures and dies under extremes of these. The thin wall is a relatively homogenous polymer and measurements are always taken in an aqueous environment. Given this extra information does it allow for a calculation to be performed or do the original problems/suggestions and constraints still apply do you think?