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I have a system where I'm dropping glass tubes filled with some sample from a certain height, along a track. I can apply a back-pressure of air to push them down faster, and in general the faster they go, the better. Additionally, the thinner the tube the better.

I'm looking for a framework for how to analyze the resistance to shock, and the relative strength of either a flat-bottomed glass tube landing on a flat-bottomed surface, or a round-bottomed glass tube landing on a round-bottomed surface. I'd also like to know how resistance to shock scales with tube thickness, because in the end I'm specifically trying to get a sense of how thick do I have to make a flat-bottomed tube before it will be able to survive the same drop speed as a round-bottomed tube.

I don't necessarily need an exact answer to this question - I realize there are a lot of parameters in the equation. I more or less just need to know how to approach each element in the problem. Ideally I'd like to set up some equation as a function of the size of the vessel and the force and some mechanical property of the glass, but if that's too complicated, a more general framework for estimating the relative strength of each tube is fine.

Hopefully this is appropriate for this SE, as there doesn't seem to be a mechanical engineering version.

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There is an ASTM standard for measuring fracture toughness

http://www.astm.org/Standards/E1820.htm

and also the famous Charpy impact test

http://en.wikipedia.org/wiki/Charpy_impact_test

Also you need Hertz Contact theory to estimate contact pressure and subsurface stress for various geometries and forces.

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I'm actually looking for a theoretical framework rather than an empirical testing method - I'm preparing a dissertation and I want potential readers (who will never materialize anyway I imagine) to be able to estimate the relative values of the flat vs rounded design in their own applications. I'll look into this Hertz Contact theory thing. –  Paul Mar 31 '13 at 22:29
    
So you need to buy a book on Contact Mechanics, like amazon.com/Contact-Mechanics-K-L-Johnson/dp/0521347963 –  ja72 Apr 1 '13 at 4:12
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