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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.

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Fracture is almost always initiated because of a stress concentration due to a microscopic defect (think - little crack becomes big crack). This means that surface finish of the tube / roughness of the surface you are hitting plays a major role in the answer. See if you can figure out tensile stress along the surface - all other things being equal that is a good proxy for likelihood of fracture (larger stress - more likely to fracture). – Floris May 28 '14 at 3:47

There is an ASTM standard for measuring fracture toughness

and also the famous 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 – ja72 Apr 1 '13 at 4:12

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