# Mechanical shock resistance as a function of shape

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

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