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I have a feeling this is actually a pretty complicated problem in detail as I know a tremendous amount of research is done on the behavior of materials under stress, and I think the way materials fracture/crack is a useful diagnostic tool.

As a starting point, waves travel at the speed of sound in a material, which is to say they are mechanical waves. Do cracks also propagate at the speed of sound?

Another related question is, do the cracks in a solid move at a constant speed? Obviously it is possible for a crack to form and stop propagating, so this might imply a dissipation of some vibrational amplitude until the energy is below the point of being able to break bonds/fragment atoms (sheets for some solids). It also might imply that the crack does not behave like a wave and spreads at a non-constant speed. Which is right?

Lastly, do all solids follow the same rules for the speed at which they fracture? I'm thinking of glass, which probably is not a good place to start on this question because it is an amorphous solid (some people say incredibly viscous liquid but this feels like semantics). Obviously some glass will crack into large pieces and some will fracture like a spiderweb. Are these processes fundamentally the same but with different microscopic details? And how does fracturing in glass relate to something simpler like the breaking of a single atom solid? I haven't seen this happen, but surely it is possible.


Obviously there were quite a few question there, but they were only meant to give a general idea of the types of questions would be nice to have answered. Maybe the question is actually quite simple and one answer will suffice, or maybe it's complicated and there are multiple good answers.

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    $\begingroup$ You are looking for work on 'fracture mechanics': it is a large area. But no, they don't: there may be an upper bound but there clearly is no lower bound. $\endgroup$ – tfb Jul 24 '17 at 7:50
  • $\begingroup$ A single-atom solid can break: diamond, silicon. There might be a lower limit: when cracks propagete slowly, the stresses are relieved by plastic deformation, caused by movements of dislocations. $\endgroup$ – Pieter Jul 24 '17 at 23:02
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fracture mechanics is a complex field in which there are few if any characteristic equations that one can derive from first principles. Here are a few observations:

the simplest case is for perfectly brittle materials stressed in tension, in which crack propagation occurs at the velocity of sound in the material and is self-propagating when the stored strain energy field surrounding the crack tip contains enough energy to furnish the requisite energy of formation of the resulting free surfaces as the crack tip advances through the material.

things get frightfully complicated however when the material possesses ductility or visco-elasticity or is anisotropic or composed of a mixture of phases or microstructures or is at elevated temperature or very low temperature. you'd need to consult a materials science text dealing with fracture mechanics for guidance in any of these "interesting" cases.

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