Effect of strain-rate dependent yield strength on crater scaling relations

Physics

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For materials whose strength is controlled by various creep processes, such as ice, the yield strength (Y) is often expressed in a power law relation to the strain rate (ɛ) Y~ɛ˙I/n, where n is a constant for some range of ɛ˙. It has been shown that, for strength-dominated craters, the crater formation time is proportional to the crater radius R and to √Y. But the strain associated with crater formation is approximately fixed in the strength regime so the strain rate controlling crater formation will vary as √YR. The result of combining these two effects is that, in materials with strain-rate dependent yield strengths, there will be a small increse in cratering efficiency (mass of ejecta/mass of explosive or impactor) as size increases in the strength-dominated regime. Explosive cratering data indicate that 1.6

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