Theoretical analysis of Richtmyer-Meshkov instability (RMI) experiments for solid strength shows that the strain rate for a given shock should be inversely proportional to the length scale of the sine wave perturbations when ${\eta }_{0}k$, the nondimensional amplitude to wavelength ratio, is held fixed. To isolate the effect of strain rate on strength, free-surface RMI specimens of annealed copper were prepared with three perturbation regions with the same ${\eta }_{0}k$ but different length scales, characterized by the wavelength $\lambda$ varying by a factor of 4.9 from 65 to 130 to $320\mu \mathrm{m}$. Three such targets with different fixed ${\eta }_0{k}^{\prime }\mathrm{s}$ were impacted to a shock pressure of 25 GPa, and the instability evolution was measured with photon Doppler velocimetry. Strengths estimated by comparing hydrocode simulation to the data increased from 700 to 1200 MPa as $\lambda$ decreased. The different ${\eta }_{0}k$ targets exercised increasing amounts of plastic strain yet showed no evidence of strain hardening. Physical regime sensitivity analysis determined that for $320-65\mu \mathrm{m}$ wavelength perturbations, the effective strain rates increased from $8.7\times {10}^6$ to $3.3\times {10}^7{\mathrm{s}}^{-1}$, a factor of 3.8. Thus, the predicted strain rate scaling was mostly achieved but slightly suppressed by increased strength at higher rates. The RMI strength estimates were plotted against constitutive testing data on copper from the literature to show striking evidence of the strength upturn at higher strain rates.

• Received 24 August 2023
• Accepted 16 November 2023

DOI:https://doi.org/10.1103/PhysRevE.109.015002

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Published by the American Physical Society