Evolution of the shock waves in polycrystalline copper at temperatures 300 and 1100 K (a), and at 1353 K under different loading (b). The numbers on the waveforms correspond to the nominal sample thickness. The inset (a) displays the elastic parts of velocity histories of thinner samples. Arrows show the velocities corresponding to the material Hugoniot elastic limit and the spall-related velocity pullback .
Free surface velocity histories of 2-mm copper samples impacted at various velocities (adjacent to the waveforms) at 1353 K.
Evolution with the impact strength of the waveforms recorded with 2-mm copper samples. Impact velocities and initial samples temperatures are shown near the waveforms and the time axis, respectively.
Front parts of the waveforms after impact of 2-mm copper samples with the velocity of 161 ± 5 m/s. Numbers at the waveforms indicate the test temperature.
Room-temperature velocity histories recorded with “as received” (solid lines) and annealed (dashed lines) copper samples of 2-mm thickness. The inset shows a 7 to 8-fold difference between amplitudes of elastic precursor waves at the two material states.
Temperature dependence of the Hugoniot elastic limit (filled circles) and yield stress (triangles) obtained with 2-mm samples after ∼160 m/s and ∼390 m/s impacts. The values of “as received” material at the same impact conditions (open circles) are shown for comparison. The spike- and minima-based values obtained in 1353-K tests are shown, respectively, by filled squares and filled circles, with the corresponding impact velocity nearby.
The spall strength of 2-mm copper samples as a function of temperature (filled symbols) and the RT values obtained with “as received” copper samples (open symbols).
Stress at HEL as a function of propagation distance at different test temperatures. The dashed lines are the power fits .
Precursor decay parameters and as a functions of normalized temperature . For comparison, the smoothed dependences and for aluminum 8 are shown by dashed lines.
(a) Shear stress at HEL as a function of plastic strain rate in polycrystalline copper shocked from different initial temperatures. Filled and open circles correspond to the states at the top of the elastic precursor waves in 2- and 0.25-mm samples, respectively. Squares with error bars are the points corresponding to the mid-height of the plastic shock wave in 2-mm samples. (b) The points at precursor top (circles) together with dependence corresponding to the initial test temperature 300 K (solid line) and the points obtained with “as received” (triangles) and annealed (squares) copper samples. Dashed lines show schematically the trajectories of the material points from the state at the top of the precursor wave to the state at the mid-height of the plastic front.
The power fit (dashed line) corresponding to the rate of decay of the elastic precursor spike estimated with use of Eq. (10) (triangles with error bars) and decay rate (dotted line) obtained by differentiating the fit of the values of the precursor spike amplitudes (circles) measured in the 1353-K tests.
1353-K tests. Shear stress in decaying spike-containing elastic precursor wave as a function of the plastic strain rate. Filled symbols correspond to the spike-based estimates with us of Eq. (11) . Open symbols correspond to the minimum-based estimates with use of Eq. (14) . Dotted lines connect the states at the spike top with those at the post-spike minima for fixed propagation distances 2 mm and 0.5 mm.
Stress at HEL as a function of propagation distance at 1353 K for elastic spikes (filled circles) and the points of the velocity minima between the elastic and plastic waves (filled and open triangles) at various impact velocities. Lines are the power fits with the same exponent, .
The density of mobile dislocations in polycrystalline copper as a function of plastic strain rate . The solid lines are the dependence corresponding to the test temperatures 300 and 1353 K, calculated using Eq. (12) . The filled diamonds correspond to the values just behind the elastic precursor shock in 2-mm samples. The filled circles, squares, and triangles are the estimates of the density of mobile dislocations , corresponding to the maximum strain rates in the plastic shock wave at different test temperatures. The open circles are the obtained with “as received” copper samples shock-loaded from room temperature. The inset shows temperature variation of the at constant plastic strain rates.
Estimates of the density of mobile dislocations (symbols) and hypothetical evolution of the dislocation density behind the spike of the elastic precursor wave (dashed lines) at 1353 K.
Parameters of planar impact experiments with pure polycrystalline copper.
Parameters and of elastic precursor decay in pure polycrystalline copper.
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