(Color online) Inverse pole figure showing the distribution of crystal directions aligned with the direction of shock propagation (horizontal in the figure).
(Color online) Free-surface velocity traces for (a) shot 1576 (nominal peak pressure 10 GPa) and (b) shot 1583 (nominal peak pressure 25 GPa) at nominal step heights of 1.0, 1.5, and 2.0 mm. Actual step heights are indicated in the figure legends.
(Color online) Inverse analysis results for shot 1576. (a-d) Normal stress, volumetric strain, deviatoric stress, and plastic strain for all steps, including estimated error bounds. (e) Normal-stress/volume curves superposed on curves for longitudinal elastic and isentropic bulk compression, including upper and lower bounds for zero dissipation and maximum dissipation. (f) Deviatoric-stress/plastic-strain curves for the three steps. (g) Deviatoric-stress/plastic-strain-rate curve for the middle step, with gray scale indicating the mean stress, ranging from light gray (2 GPa) to black (10 GPa). Equivalent points for the middle step on each graph are marked with symbols (displaced slightly for clarity in (g)): Square = arrival of HEL wave, X = peak deviatoric stress, + = level-off to post-shock plateau, O = arrival of rarefaction wave.
(Color online) As Fig. 3, for the higher-pressure shot 1583, and extending the gray scale range in (g) to 2-25 GPa.
(Color online) (a) Simulations (dashed curves) of free surface velocities using a multiscale strength model, superposed on the experimental measurements (solid curves) for shot 1576. (b) Comparison of plastic flow curves from the multiscale strength simulation with reduced initial dislocation density (dashed curve) and the inverse analysis of the experimental data (solid curve) at the 1.5-mm position. (c-d) Similar for shot 1583.
(Color online) Selected examples of algorithmic validation through comparison of simulated in situ quantities (solid curves) and the estimates derived from the inverse analysis (dashed curves). Results are from the HRD parameters on shot 1576 using the Gilman model for strength.
Rate-dependent material parameters used in the test calculations, including scenarios with unrealistically high and low rate dependence (HRD and LRD, respectively) intended to bracket all likely real-world behavior. Parameters are defined by a form of Gilman’s (Ref. 34) plasticity model, specifically . Early in the deformation, before the dislocation multiplication and hardening terms (Bψ and Hψ, respectively) are dominant, the relation is approximately . Thus D sets the scale for the deviatoric stress required to approach the velocity-saturation strain rate A at the low initial dislocation density, thereby controlling the quasi-elastic overshoot magnitude. The multiplication term then rapidly becomes dominant as the material relaxes to a more steady-state flow regime.
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