Strain-rate dependence of ramp-wave evolution and strength in tantalum

We have conducted molecular dynamics (MD) simulations of quasi-isentropic ramp-wave compression to very high pressures over a range of strain rates from ${10}^{11}$ down to ${10}^8$ 1/s. Using scaling methods, we collapse wave profiles from various strain rates to a master profile curve, which shows deviations when material response is strain-rate dependent. Thus, we can show with precision where, and how, strain-rate dependence affects the ramp wave. We find that strain rate affects the stress-strain material response most dramatically at strains below 20%, and that above 30% strain the material response is largely independent of strain rate. We show good overall agreement with experimental stress-strain curves up to approximately 30% strain, above which simulated response is somewhat too stiff. We postulate that this could be due to our interatomic potential or to differences in grain structure and/or size between simulation and experiment. Strength is directly measured from per-atom stress tensor and shows significantly enhanced elastic response at the highest strain rates. This enhanced elastic response is less pronounced at higher pressures and at lower strain rates.

Figure 1

Periodic cells of polycrystalline tantalum created for ramp-wave compression. The smaller sample has transverse dimensions of 19.73 nm, while the larger sample has 39.12 nm. The smaller sample was used in most of the simulations described.

Figure 2

Plots of piston loading paths for original (black) and scaled (red) variables as a function of time. The top two images are the velocity (left) and position (right) for a linear ramp. The bottom two images are the same plots for a stairstep ramp.

Figure 3

Spatial profiles of particle velocity in the evolution of a nonlinear ramp wave imposed at three compression rates. The strain rates are distinguished by colors shown in the legend. Each rate has its own position scale to allow superposition of the data. Five temporal snapshots are shown at time increments of one fifth of the total ramp duration, which varied for each rate from 40 ps to 4 ns. The piston drives from the left and profiles are moving with each snapshot from left to right.

Figure 4

Stress vs strain from various strain rates compared to statistical analysis from experimental measurements from the Z-machine from Davis et al. [7]. The experimental average is in black, with dashed lines showing the experimental uncertainty range. The inset shows the trend with strain rate.

Figure 5

Atomistic views of sample compression after (from left to right) approximately 0.0, 0.1, 0.2, and 0.35 strain. Contiguous grains are shown in teal, with grain boundaries pink.

Figure 6

$2\times \tau$ or the dynamic strength calculated from the stress tensor for strain rates from ${10}^{10}$ to ${10}^8$ 1/s compared to the continuum PTW and KP models.

Figure 7

$2\times \tau$ or the dynamic strength calculated from the stress tensor for strain rates ${10}^{10}$ showing inverse Hall-Petch strengthening with grain size.