A molecular dynamics study on the Mie-Grüneisen equation-of-state and high strain-rate behavior of equiatomic CoCrFeMnNi

Figures & data

Figure 1. (a) Points on the principle shock Hugoniot in $P-\rho$ space. The dashed red line only serves to indicate the trend of the data. (b) Points on the principle shock Hugoniot in $U_s-U_p$ space along with available experimental data. The solid red line represents the fitted analytic reference curve, Equation (6(6) $\begin{array}{rl}{U}_s& =2C_s{[1-S_1\mu +\sqrt{{(1-S_1\mu )}^2-4S_2{\mu }^2}]}^{-1}\\ & -B\exp [-{\left(\frac{\mu }{{\mu }^{\ast }}\right)}^N],\end{array}$(6) ).

Table 1. Calibrated Mie-Grüneisen EOS model parameters. The fitting parameter N was chosen to be fixed at 1.0.

Quantity	Value
Reference density, ${\rho }_0$ (g/cm${}^3$)	8.03640
Grüneisen parameter, ${\gamma }_0$	1.75210
Specific heat, $C_v$ (J/g · K)	0.43167
Bulk sound speed, $C_s$ (km/s)	4.78463
Linear coefficient, $S_1$	1.66206
Quadratic coefficient, $S_2$	−0.08539
Low-pressure parameter, B (km/s)	2.41519
Low-pressure parameter, ${\mu }^{\ast }$	0.03635
Low-pressure parameter, N	1.0

Figure 2. Free surface velocity, $u_{\mathrm{f}\mathrm{s}}$, traces for the NEMD simulations.

Table 2. Strain-rate dependent spall strengths for CoCrFeMnNi calculated using Equation (7(7) ${\sigma }_{\mathrm{s}\mathrm{p}}=\frac{1}{2}{\rho }_0{C}_s\mathrm{\Delta }{u}_{\mathrm{f}\mathrm{s}}$(7) ).

$u_0$ (km/s)	Strain rate (s${}^{-1}$)	Spall strength (GPa)
0.25	$8.466\times {10}^8$	–
0.50	$1.673\times {10}^9$	–
0.75	$2.505\times {10}^9$	–
1.00	$3.330\times {10}^9$	–
1.25	$4.158\times {10}^9$	15.664
1.50	$4.991\times {10}^9$	13.894
1.75	$5.816\times {10}^9$	13.807
2.00	$6.639\times {10}^9$	11.134

Figure 3. Space-time-density diagrams showing the initial shock wave propagation and subsequent rarefaction waves along with the corresponding phase fraction evolution for (a) no spallation with $u_0=1.00$ km/s and (b) spallation with $u_0=1.50$ km/s.

Data availability

The data that support the findings of this study are available from the authors upon reasonable request.