Molecular dynamics simulations of shock-induced deformation twinning of a body-centered-cubic metal

Despite a number of previous nonequilibrium molecular dynamics (MD) studies into plasticity in face-centered-cubic metals, and phase transitions in body-centered-cubic (bcc) metals, the plastic response to rapid compression of bcc metals remains largely unexplored. Key questions remain as to the relative importance of dislocation motion and twinning in shear stress release and consequent strength. We present here large scale MD simulations of shock compressed bcc metal, using an extended Finnis-Sinclair potential for tantalum, and demonstrate the presence of significant deformation twinning for pressures above the Hugoniot elastic limit for shock waves propagating along the $\left[001\right]$ direction. The twinned variants are separately identified by a per atom order parameter, allowing the strain and stress states of the rotated material to be studied. The atomic motion during twinning, and thus its mechanism, for this potential, is identified by use of a three-dimensional pair-correlation function.

Figure 1

The experimentally determined Hugoniot compared with that for the EFS potential for shocks along $\left[001\right]$. Experimental data come from McQueen et al. (Ref. 24) and Mitchell et al. (Ref. 25), with the solid line being a fit to both data sets.

Figure 2

Wave profiles for the $U_p=0.9$ km s${}^{-1}$ simulation at an initial temperature of 5 K. The upper graph shows particle velocity profiles for several time steps, with labels indicating the time passed since the initial piston impact. The lower graph shows the pressure $p_{zz}$ and shear stress for the 115 ps step. For this step the elastic front is seen around 5400 Å and the plastic (twinning) front at around 3500 Å. The profiles were calculated by averaging over atoms in 40 Å thick slabs (in the $z$ direction).

Figure 3

Intensity in the $k_z=1.16\frac{2\pi }{a}$ and $k_z=1.36\frac{2\pi }{a}$ planes showing the presence of a twinned region within the simulation. The lattice parameter for the unshocked material is used. The area shown ranges from $-3\le k\left(\frac{2\pi }{a}\right)\le 3$ in both $k_x$ and $k_y$, with color indicating intensity, blue being lowest and red being highest. The right hand plots show the various contributions to each peak from the four twin variants (red, yellow, green, and cyan). Note that many “diffraction spots” have contributions from more than one twin variant. Peaks seen in the intensity plot that are not identified in the right hand plot can be attributed to the finite width of other twin peaks lying slightly above or below the plane.

Figure 4

Two MD simulations with piston velocities of $0.8$ and $0.9$ km s${}^{-1}$, initially thermalized at 5 K. The shown sample cross section is $425\times 425$ Å${}^2$. Color denotes the results of a categorization algorithm based on the PASF. Blue represents the untwinned orientation with green, red, cyan, and yellow denoting the twinned orientations. The atoms colored pink denote atoms where the orientation is not resolved, predominantly lying on the twin boundaries.

Figure 5

3D pair-correlation function for atoms evolving from the host lattice to one of the four twin variants in the $U_p=0.9$ km s${}^{-1}$ simulation. (a)–(c) show structure factors for the same atoms at simulation times of 10, 30, and 60 ps, respectively. Atoms chosen were those identified as being in the chosen twin at 140 ps as determined by the PASF. The coloring represents distance in the $\left[\overline{1}10\right]$ direction, where green is in the plane, blue is one plane out of the page, and red is one plane below the page. The same pattern is observed for $U_p=0.8$ km s${}^{-1}$.

Figure 6

The proposed shuffle mechanism for shock compression with this potential, with an initial compression of 18.4%. Squares and circles represent two neighboring $\left(1\overline{1}0\right)$ planes. Gray sites denote the host lattice, with white and black sites indicating the initial and final positions of the twinned atoms. Twin boundaries are indicated by solid lines with a dashed line highlighting the twin. The red and blue arrows indicate two potential shuffle mechanisms that cause the $\left(\overline{1}12\right)$ planes to shift in the same or alternating $\langle 111\rangle$ directions.

Figure 7

Relative displacements for a small region of one twin variant. The arrows indicate the change in position, between 80 and 120 ps, for each atom with respect to its nearest neighbor in the $\left[0\overline{1}0\right]$ direction. Red and blue spheres represent atoms in two neighboring $\left(1\overline{1}0\right)$ planes.

Figure 8

Twinning mechanism showing the path taken by the atoms, implying two partial dislocations with Burgers vectors $\frac{1}{6}\left[110\right]$ and $\frac{1}{12}\left[11\overline{3}\right]$. The right part of the figure shows the 3D pair-correlation function for this idealized mechanism, which can be compared to Fig. 5b.