Shock-induced plasticity in nanocrystalline iron: Large-scale molecular dynamics simulations

Large-scale nonequilibrium molecular dynamics (MD) simulations of shock waves in nanocrystalline iron show evidence of plasticity before the polymorphic transformation takes place. The atomistic structure in the shock direction shows an elastic precursor, plastic deformation, and shock-induced phase transformation from bcc to hcp iron. In this Rapid Communication, large-scale MD models show that the shock response of iron is highly related to the ramp time of the applied shocks. For long ramp times we observe significant plastic relaxation and formation of microstructure defects. Pressure-induced phase transformations in iron are accompanied by stress relaxation achieving almost fully relaxed three-dimensional hydrostatic final states. The evolution of the stress relaxation is in agreement with theory and experiments. Analysis of the x-ray diffraction patterns calculated from the atomistic structure using the Debye equation revealed pronounced anisotropy of the line broadening that is caused by stacking faults in hcp Fe and by dislocations in bcc Fe.

Figure 1

Response of nanocrystalline iron under shock loading after 120 ps. In snapshots of the sample with the ramp times (a) $t_{\text{ramp}}=20$ ps and (b) 50 ps, noncentrosymmetric atoms are highlighted; the black area is the background of the simulation domain. In (c) and (d), the grains are colored according to their local orientation with respect to the shock direction. (e) shows the longitudinal pressure and shear stress along the shock wave direction, $P_{\mathrm{shear}}=\frac{1}{2}[P_{zz}-\frac{1}{2}(P_{xx}+P_{yy})]$. Elastic, plastic, and transition periods are plotted as blue, green, and yellow areas. For the 20-ps ramp, these areas are shown above the black dashed line, and for the 50-ps simulation below the blue dashed line. (f) Density along the sample; the distribution of energies is embedded in (g). The energy per atom and transition stages of both simulations are almost identical except at the beginning of the phase transition. Here, the energy per atom for the 50-ps ramp is 0.01 eV less than for the other case.

Figure 2

XRD patterns calculated using the Debye equation [26] for slabs cut from the sample displayed in Fig. 1. The thickness of the slabs in the $z$ direction was 30 nm; their starting positions were 100, 130, 330, 360, and 390 nm (from bottom to top). Vertical lines indicate positions of the diffraction lines from hcp Fe (dashed lines) and bcc Fe (solid lines). Diffraction indices are attached. The x-ray wavelength used for calculation of the XRD patterns was 0.140 891 nm. The intensities are plotted in a square-root scale.

Figure 3

Phases and microstructure defects in the transition area at 120 ps. (a) Snapshot of a simulation with $t_{\text{ramp}}=50$ ps. Atoms are colored according to the local crystal structure—blue: bcc; green: fcc; yellow: hcp; gray: disordered atoms. (b) A 7-nm-thick slice of the sample showing the propagation of dislocations of type $\frac{1}{2}〈111〉$. Only atoms of the grain boundaries and disordered atoms are shown. The color code indicates the depth of the atoms. The visualization has been done by ovito [36]. (c) and (d) Dislocation densities for a ramp time $t_{\text{ramp}}$ of 50 and 20 ps (left and right). Only dislocation segments which are generated by the shock wave are used to calculate the dislocation density. Background color: Blue, green, and yellow represent elastic, plastic, and transition periods of the sample. (e) and (f) Snapshots of the transition area where dislocations with proceeding laths of the fcc phase are shown.