Femtosecond Visualization of hcp-Iron Strength and Plasticity under Shock Compression

Iron is a key constituent of planets and an important technological material. Here, we combine in situ ultrafast x-ray diffraction with laser-induced shock compression experiments on Fe up to 187(10) GPa and 4070(285) K at ${10}^8{\mathrm{s}}^{-1}$ in strain rate to study the plasticity of hexagonal-close-packed (hcp)-Fe under extreme loading states. $\{10\overline{1}2\}$ deformation twinning controls the polycrystalline Fe microstructures and occurs within 1 ns, highlighting the fundamental role of twinning in hcp polycrystals deformation at high strain rates. The measured deviatoric stress initially increases to a significant elastic overshoot before the onset of flow, attributed to a slower defect nucleation and mobility. The initial yield strength of materials deformed at high strain rates is thus several times larger than their longer-term flow strength. These observations illustrate how time-resolved ultrafast studies can reveal distinctive plastic behavior in materials under extreme environments.

Figure 1

Geometry for x-ray stress and texture analysis under dynamic compression. (a) The x-ray free-electron laser (XFEL) probe is 65° away from the shock propagation direction and diffraction measured on six Cornell-SLAC pixel array detectors (CSPADs, $q_{1,\dots ,3}$ and $d_{1,\dots ,3}$) optimized to cover wider and key directions. Inset: target stack. (b) Pole figure coverage with the compression direction in the center. (c) Original diffraction data at run 149 (193 GPa, 4230 K), 1.12 ns after hcp-Fe synthesis and (d) MAUD reconstruction with labels for the diffraction peaks of the remaining untransformed bcc-Fe and high-pressure hcp-Fe. Variations of peak intensities and positions with orientation are representative of texture and stress, respectively.

Figure 2

Results for time series (a),(b) 1, (c),(d) 4, (e),(f) 5, and (g),(h) 6. Times have been rescaled to set $t=0$ when hcp-Fe is formed. (a),(c),(e),(g) Differential stress vs time in hcp-Fe. Circles, experimental data with $\pm 1\sigma$ error bars; blue shaded areas, guides to the eye through the experimental data. ${\sigma }_y$ indicate potential values for the yield strength and ${\sigma }_{\mathrm{flt}}$ is the long-term flow strength. (b),(d),(f),(h) Inverse pole figures of the compression direction representing texture in hcp-Fe. We observe components at $⟨2\overline{11}0⟩$, $⟨10\overline{1}0⟩$, [0001], and approximately 30° off [0001]. Texture 0.34 ns after hcp-Fe synthesis in time series 6 could not be fit due to a significant peak overlap with the remaining ambient conditions bcc-Fe. (i) Sketch of hcp-crystals with the shock direction, shown by the pink arrow, aligned with $[2\overline{11}0]$, $[10\overline{1}0]$, [0001], and approximately 30° off [0001].

Figure 3

Viscoplastic self-consistent simulations for texture evolution in hcp-Fe. (a) Inverse pole figure of the compression direction after 10% axial plastic strain and easy basal, prismatic, pyramidal $⟨a⟩$, and pyramidal $⟨c+a⟩$ slip, in addition to $\{10\overline{1}1\}$ compression and $\{10\overline{1}2\}$ extension twinning starting from the transformation texture in time series 1. (b) Simulation with dominant $\{10\overline{1}2\}$ twinning and starting from the transformation texture in time series 4.

Figure 4

Static and dynamic strength of hcp-Fe at high $P\text{−}T$. Trend lines, Refs. [22, 23, 53]; red circles, this Letter. The time-dependent stresses recorded here in situ using x-ray diffraction plot far below previous dynamic compression estimates and closer to static measurements at 300 K. For strain rates above ${10}^7{\mathrm{s}}^{-1}$, however, the true yield strength of Fe—the stress at the elastic-to-plastic transition—may be several times larger than the longer-term flow strength, which is highlighted by the blue arrows. This is due to an insufficient quantity of defects to accommodate plastic strain in the initial compression and a phonon-drag-controlled defect kinetics.