Phase transformations and plasticity in single-crystal iron from shock compression to spall fracture

Nonequilibrium molecular dynamics simulations have been used to investigate phase transformations and plasticity in single-crystal iron from shock compression to dynamic tension and subsequent spall fracture. In consistence with experimental observations, the unloading wave following the compression front is found to evolve into a rarefaction shock at the reverse hexagonal-close-packed to body-centered-cubic (bcc) phase transformation, and a pressure hysteresis between the direct and reverse phase transformations is evidenced. The interaction of this unloading wave with the rarefaction wave reflected from the sample free surface classically induces tension within the crystal, which is found to drive a bcc to face-centered-cubic (fcc) phase transformation in agreement with very recent experimental observation under subnanosecond laser shock loading. At the atomic scale, the mechanism governing this bcc to fcc phase transformation is consistent with a Bain transformation path. The spall fracture process is observed to occur through voids nucleation and growth either at favorable sites (twin boundaries, bcc-fcc grain boundaries after partial transformation) or within the defect-free fcc crystal (after full transformation). Thus, the spall strength increases with the fcc phase fraction near the plane of maximum tension. An amorphous microstructure is observed around the voids, likely due to significant heating upon severe plastic deformation, in consistence with experimental clues from the literature.

Figure 1

Wave profiles for piston maximum velocity $U_p$ of 800 m/s (a) and 1000 m/s (b) showing two-wave (a) or single compression front (b), as well as propagation of shock upon release (see text for details).

Figure 2

Mean stress spatial profile (top) at 17 ps for $U_p=800$ m/s with associated atomic configuration (bottom). bcc atoms are colored according to local pressure, atoms associated with defects are colored in brown, while hcp and fcc phases are colored in violet and cyan, respectively. Insets show microstructure within sections in compressed state (1) and during release (2) of hcp phase.

Figure 3

Mean stress spatial profile (top) at 17 ps for piston maximum velocity of 1000 m/s with associated atom configuration (bottom) where color meaning is same as in Fig. 2. Insets show evolution of microstructure in hcp phase from compressed state (1) to successive stages during release (2 and 3).

Figure 4

Mean stress distribution along the $Z$ axis (a) at 31 ps showing tensile (negative pressure) wave spatial profile for piston velocity of 800 m/s with corresponding atomic configuration (b). Atoms are colored as in Fig. 2; cyan corresponds to fcc phase.

Figure 5

Mean stress distribution at 28 ps (a) showing tensile wave spatial profile for piston velocity of 1000 m/s with corresponding atomic configuration (b), where atoms are colored as in Fig. 2. Extensive phase transition from bcc to fcc phase (cyan) is observed under tension.

Figure 6

Detail extracted from cyan zone in simulation of Fig. 5, showing fcc arrangement resulting from bcc-fcc transition observed under dynamic tension along $Z$ direction. X, Y, Z axes are [100], [010], and [001] orientations of initial bcc crystal. fcc cell is displayed as colored atoms. While its [001] orientation (green dotted line) still matches $X$ axis, its [110] orientation (blue dotted line) is parallel to $Z$ axis. Equivalently, and given crystal symmetries, [011] direction in parent bcc is [100] orientation in daughter fcc (yellow dotted line), so that this bcc-fcc transition is consistent with Bain transformation path.

Figure 7

Snapshots at successive times showing voids (forest-green colored surface) nucleation and growth for piston maximum velocity of 800 m/s (a) and 1000 m/s (b).

Figure 8

Pressure distribution at successive times for piston velocity of 800 m/s (a) and 1000 m/s (b), showing tensile pulse (negative pressure) induced within sample (black), then progressive stress relaxation accompanying nucleation and growth of spall damage.

Figure 9

Longitudinal cut within sample at 33 ps for 800-m/s piston velocity, showing voids (green colored surface) nucleated mainly at twin boundaries and phase boundaries.

Figure 10

Spall strength (black) and fcc phase fraction (red) evolution as functions of maximum shock pressure.

Figure 11

Late-time snapshots showing extensive voids growth and coalescence for piston velocities 800 m/s (a) and 1000 m/s (b), with intense plastic activity in their vicinity, which is found to be dislocation mediated (green loops in bottom pictures).

Figure 12

Snapshots showing microstructure evolution around voids (forest-green colored surface) at different simulation times for piston velocity of 800 m/s (a) and 1000 m/s (b). Atoms are colored according to local phase structure: bcc, fcc, and hcp atoms are blue, cyan, and violet, respectively, while white color represents atoms with no identified local phase structure according to PTM analysis, i.e., regions which can be considered amorphous.

Figure 13

Free-surface velocity profiles for piston velocity of 800, 900, and 1000 m/s, respectively.