Evolution of metastable elastic shockwaves in nickel

Evolution of metastable elastic shockwaves in nickel Brian J. Demaske, Vasily V. Zhakhovsky, Carter T. White, and Ivan I. Oleynik Citation: AIP Conference Proceedings 1426, 1303 (2012); doi: 10.1063/1.3686520 View online: http://dx.doi.org/10.1063/1.3686520 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1426?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Evolution of the conductivity type in germania by varying the stoichiometry Appl. Phys. Lett. 103, 232904 (2013); 10.1063/1.4838297 Three-dimensional ferromagnetic architectures with multiple metastable states Appl. Phys. Lett. 98, 222506 (2011); 10.1063/1.3595339 Monitoring microstructure evolution of nickel at high temperature AIP Conf. Proc. 615, 1518 (2002); 10.1063/1.1472973 Spatial electron distribution of CO adsorbed on Ni(100) and Ni(111) surfaces probed by metastable impact electron spectroscopy J. Chem. Phys. 114, 8546 (2001); 10.1063/1.1365151 Local electron distribution of N 2 adsorbed on a Ni(111) surface probed by metastable impact electron spectroscopy J. Chem. Phys. 113, 3864 (2000); 10.1063/1.1287717

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 54.210.20.124 On: Thu, 29 Oct 2015 16:00:02

EVOLUTION OF METASTABLE ELASTIC SHOCK WAVES IN NICKEL Brian J. Demaske∗ , Vasily V. Zhakhovsky∗ , Nail A. Inogamov† , Carter T. White∗∗ and Ivan I. Oleynik∗ ∗

†

Department of Physics, University of South Florida, Tampa, FL 33620, USA Landau Institute for Theoretical Physics, RAS, Chernogolovka 142432, Russia ∗∗ Naval Research Laboratory, Washington, DC 20375, USA

Abstract. Shock waves in nickel were simulated by molecular dynamics using a new EAM potential. Three distinct regimes of shock propagation were observed, including a single elastic shock wave, two split elastic and plastic shock waves, and a single two-zone elastic-plastic shock wave, in order of increasing piston velocity. The single two-zone wave consists of a leading lower-pressure elastic zone, followed by a higher-pressure plastic wave, both moving with the same average speed. The elastic zone of this wave is compressed to a metastable state having an average pressure above the Hugoniot elastic limit. Similar metastable states appear in the elastic precursor during the early stage of split wave development. The mechanism for relaxation of the metastable elastic state is discussed. Keywords: Shock wave in solid, Hugoniot elastic limit, molecular dynamics PACS: 62.50.Ef, 02.70.Ns

INTRODUCTION Within the traditional picture of shock response of solids, the final material state lies on the Hugoniot curve [1–3]. For crystals, there exists an elastic and plastic branch of the Hugoniot that meet at a cusp known as the Hugoniot elastic limit (HEL) beyond which stable elastic states cannot exist. For shock intensities below the HEL, only a single elastic shock wave can form with a speed given by the slope of the Rayleigh line connecting the initial and final material states. As shock intensity is increased beyond the HEL, both elastic and plastic waves will form with different initial and final states and, by the slopes of their respective Rayleigh lines, different speeds. Because the elastic response is thought to be limited to final states below the HEL, the elastic wave should be pinned by the HEL, whereas the plastic wave is not. At the overdriven (OD) point, shown in Fig. 1, the speeds of the elastic and plastic shock waves become equal. Above the OD point, the faster plastic

front should eventually reach and overrun the leading elastic front leaving a single overdriven plastic shock wave. However, it is known that elastic-plastic transformations are not instantaneous, but have a characteristic time τ p . Using Orowan’s equation [5], a previous work estimated this time for copper, where τ p ∼ 100 ps [6]. If the compression time tc τ p , then materials will respond elastically. With increasing applied pressure, τ p decreases yet remains finite. In terms of shock response, we should expect elastic states above the HEL to persist until plastic deformations have had enough time to develop. The metastability of these states is determined by their respective positions along the Hugoniot relative to the HEL [7]. States far above the HEL will have a smaller value for τ p than those closer to it. At the limit of the elastic branch HEL∗ , τ p ∼ 0.1 ps and elastic states transform into plastic states during the time of shock propagation of one crystal unit cell. Herein, molecular dynamics (MD) simulations of nickel crystals are used

Shock Compression of Condensed Matter - 2011 AIP Conf. Proc. 1426, 1303-1306 (2012); doi: 10.1063/1.3686520 © 2012 American Institute of Physics 978-0-7354-1006-0/$0.00

This article is copyrighted as indicated in the article. Reuse of AIP content is 1303 subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 54.210.20.124 On: Thu, 29 Oct 2015 16:00:02

'(!

'(

" # # $ %&

!

FIGURE 1. Hugoniot for a Ni crystal with SW propagation in the [111] direction. Squares give simulated points along elastic branch and circles along plastic branch. Crosses are taken from experiments [4]. Dashed line shows extension of the elastic branch of Hugoniot to metastable states up to the HEL∗ , which corresponds to the upper limit of pressure within the elastic zone before complete disappearance of the elastic response. Shaded region shows single two-zone elastic-plastic SW regime.

to investigate shock wave propagation regimes in the context of finite times of elastic-plastic transformations.

SIMULATION TECHNIQUES AND RESULTS Large-scale simulations were performed in singlecrystal nickel oriented in the [111] direction. Shock waves were generated in standard piston MD simulations as well as in moving window MD (MW-MD) simulations that place the steady shock front with velocity us in the reference frame of the MD box [7, 8]. In MW-MD simulations, material with a given density and velocity u0 = −us is fed into the MD cell in front of the shock and erased behind it. By adjusting the position of the erasing plane, the supporting pressure of a semi-permeable piston can be controlled and the shock front kept inside the MW frame. This method of shock wave simulation effectively decouples the limited time and length scales inherent in standard piston simulations. The nickel crystals were described by a new embedded atom method (EAM) interatomic potential

specifically designed for use in wide ranges of pressures and temperatures [9]. The potential was fit to first-principles zero-temperature equations of state (uniform and uniaxial cold pressure curves), which ensures correct material response to high compressions. The simulated plastic branch of the Hugoniot is shown in Fig. 1 plotted against experimental data [4]. Based on this figure, one can expect an accurate description of shock response by the new EAM potential for pressures up to 200 GPa. Results of MD simulations are summarized in Fig. 1. For applied pressures below PHEL = 45 GPa, we observed only a single elastic shock wave in both piston and MW-MD simulations. However, as pressure was increased beyond PHEL , both elastic and plastic shock waves formed, which separated/split over time. Figure 2 shows two pressure profiles along the propagation direction (black and blue lines) within the split wave regime for two piston velocities u p = 1.25 and 1.5 km/sec. At the higher piston velocity u p = 1.75 km/sec, shown in Fig. 2 by the red line, splitting of the elastic and plastic fronts was not observed. Pressure in the plastic wave was above POD , but instead of an overdriven single plastic shock wave, we observed a complex two-zone shock wave consisting of an elastic precursor followed by a plastic front. Both elastic and plastic waves moved with the same average speed, thereby ensuring that the net width of the elastic zone remained constant. We refer to such waves as single two-zone elastic-plastic shock waves [7]. It was found that the pressure and speed of the leading elastic precursor in the split wave regime was not initially fixed at the HEL, but was a function of applied pressure (piston velocity u p ). See Fig. 2. States behind the elastic shock lie on the metastable elastic branch above the HEL, shown by the dashed line in Fig. 1, while the final pressure behind the plastic front lies somewhere on the plastic branch below POD . For the case of a single two-zone shock wave, the pressure within the elastic zone is still greater than PHEL , but now the pressure within the plastic zone is greater than POD . If the time the material remains in the metastable state is near τ p , then dislocations will be generated within the elastic zone. Thus, the mechanism of stress relaxation within a metastable elastic wave is identical in both shock propagation regimes: two split shock waves and single two-zone elastic-plastic waves. Although such transformations to plastic flow are


-)* %. *$ +,

)*$ +, +,

) .

) .

&

&

random, they become increasingly more likely for material that has spent a longer time in the metastable state. As the waves separate, eventually dislocations will be generated within the elastic zone, as shown in Fig. 3a. The transformation is accompanied by a drop in pressure, which leads to the creation of two oppositely-traveling rarefaction waves, represented by WL and WR in panel (b). The right-moving wave WR , shown in panel (c), attenuates the leading elastic front significantly. In both split and two-zone regimes, the plastic front emits elastic pulses that propagate towards the elastic front, as in Fig. 4. However, within the split wave regime these relatively small boosts in pressure are outweighed by the decrease caused by plastic deformation. Thus, the pressure within the elastic zone continues to drop until reaching PHEL . The many cycles necessary to complete this process ensures that the elastic wave in the split regime may remain metastable for a relatively long period of time, thereby opening the door to experimental confirmation. Figure 4 shows the complex structure of a twozone shock wave consisting of an elastic zone followed by plastic zone obtained by MW-MD. We were able to track the progression of the fronts to their stable state, a process that might prove too costly for standard piston MD simulations. Eventually, the two fronts attain a common speed and move

) . ) .

FIGURE 2. Snapshots of the pressure profiles from MD shock simulations at different piston velocities: split wave regime with u p = 1.25, and 1.50 km/sec (black and blue lines) and single two-zone wave regime with 1.75 km/s (red line). Pressure and speed of leading metastable elastic shock wave is a function of u p .

FIGURE 3. Mechanism of elastic-plastic relaxation in the elastic zone of a single two-zone SW observed in MWMD simulation for us = 7.35 km/s. (a) Onset of plasticity within the metastable elastic zone. (b) The drop in pressure leads to formation of two rarefaction waves WL and WR traveling in opposite directions. (c) WR causes significant attenuation of the leading elastic front, Pxx = 80 → 45 GPa. At (c) the speed of the elastic SW is less than that of the plastic SW but soon increases due to supporting elastic pulses. Whereupon, the elastic zone begins to increase in size until a profile similar to (a) is restored. Because of repeated cycling, (a)→(c)→(a), a dynamic equilibrium is reached with elastic and plastic shock fronts moving at the same average speed.

in tandem maintaining a finite separation width del . In contrast to the split wave regime, the elastic pulses produced by the plastic front, shown in Fig. 4, are large enough to counteract the attenuation caused by plastic deformation within the metastable elastic zone. The dynamic balance between these two processes ensures that the pressure in the elastic zone remains, on average, along the metastable elastic branch of the Hugoniot on the line connecting the initial state and final plastic state. This regime of single two-zone elastic-plastic shock propagation is highlighted in Fig. 1. By performing several MW-MD simulations within the single two-zone regime, we found that the net width of the elastic zone del was not constant, but was instead a function of the applied pressure (pis-


39.9 nm 25

-5000

flow velocity ux (m/s)

ux

τ

-5500

20

-6000

15

-6500

10

-7000 -7500 -20

τ

us = 7400 m/s up = 1997 m/s -10

0

10

position x (nm)

5

20

30

shear stress τ (GPa)

shear stress τ

plastic zone ~ 40 nm

0

FIGURE 4. Top: Snapshot of shear stress profile for single two-zone elastic-plastic SW in the Ni crystal. Light (red) color corresponds to regions of high shear stress (elastic zone) while dark color corresponds to low shear stress. Bottom: The profiles show propagation of elastic pulses inside the metastable elastic zone. The drop in shear stress indicates the position of the plastic front.

tions of perfect single crystals, we performed MWMD shock wave simulations of nickel samples with defects. The defects consisted of a vacancy concentration of 0.1% and a grain boundary running along the direction of shock wave propagation. The grain boundary was simulated by an 8 Å separating layer with a 1% vacancy concentration between twin stacking faults. Although PHEL was reduced significantly (45 → 30 GPa), we found that the single twozone elastic-plastic shock wave regime remained. Based on these and similar results for Al, Au, diamond, and Lennard-Jones crystals, two-zone elasticplastic shock waves are a general phenomenon that exists for a broad class of crystalline materials [7].

ACKNOWLEDGMENTS This work was supported by ONR, NRL and NSF. N.A.I. was supported by the Russian Foundation for Basic Research. B.J.D. thanks APS GSCCM (D.S. Moore and M. Furnish), NNSA ASC (R.C. Little) and DTRA (S. Peiris) for travel support. Calculations were performed using NSF TeraGrid facilities, the USF Research Computing Cluster, and computational facilities of the Materials Simulation Laboratory at USF Physics Department.

REFERENCES ton velocity u p ). As applied pressure was decreased towards POD , del became larger. Since the pressure in the elastic zone approaches PHEL , plastic deformations take a longer time to develop and the elastic zone grows. In the opposite case, as applied pressure is increased, del diminishes. At the HEL∗ , where τ p becomes less than the shock wave propagation time of one crystal unit cell, further increasing the applied pressure results in saturation of del to the interatomic distance. Shown at the top of the elastic branch in Fig. 1, HEL∗ corresponds to the limit of mechanical stability of a crystalline solid under uniaxial loading in which crystal unit cells are destroyed within a few atomic oscillations. For shock intensities above HEL∗ , a remnant of the elastic zone persists up until the transition to a melting shock wave. To show that the existence of the single two-zone elastic-plastic regime is not a byproduct of simula-

1. Graham, R. A., Solids under high-pressure shock compression, Springer, 1993. 2. Zel’dovich, Y. B., and Raizer, Y. P., Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Dover, 2002. 3. Caldirola, P., and Knoepfel, H., editors, Shock waves in condensed media, Academic Press, 1971. 4. Shock wave database: http://teos.ficp.ac.ru/rusbank/. 5. Orowan, E., Dislocations in Metals, AIME, 1964. 6. Loveridge-Smith, A., Allen, A., Belak, J., et al, Phys. Rev. Lett., 86, 2349–2352 (2001). 7. Zhakhovsky, V. V., Budzevich, M. M., Inogamov, N. A., Oleynik, I. I., and White, C. T., (in press, Phys. Rev. Lett.); see also in AIP SCCM Conf. Proc., J3.1 (2011). 8. Zhakhovskii, V. V. and Nishihara, K. and Anisimov, S. I., JEPT Lett., 66, 99–105 (1997). 9. Demaske, B. J., Zhakhovsky, V. V., White, C. T., and Oleynik, I. I., AIP SCCM Conf. Proc., F1.151 (2011).
