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Shock compression behavior of low density powder materials and the double-shock Hugoniot
Mechanics of Materials 111 (2017) 15–20
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Shock compression behavior of low density powder materials and the double-shock Hugoniot Takamichi Kobayashi National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
a r t i c l e
i n f o
Article history: Received 24 May 2016 Revised 9 May 2017 Available online 13 May 2017 Keywords: Shock compression Powder material Shock impedance Particle velocity
a b s t r a c t Particle velocity measurements of window/sample interface by velocity interferometer have been performed on a low density powder material, Ce:YAG, under various shock loading conditions generated by plate impact with a maximum impact velocity of 1.564 km/s (SUS304). The observed interface velocities and the reshock pressures are very high, indicating that the shock impedance of shock-compressed powder in the first-shock state is much higher than that of the initial powder because the density and the shock velocity for the first-shock state are largely increased. Measurements with three different window materials with almost the same impact velocities have been carried out to determine the reshock (double-shock) Hugoniot which is much stiffer than the principle Hugoniot, leading to a characteristic shock reverberation behavior of low density powder materials. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Behavior of shock-compressed powder and porous materials with high compressibility is difficult to describe, especially at very high pressures. The primary reason for this is the extreme temperature produced under the fast adiabatic shock compression where intense interparticle collisions induce deformation, damage, surface jetting, production of gaseous products, and so forth (Shang et al., 1994; Zhao et al., 2013). It is made further complicated by the existence of interstitial gas in pores, which is considered responsible for the excessive heat observed under shock compression of powder materials. The generation of excessive heat cannot be attributed solely to shock-compressed condensed constituent (Resnyansky, 2016). Analytical models to describe the shock response of powder materials have been proposed (Herrman, 1969; Petrie and Page, 1991; Dijken and De Hosson, 1994; Dai et al., 2008; Fredenburg and Thadhani, 2013). Shock compression of powder materials has been the subject of interest for its unique shock-compression response such as shock dissipation property and shock-induced chemical reaction (Vandersall and Thadhani, 2003; Dai et al., 2008). Extensive densification is known to occur even at relatively low shock pressures because of their very high compressibility. Low density powder materials have a low shock impedance (ρ Us ) because of low density (ρ ) and low shock velocity (Us ), whereas powder materials under shock compression should have a much higher shock
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impedance because of largely increased density and shock velocity (Gourdin and Weinland, 1985; Kobayashi, 2014), suggesting that the shock reverberation behavior of low density powder materials can be quite different from that of incompressible materials. There have been a few studies examining the shock impedance of powder materials in the first-shock states at low shock pressures less than ∼6 GPa (Gourdin and Weinland, 1985; Vogler et al., 2007). They observed large increases in powder density (30 ∼ 120%) and also in shock impedance (110 ∼ 280%) for the first-shock states. For fully-dense ceramic samples (Alumina), the reshock states were found to lie above the P-Up (particle velocity) principle Hugoniot (loci of final shock states) of the ceramic sample, which was explained by material strength (Reinhart and Chhabildas, 2003). On the other hand, the classic assumption for calculating reshock states from a first-shock state on the principal Hugoniot of the sample is to approximate them in P-Up space with the mirror reflection of the Hugoniot about the vertical axis through the firstshock state Up . This was experimentally confirmed for some metals (Al, Cu, and Ta) over a wide pressure range up to 440 GPa (Nellis et al., 2003). In this paper, results of particle velocity measurements of a low density powder material under shock compression up to ∼20 GPa (reshock pressure) are presented. Observed shock reverberation behavior with an extremely large increase in shock impedance of up to ∼820% for the first-shock state is analyzed and the corresponding reshock Hugoniot is determined using three different window materials from essentially the same first-shock state. The obtained reshock Hugoniot for the low density powder is much stiffer than the initial unpressed powder Hugoniot (principle Hugoniot).
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Fig. 2. Window/sample interface particle velocity profiles for LiF window and Ce:YAG powder sample. The impact velocities (Vimp ) are indicated in the figure. The initial sample thicknesses were (a) 0.618 mm, (b) 0.562 mm, and (c) 0.619 mm. The plateau values agree well with those at equilibrium states predicted by the shockimpedance-match principle.
Fig. 1. (a) Schematic of target assemblage for VISAR measurement. The second harmonic of a CW Nd:YAG laser (532 nm) was used with a Fiber Optic Probe (F.O.P.). (b) A microscope image of the powder specimen. The full scale corresponds to 50 μm.
2. Experiment Impact experiments were conducted using a propellant gun with a 30 mm inner-bore diameter (Sekine, 1997). An unpressed powder sample with a thickness of 0.46 ∼ 0.64 mm and a diameter of 15 ∼ 18 mm was sandwiched between a 1-mm-thick metal base-plate (SUS304 or A6061) and a 5 ∼ 8-mm-thick window (sapphire or LiF or silica). Powder sample used was a wellknown phosphor, Ce: YAG (NICHIA corporation, < 5 μm) with the sample density (ρ 0 ) of ∼1.45 g/cm3 . The porosity of the powder samples was ∼68% since the density of crystalline YAG is 4.56 g/cm3 . A 3-mm-thick stainless steel or aluminum impactor was accelerated by the propellant gun and struck the base-plate (the same material as the impactor) with the maximum impact velocity (Vimp ) of 1.564 km/s. Window/sample interface particle velocities were measured with a VISAR (VALYN MULTI-BEAM VISAR System) (Barker and Hollenbach, 1972). The second harmonic of a CW Nd: YAG laser (VERDI-5 W, COHERENT) was used with a Fiber Optic Probe (F.O.P.). The target assemblage and a microscope image of the powder specimen are shown in Fig. 1. A thin aluminum foil (10 mm × 10 mm, 12 μm thick) was placed between the sample and the window to reflect the laser light (532 nm, 0.5 W CW). The aluminum foil is quickly equilibrated to the peak shock pressure within ∼5 ns. The time resolution for this measurement was about a few nanoseconds. The Hugoniots used were
Us = 4.58 + 1.49Up for SUS304, Us = 5.35 + 1.34Up for A6061 (Marsh, 1980), Us = 11.213 + 0.97Up for sapphire in the elastic region (Jones et al., 2001), Us = 5.15 + 1.35Up for LiF, and Us ∼ 5.0 for silica (Up < 2.0 km/s) (Marsh, 1980). The Hugoniot for the powder sample, Ce: YAG, is not known. We have previously measured the approximate shock velocity of this powder (Kobayashi, 2014). The shock velocity was 2.36 (± 0.16) km/s for the impact velocity of 1.63 km/s (SUS304) and the partic1e velocity was determined to be 1.50 (± 0.10) km/s using the shock-impedance-match principle. The Hugoniot based on this measurement was used for the powder sample in this study, which should give the upper limit because all the data points presented here were measured below the impact velocity of 1.63 km/s. In order to confirm the reliability of the particle velocity measurements, we carried out the ruby luminescence measurements under shock compression to measure the shock pressures with a ruby window using the same sample assemblage as in Fig. 1 and compared the results with the particle velocity measurements with a sapphire window. Their results were consistent with each other. The detailed description on this technique to measure shock pressures and particle velocities is presented elsewhere (Kobayashi, 2014). 3. Results Window/sample interface particle velocity profiles for LiF window are shown in Fig. 2 for three different flyer impact velocities. The flyers and the base-plates were SUS304. Each profile looks a two-wave structure. The window/sample interface starts moving when the first shock wave strikes the LiF window. The first particle velocities observed are (a) ∼1.03 km/s, (b) ∼0.65 km/s, and (c) ∼0.35 km/s, which last for 0.07 - 0.16 μs. These time intervals correspond to the times required for the shock wave reflected at the window/sample interface to reverberate between the window and the base-plate and strike the LiF window again. Then the interface particle velocity jumps up and converges to (a) ∼1.08 km/s, (b) ∼0.71 km/s, and (c) ∼0.49 km/s, which suggests that the equilibrium state is reached very quickly within a couple of shock wave
T. Kobayashi / Mechanics of Materials 111 (2017) 15–20
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Table 1 Shock experiment conditions. Uncertainties in impact velocities are less than 1% and those in sample thickness are less than 3.0% which were used to estimate uncertainties in sample densities of less than 5.8%. Uncertainties in interface particle velocities (Up ) are about 2%. Up represents the sample/window interface velocity. Impactor
Impact velocity (km/s)
Sample thickness (mm)
Sample density (g/cm3 )
Window material
1st Up (km/s)
2nd Up (km/s)
SUS304 (3mmt) SUS304 (3mmt) SUS304 (3mmt) SUS304 (3mmt) SUS304 (3mmt) SUS304 (3mmt) A6061 (8mmt)
1.564 0.997 0.676 0.958 0.962 0.960 1.133
0.62 0.56 0.62 0.46 0.57 0.63 0.63
1.45 1.41 1.40 1.51 1.46 1.45 1.50
LiF LiF LiF Sapphire LiF Silica LiF
1.03 0.65 0.35 0.36 0.60 0.68 0.64
1.08 0.71 0.49 0.45 0.68 0.72 0.60
Fig. 3. P-Up diagram showing the results of Fig. 2. Dotted lines are the Hugoniots of SUS304 flyers with three different impact velocities. Observed first interface particle velocities are plotted with open circles on the LiF Hugoniot curve. The error bars for these measurements (∼2%) are not shown in the figure because they are smaller than the circle size. The low-lying line is an estimated P-Up relation for the initial powder sample. The arrows drawn from the intersection points of the sample Hugoniot and the SUS304 Hugoniots to the open circles represent the process where the first shock wave specified by the intersection point is reflected at the window/sample interface and the interface starts moving at the velocity indicated by the open circle. The slopes of these arrows may be considered as the shock impedance for the powder in the first-shock state.
reflections at the sample interfaces. Experimental specifics and interface particle velocities are given in Table 1. Fig. 3 is a P-Up diagram with the first interface velocities from Fig. 2 indicated by open circles (◦). Dotted lines are the Hugoniots of SUS304 flyers with three different impact velocities, and their intersection points with the LiF Hugoniot correspond to the equilibrium states which agree well with above mentioned convergence values of the particle velocities in Fig. 2. The low-lying line is an estimated P-Up relation for the powder sample based on a shock velocity measurement at Vimp = 1.63 km/s. The slope of this line corresponds to the shock impedance of the initial powder sample. The actual shock impedance of the initial powder should be somewhat smaller, especially for lower Vimp shots. The arrows to the first interface velocities (◦) represent the process where the first shock wave is reflected at the window/sample interface and the interface starts moving at the velocity indicated by the open circle. The slopes of these arrows may be considered as the shock impedance of shock-compressed powder in the first-shock state. It is seen that the slopes of the arrows are much steeper than that of the initial powder and increase with the impact velocity. The observed shock impedance jump when changing from the initial uncompressed state to the first-shock states are calculated to be more
Fig. 4. Interface particle velocity measurements with three different window materials (sapphire, LiF, and silica). The Hugoniots of sapphire, LiF, silica, and the powder sample are indicated by solid curves and that of the SUS304 flyer at Vimp = 0.960 km/s is shown by a broken curve. Measured first interface particle velocities for three different windows are plotted with open circles and the intersection point of the powder sample Hugoniot and the SUS304 Hugoniot is indicated with an open square.
than 3.3 times (230% increase), 7.9 times (690% increase), and 9.2 times (820% increase) for (c), (b), and (a), respectively. Fig. 4 shows the results of interface particle velocity measurements with three different window materials, namely, sapphire, LiF, and silica. All the other experimental conditions were kept as identical to each other as possible. The Hugoniots of sapphire, LiF, silica, and the powder sample are indicated by solid curves and that of the SUS304 flyer at Vimp = 0.960 km/s is shown by a broken curve. Measured first interface particle velocities for three different windows are plotted with open circles. These three points together with the intersection point of the Hugoniots for the powder sample and the SUS304 flyer (indicated with an open square in Fig. 4) appear to be located nearly on a straight line (slightly curved to be more precise). This suggests that the shock impedances of compressed powder samples in the first-shock states are almost the same and appear only weakly dependent on the window materials. It is important to notice here that almost exactly the same first-shock state was realized in the powder sample when the first shock wave propagated in each sample. This first-shock state is specified by the intersection point indicated by in Fig. 4. On the other hand, exactly the same first-shock state can also be realized even when the experimental conditions are different. For example, an impact of a SUS304 flyer at a certain Vimp can create the same first-shock state in the sample as an impact of an A6061 flyer
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ties in Fig. 6 agree well with those at equilibrium points predicted by the shock-impedance-match principle, indicated by the intersection points of the two flyer Hugoniots and the LiF Hugoniot in Fig. 5. The first interface particle velocity for the A6061 impact is already beyond the equilibrium point, and thus the shock wave is reflected back at the sample/base-plate interface into the sample as a partial release wave, whereas in the SUS impact case the reflected wave is a reshock wave. 4. Discussion 4.1. Large increase in shock impedance and density
Fig. 5. Interface particle velocity measurements with different flyer materials but with the same window material (LiF). Vimp (SUS304) = 0.997 km/s and Vimp (A6061) = 1.133 km/s. Observed interface particle velocities are indicated by an open circle for the SUS304 impact and by an open square for the A6061 impact.
The shock impedance of the powder in the first-shock state shown in Fig. 3 (the slope of the arrows) is much larger than that of the initial unpressed powder. The slope of the arrows increases as the shock strength is increased and the increasing rate is higher in the weak shock region, which seems reasonable because the compression ratio of low density powder materials increases drastically in the low pressure region but quickly levels off in the higher pressure region (Gourdine and Weinland, 1985). For the shot (a) in Fig. 2, the first-shock state of the powder sample is specified with Up ∼ 1.44 km/s, Us ∼ 2.3 km/s, and thus ρ ∼ 2.7·ρ 0 = 3.9 g/cm3 (∼170% increase). The density is largely increased and accordingly the shock velocity is largely increased as well, which leads to the drastic increase of shock impedance for the compressed powder in the first-shock state. The reshock states generated by the reflected shock waves at the LiF window are indicated by the open circles in Fig. 3. They are close to the equilibrium points and the following reflected shock waves at the sample/base-plate interface should have taken the sample to the equilibrium points. This shock reverberation behavior is considered characteristic of low density powder materials (or compressible porous materials in general) (Vogler et al., 2007) and is quite different from typical behavior of materials such as metals where shock impedance change is insignificant during shock reverberation even for the cases where the density increase is as much as several tens of percent (Nellis et al., 2003). 4.2. Reshock Hugoniot of powder specimen
Fig. 6. Interface particle velocity profiles corresponding to the results in Fig. 5. The initial sample thicknesses were (a) 0.562 mm and (b) 0.625 mm.
at somewhat higher Vimp . Fig. 5 depicts such an example where shock compression by a SUS304 impactor with Vimp = 0.997 km/s and that by an A6061 impactor with Vimp = 1.133 km/s created almost the same first-shock state in the powder sample. Since the window was LiF in both cases, similar first particle velocities were expected to be observed. Observed particle velocities are indicated in Fig. 5 by an open circle for the SUS304 impact and by an open square for the A6061 impact, which are close to each other as expected. Corresponding interface particle velocity profiles are shown in Fig. 6. It is seen that the first particle velocities are almost the same (∼0.64 km/s) as mentioned above, but they converge to their equilibrium values in an opposite way, which is understood from Fig. 5 because the equilibrium point for the A6061 impact is below the first particle velocity () and that for the SUS304 impact is above the first particle velocity (◦). Converged particle veloci-
In Fig. 4, results of particle velocity measurements performed under almost exactly the same experimental conditions except window materials are shown. Observed three points (open circles) must be on the same curve which passes through the intersection point of the initial powder Hugoniot and the SUS304 Hugoniot for Vimp = 0.960 km/s (indicated by the open square). This curved line should correspond to the reshock or double-shock Hugoniot and may be fitted by a quadratic equation with respect to Up . Such a fit is shown by a thick solid curve in Fig. 7, which was then mirror reversed left and right to obtain a usual P-Up relation for the powder specimen in the first-shock state (drawn with a dotted curve). This method is applicable to any material for determination of reshock Hugoniots. It is clearly seen that the shock impedance for the firstshock state is about several times larger than that for the initial unpressed state and even larger than that of LiF. It should be noted here, however, that the Hugoniot obtained this way is not simply the one for a higher density powder but the one under shock compression with increased temperature and entropy. This reshock Hugoniot is good only for the particular first-shock state specified by in Fig. 7. Different Hugoniots are assigned for different first-shock states of the powder specimen. The reshock Hugoniot in Fig. 7 should be slightly different from the actual one because the intersection point () was obtained using an approximate Hugoniot for the initial unpressed powder, which was determined by a previously measured data point (Us = 2.36 km/s at Up = 1.50 km/s)
T. Kobayashi / Mechanics of Materials 111 (2017) 15–20
Fig. 7. Reshock Hugoniot (P-Up ) for the powder in the first-shock state generated by the Vimp = 0.960 km/s impact. The thick solid curve represents the reshock Hugoniot obtained by a quadratic fit which passes through the observed interface velocities (◦) and the intercept (). The dotted curve is the P-V relation obtained by horizontal inversion of the quadratic fit.
with a relatively large uncertainty in Us (∼14%). It is clearly seen that the reshock Hugoniot is several times steeper than the principle Hugoniot of powder specimen and cannot be approximated by the mirror reflection of the principle Hugoniot. The steeper reshock Hugoniot appears reasonable because the specimen density of the first-shock state is drastically increased compared to the initial unpressed powder density. In this respect, it is rather interesting that the reshock Hugoniots of metals at high shock pressures with several tens of percent increase in the first-shock state density are well represented by the mirror reflected principle Hugoniot about the vertical axis (Nellis et al., 2003). It may have something to do with the fact that metals lose their strength significantly at high shock pressures and temperatures, which may not always be the case with ceramic materials in the pressure and the temperature range of the present study. 4.3. Shock reverberation behavior of low density powder The reshock Hugoniot is solely dependent on the first-shock state which is represented by the intersection of the initial powder Hugoniot and the base-plate Hugoniot indicated by in Fig. 7. This is well illustrated in Figs. 5 and 6 which show that almost the same first-shock states generated by different impactors with different impact velocities give rise to almost the same first interface particle velocities. The shock reverberation behavior for the Al impactor shot (Fig. 6(b)) is quite different from commonly known behavior in which reflected shocks lift up the sample pressure stepwise before reaching the equilibrium pressure. The reshock state is determined by the reshock Hugoniot and the window Hugoniot. The shock impedance of the compressed powder in the first-shock state is essentially determined by the reshock Hugoniot, and its weak window material dependence is introduced through the fact that the reshock Hugoniot (P-Up ) is not a straight line. In order to understand the shock reverberation behavior of low density powder materials in more detail, it would be helpful to construct a P-V diagram. We start by obtaining a bit more realistic Hugoniot for the initial powder sample. Most Hugoniot data for solids follow the relation Us = C + SUp where C is bulk sound
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Fig. 8. P-V relations for the principle Hugoniot (dotted curve) and the shock reverberation behavior for the Vimp = 0.676 km/s measurement (arrows). The solid line represents the shock-compression curve for YAG single crystal. Uncertainties in open squares mainly come from those in the estimated Hugoniot of the initial powder (Us = 0.42 + 1.29 Up ) . Uncertainties for open circles also originate mainly from those in the Hugoniot which are used to calculate the uncertainties in the shock impedance, the reshock velocity, and the volume. Uncertainties in P are significantly smaller than the circle size and not indicated.
speed at P = 0 and S is the slope of the linear relation between Us and Up . Since C is expressed as the square root of bulk modulus/density and bulk modulus is the inverse of compressibility, a simple compressibility measurement of the powder sample using a hydraulic pump in a low pressure region (< 0.2 GPa) was carried out to estimate the bulk modulus (∼0.26 GPa) which then gave the bulk sound speed of ∼0.42 km/s with a relatively large uncertainty of ∼30%. Using the measured shock velocity data (Us = 2.36 km/s at Up = 1.50 km/s), the Hugoniot for the initial powder was obtained as Us = 0.42 + 1.29 Up . The modified powder Hugoniot with this Us -Up relation is located slightly below the straight line Hugoniot used in Figs. 3–5. We can now calculate pressures and volumes for the first-shock states which are represented by the intersections of the SUS304 Hugoniots and the initial powder Hugoniot obtained above. Results are (V, P) = (0.25 cm3 /g, 4.82 GPa) for (a), (0.30 cm3 /g, 2.18 GPa) for (b), and (0.35 cm3 /g, 1.12 GPa) for (c), and they are plotted in Fig. 8 with open squares. The P-V relation appears the typical shock-compression curve of highly compressible powder materials, namely, the volume decreases drastically in the low pressure region and then becomes almost incompressible at higher pressures. The isentrope should lie below this P-V curve. After the first shock wave strikes the window/sample interface, the reflected shock waves move back and forth between the two sample boundaries. In order to obtain the volume and the pressure of the reshock states, we take the Vimp = 0.676 km/s experiment indicated as (c) in Figs. 2 and 3 as an example to explain how V and P are determined. Note that the straight sample Hugoniot in Fig. 3 is now replaced by the curved line obtained from Us = 0.42 + 1.29 Up . The first shock state specified by the intersection of the initial powder Hugoniot and the SUS304 Hugoniot for Vimp = 0.676 km/s has (Up , P) = (0.64 km/s, 1.12 GPa). The Us and the shock impedance (ρ 0 Us ) are calculated to be 1.25 km/s and 1.81 g·km/cm3 /s, respectively. The first reshock state shown by ◦ in Fig. 3(c) has (Up , P) = (0.35 km/s, 5.19 GPa), and the shock impedance (slope of the arrow) is 14.0 g·km/cm3 /s which can be
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T. Kobayashi / Mechanics of Materials 111 (2017) 15–20
used to estimate the reshock velocity as 4.70 km/s which is nearly 4 times of the first shock velocity. Since the actual particle velocity in the reshock state is 0.64–0.35 = 0.29 km/s, the volume of the reshock state is calculated to be 0.32 cm3 /g. The second reshock should have brought the sample to the equilibrium state as Figs. 2 and 3 suggest, and thus it has (Up , P) = (0.48 km/s, 7.34 GPa). The pressure jump is 7.34–5.19 = 2.15 GPa and the actual particle velocity is 0.48–0.35 = 0.13 km/s, which leads to Us = 5.21 km/s and V = 0.31 cm3 /g for the second reshock state. The results are plotted in Fig. 8 with open circles. The shock reverberation behavior of the powder sample is indicated by the arrows, and it appears quite different from commonly known reverberation behavior which is usually located near the isentrope lying below the principle Hugoniot, and thus the observed shock reverberation behavior is characteristic of low density powder materials. 5. Conclusions Particle velocity measurements on a low density powder material under shock loading were performed. It was indicated that the observed first window/sample interface velocities were very fast and the shock impedance for the first-shock state of the powder specimen was much larger than that for the initial powder due to the drastic increase in density and shock velocity even for weak shock loadings. The reshock Hugoniot for Vimp ∼ 0.960 km/s was successfully determined experimentally using three different window materials. The obtained reshock Hugoniot in P-Up space is much steeper than the principle powder Hugoniot because the first-shock state density is drastically increased, and thus the reshock Hugoniot cannot be approximated by the mirror reflection of the principle Hugoniot, which is in contrast to the metal cases where the strength is significantly reduced under high temperatures. This may be suggesting that ceramic powders such as YAG do not lose their strength very much in the pressure and the temperature range investigated in the present study. The reshock Hugoniot depends only on the first-shock state which is specified by the intersection of the initial powder Hugoniot and the baseplate Hugoniot in P-Up space. The P-V behavior corresponding to the shock reverberation of low density powder was also determined and indicated that it does not approach the isentrope.
Acknowledgment This work was supported in part by JSPS KAKENHI (26400439). Refrences Barker, L.M., Hollenbach, R.E., 1972. Laser interferometer for measuring high velocities of any reflecting surface. J. Appl. Phys. 43, 4669–4675. Dai, C.D., Eakins, D.E., Thadhani, N.N., 2008. Dynamic densification behavior of nanoiron powders under shock compression. J. Appl. Phys. 103 093503-1–093503-12. Dijken, D.K., De Hosson, J.Th.M., 1994. Shock wave velocity and shock pressure for low density powders: A novel approach. Appl. Phys. Lett. 64, 933–935. Gourdin, W.H., Weinland, S.L., 1985. Dynamic compaction of aluminum nitride powder: Hugoniot measurement and comparison with static behavior. J. Am. Ceram. Soc. 68, 674–679. Fredenburg, D.A., Thadhani, N.N., 2013. Predicting the shock compression response of heterogeneous powder mixtures. J. Appl. Phys. 113 223513-1–223513-9. Herrman, W., 1969. Constitutive equation for the dynamic compaction of ductile porous materials. J. Appl. Phys. 40, 2490–2499. Jones, S.C., Vaughan, B.A.M., Gupta, Y.M., 2001. Refractive indices of sapphire under elastic, uniaxial strain compression along the a axis. J. Appl. Phys. 90, 4990–4996. Kobayashi, T., 2014. Direct observation of large shock impedance jump upon shock-induced densification of powdered materials confirmed by in situ shock pressure and particle velocity measurements. Chem. Phys. Lett. 608, 157–160. Marsh, S.P., 1980. LASL Shock Hugoniot Data. University of California Press. Nellis, W.J., Mitchell, A.C., Young, D.A., 2003. Equation-of-state measurements for aluminum, copper, and tantalum in the pressure range 80-440 GPa (0.8-4.4 Mbar). J. Appl. Phys. 93, 304–310. Petrie, M.W., Page, N.W., 1991. An equation of state for shock loaded powders. J. Appl. Phys. 69, 3517–3524. Reinhart, W.D., Chhabildas, L.C., 2003. Strength properties of Coors AD995 alumina in the shocked state. Int. J. Impact Eng. 29, 601–619. Resnyansky, A.D., 2016. Two-zone Hugoniot for porous materials. Phys. Rev. B 93 054103-1–054103-12. Sekine, T., 1997. Shock wave chemical synthesis. Eur. J. Solid State Inorg. Chem. 34, 823–833. Shang, S.S., Benson, D.J., Meyers, M.A., 1994. Microstructurally-based analysis and computational modeling of shock consolidation. J. Phys. IV 4 C8-521–C8-526. Vandersall, K.S., Thadhani, N.N., 2003. Time-resolved measurements of the shock– compression response of Mo+2Si elemental powder mixtures. J. Appl. Phys. 94, 1575–1583. Vogler, T.J., Lee, M.Y., Grady, D.E., 2007. Static and dynamic compaction of ceramic powders. Int. J. Solids Structures 44, 636–658. Zhao, F.P., An, Q., Li, B., Wu, H.A., Goddard III, W.A., Luo, S.N., 2013. Shock response of a model structured nanofoam of Cu. J. Appl. Phys. 113 063516-1–063516-8.
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Mechanics of Materials journal homepage: www.elsevier.com/locate/mechmat
Shock compression behavior of low density powder materials and the double-shock Hugoniot Takamichi Kobayashi National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
a r t i c l e
i n f o
Article history: Received 24 May 2016 Revised 9 May 2017 Available online 13 May 2017 Keywords: Shock compression Powder material Shock impedance Particle velocity
a b s t r a c t Particle velocity measurements of window/sample interface by velocity interferometer have been performed on a low density powder material, Ce:YAG, under various shock loading conditions generated by plate impact with a maximum impact velocity of 1.564 km/s (SUS304). The observed interface velocities and the reshock pressures are very high, indicating that the shock impedance of shock-compressed powder in the first-shock state is much higher than that of the initial powder because the density and the shock velocity for the first-shock state are largely increased. Measurements with three different window materials with almost the same impact velocities have been carried out to determine the reshock (double-shock) Hugoniot which is much stiffer than the principle Hugoniot, leading to a characteristic shock reverberation behavior of low density powder materials. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Behavior of shock-compressed powder and porous materials with high compressibility is difficult to describe, especially at very high pressures. The primary reason for this is the extreme temperature produced under the fast adiabatic shock compression where intense interparticle collisions induce deformation, damage, surface jetting, production of gaseous products, and so forth (Shang et al., 1994; Zhao et al., 2013). It is made further complicated by the existence of interstitial gas in pores, which is considered responsible for the excessive heat observed under shock compression of powder materials. The generation of excessive heat cannot be attributed solely to shock-compressed condensed constituent (Resnyansky, 2016). Analytical models to describe the shock response of powder materials have been proposed (Herrman, 1969; Petrie and Page, 1991; Dijken and De Hosson, 1994; Dai et al., 2008; Fredenburg and Thadhani, 2013). Shock compression of powder materials has been the subject of interest for its unique shock-compression response such as shock dissipation property and shock-induced chemical reaction (Vandersall and Thadhani, 2003; Dai et al., 2008). Extensive densification is known to occur even at relatively low shock pressures because of their very high compressibility. Low density powder materials have a low shock impedance (ρ Us ) because of low density (ρ ) and low shock velocity (Us ), whereas powder materials under shock compression should have a much higher shock
E-mail address: [email protected] http://dx.doi.org/10.1016/j.mechmat.2017.05.004 0167-6636/© 2017 Elsevier Ltd. All rights reserved.
impedance because of largely increased density and shock velocity (Gourdin and Weinland, 1985; Kobayashi, 2014), suggesting that the shock reverberation behavior of low density powder materials can be quite different from that of incompressible materials. There have been a few studies examining the shock impedance of powder materials in the first-shock states at low shock pressures less than ∼6 GPa (Gourdin and Weinland, 1985; Vogler et al., 2007). They observed large increases in powder density (30 ∼ 120%) and also in shock impedance (110 ∼ 280%) for the first-shock states. For fully-dense ceramic samples (Alumina), the reshock states were found to lie above the P-Up (particle velocity) principle Hugoniot (loci of final shock states) of the ceramic sample, which was explained by material strength (Reinhart and Chhabildas, 2003). On the other hand, the classic assumption for calculating reshock states from a first-shock state on the principal Hugoniot of the sample is to approximate them in P-Up space with the mirror reflection of the Hugoniot about the vertical axis through the firstshock state Up . This was experimentally confirmed for some metals (Al, Cu, and Ta) over a wide pressure range up to 440 GPa (Nellis et al., 2003). In this paper, results of particle velocity measurements of a low density powder material under shock compression up to ∼20 GPa (reshock pressure) are presented. Observed shock reverberation behavior with an extremely large increase in shock impedance of up to ∼820% for the first-shock state is analyzed and the corresponding reshock Hugoniot is determined using three different window materials from essentially the same first-shock state. The obtained reshock Hugoniot for the low density powder is much stiffer than the initial unpressed powder Hugoniot (principle Hugoniot).
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Fig. 2. Window/sample interface particle velocity profiles for LiF window and Ce:YAG powder sample. The impact velocities (Vimp ) are indicated in the figure. The initial sample thicknesses were (a) 0.618 mm, (b) 0.562 mm, and (c) 0.619 mm. The plateau values agree well with those at equilibrium states predicted by the shockimpedance-match principle.
Fig. 1. (a) Schematic of target assemblage for VISAR measurement. The second harmonic of a CW Nd:YAG laser (532 nm) was used with a Fiber Optic Probe (F.O.P.). (b) A microscope image of the powder specimen. The full scale corresponds to 50 μm.
2. Experiment Impact experiments were conducted using a propellant gun with a 30 mm inner-bore diameter (Sekine, 1997). An unpressed powder sample with a thickness of 0.46 ∼ 0.64 mm and a diameter of 15 ∼ 18 mm was sandwiched between a 1-mm-thick metal base-plate (SUS304 or A6061) and a 5 ∼ 8-mm-thick window (sapphire or LiF or silica). Powder sample used was a wellknown phosphor, Ce: YAG (NICHIA corporation, < 5 μm) with the sample density (ρ 0 ) of ∼1.45 g/cm3 . The porosity of the powder samples was ∼68% since the density of crystalline YAG is 4.56 g/cm3 . A 3-mm-thick stainless steel or aluminum impactor was accelerated by the propellant gun and struck the base-plate (the same material as the impactor) with the maximum impact velocity (Vimp ) of 1.564 km/s. Window/sample interface particle velocities were measured with a VISAR (VALYN MULTI-BEAM VISAR System) (Barker and Hollenbach, 1972). The second harmonic of a CW Nd: YAG laser (VERDI-5 W, COHERENT) was used with a Fiber Optic Probe (F.O.P.). The target assemblage and a microscope image of the powder specimen are shown in Fig. 1. A thin aluminum foil (10 mm × 10 mm, 12 μm thick) was placed between the sample and the window to reflect the laser light (532 nm, 0.5 W CW). The aluminum foil is quickly equilibrated to the peak shock pressure within ∼5 ns. The time resolution for this measurement was about a few nanoseconds. The Hugoniots used were
Us = 4.58 + 1.49Up for SUS304, Us = 5.35 + 1.34Up for A6061 (Marsh, 1980), Us = 11.213 + 0.97Up for sapphire in the elastic region (Jones et al., 2001), Us = 5.15 + 1.35Up for LiF, and Us ∼ 5.0 for silica (Up < 2.0 km/s) (Marsh, 1980). The Hugoniot for the powder sample, Ce: YAG, is not known. We have previously measured the approximate shock velocity of this powder (Kobayashi, 2014). The shock velocity was 2.36 (± 0.16) km/s for the impact velocity of 1.63 km/s (SUS304) and the partic1e velocity was determined to be 1.50 (± 0.10) km/s using the shock-impedance-match principle. The Hugoniot based on this measurement was used for the powder sample in this study, which should give the upper limit because all the data points presented here were measured below the impact velocity of 1.63 km/s. In order to confirm the reliability of the particle velocity measurements, we carried out the ruby luminescence measurements under shock compression to measure the shock pressures with a ruby window using the same sample assemblage as in Fig. 1 and compared the results with the particle velocity measurements with a sapphire window. Their results were consistent with each other. The detailed description on this technique to measure shock pressures and particle velocities is presented elsewhere (Kobayashi, 2014). 3. Results Window/sample interface particle velocity profiles for LiF window are shown in Fig. 2 for three different flyer impact velocities. The flyers and the base-plates were SUS304. Each profile looks a two-wave structure. The window/sample interface starts moving when the first shock wave strikes the LiF window. The first particle velocities observed are (a) ∼1.03 km/s, (b) ∼0.65 km/s, and (c) ∼0.35 km/s, which last for 0.07 - 0.16 μs. These time intervals correspond to the times required for the shock wave reflected at the window/sample interface to reverberate between the window and the base-plate and strike the LiF window again. Then the interface particle velocity jumps up and converges to (a) ∼1.08 km/s, (b) ∼0.71 km/s, and (c) ∼0.49 km/s, which suggests that the equilibrium state is reached very quickly within a couple of shock wave
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Table 1 Shock experiment conditions. Uncertainties in impact velocities are less than 1% and those in sample thickness are less than 3.0% which were used to estimate uncertainties in sample densities of less than 5.8%. Uncertainties in interface particle velocities (Up ) are about 2%. Up represents the sample/window interface velocity. Impactor
Impact velocity (km/s)
Sample thickness (mm)
Sample density (g/cm3 )
Window material
1st Up (km/s)
2nd Up (km/s)
SUS304 (3mmt) SUS304 (3mmt) SUS304 (3mmt) SUS304 (3mmt) SUS304 (3mmt) SUS304 (3mmt) A6061 (8mmt)
1.564 0.997 0.676 0.958 0.962 0.960 1.133
0.62 0.56 0.62 0.46 0.57 0.63 0.63
1.45 1.41 1.40 1.51 1.46 1.45 1.50
LiF LiF LiF Sapphire LiF Silica LiF
1.03 0.65 0.35 0.36 0.60 0.68 0.64
1.08 0.71 0.49 0.45 0.68 0.72 0.60
Fig. 3. P-Up diagram showing the results of Fig. 2. Dotted lines are the Hugoniots of SUS304 flyers with three different impact velocities. Observed first interface particle velocities are plotted with open circles on the LiF Hugoniot curve. The error bars for these measurements (∼2%) are not shown in the figure because they are smaller than the circle size. The low-lying line is an estimated P-Up relation for the initial powder sample. The arrows drawn from the intersection points of the sample Hugoniot and the SUS304 Hugoniots to the open circles represent the process where the first shock wave specified by the intersection point is reflected at the window/sample interface and the interface starts moving at the velocity indicated by the open circle. The slopes of these arrows may be considered as the shock impedance for the powder in the first-shock state.
reflections at the sample interfaces. Experimental specifics and interface particle velocities are given in Table 1. Fig. 3 is a P-Up diagram with the first interface velocities from Fig. 2 indicated by open circles (◦). Dotted lines are the Hugoniots of SUS304 flyers with three different impact velocities, and their intersection points with the LiF Hugoniot correspond to the equilibrium states which agree well with above mentioned convergence values of the particle velocities in Fig. 2. The low-lying line is an estimated P-Up relation for the powder sample based on a shock velocity measurement at Vimp = 1.63 km/s. The slope of this line corresponds to the shock impedance of the initial powder sample. The actual shock impedance of the initial powder should be somewhat smaller, especially for lower Vimp shots. The arrows to the first interface velocities (◦) represent the process where the first shock wave is reflected at the window/sample interface and the interface starts moving at the velocity indicated by the open circle. The slopes of these arrows may be considered as the shock impedance of shock-compressed powder in the first-shock state. It is seen that the slopes of the arrows are much steeper than that of the initial powder and increase with the impact velocity. The observed shock impedance jump when changing from the initial uncompressed state to the first-shock states are calculated to be more
Fig. 4. Interface particle velocity measurements with three different window materials (sapphire, LiF, and silica). The Hugoniots of sapphire, LiF, silica, and the powder sample are indicated by solid curves and that of the SUS304 flyer at Vimp = 0.960 km/s is shown by a broken curve. Measured first interface particle velocities for three different windows are plotted with open circles and the intersection point of the powder sample Hugoniot and the SUS304 Hugoniot is indicated with an open square.
than 3.3 times (230% increase), 7.9 times (690% increase), and 9.2 times (820% increase) for (c), (b), and (a), respectively. Fig. 4 shows the results of interface particle velocity measurements with three different window materials, namely, sapphire, LiF, and silica. All the other experimental conditions were kept as identical to each other as possible. The Hugoniots of sapphire, LiF, silica, and the powder sample are indicated by solid curves and that of the SUS304 flyer at Vimp = 0.960 km/s is shown by a broken curve. Measured first interface particle velocities for three different windows are plotted with open circles. These three points together with the intersection point of the Hugoniots for the powder sample and the SUS304 flyer (indicated with an open square in Fig. 4) appear to be located nearly on a straight line (slightly curved to be more precise). This suggests that the shock impedances of compressed powder samples in the first-shock states are almost the same and appear only weakly dependent on the window materials. It is important to notice here that almost exactly the same first-shock state was realized in the powder sample when the first shock wave propagated in each sample. This first-shock state is specified by the intersection point indicated by in Fig. 4. On the other hand, exactly the same first-shock state can also be realized even when the experimental conditions are different. For example, an impact of a SUS304 flyer at a certain Vimp can create the same first-shock state in the sample as an impact of an A6061 flyer
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ties in Fig. 6 agree well with those at equilibrium points predicted by the shock-impedance-match principle, indicated by the intersection points of the two flyer Hugoniots and the LiF Hugoniot in Fig. 5. The first interface particle velocity for the A6061 impact is already beyond the equilibrium point, and thus the shock wave is reflected back at the sample/base-plate interface into the sample as a partial release wave, whereas in the SUS impact case the reflected wave is a reshock wave. 4. Discussion 4.1. Large increase in shock impedance and density
Fig. 5. Interface particle velocity measurements with different flyer materials but with the same window material (LiF). Vimp (SUS304) = 0.997 km/s and Vimp (A6061) = 1.133 km/s. Observed interface particle velocities are indicated by an open circle for the SUS304 impact and by an open square for the A6061 impact.
The shock impedance of the powder in the first-shock state shown in Fig. 3 (the slope of the arrows) is much larger than that of the initial unpressed powder. The slope of the arrows increases as the shock strength is increased and the increasing rate is higher in the weak shock region, which seems reasonable because the compression ratio of low density powder materials increases drastically in the low pressure region but quickly levels off in the higher pressure region (Gourdine and Weinland, 1985). For the shot (a) in Fig. 2, the first-shock state of the powder sample is specified with Up ∼ 1.44 km/s, Us ∼ 2.3 km/s, and thus ρ ∼ 2.7·ρ 0 = 3.9 g/cm3 (∼170% increase). The density is largely increased and accordingly the shock velocity is largely increased as well, which leads to the drastic increase of shock impedance for the compressed powder in the first-shock state. The reshock states generated by the reflected shock waves at the LiF window are indicated by the open circles in Fig. 3. They are close to the equilibrium points and the following reflected shock waves at the sample/base-plate interface should have taken the sample to the equilibrium points. This shock reverberation behavior is considered characteristic of low density powder materials (or compressible porous materials in general) (Vogler et al., 2007) and is quite different from typical behavior of materials such as metals where shock impedance change is insignificant during shock reverberation even for the cases where the density increase is as much as several tens of percent (Nellis et al., 2003). 4.2. Reshock Hugoniot of powder specimen
Fig. 6. Interface particle velocity profiles corresponding to the results in Fig. 5. The initial sample thicknesses were (a) 0.562 mm and (b) 0.625 mm.
at somewhat higher Vimp . Fig. 5 depicts such an example where shock compression by a SUS304 impactor with Vimp = 0.997 km/s and that by an A6061 impactor with Vimp = 1.133 km/s created almost the same first-shock state in the powder sample. Since the window was LiF in both cases, similar first particle velocities were expected to be observed. Observed particle velocities are indicated in Fig. 5 by an open circle for the SUS304 impact and by an open square for the A6061 impact, which are close to each other as expected. Corresponding interface particle velocity profiles are shown in Fig. 6. It is seen that the first particle velocities are almost the same (∼0.64 km/s) as mentioned above, but they converge to their equilibrium values in an opposite way, which is understood from Fig. 5 because the equilibrium point for the A6061 impact is below the first particle velocity () and that for the SUS304 impact is above the first particle velocity (◦). Converged particle veloci-
In Fig. 4, results of particle velocity measurements performed under almost exactly the same experimental conditions except window materials are shown. Observed three points (open circles) must be on the same curve which passes through the intersection point of the initial powder Hugoniot and the SUS304 Hugoniot for Vimp = 0.960 km/s (indicated by the open square). This curved line should correspond to the reshock or double-shock Hugoniot and may be fitted by a quadratic equation with respect to Up . Such a fit is shown by a thick solid curve in Fig. 7, which was then mirror reversed left and right to obtain a usual P-Up relation for the powder specimen in the first-shock state (drawn with a dotted curve). This method is applicable to any material for determination of reshock Hugoniots. It is clearly seen that the shock impedance for the firstshock state is about several times larger than that for the initial unpressed state and even larger than that of LiF. It should be noted here, however, that the Hugoniot obtained this way is not simply the one for a higher density powder but the one under shock compression with increased temperature and entropy. This reshock Hugoniot is good only for the particular first-shock state specified by in Fig. 7. Different Hugoniots are assigned for different first-shock states of the powder specimen. The reshock Hugoniot in Fig. 7 should be slightly different from the actual one because the intersection point () was obtained using an approximate Hugoniot for the initial unpressed powder, which was determined by a previously measured data point (Us = 2.36 km/s at Up = 1.50 km/s)
T. Kobayashi / Mechanics of Materials 111 (2017) 15–20
Fig. 7. Reshock Hugoniot (P-Up ) for the powder in the first-shock state generated by the Vimp = 0.960 km/s impact. The thick solid curve represents the reshock Hugoniot obtained by a quadratic fit which passes through the observed interface velocities (◦) and the intercept (). The dotted curve is the P-V relation obtained by horizontal inversion of the quadratic fit.
with a relatively large uncertainty in Us (∼14%). It is clearly seen that the reshock Hugoniot is several times steeper than the principle Hugoniot of powder specimen and cannot be approximated by the mirror reflection of the principle Hugoniot. The steeper reshock Hugoniot appears reasonable because the specimen density of the first-shock state is drastically increased compared to the initial unpressed powder density. In this respect, it is rather interesting that the reshock Hugoniots of metals at high shock pressures with several tens of percent increase in the first-shock state density are well represented by the mirror reflected principle Hugoniot about the vertical axis (Nellis et al., 2003). It may have something to do with the fact that metals lose their strength significantly at high shock pressures and temperatures, which may not always be the case with ceramic materials in the pressure and the temperature range of the present study. 4.3. Shock reverberation behavior of low density powder The reshock Hugoniot is solely dependent on the first-shock state which is represented by the intersection of the initial powder Hugoniot and the base-plate Hugoniot indicated by in Fig. 7. This is well illustrated in Figs. 5 and 6 which show that almost the same first-shock states generated by different impactors with different impact velocities give rise to almost the same first interface particle velocities. The shock reverberation behavior for the Al impactor shot (Fig. 6(b)) is quite different from commonly known behavior in which reflected shocks lift up the sample pressure stepwise before reaching the equilibrium pressure. The reshock state is determined by the reshock Hugoniot and the window Hugoniot. The shock impedance of the compressed powder in the first-shock state is essentially determined by the reshock Hugoniot, and its weak window material dependence is introduced through the fact that the reshock Hugoniot (P-Up ) is not a straight line. In order to understand the shock reverberation behavior of low density powder materials in more detail, it would be helpful to construct a P-V diagram. We start by obtaining a bit more realistic Hugoniot for the initial powder sample. Most Hugoniot data for solids follow the relation Us = C + SUp where C is bulk sound
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Fig. 8. P-V relations for the principle Hugoniot (dotted curve) and the shock reverberation behavior for the Vimp = 0.676 km/s measurement (arrows). The solid line represents the shock-compression curve for YAG single crystal. Uncertainties in open squares mainly come from those in the estimated Hugoniot of the initial powder (Us = 0.42 + 1.29 Up ) . Uncertainties for open circles also originate mainly from those in the Hugoniot which are used to calculate the uncertainties in the shock impedance, the reshock velocity, and the volume. Uncertainties in P are significantly smaller than the circle size and not indicated.
speed at P = 0 and S is the slope of the linear relation between Us and Up . Since C is expressed as the square root of bulk modulus/density and bulk modulus is the inverse of compressibility, a simple compressibility measurement of the powder sample using a hydraulic pump in a low pressure region (< 0.2 GPa) was carried out to estimate the bulk modulus (∼0.26 GPa) which then gave the bulk sound speed of ∼0.42 km/s with a relatively large uncertainty of ∼30%. Using the measured shock velocity data (Us = 2.36 km/s at Up = 1.50 km/s), the Hugoniot for the initial powder was obtained as Us = 0.42 + 1.29 Up . The modified powder Hugoniot with this Us -Up relation is located slightly below the straight line Hugoniot used in Figs. 3–5. We can now calculate pressures and volumes for the first-shock states which are represented by the intersections of the SUS304 Hugoniots and the initial powder Hugoniot obtained above. Results are (V, P) = (0.25 cm3 /g, 4.82 GPa) for (a), (0.30 cm3 /g, 2.18 GPa) for (b), and (0.35 cm3 /g, 1.12 GPa) for (c), and they are plotted in Fig. 8 with open squares. The P-V relation appears the typical shock-compression curve of highly compressible powder materials, namely, the volume decreases drastically in the low pressure region and then becomes almost incompressible at higher pressures. The isentrope should lie below this P-V curve. After the first shock wave strikes the window/sample interface, the reflected shock waves move back and forth between the two sample boundaries. In order to obtain the volume and the pressure of the reshock states, we take the Vimp = 0.676 km/s experiment indicated as (c) in Figs. 2 and 3 as an example to explain how V and P are determined. Note that the straight sample Hugoniot in Fig. 3 is now replaced by the curved line obtained from Us = 0.42 + 1.29 Up . The first shock state specified by the intersection of the initial powder Hugoniot and the SUS304 Hugoniot for Vimp = 0.676 km/s has (Up , P) = (0.64 km/s, 1.12 GPa). The Us and the shock impedance (ρ 0 Us ) are calculated to be 1.25 km/s and 1.81 g·km/cm3 /s, respectively. The first reshock state shown by ◦ in Fig. 3(c) has (Up , P) = (0.35 km/s, 5.19 GPa), and the shock impedance (slope of the arrow) is 14.0 g·km/cm3 /s which can be
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used to estimate the reshock velocity as 4.70 km/s which is nearly 4 times of the first shock velocity. Since the actual particle velocity in the reshock state is 0.64–0.35 = 0.29 km/s, the volume of the reshock state is calculated to be 0.32 cm3 /g. The second reshock should have brought the sample to the equilibrium state as Figs. 2 and 3 suggest, and thus it has (Up , P) = (0.48 km/s, 7.34 GPa). The pressure jump is 7.34–5.19 = 2.15 GPa and the actual particle velocity is 0.48–0.35 = 0.13 km/s, which leads to Us = 5.21 km/s and V = 0.31 cm3 /g for the second reshock state. The results are plotted in Fig. 8 with open circles. The shock reverberation behavior of the powder sample is indicated by the arrows, and it appears quite different from commonly known reverberation behavior which is usually located near the isentrope lying below the principle Hugoniot, and thus the observed shock reverberation behavior is characteristic of low density powder materials. 5. Conclusions Particle velocity measurements on a low density powder material under shock loading were performed. It was indicated that the observed first window/sample interface velocities were very fast and the shock impedance for the first-shock state of the powder specimen was much larger than that for the initial powder due to the drastic increase in density and shock velocity even for weak shock loadings. The reshock Hugoniot for Vimp ∼ 0.960 km/s was successfully determined experimentally using three different window materials. The obtained reshock Hugoniot in P-Up space is much steeper than the principle powder Hugoniot because the first-shock state density is drastically increased, and thus the reshock Hugoniot cannot be approximated by the mirror reflection of the principle Hugoniot, which is in contrast to the metal cases where the strength is significantly reduced under high temperatures. This may be suggesting that ceramic powders such as YAG do not lose their strength very much in the pressure and the temperature range investigated in the present study. The reshock Hugoniot depends only on the first-shock state which is specified by the intersection of the initial powder Hugoniot and the baseplate Hugoniot in P-Up space. The P-V behavior corresponding to the shock reverberation of low density powder was also determined and indicated that it does not approach the isentrope.
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