Some meteorites consist of a mix of components of various parent bodies that were presumably brought together by past collisions. Impact experiments have been performed to investigate the degree of target fragmentation during such collisions. However, much less attention has been paid to the fate of the impactors. Here, we report the results of our study of the empirical relationship between the degree of projectile fragmentation and the impact conditions. Millimeter-sized pyrophyllite and basalt projectiles were impacted onto regolith-like sand targets and an aluminum target at velocities of up to 960 m s−1. Experiments using millimeter-sized pyrophyllite blocks as targets were also conducted to fill the gap between this study and the previous studies of centimeter-sized rock targets. The catastrophic disruption threshold for a projectile is defined as the energy density at which the mass of the largest fragment is the half of the original mass. The thresholds with the sand target were 4.5 ± 1.1 × 104 and 9.0 ± 1.9 × 104 J kg−1, for pyrophyllite and basalt projectiles, respectively. These values are two orders of magnitude larger than the threshold for impacts between pyrophyllite projectiles onto aluminum targets, but are qualitatively consistent with the fact that the compressive and tensile strengths of basalt are larger than those of pyrophyllite. The threshold for pyrophyllite projectiles and the aluminum target agrees with the threshold for aluminum projectiles and pyrophyllite targets within the margin of error. Consistent with a previous result, the threshold depended on the size of the rocks with a power of approximately −0.4 (Housen and Holsapple 1999). Destruction of rock projectiles occurred when the peak pressure was about ten times the tensile strength of the rocks.
Most meteorites are fragments of asteroids. They provide information about the early stages of the solar system, because thermal activity ceased early in the meteorite parent bodies. In some meteorites, the components of various parent bodies are mixed. For example, fine-grained angular black clasts up to 800 μm in their longest dimension were observed in a brecciated region of the Tsukuba meteorite. Mineralogically and compositionally, the clasts in the host H5—6 chondrite Tsukuba resemble CI chondrites (Nakashima et al. 2003). The Almahata Sitta meteorite is a fine-grained fragmental breccia, polymict ureilite. Aggregates of carbonaceous material up to 500 μm were observed, consisting primarily of fine-grained graphite (Jenniskens et al. 2009). HED meteorites are recognized to have originated from asteroid 4 Vesta, and contain carbonaceous chondrite clasts (Zolensky et al. 1996 and references therein). Meteorites containing the fragments of material from other bodies were likely formed as follows. The surface of parent bodies (composed of regolith and boulders) was impacted by bodies that originated from other parent bodies. Some of the impactor fragments were then captured in the regolith. The regolith containing the fragments was lithified by further impacts. In fact, dark material having similar spectra to carbonaceous chondrite meteorites mixed with materials indigenous to asteroid 4 Vesta was found on the surface of Vesta (Reddy et al. 2012). In addition, a black boulder found on the surface of asteroid 25143 Itokawa (Hirata, personal communication) is possibly a fragment derived from the parent body of a carbonaceous chondrite. Such evidence suggests that the acquisition of material from other parent bodies was a universal process on asteroid surfaces.
Many laboratory impact-disruption experiments have been performed to investigate the degree of target fragmentation, where the target is defined as the larger of the two colliding bodies (Holsapple et al. 2002 and references therein). The catastrophic disruption threshold Q* is defined as the projectile kinetic energy per unit target mass Mt or the total mass of the system, i.e., Mt + Mp, where Mp is the projectile mass, when the largest fragment mass mL,t is half of the original target mass, i.e., mL,t/Mt = 0.5. Experimental values of Q* have been determined for competent silicate rocks, water ice, metal, and porous materials. However, much less attention has been paid to the fate of impactors. For example, the threshold projectile kinetic energy per unit projectile mass , of catastrophic projectile destruction, i.e., mL,p/Mp = 0.5, where mL,p is the largest fragment of the projectile, has not been determined for the same materials for which Q* was determined.
In this study, we investigated the empirical relationship between the degree of projectile fragmentation and the impact condition. Specifically, we examined the case in which the projectile collides with a regolith-like surface. Millimeter-sized rock projectiles were impacted into a sand target, and the largest fragment mass fraction of the projectile was studied. The projectile materials were pyrophyllite and basalt, which were used in previous experiments of target destruction (Fujiwara and Tsukamoto 1980; Takagi et al. 1984). To compare our work with previous results that involved centimeter-sized targets, we also conducted impact-disruption experiments using millimeter-sized targets, because the disruption threshold of a rocky body depends on the event size scale (Housen and Holsapple 1999). Disruption experiments of millimeter-sized pyrophyllite projectiles with a larger aluminum target were performed for further comparison with previous results. In the 'Experiments' section, we describe the experimental procedure. In the 'Results' section, we present the results of the impact-disruption experiments. In the 'Discussion' section, the comparison of the disruption threshold under different impact conditions is discussed.
Impact Experiments of Rock Projectiles onto Simulated Regolith
Impact experiments were performed using a 15 mm diameter bore vertical powder gun (Matsui et al. 1982; Kani and Yamada 1984) that was transferred from Kyoto University to Okayama University in the 1980s, and then to Kobe University in the 2000s. We also used a 3.2 mm diameter bore He gas gun (Setoh et al. 2010) at Kobe University. Rock projectiles simulating meteorites were impacted onto regolith-like sand targets at velocities between 177 and 960 m s−1 with the powder gun, and between 167 and 207 m s−1 with the gas gun. The experimental velocity range only corresponds to the low-speed tail of the collisional speed distribution because the mean collision speed in the asteroid belt is approximately 5 km s−1 (Bottke et al. 1994). We expected the survival of the impactor to be greatest at these low velocities.
In the vertical powder-gun experiments, we glued a 15 mm diameter polycarbonate (PC) cylinder to the rear side of the projectile to prevent the projectile from rubbing against the inner wall of the barrel and being damaged through acceleration. We set a stopper for the PC cylinder, a plate with a hole of diameter 10 or 12 mm, for the projectile to separate the PC cylinder from the projectile. Figure 1a shows a projectile image. The projectile materials were pyrophyllite (Gestoptefontein, S.E. Transvaal, South Africa), which will henceforth be referred to as weak pyrophyllite (WP), and basalt (Yakuno, Kyoto, Japan). The porosity of the projectile was negligible, although the porosity is generally higher (up to >20%) in the carbonaceous chondrites (Britt and Consolmagno 2003), which are the type of clasts found in the Tsukuba meteorite, Almahata Sitta meteorite, and HED meteorites. All projectiles were cylindrical in shape. It was reported that the rock's shape did not influence the largest fragment mass fraction (Fujiwara and Tsukamoto 1980). The WP projectiles were 0.25–3.05 g in weight, 5–10 mm in diameter, and 5–15 mm in length. The basalt projectiles were 0.26–0.27 g in weight, 5 mm in diameter, and 5 mm in length. The ambient pressure in the target chamber was maintained lower than 0.01 MPa for the powder-gun shots.
The horizontal gas-gun shots were conducted under atmospheric pressure. We launched cylindrical projectiles of pyrophyllite, 0.058–0.059 g in weight, 3 mm in diameter, and 3 mm in length.
The sample used as target was fine-grained silica sand, as shown in Fig. 1b. According to the supplier, the material consists of 99.85% SiO2, 0.038% Al2O3, 0.025% Fe2O3, and other ingredients. The grain size of the sand ranged from less than 10 microns to several tens of microns. In the powder-gun experiments, the sand grains were poured into a cylindrical container 12.6 cm in inner diameter and 18.2 cm in height. Using a grain density of 2600 kg m−3 of quartz, the porosity of the sand target was 64 ± 1%. We measured the bulk porosity of the target using a smaller cylindrical container, 6.4 cm in inside diameter and 7 cm in height; we regard this porosity as the target porosity for the powder-gun experiment because we used the same procedure for the target preparation. The porosity of the sand target was within the range of the near-surface bulk porosities of the 36 main-belt asteroids and the 9 near-Earth asteroids, measured with radar to be 51 ± 14% (Magri et al. 2001). In the gas-gun experiments, this smaller target container was used. It was suspended horizontally, i.e., with the top opening of the container facing toward the projectile trajectory, using a thread. We prevented the sand target from collapsing by pushing the sand from the surface. Therefore, the porosity of the target decreased to 45%, although the influence of this change on the results was negligible because all the projectiles in the gas-gun shot were almost intact.
The experimental conditions for individual runs are listed in Table 1. The projectile velocities were determined by high-speed camera images. Recovered fragments were sorted using a 500 μm mesh and the masses of the fragments were measured. In the powder-gun experiment, high-speed camera images showed that about half of the WP projectiles were destroyed before they hit the targets. We speculated that this predestruction was due to a misalignment of the projectiles to the PC cylinders and the resulting contact with the PC cylinder's stopper. The masses of the largest fragment of the predestructed projectiles probably are at the lower limit and were therefore included in Table 1. We did not include the data for the predestructed projectiles when calculating the disruption threshold or when curve-fitting the data.
Table 1. Experimental conditions and the results of an impact into a regolith target
Numbers with > indicate lower limit, because preimpact breakup of the projectile was observed on the high-speed camera images.
WP projectile, gas gun
2.14 × 104
1.39 × 104
1.92 × 104
1.86 × 104
WP projectile, powder gun
3.20 × 104
1.81 × 104
2.83 × 104
3.75 × 104
2.88 × 104
4.62 × 104
3.18 × 104
2.67 × 104
6.99 × 104
6.44 × 104
9.20 × 104
7.22 × 104
8.53 × 104
1.29 × 105
8.86 × 104
2.23 × 104
2.12 × 104
3.54 × 104
6.99 × 104
4.93 × 104
9.86 × 104
4.65 × 104
3.43 × 104
4.09 × 104
1.57 × 105
1.57 × 104
Basalt projectile, powder gun
6.23 × 104
1.36 × 105
3.85 × 105
3.16 × 105
4.61 × 105
1.46 × 105
Impact Experiments of Pyrophyllite Projectiles with an Aluminum Plate as a Target
Cylindrical projectiles of WP used in the gas-gun shots described above were also used in this study. The target was a 65 × 50 × 10 mm aluminum plate. The impact velocity was determined from high-speed images and ranged from 9.8 to 106 m s−1. The fragments of the projectile were collected and weighed after each shot. The experimental conditions are listed in Table 2.
Table 2. Experimental conditions and the results of a WP projectile into an aluminum target
Size (diam., height)
Vi (m s−1)
Qp (J kg−1)
Peak pressure (MPa)
5.62 × 103
1.51 × 103
4.10 × 103
3.65 × 103
8.32 × 103
7.44 × 103
5.45 × 103
4.79 × 103
5.35 × 103
1.10 × 103
Experiments on the Effect of Size on Impact Disruption
We performed impact-disruption experiments with different sized pyrophyllite targets. We defined three different experimental groups according to the size scale. The geometric average size of the targets (La), the ratio of the projectile mass to the target mass (Mp/Mt), and the impact velocities (Vi) are summarized for each of three experimental groups in Table 3. The collisional conditions, i.e., the range of the mass ratio and the impact velocity, were similar for the three groups following the procedure in Housen and Holsapple (1999) for larger targets. In this study, cube-shaped pyrophyllite blocks were used as targets.
Table 3. Conditions and results of the size-effect disruption experiment for pyrophyllite targets
Group III projectile: 15diam. × 20 mm height aluminum cylinder, target: WP
Summary of group III
La = 32.8
Projectiles in groups I and II were accelerated using the gas gun. The targets of groups I and II were cut from a leftover pyrophyllite block from the impact experiments of Takagi et al. (1984). Hereafter, in this article, we call this material strong pyrophyllite (SP). In group I, 1.0 mm diameter aluminum spheres were used as projectiles. The projectile was attached to a 3 mm diameter PC cylinder and accelerated. The PC cylinder was stopped at the gun muzzle by a stopper with a 2 mm diameter pinhole. Consequently, only the projectile came in contact with the target. The target was put on the top of a pick supported by grease. The projectile collided with the target, which was 1.0–2.5 mm on a side, at a velocity of approximately 210 m s−1. The projectile velocity was determined from high-speed images. Figure 2 shows an example image of the impact experiments using a 1 mm projectile. The experimental conditions are given in Table 3. In group II, 3.2 mm diameter soda-lime glass spheres were shot at targets with sides of 2.8–7.3 mm. The target was suspended using a thread. The projectile velocity was determined to be about 240 m s−1 for other experiments conducted using this gas gun.
To compare the two pyrophyllite materials and to study the size dependence of the static strength, we conducted a Brazilian disc test (Housen and Holsapple 1999; Nakamura et al. 2007) using a compressive testing machine installed at Kobe University.
Disc-shaped specimens were cut from the SP used in the gas-gun shots described in the 'Experiments on the Effect of Size on Impact Disruption' section. The sizes of the specimens were 9.97 ± 0.01 mm in diameter and 4.985 ± 0.009 mm in thickness. The loading rate was 1 μm s−1. Seventeen specimens were used.
It has been shown that the size dependence of static strength is expressed by the Weibull modulus φ (Weibull 1939) as Yt α V−1/φ, where V is the volume of the specimen. Nakamura et al. (2007) obtained the Weibull modulus of Yakuno basalt, which was used in previous impact experiments, as well as this study. Similarly, we obtained the Weibull modulus of medium-sized SP based on our 17 measurements. The result was
where φ = 10.9 ± 1.4. The Weibull modulus was less than the value of Yakuno basalt, φ = 15–17 (Nakamura et al. 2007), and Georgia Keystone granite, φ = 12, determined using different size samples (Housen and Holsapple 1999). The characteristic tensile strength at which 63.2% of the specimens are broken up,Yt0, was found to be 9.2 MPa. The arithmetic mean of the 17 measurements was 8.7 MPa. These values are larger than the average value of the WP specimen, 5.7 MPa.
We also measured the uniaxial compressive strength, Yc, of WP using the same machine. Cylinder-shaped specimens were cut from a block of WP. The specimen size was 10.01 ± 0.02 mm in diameter and 20.02 ± 0.03 mm in height. The loading rate was 1 μm s−1. Four specimens were used. The compressive strength of WP was about half of the value of SP. WP is lighter and weaker than SP. The rocks used in this experiment have strengths within the range of the value of ordinary chondrite meteorites (Kimberley and Ramesh 2011) and even carbonaceous chondrite that were reported to have tensile strength of 0.3–30 MPa (Tsuchiyama et al. 2009). Their sound velocities are also within the range of those of ordinary chondrites (Nakamura et al. 2009 and references therein). However, measured physical properties of meteorites are probably biased toward stronger ones: estimated bulk strengths of pre-entry, meter-scale interplanetary meteoroids are of the order of 10–2 to 10–1 times the tensile strengths of recovered samples (Popova et al. 2011).
Table 4 summarizes the strengths of the materials used in this study.
Table 4. Mechanical properties of pyrophyllite and basalt
We derived the relationship of the largest fragment mass ratio mL,p/Mp with the projectile impact energy density Qp defined as
for the 5 mm projectiles of WP and basalt shown in Fig. 3. The lines represent the least-squares fits to the data used in this study. The catastrophic disruption threshold, Q*p, is defined as the energy density at which catastrophic disruption of the projectile of mass occurs, i.e., the largest fragment mass is half of the original mass, mL,p/Mp = 0.5. Table 5 summarizes the fitting results of the following equation to the data.
Q*p was found to be 4.5 ± 1.1 × 104 and 9.0 ± 1.9 × 104 J kg−1 for WP and basalt projectiles, respectively. This result is qualitatively consistent with the fact that the compressive and tensile strengths of basalt are larger than those of WP.
In Fig. 4, we show the result of the size-effect experiments. The largest fragment mass fraction of the target (mL,t/Mt) versus the energy density, that is the projectile's kinetic energy per unit total mass of the system defined as
The data for each group shift to the right as the average target size La decreases, indicating the strengthening of the target against collisional destruction with decreasing target size. The dashed lines represent the least-squares fits to the data. The solid line corresponds to the result of previous impact experiments of SP targets that were 42–60 mm on a side with impact velocities between 258 and 950 m s−1 (Takagi et al. 1984), where the energy density was defined as
The difference in the definitions of Q in Equations (4) and (5) is small for the previous experiment because the mass ratio of the projectile and the target was 5% or less. The result was similar to the result for group III, probably because the differences in target size, impact velocity, and strength of the target material between two experiments were rather small. The fitting results of this equation
To examine the influence of the projectile size on the degree of WP projectile fragmentation, we plotted the results of the WP impact on the sand target according to the size of the WP projectiles, as shown in Fig. 5. The size range of the pyrophillite targets was between 1.6 and 32.8 mm, which encompasses more than one order of magnitude. We confirmed that the disruption threshold depends on the size of the targets. However, in the WP projectile and sand target experiment, the range of the projectile diameter was between 3 and 10 mm, which is only a factor of three. Due probably to the small size range, we did not observe any size dependence of the disruption threshold for the WP projectiles.
Figure 6 shows the mass fraction of the largest fragment of the WP projectile mL,p/Mp versus the energy density Qp for impacts with an aluminum plate. The solid line represents the least-squares fit to the data. The fitting parameters are shown in Table 5. We compared this result with the result of our group III experiments in which aluminum projectiles impacted WP targets. The data are mostly in agreement.
To compare the catastrophic disruption threshold for rocks under different impact conditions, especially the threshold, Q*p, with the threshold, Q*, we plotted our results with previous results for targets made of SP (Takagi et al. 1984) and Yakuno basalt (Fujiwara and Tsukamoto 1980) in Fig. 7. The horizontal axis is the equivalent diameter of the rocks used in the disruption experiments. The four data points for the aluminum projectile and SP and WP targets show that Q* depends on the event scale as already shown in Fig. 4. The solid line represents the least-squares fit to the three SP data points. The slope of the curve was −0.404 ± 0.035, which is similar to the slope of −0.405 ± 0.023 found in the previous study of large targets (Housen and Holsapple 1999). The catastrophic disruption threshold Q*p for the WP projectile and aluminum target agrees with the threshold Q* for the aluminum projectile and WP targets within the margin of error, as shown in Fig. 6, although the definition of the threshold is slightly different. On the other hand, the catastrophic disruption threshold Q*p for the WP and basalt projectiles with a sand target is about two orders of magnitude larger than the threshold for WP projectiles impacting with an aluminum target. This is probably because the sand target was “soft,” i.e., the peak pressure did not reach the level that was attained in the experiments with aluminum targets.
We plotted the largest fragment mass ratio versus the roughly estimated peak pressure divided by the static tensile strength of the projectile material in Fig. 8. For impact experiments conducted with 64% porosity sand, the peak pressure was estimated assuming a one-dimensional planar impact and a linear relationship between the wave velocity U and the particle velocity up, i.e., U = C + sup, where C is the bulk sound velocity and s is a constant (e.g., Melosh 1989). We adopted a bulk density of 945 kg m−3 and assumed unity for s. We assumed that C =0.25 km s−1, which is 1/6.7 times the value of sand with a density of 1610 kg m−3 (1.7 km s−1), based on the ratio of the bulk sound velocities, 0.41 and 2.75 km s−1, of porous quartz with densities of 1150 and 1877 kg m−3, respectively (Ahrens and Johnson 1995). For Yakuno basalt and aluminum, we used the values from the previous study (Takagi et al. 1984). For the Hugoniot parameters for WP, we modified the previous values of SP, using a measured density of 2620 kg m−3 and assumed a bulk sound velocity of 2100 m s−1 based on the measured value of the longitudinal wave velocity of 2800 m s−1 for WP. The result shows that the difference between the sand target and the aluminum target was within a factor of one and was much less significant than that found in Q*p. It is notable that destruction started to occur when the ratio of the peak pressure was about ten times the tensile strength. Similar results were found for the impact penetration of projectiles into highly porous sintered glass beads targets (Okamoto et al. 2013). The empirical relationship between the largest fragment mass fraction and the peak pressure Pi normalized by the tensile strength of the target Yt is given as follows:
where a =2.16 ± 0.93 and 2.26 ± 0.53, b =−1.81 ± 0.65 and −2.37 ± 0.38, for WP and basalt projectiles versus sand, respectively. Assuming similar shape and bulk density of the boulder and the parent body, Equation (7) gives
where dL, p and Dp are the size of the largest fragment and the impactor.
Here, we extrapolate this result to a larger size scale and a higher velocity regime. On asteroid 25143 Itokawa, a unique and remarkably dark boulder about 6 m in size, called Black Boulder, was found (Hirata, personal communication). One of possible origins is that the Black Boulder is a xenolith from another body that consisted of a low-albedo material. We estimate the size of the parent body of the Black Boulder assuming it was the largest fragment of a dark body that impacted onto a regolith surface. We assumed a spherical shape and bulk density of 2200 kg m−3, resulting in an estimated mass of the Black Boulder of 2.5 × 105 kg. Because Itokawa is expected to have spent most of its time in the asteroid Main Belt (Michel et al. 2008) and the average velocity of collisions in the asteroid main belt is about 5 km s−1 (Bottke et al. 1994), we estimated the peak pressure of the impact to be 13 GPa, using the Hugoniot parameters of the Murchison meteorite (Anderson and Ahrens 1998) and planar approximation. Adopting the tensile strength of Murchison, 3 MPa (Tsuchiyama et al. 2009), and using Equation (8), we estimated that the size of the impacting body was approximately 200 and 800 m based on the parameters of WP and basalt, respectively. Note that these are the lower size limits of an impactor, because the Black Boulder may not be the largest fragment of the impacting dark body, i.e., there may be larger fragments. Furthermore, the strength of the parent body probably depends on the strain rate (Kimberley and Ramesh 2011), and the estimated size of 200 m is a lower limit. This size is at the border of the strength–gravity regime transition of catastrophic disruption of nonporous and porous bodies (Jutzi et al. 2010). Because the size of Itokawa is 535 × 294 × 209 m (Fujiwara et al. 2006), and it cannot survive an impact with a 200 m body at 5 km s−1, the impact that created the Black Boulder must have occurred on a much larger body that may have been an ancestor of Itokawa.
Millimeter-sized rock projectiles simulating meteorites were impacted onto regolith-like sand targets at velocities of 167–960 m s−1. The rocks used in the experiments were strong pyrophyllite (SP), weak pyrophyllite (WP), and basalt. Recovered fragments were sorted using a 500 μm mesh and the masses of the largest fragments were obtained. Disruption experiments of millimeter-sized pyrophyllite projectiles with a larger aluminum target and impact-disruption experiments of millimeter-sized targets were also performed for comparison with previous results.
In this study, the energy density, Qp, was defined as the kinetic energy of the projectile per unit mass of the projectile. The catastrophic disruption threshold of the projectile, Q*p, was defined as the energy density at which the largest mass fragment of a projectile was half of the projectile's original mass. The threshold Q*p of an impact into a sand target was 4.5 ± 1.1 × 104 J kg−1 for WP projectiles and 9.0 ± 1.9 × 104 J kg−1 for basalt projectiles. The higher threshold for basalt compared with WP is qualitatively consistent with the fact that the compressive and tensile strengths of basalt are greater than those of WP. The catastrophic disruption threshold of the target Q* of the SP target depended on the size of the target rocks with a power of −0.404 ± 0.035. This is similar to the power of −0.405 ± 0.023 found in a previous study of impacts into granite targets (Housen and Holsapple 1999). We did not observe any size dependence of Q*p, which was probably due to the limited range in size of the rock projectiles.
The threshold Q*p for the WP projectile and the aluminum target was within a factor of the threshold Q* for the aluminum projectile and the WP target, although the definition of the threshold was slightly different. In contrast, the threshold Q*p for the rock projectile and sand target was about two orders of magnitude higher than the threshold for the same material impacting with aluminum. This was probably because the peak pressure in the collisions with the sand target was much lower than in the collisions with solid targets. Destruction of projectile was found to occur when the ratio of the peak pressure was about ten times the tensile strength of the rocks.
The authors are grateful to K. Kani and K. Tomeoka for their cooperation and support for our operation of the powder gun at Kobe University. We are also thankful to Y. Takagi for giving us a leftover pyrophyllite block. This work was supported by the grants-in-aid for science research (21244069) from the Japanese Society for the Promotion of Science (JSPS).