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Comparison of Crater Behavior of Water Ice by Low and High Density Projectiles under Hypervelocity Impact
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ScienceDirect Available online at www.sciencedirect.com Procedia Engineering 00 (2017) 000–000
ScienceDirect
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Procedia Engineering 204 (2017) 329–336
14th Hypervelocity Impact Symposium 2017, HVIS2017, 24-28 April 2017, Canterbury, Kent, UK
Comparison of Crater Behavior of Water Ice by Low and High Density Projectiles under Hypervelocity Impact Lan Sheng-wei*, Liu Sen, Qin Jin-gui, Ren Lei-sheng, Huang Jie
Hypervelocity Impact Research Center, CARDC, NO.6 Er Huan Lu Nan Duan, Mianyang, 621000, P.R.China
Abstract Hypervelocity impact tests have been performed on water ice in the velocity range of 3 to 7 km/s, by using low and high density projectiles. The projectile materials included polycarbonate and stainless steel, with diameter of 1.0 mm. The ice targets were solid cylinders at 253K made from pure water. The crater morphology in the solid ice caused by different projectile and different velocity were observed. The crater sizes were measured and compared with previous tests impacted by aluminum projectiles. The results showed that: 1) the crater diameter and crater depth were dominated by different mechanisms, the crater depth was mainly caused by the projectile penetration, while the crater diameter was mainly caused by the ice spallation; 2) the crater depth showed stronger projectile density dependence than crater diameter, while the crater diameter by higher density projectile showed stronger velocity dependence than that by lower density projectile; 3) the crater volume scaled with the impact energy, the crater diameter by high density projectile showed ‘energy scaling’ behavior, while the crater diameter by lower density projectile showed ‘momentum scaling’ behavior. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 14th Hypervelocity Impact Symposium 2017. Keywords: impact crater; water ice; hypervelocity impact; planet
* Corresponding author. Tel.: +86-816-2465387. E-mail address: [email protected] 1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 14th Hypervelocity Impact Symposium 2017.
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 14th Hypervelocity Impact Symposium 2017. 10.1016/j.proeng.2017.09.754
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Lan Sheng-wei et al. / Procedia Engineering 204 (2017) 329–336 Lan Sheng-wei et al./ Procedia Engineering 00 (2017) 000–000
1. Introduction Impact craters are one of the most important visible features on the surfaces of most icy bodies in Solar System. It is therefore significant for understanding the formation and evolution of planets in the outer Solar System to study the impact cratering behaviour of water ice. A large amount of laboratory experiments have been performed to study the craters on icy bodies. In early 1980s, Croft (1979, 1981), Kawakami et al (1983), Cintala et al (1985) and Lange (1987) conducted a series of impact cratering tests on water ice [1~5]. They compared the differences of craters in water ice and rocks, and explored the influences of ice strength, projectile densities and impact energies to the crater size. However, most of these works were restricted to lower velocity range (below 1 km/s), which was much lower than the velocities in realistic planetary impact events (from several to dozens of km/s). From the middle 1990s, M J Burchell and his team [6~10] conducted a series of hypervelocity (up to 7 km/s) impact tests on water ice, attempting to construct the scaling laws of the crater size with the impact conditions. All of these works above have greatly enriched the understanding of the cratering behavior in water ice. One of the main results from these studies is the scaling laws of the crater volume (or mass) with the impact energy. However, it is not sufficient to model the craters just by the combined energy dependence. Other conditions, such as projectile/target properties, impact velocity and incline, ambient temperature, should also be taken into account. Therefore, to better understanding the cratering behavior of water ice under different projectile and different velocities, the hypervelocity impact cratering tests have been performed by using two types of projectiles with different density. Nomenclature D crater diameter H crater depth V crater volume E impact energy projectile density
2. Experiment method 2.1. Ice preparation The ice targets were made by pure water. First, the water was boiled to exclude the dissolved gases. Then it was put into the ice bath. When the water was cooled to about 277K, it was transferred to a special container. The container was consisted of a plastic cylinder shell, a metal bottom and a plastic top. The inner size of the container was Φ200mm×120mm, the height of the water is about 92mm. The container with cold water was then put into a freezer in which the temperature was kept at 253K. During the freezing process, heat sources were mounted on the top plate and the upper portion of the side shell. The ice grew from the bottom to the top. When the water was frozen completely, a clear and solid ice target was formed. Then it was taken out from the container and stored in a freezer with temperature of 253K. 2.2. Experiment facility The tests were performed at the hypervelocity impact range (Range A) of the China Aerodynamics Research and Development Center (CARDC). Range A consists of a 7.6mm caliber two stage light gas gun (TSLGG) and an impact chamber, as shown in Fig. 1. The TSLGG uses powder as energy source. A piston is accelerated by the powder gas and then presses the hydrogen gas in the pump tube. The hydrogen is pressed to extremely high pressure and entered into the launch tube, driving the projectile to move forward. The projectile then flies into the chamber and impacts on the ice target. A laser velocimeter system was used to measure the projectile velocity.
Author name / Procedia Engineering 00 (2017) 000–000 Lan Sheng-wei et al. / Procedia Engineering 204 (2017) 329–336
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1——powder chamber；2——piston；3——pump tube；4——launch tube； 5——projectile；6——impact chamber；7——ice target Fig. 1. Sketch of TSLGG.
2.3. Crater measurement The crater diameter, depth and volume were measured after impact. The diameter was measured by a caliper, the depth was measured by a depth gauge. The crater volume was measured by filling the crater with fine glass balls. To study the crater morphology, the crater profiles were measured. Four profiles were selected by 45 degree space. For each profile, the depth was measured by every 1 or 2 mm along the diameter. 3. Experiment parameters and crater results The diameter of the projectiles kept 1.0 mm. The projectile materials included polycarbonate and stainless steel. The impact velocities included 3 km/s, 5 km/s and 7 km/s. The experiments lists and crater sizes were showed in Table 1. Table 1. Experiment parameters and crater size NO
Projectile Material
V (km/s)
D (mm)
D-error (mm)
H (mm)
H-error (mm)
V (cm3)
V-error (cm3)
1 4 7 2 3 8
Steel Steel Steel Polycarbonate Polycarbonate Polycarbonate
5.12 3.12 7.05 5.17 3.01 7.26
81.75 69.50 120.25 47.10 38.75 46.25
8.54 12.12 10.44 10.09 5.50 9.13
21.85 16.84 18.35 7.04 7.41 5.78
0.13 1.26 0.25 0.05 0.18 0.17
22.96 17.85 51.58 3.57 1.72 3.72
3.52 4.72 0.88 0.76 -
Typical crater morphology is shown in Fig.2. It was found that, the crater was mainly caused by the spallation of the ice material in the crater. The inner surface of the crater was not smooth, and the circle of the crater was irregular. The main morphological features of the craters included the spallation on the top surface and the central pit in the crater bottom. Several cracks can be found surrounding the crater by a steel sphere, some of them extended to the edge of the top surface and propagated toward the back surface. These morphological features were consistent with many previous work such as Kato (1995) [11], Grey (2001) [7], and Shrine (2002) [9]. Although no large crack was found in the craters by polycarbonate projectiles, even at 7 km/s, the material spallation and irregular crater circle were still observed. Thus, the ice showed brittle behaviour in the cratering process. Fig.3 shows the profiles of the craters. It can be found that a pit in the center of the crater bottom, especially for the crater at lower velocities. With the velocity increase, the crater became flat. At 7 km/s velocity, the central pit nearly disappeared. The ratio of crater depth to diameter (H/D) was used to characterize the crater shape, as shown in Fig.4. The H/D ratio decreased with the velocity increasing, for both two types of projectiles, this is similar to the aluminum projectiles impacts in Shrine (2002) [9]. This indicates that the craters at higher impact velocity were shallower than which at lower velocity. Moreover, the H/D ratio of craters by steel projectiles was higher than that by polycarbonate projectiles at the same impact velocity, while the craters by aluminum projectiles showed the opposite behavior.
Lan Sheng-wei et al. / Procedia Engineering 204 (2017) 329–336 Lan Sheng-wei et al./ Procedia Engineering 00 (2017) 000–000
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Fig. 2. Typical morphology of impact crater in ice (left: steel projectile, V=7.05 km/s; right: polycarbonate projectile, V=7.26km/s). 100
PC 3.01 km/s PC 5.17 km/s
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PC 7.26 km/s
Depth (mm)
Steel 3.12 km/s 60 Steel 5.12 km/s 40
Steel 7.05 km/s
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Diameter (mm) Fig. 3. Crater profiles comparison.
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Fig. 4. Crater shape comparison. (Left: H/D ratio versus impact velocity; right: H/D ratio versus projectile density)
4. Discussion 4.1. Influence of impact velocity The crater dimensions of the present tests, combined with early data for aluminum projectiles (Shrine, 2002) [9], were plotted versus impact velocity and projectile density respectively, as shown in Fig.5. As shown in Fig.5a, the crater diameter by polycarbonate and steel projectiles scaled with the velocity in power laws, similar to craters by aluminum projectiles. The relationships were fitted as below: For steel projectiles, For aluminum projectiles, For polycarbonate projectiles,
D 27.8V 0.71
(1)
D 17V 0.72
(2)
D 23.9V 0.33
(3) The velocity exponents of the crater diameter for steel and aluminum projectiles were 0.71 and 0.72 respectively, close to exponents in many previous works of 0.66. The velocity exponent for polycarbonate projectile was 0.33, nearly half the above values. It is thus observed that the crater formed by high density projectiles shows more velocity dependence than low density ones. There was no consistent scaling law with velocity for crater depth as shown in Fig.5b, with the depth by different projectiles showing different behaviors. For polycarbonate projectile, the depth decreased with the velocity, while for aluminum and steel projectiles, it increased from 3km/s to 5km/s and decreased from 5km/s to 7km/s. It can-not be concluded as an essential behavior nor just a data scatter due to the lack of data.
Lan Sheng-wei et al. / Procedia Engineering 204 (2017) 329–336 Lan Sheng-wei et al./ Procedia Engineering 00 (2017) 000–000
334 6 140
120
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D =17 *V 0.72
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D =23.9 *V 0.33 2
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Velocity (km/s)
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D =42.62 0.48
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D =40.03 0.41
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D =30.59 0.36
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(a)
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aluminum (shrine,2002) fit by shrine pc steel
24 20 16 12 8
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V=3km/s V=5km/s V=7km/s Burchell 2001 fit 7km/s fit 5km/s
20
Cater Depth (mm)
Crater Depth (mm)
3
V= 7km/s V= 3km/s V= 5km/s
120
D =27.8*V 0.71
Crater Diameter (mm)
Crater Diameter (mm)
140
steel PC aluminum (shrine,2002)
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Projectile Density (g/cm3)
7
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H 0.62
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H 0.24
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(d) 0
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Projectile Density (g/cm3)
7
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Fig. 5. Crater dimensions versus impact velocity and projectile density.
4.2. Influence of projectile density Fig.5c shows the dependence on projectile density. The crater diameter at 5km/s agreed well with the fit by Burchell (2001) [6], increasing with the projectile density in a power law. The crater diameter at 3km/s and 7km/s followed a similar way. The fitted relationships were
D 42.62 0.48 for 7 km/s D 40.03 0.41 for 5 km/s D 30.59 0.36 for 3 km/s
(4) (5)
(6) It can be found that the density exponents increased with the velocity increasing, indicating that the crater diameter would show more density dependence at higher impact velocity. The crater depth with the projectile density was shown in Fig. 5d. The crater depth increased with the projectile density but it did not agree with the fit by Burchell (2001) [6]. Since the depth at 3km/s showed an unusual scatter, just data at 5km/s and 7km/s were fitted. The density exponents of depth for both two velocities almost equaled to each other, and obviously higher than that of diameter. It may be induced that the projectile density affect crater depth more than diameter. 4.3. Influence of impact energy The crater diameter and volume versus the impact energy was plotted as Fig.6, combined with previous aluminum projectile data (Shrine, 2002) [9] and polycarbonate projectile data at low velocity (Lange, 1987) [7]. The
Lan Sheng-wei et al. / Procedia Engineering 204 (2017) 329–336 Author name / Procedia Engineering 00 (2017) 000–000
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crater volume showed a good agreement with the fit by Burchell (2005) [12]. This indicates an ‘energy scaling’ [13], which was compatible with many previous works. However, it can-not simply be assumed that the crater dimensions scale with the cubic-root energy. As shown in Fig.6b, the energy exponents of crater diameters for steel and aluminum projectiles were 0.36, nearly one third of volume-energy exponent (about 0.33). This is compatible with the diameter versus velocity relationship, indicating ‘energy scaling’. However, the exponent for polycarbonate projectiles was 0.17, just about half of 0.33. This implies that the velocity exponent for polycarbonate projectiles would be half of the exponent for steel/aluminum projectiles. Thus it means the crater diameter for polycarbonate projectile should show ‘momentum scaling’. 200
1000
U E1.01 0.08
D E 0.36 100
10
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steel PC aluminum (shrine, 2002) PC (Lange, 1987) steel (Burchell, 1998/2005) fit by Burchell 2005
0.1
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100
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1000 2000
Crater Diameter (mm)
Volume (cm3)
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D E 0.24 D E 0.17
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steel pc pc (Lange,1987) aluminum(shrine, 2002) fit for aluminum (shrine, 2002) fit for present steel data fit for present PC data fit for pc data of Lange(1987)
D E 0.36 1
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Energy (J)
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1000 2000
Fig. 6. Scale crater diameter and crater volume with impact energy.
5. Conclusions Based on hypervelocity impacts with low and high density projectiles over velocity range 3 km/s to 7 km/s, the effect of projectile materials to ice crater behavior had been investigated. The crater size was affected by both projectile density and impact velocity. However, the influences of the two factors showed in different ways and mainly influenced different crater dimensions. It was found that crater diameter showed an increasing dependence on projectile density with the velocity increase, and the crater depth seemed more dependent on projectile density than crater diameter. This is well explained by the formation mechanism of impact craters, that is, the crater depth mainly caused by projectile penetration, while the crater diameter mainly caused by the wave propagation and material spallation. For the crater scaling, the crater diameter by high density projectile showed ‘energy scaling’ while the low density projectile was more like ‘momentum scaling’. Nevertheless all of the crater volumes by different projectiles were proportional with impact energy. These conclusions may be helpful to understand the geological characteristics of icy bodies, and could be used to analyse the formation of impact craters on icy surfaces. However, these conclusions were reached from a limited data set taken in the strength regime. More tests over a wider range of projectile densities and impact velocities should be carried out for further investigation. Acknowledgements This work was supported by the National Natural Science Foundation of China (NO. 41304138). The authors thank Mr. Li Wen-guang and Dr. Wang Ma-fa for the help in the ice impact tests. References [1] Croft, S. K., S. W. Kieffer, T. J. Ahrens. Low-velocity impact craters in ice and ice-saturated sand with implications for Martian crater count ages [J]. Journal of Geophysical Research, 1979, 84(B14): 8023–8032. [2] Croft S K. Hypervelocity impact craters in icy media[C]//Lunar and Planetary Science Conference. 1981, 12: 190-192.
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[3] Kawakami S I, Mizutani H, Takagi Y, et al. Impact experiments on ice [J]. Journal of Geophysical Research: Solid Earth, 1983, 88(B7): 5806-5814. [4] Cintala M J, Smrekar S, Horz F, et al. Impact experiments in H2O ice, I: cratering [C] // Lunar and Planetary Science Conference. 1985, 16: 131-132. [5] Lange M A, Ahrens T J. Impact experiments in low-temperature ice [J]. Icarus, 1987, 69(3): 506-518. [6] Burchell M J, Grey I D S, Shrine N R G. Laboratory investigations of hypervelocity impact cratering in ice [J]. Advances in Space Research, 2001, 28(10): 1521-1526. [7] Grey I D S, Burchell M J, Shrine N R G. Laboratory investigations of the temperature dependence of hypervelocity impact cratering in ice [J]. Advances in Space Research, 2001, 28(10): 1527-1532. [8] Grey I D S, Burchell M J, Shrine N R G. Scaling of hypervelocity impact craters in ice with impact angle [J]. Journal of Geophysical Research-Planets, 2002, 107(E10): 6-11. [9] Shrine N R G, Burchell M J, Grey I D S. Velocity Scaling of Impact Craters in Water Ice over the Range 1 to 7.3 km s− 1[J]. Icarus, 2002, 155(2): 475-485. [10] Grey I D S, Burchell M J. Hypervelocity impact cratering on water ice targets at temperatures ranging from 100 K to 253 K[J]. Journal of Geophysical Research (Planets), 2003, 108(E3): 5019. [11] M Kato, Y Iijima. Ice-on-ice impact experiments. Icarus, 1995, 113: 423-441 [12] Burchell M J, Johnson E. Impact craters on small icy bodies such as icy satellites and comet nuclei [J]. Monthly Notices of the Royal Astronomical Society, 2005, 360(2): 769-781. [13] K A Holsapple, R M Schmidt. On the scaling of crater dimensions 2. Impact Processes [J]. Journal of Geophysical Research, 1982, 87 (B3): 1849-1870
ScienceDirect Available online at www.sciencedirect.com Procedia Engineering 00 (2017) 000–000
ScienceDirect
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Procedia Engineering 204 (2017) 329–336
14th Hypervelocity Impact Symposium 2017, HVIS2017, 24-28 April 2017, Canterbury, Kent, UK
Comparison of Crater Behavior of Water Ice by Low and High Density Projectiles under Hypervelocity Impact Lan Sheng-wei*, Liu Sen, Qin Jin-gui, Ren Lei-sheng, Huang Jie
Hypervelocity Impact Research Center, CARDC, NO.6 Er Huan Lu Nan Duan, Mianyang, 621000, P.R.China
Abstract Hypervelocity impact tests have been performed on water ice in the velocity range of 3 to 7 km/s, by using low and high density projectiles. The projectile materials included polycarbonate and stainless steel, with diameter of 1.0 mm. The ice targets were solid cylinders at 253K made from pure water. The crater morphology in the solid ice caused by different projectile and different velocity were observed. The crater sizes were measured and compared with previous tests impacted by aluminum projectiles. The results showed that: 1) the crater diameter and crater depth were dominated by different mechanisms, the crater depth was mainly caused by the projectile penetration, while the crater diameter was mainly caused by the ice spallation; 2) the crater depth showed stronger projectile density dependence than crater diameter, while the crater diameter by higher density projectile showed stronger velocity dependence than that by lower density projectile; 3) the crater volume scaled with the impact energy, the crater diameter by high density projectile showed ‘energy scaling’ behavior, while the crater diameter by lower density projectile showed ‘momentum scaling’ behavior. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 14th Hypervelocity Impact Symposium 2017. Keywords: impact crater; water ice; hypervelocity impact; planet
* Corresponding author. Tel.: +86-816-2465387. E-mail address: [email protected] 1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 14th Hypervelocity Impact Symposium 2017.
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 14th Hypervelocity Impact Symposium 2017. 10.1016/j.proeng.2017.09.754
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Lan Sheng-wei et al. / Procedia Engineering 204 (2017) 329–336 Lan Sheng-wei et al./ Procedia Engineering 00 (2017) 000–000
1. Introduction Impact craters are one of the most important visible features on the surfaces of most icy bodies in Solar System. It is therefore significant for understanding the formation and evolution of planets in the outer Solar System to study the impact cratering behaviour of water ice. A large amount of laboratory experiments have been performed to study the craters on icy bodies. In early 1980s, Croft (1979, 1981), Kawakami et al (1983), Cintala et al (1985) and Lange (1987) conducted a series of impact cratering tests on water ice [1~5]. They compared the differences of craters in water ice and rocks, and explored the influences of ice strength, projectile densities and impact energies to the crater size. However, most of these works were restricted to lower velocity range (below 1 km/s), which was much lower than the velocities in realistic planetary impact events (from several to dozens of km/s). From the middle 1990s, M J Burchell and his team [6~10] conducted a series of hypervelocity (up to 7 km/s) impact tests on water ice, attempting to construct the scaling laws of the crater size with the impact conditions. All of these works above have greatly enriched the understanding of the cratering behavior in water ice. One of the main results from these studies is the scaling laws of the crater volume (or mass) with the impact energy. However, it is not sufficient to model the craters just by the combined energy dependence. Other conditions, such as projectile/target properties, impact velocity and incline, ambient temperature, should also be taken into account. Therefore, to better understanding the cratering behavior of water ice under different projectile and different velocities, the hypervelocity impact cratering tests have been performed by using two types of projectiles with different density. Nomenclature D crater diameter H crater depth V crater volume E impact energy projectile density
2. Experiment method 2.1. Ice preparation The ice targets were made by pure water. First, the water was boiled to exclude the dissolved gases. Then it was put into the ice bath. When the water was cooled to about 277K, it was transferred to a special container. The container was consisted of a plastic cylinder shell, a metal bottom and a plastic top. The inner size of the container was Φ200mm×120mm, the height of the water is about 92mm. The container with cold water was then put into a freezer in which the temperature was kept at 253K. During the freezing process, heat sources were mounted on the top plate and the upper portion of the side shell. The ice grew from the bottom to the top. When the water was frozen completely, a clear and solid ice target was formed. Then it was taken out from the container and stored in a freezer with temperature of 253K. 2.2. Experiment facility The tests were performed at the hypervelocity impact range (Range A) of the China Aerodynamics Research and Development Center (CARDC). Range A consists of a 7.6mm caliber two stage light gas gun (TSLGG) and an impact chamber, as shown in Fig. 1. The TSLGG uses powder as energy source. A piston is accelerated by the powder gas and then presses the hydrogen gas in the pump tube. The hydrogen is pressed to extremely high pressure and entered into the launch tube, driving the projectile to move forward. The projectile then flies into the chamber and impacts on the ice target. A laser velocimeter system was used to measure the projectile velocity.
Author name / Procedia Engineering 00 (2017) 000–000 Lan Sheng-wei et al. / Procedia Engineering 204 (2017) 329–336
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1——powder chamber；2——piston；3——pump tube；4——launch tube； 5——projectile；6——impact chamber；7——ice target Fig. 1. Sketch of TSLGG.
2.3. Crater measurement The crater diameter, depth and volume were measured after impact. The diameter was measured by a caliper, the depth was measured by a depth gauge. The crater volume was measured by filling the crater with fine glass balls. To study the crater morphology, the crater profiles were measured. Four profiles were selected by 45 degree space. For each profile, the depth was measured by every 1 or 2 mm along the diameter. 3. Experiment parameters and crater results The diameter of the projectiles kept 1.0 mm. The projectile materials included polycarbonate and stainless steel. The impact velocities included 3 km/s, 5 km/s and 7 km/s. The experiments lists and crater sizes were showed in Table 1. Table 1. Experiment parameters and crater size NO
Projectile Material
V (km/s)
D (mm)
D-error (mm)
H (mm)
H-error (mm)
V (cm3)
V-error (cm3)
1 4 7 2 3 8
Steel Steel Steel Polycarbonate Polycarbonate Polycarbonate
5.12 3.12 7.05 5.17 3.01 7.26
81.75 69.50 120.25 47.10 38.75 46.25
8.54 12.12 10.44 10.09 5.50 9.13
21.85 16.84 18.35 7.04 7.41 5.78
0.13 1.26 0.25 0.05 0.18 0.17
22.96 17.85 51.58 3.57 1.72 3.72
3.52 4.72 0.88 0.76 -
Typical crater morphology is shown in Fig.2. It was found that, the crater was mainly caused by the spallation of the ice material in the crater. The inner surface of the crater was not smooth, and the circle of the crater was irregular. The main morphological features of the craters included the spallation on the top surface and the central pit in the crater bottom. Several cracks can be found surrounding the crater by a steel sphere, some of them extended to the edge of the top surface and propagated toward the back surface. These morphological features were consistent with many previous work such as Kato (1995) [11], Grey (2001) [7], and Shrine (2002) [9]. Although no large crack was found in the craters by polycarbonate projectiles, even at 7 km/s, the material spallation and irregular crater circle were still observed. Thus, the ice showed brittle behaviour in the cratering process. Fig.3 shows the profiles of the craters. It can be found that a pit in the center of the crater bottom, especially for the crater at lower velocities. With the velocity increase, the crater became flat. At 7 km/s velocity, the central pit nearly disappeared. The ratio of crater depth to diameter (H/D) was used to characterize the crater shape, as shown in Fig.4. The H/D ratio decreased with the velocity increasing, for both two types of projectiles, this is similar to the aluminum projectiles impacts in Shrine (2002) [9]. This indicates that the craters at higher impact velocity were shallower than which at lower velocity. Moreover, the H/D ratio of craters by steel projectiles was higher than that by polycarbonate projectiles at the same impact velocity, while the craters by aluminum projectiles showed the opposite behavior.
Lan Sheng-wei et al. / Procedia Engineering 204 (2017) 329–336 Lan Sheng-wei et al./ Procedia Engineering 00 (2017) 000–000
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Fig. 2. Typical morphology of impact crater in ice (left: steel projectile, V=7.05 km/s; right: polycarbonate projectile, V=7.26km/s). 100
PC 3.01 km/s PC 5.17 km/s
80
PC 7.26 km/s
Depth (mm)
Steel 3.12 km/s 60 Steel 5.12 km/s 40
Steel 7.05 km/s
20
0 -80
-60
-40
-20
0
20
Diameter (mm) Fig. 3. Crater profiles comparison.
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Lan Sheng-wei et al. / Procedia Engineering 204 (2017) 329–336 Author name / Procedia Engineering 00 (2017) 000–000 0.3
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Fig. 4. Crater shape comparison. (Left: H/D ratio versus impact velocity; right: H/D ratio versus projectile density)
4. Discussion 4.1. Influence of impact velocity The crater dimensions of the present tests, combined with early data for aluminum projectiles (Shrine, 2002) [9], were plotted versus impact velocity and projectile density respectively, as shown in Fig.5. As shown in Fig.5a, the crater diameter by polycarbonate and steel projectiles scaled with the velocity in power laws, similar to craters by aluminum projectiles. The relationships were fitted as below: For steel projectiles, For aluminum projectiles, For polycarbonate projectiles,
D 27.8V 0.71
(1)
D 17V 0.72
(2)
D 23.9V 0.33
(3) The velocity exponents of the crater diameter for steel and aluminum projectiles were 0.71 and 0.72 respectively, close to exponents in many previous works of 0.66. The velocity exponent for polycarbonate projectile was 0.33, nearly half the above values. It is thus observed that the crater formed by high density projectiles shows more velocity dependence than low density ones. There was no consistent scaling law with velocity for crater depth as shown in Fig.5b, with the depth by different projectiles showing different behaviors. For polycarbonate projectile, the depth decreased with the velocity, while for aluminum and steel projectiles, it increased from 3km/s to 5km/s and decreased from 5km/s to 7km/s. It can-not be concluded as an essential behavior nor just a data scatter due to the lack of data.
Lan Sheng-wei et al. / Procedia Engineering 204 (2017) 329–336 Lan Sheng-wei et al./ Procedia Engineering 00 (2017) 000–000
334 6 140
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Fig. 5. Crater dimensions versus impact velocity and projectile density.
4.2. Influence of projectile density Fig.5c shows the dependence on projectile density. The crater diameter at 5km/s agreed well with the fit by Burchell (2001) [6], increasing with the projectile density in a power law. The crater diameter at 3km/s and 7km/s followed a similar way. The fitted relationships were
D 42.62 0.48 for 7 km/s D 40.03 0.41 for 5 km/s D 30.59 0.36 for 3 km/s
(4) (5)
(6) It can be found that the density exponents increased with the velocity increasing, indicating that the crater diameter would show more density dependence at higher impact velocity. The crater depth with the projectile density was shown in Fig. 5d. The crater depth increased with the projectile density but it did not agree with the fit by Burchell (2001) [6]. Since the depth at 3km/s showed an unusual scatter, just data at 5km/s and 7km/s were fitted. The density exponents of depth for both two velocities almost equaled to each other, and obviously higher than that of diameter. It may be induced that the projectile density affect crater depth more than diameter. 4.3. Influence of impact energy The crater diameter and volume versus the impact energy was plotted as Fig.6, combined with previous aluminum projectile data (Shrine, 2002) [9] and polycarbonate projectile data at low velocity (Lange, 1987) [7]. The
Lan Sheng-wei et al. / Procedia Engineering 204 (2017) 329–336 Author name / Procedia Engineering 00 (2017) 000–000
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crater volume showed a good agreement with the fit by Burchell (2005) [12]. This indicates an ‘energy scaling’ [13], which was compatible with many previous works. However, it can-not simply be assumed that the crater dimensions scale with the cubic-root energy. As shown in Fig.6b, the energy exponents of crater diameters for steel and aluminum projectiles were 0.36, nearly one third of volume-energy exponent (about 0.33). This is compatible with the diameter versus velocity relationship, indicating ‘energy scaling’. However, the exponent for polycarbonate projectiles was 0.17, just about half of 0.33. This implies that the velocity exponent for polycarbonate projectiles would be half of the exponent for steel/aluminum projectiles. Thus it means the crater diameter for polycarbonate projectile should show ‘momentum scaling’. 200
1000
U E1.01 0.08
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steel PC aluminum (shrine, 2002) PC (Lange, 1987) steel (Burchell, 1998/2005) fit by Burchell 2005
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steel pc pc (Lange,1987) aluminum(shrine, 2002) fit for aluminum (shrine, 2002) fit for present steel data fit for present PC data fit for pc data of Lange(1987)
D E 0.36 1
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Fig. 6. Scale crater diameter and crater volume with impact energy.
5. Conclusions Based on hypervelocity impacts with low and high density projectiles over velocity range 3 km/s to 7 km/s, the effect of projectile materials to ice crater behavior had been investigated. The crater size was affected by both projectile density and impact velocity. However, the influences of the two factors showed in different ways and mainly influenced different crater dimensions. It was found that crater diameter showed an increasing dependence on projectile density with the velocity increase, and the crater depth seemed more dependent on projectile density than crater diameter. This is well explained by the formation mechanism of impact craters, that is, the crater depth mainly caused by projectile penetration, while the crater diameter mainly caused by the wave propagation and material spallation. For the crater scaling, the crater diameter by high density projectile showed ‘energy scaling’ while the low density projectile was more like ‘momentum scaling’. Nevertheless all of the crater volumes by different projectiles were proportional with impact energy. These conclusions may be helpful to understand the geological characteristics of icy bodies, and could be used to analyse the formation of impact craters on icy surfaces. However, these conclusions were reached from a limited data set taken in the strength regime. More tests over a wider range of projectile densities and impact velocities should be carried out for further investigation. Acknowledgements This work was supported by the National Natural Science Foundation of China (NO. 41304138). The authors thank Mr. Li Wen-guang and Dr. Wang Ma-fa for the help in the ice impact tests. References [1] Croft, S. K., S. W. Kieffer, T. J. Ahrens. Low-velocity impact craters in ice and ice-saturated sand with implications for Martian crater count ages [J]. Journal of Geophysical Research, 1979, 84(B14): 8023–8032. [2] Croft S K. Hypervelocity impact craters in icy media[C]//Lunar and Planetary Science Conference. 1981, 12: 190-192.
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[3] Kawakami S I, Mizutani H, Takagi Y, et al. Impact experiments on ice [J]. Journal of Geophysical Research: Solid Earth, 1983, 88(B7): 5806-5814. [4] Cintala M J, Smrekar S, Horz F, et al. Impact experiments in H2O ice, I: cratering [C] // Lunar and Planetary Science Conference. 1985, 16: 131-132. [5] Lange M A, Ahrens T J. Impact experiments in low-temperature ice [J]. Icarus, 1987, 69(3): 506-518. [6] Burchell M J, Grey I D S, Shrine N R G. Laboratory investigations of hypervelocity impact cratering in ice [J]. Advances in Space Research, 2001, 28(10): 1521-1526. [7] Grey I D S, Burchell M J, Shrine N R G. Laboratory investigations of the temperature dependence of hypervelocity impact cratering in ice [J]. Advances in Space Research, 2001, 28(10): 1527-1532. [8] Grey I D S, Burchell M J, Shrine N R G. Scaling of hypervelocity impact craters in ice with impact angle [J]. Journal of Geophysical Research-Planets, 2002, 107(E10): 6-11. [9] Shrine N R G, Burchell M J, Grey I D S. Velocity Scaling of Impact Craters in Water Ice over the Range 1 to 7.3 km s− 1[J]. Icarus, 2002, 155(2): 475-485. [10] Grey I D S, Burchell M J. Hypervelocity impact cratering on water ice targets at temperatures ranging from 100 K to 253 K[J]. Journal of Geophysical Research (Planets), 2003, 108(E3): 5019. [11] M Kato, Y Iijima. Ice-on-ice impact experiments. Icarus, 1995, 113: 423-441 [12] Burchell M J, Johnson E. Impact craters on small icy bodies such as icy satellites and comet nuclei [J]. Monthly Notices of the Royal Astronomical Society, 2005, 360(2): 769-781. [13] K A Holsapple, R M Schmidt. On the scaling of crater dimensions 2. Impact Processes [J]. Journal of Geophysical Research, 1982, 87 (B3): 1849-1870