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Efficiency of needle structure at hypervelocity impact
Acta Astronautica xxx (2017) 1–8
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Efficiency of needle structure at hypervelocity impact Mikhail Silnikov a, Igor Guk a, *, Andrey Mikhaylin a, Alexey Nechunaev b a b
Special Materials Corp, St Petersburg, 194044, Russia St Petersburg State University, St Petersburg, 199034, Russia
A R T I C L E I N F O
A B S T R A C T
Keywords: Hypervelocity impact Spacecraft protection Heterogeneous structure Needle structure Nanowhiskers Smoothed particles hydrodynamics
The paper presents a numerical investigation of an efficiency of a needle structure at a hypervelocity impact with a spherical projectile. A modeling was performed using a smoothed particle hydrodynamics method implemented in Ansys/Ls-Dyna explicit software and a verified model. We investigated hypervelocity impacts of the spherical projectile with needle structure at different initial velocities in the range of 4190–9200 m/s and both normal and oblique impact angle. The investigations revealed efficiency of a needle structure in comparison with a solid structure of the same mass at a normal impact angle. It was shown that the character of hypervelocity impact of the spherical projectile with needle structure did not change qualitatively when the impact angle changed, and the needle structure preserved its capability to resist a hypervelocity impact.
1. Introduction Protective structures are developing fast based on advanced materials and various combinations and geometrical solutions of ceramic-carbides, nitrides, high-strength metal alloys (steel, titanium, aluminum), composite materials. Today a problem of developing new configurations of space vehicle protection against micrometeoroids and man-made debris is very important since the quantity of man-made space debris is constantly growing [1,2]. Whipple shields [3] and their modifications are widely used for space vehicle protection against hypervelocity impacts with micrometeoroids and man-made debris. “Stuffed Whipple” modification – a shield filled with various structures made of the wide spectrum of materials [4] – is used for the International Space Station protection. Whipple shields do not have any advantages over solid structures at relatively low impact velocities when even a partial melting of a projectile is not observed; it is less than 2.5 km/s for aluminum [5] or less than the ½ speed of sound in the material. This problem can be partially solved by using a great number of intermediate thin plates made of a ceramic fabric, a “multi-shock” shield [6].The multi-shock – thin, sequentially spaced plates designed for repetitive impacts with a projectile up to a high-energy state. Therefore, the projectile can melt and evaporate at velocities that usually do not cause such phenomena. Another serious disadvantage of Whipple shields is their size, for example, a thickness of a multi-shock shield can reach 15 cm and more, which is unacceptable for the ISS [7]. Since a lot of thin layers made of metal [8], fabric [9], ceramic [10] or
composite [11] materials. Some materials can be reinforced by nanotubes [12] in the form of flat sheets [13] or meshes [14] with various cell sizes [15], are used for protective structures. So, investigating the efficiency of volume structures at hypervelocity impacts is interesting. Thus, it is suggested to attenuate a projectile energy using spherical envelopes filled with the two-phase gas-liquid medium [16] and transforming this energy into a shock wave energy which intensity can be decreased by rarefaction waves [17]. The efficiency of «egg-box panels » structures [18] at hypervelocity impact is investigated as well as porous structures or foams made of various materials – aluminum [19, 20], ceramic [21] with the addition of a shear thickening liquid [22], «honeycomb » structures [23]. The structures above can be used for protection on their own [24] and as fillers for stuffed Whipple shields [25]. It is obvious, that full-scale experiments with various geometry and combinations of protective structures are very laborious, timeconsuming and expensive. A computational modeling is an efficient way of developing new geometries; it is free of safety regulations, allows investigating impacts at velocities that are impossible to achieve in fullscale experiments using gas cannons or railguns. Computational modeling can give information on various physical parameters in any point of the model at any discrete time step – on temperatures, pressures, velocities, strains, stresses. Numerical comparison of various geometry structures at identical initial conditions such as impact velocity, projectile size, and mass, impact angle, pressure, temperature is possible.
* Corresponding author. E-mail address: [email protected] (I. Guk). https://doi.org/10.1016/j.actaastro.2017.10.026 Received 4 October 2017; Accepted 19 October 2017 Available online xxxx 0094-5765/© 2017 IAA. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: M. Silnikov, et al., Efficiency of needle structure at hypervelocity impact, Acta Astronautica (2017), https://doi.org/ 10.1016/j.actaastro.2017.10.026
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Acta Astronautica xxx (2017) 1–8
2. Efficiency of needle structure at hypervelocity impact and comparison with monolithic shield
Table 1 Materials' constants and parameters.
As it was shown by previous experimental and theoretical studies of the depth of compact element penetration in shielding material, the effective metallic shield should be rather thick to withstand even mm sizing elements at an impact velocity of the order of 10 km/s [26]. The crater example with an equivalent metallic impactor placed in the crater after the experiment is shown in Fig. 1. The ruler with millimeter cuts on the right-hand side illustrates the scale. It is understandable that this type of shield though being reliable is too heavy for being used by a spacecraft. Perspective geometry being much lighter, that is capable of resisting hypervelocity impacts, is a needle structure– needle array on a thin backing plate. Such a structure can be investigated by computational modeling techniques. It is possible to perform numerically a series of calculations changing only one key parameter, for example, impact angle, preserve invariable all other boundary and initial conditions, and based on this calculation conclude efficiency of a given configuration. The modeling was performed using smoothed particles hydrodynamics method implemented in Ansys/Ls-Dyna explicit software [27,28]. Efficiency and adequacy of this method for solving hypervelocity impact problems have been proved before [29–31]. Jonson- Cook equations of plasticity and failure (*MAT_JOHNSON_COOK) supplemented by MieGruneisen and linear polynomial equations of state (*EOS_GRUNEISEN, *EOS_LINEAR_POLYNOMIAL) [32] were used to describe the behavior of a needle structure and a projectile. Constants and materials' parameters, Table1–3 had been verified before [33] in comparison with the known full-scale experiment [34], in which the hypervelocity impact of the spherical projectile with thin plate had been investigated. In the verified calculation [33] the diameter and the thickness of the debris cloud, the velocities of their propagation, the distribution of the projectile and the plate particles in the debris cloud, and all their key characteristics coincided with the experimental data with good accuracy. It shows correctness and adequacy of the chosen parameters, method, and approach. The needle structure is an array of equidistant, mutually parallel rows of needles on a flat backing plate. An angle between each needle and the backing plate is 90 . The considered needle structure consists of a backing plate of 3.1 mm thickness and 51 51array of needles of 50 mm length each. A needle diameter is 0.31 mm, a distance between needles is 0.31 mm 2601 needles all in all in the array. The needles and the backing plate are made of Al-6061-T6. The surface density of this structure is 35.96 kg/m2 - the total surface density of the needles is 27.33 kg/m2, the surface density of the backing plate is 8.63 kg/m2. To estimate the efficiency of the above-described structure at a hypervelocity impact, its impact with a spherical projectile made of Al1100, 5-mm diameter at a normal angle to the backing plate and different velocities was investigated. We calculated impacts at initial projectile velocities of 6200 m/s, 7200 m/s, 8200 m/s, 8500 m/s and 9200 m/s.
Parameter
Unit
Al-1100
Al-6061-T6
Density, ρ Shear modulus, G Yield stress, A Material hardening, B Strain hardening, n Johnson-Cook constant, c Thermal softening, m Testing temperature Melting temperature Testing strain rate Specific heat capacity, Cp
kg/m3 Pa Pa Pa
2770 25.9 109 4.1 107 1.25 108 0.183 0.001 0.859 293 893 1 910
2770 25 109 3.241 108 1.138 108 0.42 0.002 1.34 293 893 1 910
0.071
0.77
1.248 1.142 0.0097 0
1.45 0.47 0 1.6
K K 1/s J/(kg K kg K)
Coefficients in the Johnson-Cook destruction model, D1 D2 D3 D4 D5
Table 2 Linear polynomial equation of state coefficients. Material
C0
C1, GPa
C2, GPa
C3, GPa
C4
C5
C6
E0
V0
Al-1100
0
74.2
60.5
36.5
1.96
0
0
0
1
Table 3 Mie-Gruneisen equation of state coefficients. Material
C, m/s
S1
S2
S3
a
E0
Γ0
V0
Al-6061-T6
3935
1.578
0
0
0
0
1.69
1
The cross-section of the model is given in Fig. 2. The needles, backing plate, and the sphere are divided into identical particles of 0.31 mm diameter. The diameter of one particle coincides with the needle diameter. The backing plate is divided into ten particles on its thickness, and the spherical projectile – into 16 particles on its diameter. The backing plate is fixed rigidly at four sides. The impact occurs in an absolute vacuum. Figs. 3.1, 3.2, 3.3 represent pairs of sequential images, at 0 μs, 6 μs, and 80 μs after the impact, of 5-mm diameter spherical projectile propagation through the needle structure at 8200 m/s and 9200 m/s initial velocity. The palette shows the ratio between the particles color and their velocities along Y axis in the direction, perpendicular to the backing plate. Our calculations show that considered needle structure successfully withstands hypervelocity impacts with a spherical projectile at a
Fig. 1. Cross section of the experimental steel shield after being impacted by a 2.5 mm element [26].
Fig. 2. Cross section of the model. 2
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Fig. 3.1. Initial state, 0 μs. (a) – initial projectile velocity is 8200 m/s, (b) – initial projectile velocity is 9200 m/s.
Fig. 3.2. Propagation of the projectile through the needle structure. 6 μs after the impact. (a) – initial projectile velocity is 8200 m/s, (b) – initial projectile velocity is 9200 m/s.
backing plate on axis Y. It reveals that in 25 μs after the impact the shock wave caused by projectile movement reaches the backing plate, deforms it and cause its oscillations on axis Y with maximum velocity up to 105 m/s. After 35–40 μs backing plate interacts with secondary debris cloud. After 80 μs the main part of the secondary debris is fully stopped, and the backing plate begins to elastic recovery. The investigated needle
normal angle at velocities 6200 m/s, 7200 m/s and 8200 m/s. At an initial projectile velocity of 9200 m/s back surface of backing plate suffered damage – some longitudinal cracks were found after the main part of secondary debris, formed as a result of the interaction of spherical projectile with needle structure, hit the backing plate. The diagram (Fig. 4.1) shows back surface particles' velocities of the
Fig. 3.3. Propagation of the projectile through the needle structure. 80 μs after the impact. (a) – initial projectile velocity is 8200 m/s, (b) – initial projectile velocity is 9200 m/s. 3
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Fig. 4.2. Group diagram back surface particles' velocity of backing plate. Initial projectile velocity is 9200 m/s.
surface density of considered needle structure is 35.96 kg/m2. The relation between the solid shield surface density and the needle structure surface density reveals that the aluminum needle structure is 3–4 times more efficient by weight than the solid aluminum shield.
Fig. 4.1. Group diagram back surface particles' velocity of backing plate. Initial projectile velocity is 8200 m/s.
structure successfully withstood the impact with the 5 mm diameter projectile at 8200 m/s initial velocity. When initial projectile velocity is 9200 m/s, the interaction of projectile with needle structure is qualitatively the same (Fig. 4.2). The shock wave traveling along the needles from moving projectile also causes oscillations on axis Y of the backing shield with maximum velocity up to 120 m/s in 25 μs after the impact. These initial oscillations are followed by oscillations up to 90 m/s in 35–80 μs, which are caused by the secondary debris. However, elastic recovery of the backing shield does not occur, and longitudinal cracks on the back surface of the backing shield are formed. Further clarifying calculations show that the maximum impact velocity of the spherical aluminum projectile with 5-mm diameter at a normal angle that considered needle structure can withstand, so no perforation is observed and back surface of the backing plate remains undamaged, is 8500 m/s. For being used in space vehicle's protective systems, the needle structure, apart from its capability to withstand hypervelocity impacts with a projectile, is to have advantage in its mass over a solid, monolithic shield made of the same material. To evaluate the thickness of aluminum monolithic protective shield, which is capable of withstanding hypervelocity impact of the spherical projectile with 5-mm diameter and 8500 m/s initial velocity, well-known empirical equation was used [5]. The penetration depth into a semi-infinite target, when projectile and target density is almost the same, is:
P ¼ 5:24d 19=18 H 0:25
2=3 2=3 ρp V C ρt
3. Comparison of efficiency of needle structure at normal and oblique impact The scenario described above is degenerate because the angle of impact is 90 to the backing plate surface. To find out if this needle structure preserves its efficiency at an angle different from the normal, let us compare normal hypervelocity impact of a spherical projectile with oblique hypervelocity impact of the spherical projectile with aforementioned needle structure. Two scenarios were investigated – an impact at normal to the backing plate surface angle and an impact at 5-degree angle to the surface normal (or 85 to the surface of the backing plate). Fig. 5a and b presents a general view of the problem. The calculations reveal that the investigated needle structure successfully withstand both oblique and normal hypervelocity impacts. Figs. 6.1–6.6. (a,b) present the calculation results – images of the projectile interaction with the needle structure at the same moments of time– from 0 to 80 μs after the impact. At first, we consider an impact at a normal angle to the surface. Figs. 6.1–6.6 present images of the needle structure interaction with the spherical projectile and formation of a secondary debris cloud propagating through the structure. The palette shows the ratio between the particles color and their velocities along Y axis (in the direction, perpendicular to the backing plate). At the very beginning of the propagation, when the projectile is interacting with the needles at a velocity exceeding a shock wave propagation velocity, the shock wave does not propagate through the needles, since the needles have been destroyed before the shock wave is formed. With some time, as the mutual destruction of the needles and the projectile occurs, the projectile velocity decreases. At 10 μs moment of time the shock wave propagating through the needles begins overrunning the projectile particles, and in 24 μs after the impact, the shock wave reaches the backing plate. By that moment of time, the projectile particles have moved forward to 4\7 needle length inside the structure. After that the shock wave propagates through the thickness of the backing plate and in 25 μs, it reaches the back surface of the backing plate. Then the shock wave is reflected from the back surface, in 26 μs it interferes with a shock wave propagating through the needles (shock waves caused by the projectile motion), the wave in the backing plate begins propagating to the backing plate edges (29 μs). The maximum load intensity of the backing plate is observed in the center, on the impact axis, which causes its insignificant plastic deformation. The back surface of the backing plate bugles to 1.5 mm in the line of the projectile trajectory (34 μs). At 80 μs debris resulted from the projectile and needles destruction form an elongated across cloud
(1)
where d – projectile diameter, H – Brinell hardness, ρp – projectile density, ρt – monolithic shield density, V – initial projectile velocity, C – speed of sound. Even when there is no target perforation, some damage to the back surface of the monolithic shield is possible – spallation, for example. To estimate needle structure advantage over the solid shield, we calculated monolithic shield thickness sufficient to prevent the eruption of the material from the back surface of the backing plate, since in our calculation maximum impact velocity was evaluated so that there is no damage to the back surface of the backing plate was observed. Plate thickness to prevent perforation and detached spall can be estimated as 2.2 P, and plate thickness to prevent perforation and incipient spall can be estimated as 3 P. Thus, a minimum thickness of a solid Al-6061-T6 structure required for complete cessation of a 5-mm diameter spherical Al-1100 projectile with 8500 m/s initial velocity is 3.9–5.3 cm, which means that the working surface density of the solid shield is 107.25–145.75 kg/m2. As it was mentioned previously, the working 4
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Fig. 5. Side view of the model. (a) – normal impact, (b) – oblique impact.
Fig. 6.1. Initial state, 0 μs. (a) – normal impact at 4190 m/s, (b) – oblique impact (5 to the normal) at 4190 m/s.
At oblique impact, 5 to the normal (Figs. 6.1–6.6 (b)), the spherical projectile/needle structure interaction picture is qualitatively similar to the picture of the normal impact. The secondary debris cloud is propagating through the needle structure towards the backing plate with insignificant deviation on Z axis. Approximately in 80 μs some particles get out of the side surface of the needles.
with a small leading group. The leading group is at about 5 mm distance from the backing plate, which is about 10% of the initial length of the needles. The main group of the debris is at 8 mm distance or 15% of the initial length of the needles. As that takes place, the maximum velocity of the particles does not exceed 218 m/s or 5% of the initial velocity of the projectile.
Fig. 6.2. Images of projectile propagation through the needle structure, 6 μs after the impact. (a) – normal impact at 4190 m/s, (b) – oblique impact (5 to the normal) at 4190 m/s. 5
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Fig. 6.3. Images of projectile propagation through the needle structure, 10 μs after the impact. (a) – normal impact at 4190 m/s, (b) – oblique impact (5 to the normal) at 4190 m/s.
Fig. 6.4. Images of projectile propagation through the needle structure. (a) – normal impact at 4190 m/s, 25 μs after the impact, (b) – oblique impact, 25.14 μs after the impact (5 to the normal) at 4190 m/s.
Practically at the same moment of time (10 μs) as it is for the normal impact, the shock wave begins overrunning the projectile and propagating through the needles. However, the shock wave reaches the backing plate several tenth fractions of microseconds later because the
initial velocity component on axis Y is slightly smaller for the oblique impact4174 m/s, and for the normal impact it is 4190 m/s. At 80 μs the secondary debris cloud is asymmetrical about the impact axis. The leading group is practically not seen. The group of particles
Fig. 6.5. Images of projectile propagation through the needle structure. (a) – normal impact at 4190 m/s, 25.14 μs after the impact, (b) – oblique impact, 25.29 μs after the impact (5 to the normal) at 4190 m/s. 6
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Fig. 6.6. Images of projectile propagation through the needle structure, 80 μs after the impact. (a) – normal impact at 4190 m/s, (b) – oblique impact (5 to the normal) at 4190 m/s.
5. Conclusion
propagating towards the backing plate is extended in the direction parallel to the backing plate plane at 10 mm distance or 20% of the initial length of the needles.
We have investigated the efficiency of a needle protective structure at a hypervelocity impact with a spherical projectile and showed that it was efficient at a normal impact. We have established that needle structure, made of Al-6061-T6, consisting of 3.1 mm thickness backing shield and an array of needles with a length of 50 mm, diameter 0.31 mm distance between needles of 0.31 mm, can withstand a hypervelocity impact of 5mm diameter spherical Al-1100 projectile at velocities up to 8500 m/s. In comparison with a solid monolithic protective structure of the same material, the considered needle structure was 3–4 times lighter. It was found that removal of the extinction5 deviation of the projectile velocity vector from the normal – the impact results did not change qualitatively and the needle structure preserved its capability to withstand hypervelocity impacts.
4. Discussion Comparison of pairs of images obtained at the normal impact and at 5 impact (images that illustrate propagation of the projectile particles, the particles of destructed needles, shock propagation characters in destructed needles and the backing plate) reveals a qualitative similarity of these two cases. The axial symmetry removal and the extinction along Y-axis do not seriously affect the interaction between a hypervelocity projectile and the needle structure. The images of shock wave propagation in the needles and the backing plate, the initial velocity/moment velocity ratios at the same moments of time, formation of secondary debris clouds are similar in both cases in the accuracy of the velocities' relation on the Y axis. The needle structure is efficient in the normal impact case and the oblique impact case. Insignificant quantitative differences in time of the shock wave approach to the backing plate, asymmetrical propagation of the debris resulted from the projectile, and destructed needles in the structure are explained by the sphere velocity vector component on Z axis in the case of 5 impact. The needle structure investigated is a simplified model made of polycrystalline aluminum for which a numerical model has been verified. That material possesses comparatively low strength characteristics. For example, the ultimate stress of Al-6061-T6 alloy is only 310 MPa. A perspective material for the needle structure is alumina nanowhiskers [35]. Nanowhiskers are a variety of a thread-like crystal with a cross-section diameter of μs order and a length/diameter ratio more than 100, sometimes even more than 107 [36]. Nanowhiskers possess crystallographic anisotropy characteristics and practically do not have dislocations or defects. This excludes usual mechanisms of plastic deformation and brings the strength of the needle structure made on the base of nanowhiskers to the theoretical limit for material they are made of. Nanowhiskers can be made, for example, by a molecular beam epitaxy method [37], chemical liquid deposition [38], etc. The ultimate stress of pure alumina can reach 1500 MPa, which is five times higher than of the investigated aluminum alloy. The melting temperature of alumina is 2050C, and it preserves its strength characteristics at 1800 C [39], it is two times higher than that of aluminum. It means that in case of interaction of alumina nanowhiskers with aluminum particles and space debris the aluminum particle is melted, but the alumina needles preserve their solid state and strength characteristics. Further improvement for such protective structure could be toughening of nanowhiskers by graphene covering [40].
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Efficiency of needle structure at hypervelocity impact Mikhail Silnikov a, Igor Guk a, *, Andrey Mikhaylin a, Alexey Nechunaev b a b
Special Materials Corp, St Petersburg, 194044, Russia St Petersburg State University, St Petersburg, 199034, Russia
A R T I C L E I N F O
A B S T R A C T
Keywords: Hypervelocity impact Spacecraft protection Heterogeneous structure Needle structure Nanowhiskers Smoothed particles hydrodynamics
The paper presents a numerical investigation of an efficiency of a needle structure at a hypervelocity impact with a spherical projectile. A modeling was performed using a smoothed particle hydrodynamics method implemented in Ansys/Ls-Dyna explicit software and a verified model. We investigated hypervelocity impacts of the spherical projectile with needle structure at different initial velocities in the range of 4190–9200 m/s and both normal and oblique impact angle. The investigations revealed efficiency of a needle structure in comparison with a solid structure of the same mass at a normal impact angle. It was shown that the character of hypervelocity impact of the spherical projectile with needle structure did not change qualitatively when the impact angle changed, and the needle structure preserved its capability to resist a hypervelocity impact.
1. Introduction Protective structures are developing fast based on advanced materials and various combinations and geometrical solutions of ceramic-carbides, nitrides, high-strength metal alloys (steel, titanium, aluminum), composite materials. Today a problem of developing new configurations of space vehicle protection against micrometeoroids and man-made debris is very important since the quantity of man-made space debris is constantly growing [1,2]. Whipple shields [3] and their modifications are widely used for space vehicle protection against hypervelocity impacts with micrometeoroids and man-made debris. “Stuffed Whipple” modification – a shield filled with various structures made of the wide spectrum of materials [4] – is used for the International Space Station protection. Whipple shields do not have any advantages over solid structures at relatively low impact velocities when even a partial melting of a projectile is not observed; it is less than 2.5 km/s for aluminum [5] or less than the ½ speed of sound in the material. This problem can be partially solved by using a great number of intermediate thin plates made of a ceramic fabric, a “multi-shock” shield [6].The multi-shock – thin, sequentially spaced plates designed for repetitive impacts with a projectile up to a high-energy state. Therefore, the projectile can melt and evaporate at velocities that usually do not cause such phenomena. Another serious disadvantage of Whipple shields is their size, for example, a thickness of a multi-shock shield can reach 15 cm and more, which is unacceptable for the ISS [7]. Since a lot of thin layers made of metal [8], fabric [9], ceramic [10] or
composite [11] materials. Some materials can be reinforced by nanotubes [12] in the form of flat sheets [13] or meshes [14] with various cell sizes [15], are used for protective structures. So, investigating the efficiency of volume structures at hypervelocity impacts is interesting. Thus, it is suggested to attenuate a projectile energy using spherical envelopes filled with the two-phase gas-liquid medium [16] and transforming this energy into a shock wave energy which intensity can be decreased by rarefaction waves [17]. The efficiency of «egg-box panels » structures [18] at hypervelocity impact is investigated as well as porous structures or foams made of various materials – aluminum [19, 20], ceramic [21] with the addition of a shear thickening liquid [22], «honeycomb » structures [23]. The structures above can be used for protection on their own [24] and as fillers for stuffed Whipple shields [25]. It is obvious, that full-scale experiments with various geometry and combinations of protective structures are very laborious, timeconsuming and expensive. A computational modeling is an efficient way of developing new geometries; it is free of safety regulations, allows investigating impacts at velocities that are impossible to achieve in fullscale experiments using gas cannons or railguns. Computational modeling can give information on various physical parameters in any point of the model at any discrete time step – on temperatures, pressures, velocities, strains, stresses. Numerical comparison of various geometry structures at identical initial conditions such as impact velocity, projectile size, and mass, impact angle, pressure, temperature is possible.
* Corresponding author. E-mail address: [email protected] (I. Guk). https://doi.org/10.1016/j.actaastro.2017.10.026 Received 4 October 2017; Accepted 19 October 2017 Available online xxxx 0094-5765/© 2017 IAA. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: M. Silnikov, et al., Efficiency of needle structure at hypervelocity impact, Acta Astronautica (2017), https://doi.org/ 10.1016/j.actaastro.2017.10.026
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2. Efficiency of needle structure at hypervelocity impact and comparison with monolithic shield
Table 1 Materials' constants and parameters.
As it was shown by previous experimental and theoretical studies of the depth of compact element penetration in shielding material, the effective metallic shield should be rather thick to withstand even mm sizing elements at an impact velocity of the order of 10 km/s [26]. The crater example with an equivalent metallic impactor placed in the crater after the experiment is shown in Fig. 1. The ruler with millimeter cuts on the right-hand side illustrates the scale. It is understandable that this type of shield though being reliable is too heavy for being used by a spacecraft. Perspective geometry being much lighter, that is capable of resisting hypervelocity impacts, is a needle structure– needle array on a thin backing plate. Such a structure can be investigated by computational modeling techniques. It is possible to perform numerically a series of calculations changing only one key parameter, for example, impact angle, preserve invariable all other boundary and initial conditions, and based on this calculation conclude efficiency of a given configuration. The modeling was performed using smoothed particles hydrodynamics method implemented in Ansys/Ls-Dyna explicit software [27,28]. Efficiency and adequacy of this method for solving hypervelocity impact problems have been proved before [29–31]. Jonson- Cook equations of plasticity and failure (*MAT_JOHNSON_COOK) supplemented by MieGruneisen and linear polynomial equations of state (*EOS_GRUNEISEN, *EOS_LINEAR_POLYNOMIAL) [32] were used to describe the behavior of a needle structure and a projectile. Constants and materials' parameters, Table1–3 had been verified before [33] in comparison with the known full-scale experiment [34], in which the hypervelocity impact of the spherical projectile with thin plate had been investigated. In the verified calculation [33] the diameter and the thickness of the debris cloud, the velocities of their propagation, the distribution of the projectile and the plate particles in the debris cloud, and all their key characteristics coincided with the experimental data with good accuracy. It shows correctness and adequacy of the chosen parameters, method, and approach. The needle structure is an array of equidistant, mutually parallel rows of needles on a flat backing plate. An angle between each needle and the backing plate is 90 . The considered needle structure consists of a backing plate of 3.1 mm thickness and 51 51array of needles of 50 mm length each. A needle diameter is 0.31 mm, a distance between needles is 0.31 mm 2601 needles all in all in the array. The needles and the backing plate are made of Al-6061-T6. The surface density of this structure is 35.96 kg/m2 - the total surface density of the needles is 27.33 kg/m2, the surface density of the backing plate is 8.63 kg/m2. To estimate the efficiency of the above-described structure at a hypervelocity impact, its impact with a spherical projectile made of Al1100, 5-mm diameter at a normal angle to the backing plate and different velocities was investigated. We calculated impacts at initial projectile velocities of 6200 m/s, 7200 m/s, 8200 m/s, 8500 m/s and 9200 m/s.
Parameter
Unit
Al-1100
Al-6061-T6
Density, ρ Shear modulus, G Yield stress, A Material hardening, B Strain hardening, n Johnson-Cook constant, c Thermal softening, m Testing temperature Melting temperature Testing strain rate Specific heat capacity, Cp
kg/m3 Pa Pa Pa
2770 25.9 109 4.1 107 1.25 108 0.183 0.001 0.859 293 893 1 910
2770 25 109 3.241 108 1.138 108 0.42 0.002 1.34 293 893 1 910
0.071
0.77
1.248 1.142 0.0097 0
1.45 0.47 0 1.6
K K 1/s J/(kg K kg K)
Coefficients in the Johnson-Cook destruction model, D1 D2 D3 D4 D5
Table 2 Linear polynomial equation of state coefficients. Material
C0
C1, GPa
C2, GPa
C3, GPa
C4
C5
C6
E0
V0
Al-1100
0
74.2
60.5
36.5
1.96
0
0
0
1
Table 3 Mie-Gruneisen equation of state coefficients. Material
C, m/s
S1
S2
S3
a
E0
Γ0
V0
Al-6061-T6
3935
1.578
0
0
0
0
1.69
1
The cross-section of the model is given in Fig. 2. The needles, backing plate, and the sphere are divided into identical particles of 0.31 mm diameter. The diameter of one particle coincides with the needle diameter. The backing plate is divided into ten particles on its thickness, and the spherical projectile – into 16 particles on its diameter. The backing plate is fixed rigidly at four sides. The impact occurs in an absolute vacuum. Figs. 3.1, 3.2, 3.3 represent pairs of sequential images, at 0 μs, 6 μs, and 80 μs after the impact, of 5-mm diameter spherical projectile propagation through the needle structure at 8200 m/s and 9200 m/s initial velocity. The palette shows the ratio between the particles color and their velocities along Y axis in the direction, perpendicular to the backing plate. Our calculations show that considered needle structure successfully withstands hypervelocity impacts with a spherical projectile at a
Fig. 1. Cross section of the experimental steel shield after being impacted by a 2.5 mm element [26].
Fig. 2. Cross section of the model. 2
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Fig. 3.1. Initial state, 0 μs. (a) – initial projectile velocity is 8200 m/s, (b) – initial projectile velocity is 9200 m/s.
Fig. 3.2. Propagation of the projectile through the needle structure. 6 μs after the impact. (a) – initial projectile velocity is 8200 m/s, (b) – initial projectile velocity is 9200 m/s.
backing plate on axis Y. It reveals that in 25 μs after the impact the shock wave caused by projectile movement reaches the backing plate, deforms it and cause its oscillations on axis Y with maximum velocity up to 105 m/s. After 35–40 μs backing plate interacts with secondary debris cloud. After 80 μs the main part of the secondary debris is fully stopped, and the backing plate begins to elastic recovery. The investigated needle
normal angle at velocities 6200 m/s, 7200 m/s and 8200 m/s. At an initial projectile velocity of 9200 m/s back surface of backing plate suffered damage – some longitudinal cracks were found after the main part of secondary debris, formed as a result of the interaction of spherical projectile with needle structure, hit the backing plate. The diagram (Fig. 4.1) shows back surface particles' velocities of the
Fig. 3.3. Propagation of the projectile through the needle structure. 80 μs after the impact. (a) – initial projectile velocity is 8200 m/s, (b) – initial projectile velocity is 9200 m/s. 3
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Fig. 4.2. Group diagram back surface particles' velocity of backing plate. Initial projectile velocity is 9200 m/s.
surface density of considered needle structure is 35.96 kg/m2. The relation between the solid shield surface density and the needle structure surface density reveals that the aluminum needle structure is 3–4 times more efficient by weight than the solid aluminum shield.
Fig. 4.1. Group diagram back surface particles' velocity of backing plate. Initial projectile velocity is 8200 m/s.
structure successfully withstood the impact with the 5 mm diameter projectile at 8200 m/s initial velocity. When initial projectile velocity is 9200 m/s, the interaction of projectile with needle structure is qualitatively the same (Fig. 4.2). The shock wave traveling along the needles from moving projectile also causes oscillations on axis Y of the backing shield with maximum velocity up to 120 m/s in 25 μs after the impact. These initial oscillations are followed by oscillations up to 90 m/s in 35–80 μs, which are caused by the secondary debris. However, elastic recovery of the backing shield does not occur, and longitudinal cracks on the back surface of the backing shield are formed. Further clarifying calculations show that the maximum impact velocity of the spherical aluminum projectile with 5-mm diameter at a normal angle that considered needle structure can withstand, so no perforation is observed and back surface of the backing plate remains undamaged, is 8500 m/s. For being used in space vehicle's protective systems, the needle structure, apart from its capability to withstand hypervelocity impacts with a projectile, is to have advantage in its mass over a solid, monolithic shield made of the same material. To evaluate the thickness of aluminum monolithic protective shield, which is capable of withstanding hypervelocity impact of the spherical projectile with 5-mm diameter and 8500 m/s initial velocity, well-known empirical equation was used [5]. The penetration depth into a semi-infinite target, when projectile and target density is almost the same, is:
P ¼ 5:24d 19=18 H 0:25
2=3 2=3 ρp V C ρt
3. Comparison of efficiency of needle structure at normal and oblique impact The scenario described above is degenerate because the angle of impact is 90 to the backing plate surface. To find out if this needle structure preserves its efficiency at an angle different from the normal, let us compare normal hypervelocity impact of a spherical projectile with oblique hypervelocity impact of the spherical projectile with aforementioned needle structure. Two scenarios were investigated – an impact at normal to the backing plate surface angle and an impact at 5-degree angle to the surface normal (or 85 to the surface of the backing plate). Fig. 5a and b presents a general view of the problem. The calculations reveal that the investigated needle structure successfully withstand both oblique and normal hypervelocity impacts. Figs. 6.1–6.6. (a,b) present the calculation results – images of the projectile interaction with the needle structure at the same moments of time– from 0 to 80 μs after the impact. At first, we consider an impact at a normal angle to the surface. Figs. 6.1–6.6 present images of the needle structure interaction with the spherical projectile and formation of a secondary debris cloud propagating through the structure. The palette shows the ratio between the particles color and their velocities along Y axis (in the direction, perpendicular to the backing plate). At the very beginning of the propagation, when the projectile is interacting with the needles at a velocity exceeding a shock wave propagation velocity, the shock wave does not propagate through the needles, since the needles have been destroyed before the shock wave is formed. With some time, as the mutual destruction of the needles and the projectile occurs, the projectile velocity decreases. At 10 μs moment of time the shock wave propagating through the needles begins overrunning the projectile particles, and in 24 μs after the impact, the shock wave reaches the backing plate. By that moment of time, the projectile particles have moved forward to 4\7 needle length inside the structure. After that the shock wave propagates through the thickness of the backing plate and in 25 μs, it reaches the back surface of the backing plate. Then the shock wave is reflected from the back surface, in 26 μs it interferes with a shock wave propagating through the needles (shock waves caused by the projectile motion), the wave in the backing plate begins propagating to the backing plate edges (29 μs). The maximum load intensity of the backing plate is observed in the center, on the impact axis, which causes its insignificant plastic deformation. The back surface of the backing plate bugles to 1.5 mm in the line of the projectile trajectory (34 μs). At 80 μs debris resulted from the projectile and needles destruction form an elongated across cloud
(1)
where d – projectile diameter, H – Brinell hardness, ρp – projectile density, ρt – monolithic shield density, V – initial projectile velocity, C – speed of sound. Even when there is no target perforation, some damage to the back surface of the monolithic shield is possible – spallation, for example. To estimate needle structure advantage over the solid shield, we calculated monolithic shield thickness sufficient to prevent the eruption of the material from the back surface of the backing plate, since in our calculation maximum impact velocity was evaluated so that there is no damage to the back surface of the backing plate was observed. Plate thickness to prevent perforation and detached spall can be estimated as 2.2 P, and plate thickness to prevent perforation and incipient spall can be estimated as 3 P. Thus, a minimum thickness of a solid Al-6061-T6 structure required for complete cessation of a 5-mm diameter spherical Al-1100 projectile with 8500 m/s initial velocity is 3.9–5.3 cm, which means that the working surface density of the solid shield is 107.25–145.75 kg/m2. As it was mentioned previously, the working 4
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Fig. 5. Side view of the model. (a) – normal impact, (b) – oblique impact.
Fig. 6.1. Initial state, 0 μs. (a) – normal impact at 4190 m/s, (b) – oblique impact (5 to the normal) at 4190 m/s.
At oblique impact, 5 to the normal (Figs. 6.1–6.6 (b)), the spherical projectile/needle structure interaction picture is qualitatively similar to the picture of the normal impact. The secondary debris cloud is propagating through the needle structure towards the backing plate with insignificant deviation on Z axis. Approximately in 80 μs some particles get out of the side surface of the needles.
with a small leading group. The leading group is at about 5 mm distance from the backing plate, which is about 10% of the initial length of the needles. The main group of the debris is at 8 mm distance or 15% of the initial length of the needles. As that takes place, the maximum velocity of the particles does not exceed 218 m/s or 5% of the initial velocity of the projectile.
Fig. 6.2. Images of projectile propagation through the needle structure, 6 μs after the impact. (a) – normal impact at 4190 m/s, (b) – oblique impact (5 to the normal) at 4190 m/s. 5
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Fig. 6.3. Images of projectile propagation through the needle structure, 10 μs after the impact. (a) – normal impact at 4190 m/s, (b) – oblique impact (5 to the normal) at 4190 m/s.
Fig. 6.4. Images of projectile propagation through the needle structure. (a) – normal impact at 4190 m/s, 25 μs after the impact, (b) – oblique impact, 25.14 μs after the impact (5 to the normal) at 4190 m/s.
Practically at the same moment of time (10 μs) as it is for the normal impact, the shock wave begins overrunning the projectile and propagating through the needles. However, the shock wave reaches the backing plate several tenth fractions of microseconds later because the
initial velocity component on axis Y is slightly smaller for the oblique impact4174 m/s, and for the normal impact it is 4190 m/s. At 80 μs the secondary debris cloud is asymmetrical about the impact axis. The leading group is practically not seen. The group of particles
Fig. 6.5. Images of projectile propagation through the needle structure. (a) – normal impact at 4190 m/s, 25.14 μs after the impact, (b) – oblique impact, 25.29 μs after the impact (5 to the normal) at 4190 m/s. 6
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Fig. 6.6. Images of projectile propagation through the needle structure, 80 μs after the impact. (a) – normal impact at 4190 m/s, (b) – oblique impact (5 to the normal) at 4190 m/s.
5. Conclusion
propagating towards the backing plate is extended in the direction parallel to the backing plate plane at 10 mm distance or 20% of the initial length of the needles.
We have investigated the efficiency of a needle protective structure at a hypervelocity impact with a spherical projectile and showed that it was efficient at a normal impact. We have established that needle structure, made of Al-6061-T6, consisting of 3.1 mm thickness backing shield and an array of needles with a length of 50 mm, diameter 0.31 mm distance between needles of 0.31 mm, can withstand a hypervelocity impact of 5mm diameter spherical Al-1100 projectile at velocities up to 8500 m/s. In comparison with a solid monolithic protective structure of the same material, the considered needle structure was 3–4 times lighter. It was found that removal of the extinction5 deviation of the projectile velocity vector from the normal – the impact results did not change qualitatively and the needle structure preserved its capability to withstand hypervelocity impacts.
4. Discussion Comparison of pairs of images obtained at the normal impact and at 5 impact (images that illustrate propagation of the projectile particles, the particles of destructed needles, shock propagation characters in destructed needles and the backing plate) reveals a qualitative similarity of these two cases. The axial symmetry removal and the extinction along Y-axis do not seriously affect the interaction between a hypervelocity projectile and the needle structure. The images of shock wave propagation in the needles and the backing plate, the initial velocity/moment velocity ratios at the same moments of time, formation of secondary debris clouds are similar in both cases in the accuracy of the velocities' relation on the Y axis. The needle structure is efficient in the normal impact case and the oblique impact case. Insignificant quantitative differences in time of the shock wave approach to the backing plate, asymmetrical propagation of the debris resulted from the projectile, and destructed needles in the structure are explained by the sphere velocity vector component on Z axis in the case of 5 impact. The needle structure investigated is a simplified model made of polycrystalline aluminum for which a numerical model has been verified. That material possesses comparatively low strength characteristics. For example, the ultimate stress of Al-6061-T6 alloy is only 310 MPa. A perspective material for the needle structure is alumina nanowhiskers [35]. Nanowhiskers are a variety of a thread-like crystal with a cross-section diameter of μs order and a length/diameter ratio more than 100, sometimes even more than 107 [36]. Nanowhiskers possess crystallographic anisotropy characteristics and practically do not have dislocations or defects. This excludes usual mechanisms of plastic deformation and brings the strength of the needle structure made on the base of nanowhiskers to the theoretical limit for material they are made of. Nanowhiskers can be made, for example, by a molecular beam epitaxy method [37], chemical liquid deposition [38], etc. The ultimate stress of pure alumina can reach 1500 MPa, which is five times higher than of the investigated aluminum alloy. The melting temperature of alumina is 2050C, and it preserves its strength characteristics at 1800 C [39], it is two times higher than that of aluminum. It means that in case of interaction of alumina nanowhiskers with aluminum particles and space debris the aluminum particle is melted, but the alumina needles preserve their solid state and strength characteristics. Further improvement for such protective structure could be toughening of nanowhiskers by graphene covering [40].
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