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Atomistic-scale simulations of mechanical behavior of suspended single-walled carbon nanotube bundles under nanoprojectile impact
Computational Materials Science 142 (2018) 237–243
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Atomistic-scale simulations of mechanical behavior of suspended single-walled carbon nanotube bundles under nanoprojectile impact Dongrong Liu a,1, Lin Yang b,c,⇑,1, Xiaodong He b, Rongguo Wang b, Quantian Luo c a
School of Materials Science and Engineering, Harbin University of Science and Technology, Harbin 150040, China Centre for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, China c School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia b
a r t i c l e
i n f o
Article history: Received 10 July 2017 Received in revised form 1 October 2017 Accepted 9 October 2017
Keywords: Mechanical behavior Carbon nanotube Molecular dynamic simulation
a b s t r a c t Carbon nanotube fiber (CNTF) is generally considered a strong candidate for the fabrication of bulletresistant vests due to its excellent combination of extremely high elastic modulus, high yield strain, low density, super toughness, as well as good flexibility. CNTF may also provide effective dissipation of impact energy through fibrillation within the CNTF and through disintegration of the CNTF. In this study, molecular dynamic (MD) simulations are performed to investigate the nanoprojectile impact on suspended single-walled carbon nanotube (SWCNT) bundles. The simulated results show that the fronts of impact-induced longitudinal and transverse waves travel at speeds ranging from 18 to 20 km/s and 1.5 to 1.7 km/s in the bundles that absorb most of the nanoprojectile’s initial kinetic energy. The manner in which ballistic impact energy spreads within the CNTF is predicted to be mainly through transverse waves. Acoustic vibrations of the SWCNT bundle caused by the impact-induced longitudinal and transverse waves are revealed. We propose that impact energy can be effectively dampened in a manner of generating acoustic noise and heat. The threshold of the nanoprojectile’s incidental kinetic energy is calculated and is used to evaluate the breaking of SWCNT bundle. The destructive role of a lap joint within the SWCNT bundle is demonstrated, as well as the role of local buckling in blocking the propagation of transverse and longitudinal waves. To facilitate the spreading of impact energy over a long distance, we propose that polymers may form an ideal matrix that should be infiltrated in the CNTF through capillary forces to increase the impact strength and to reinforce the wave spreading to release. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Desirable features for bullet-resistant vests are that they be lightweight, air-permeable and soft. These features make bulletresistant vests more comfortable to wear and more applicable in various occasions and circumstances. Inspired by these requirements, today’s generation of soft bullet-resistant vests are developed using tightly woven layers, such as woven Kevlar and Dyneema fibers, to protect the wearer from gun bullets and stab attacks [1,2]. When a bullet strikes fiber-textile body armor, the tightly woven layers of fiber textile can diffuse its impact through spreading impact-induced plane and shear waves over a large portion of the vest to resist the ballistic impact. The kinetic energy of the projectile is absorbed by the fiber textile, allowing the
⇑ Corresponding author at: Centre for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, China. E-mail address: [email protected] (L. Yang). 1 These authors contributed equally to this work. https://doi.org/10.1016/j.commatsci.2017.10.018 0927-0256/Ó 2017 Elsevier B.V. All rights reserved.
projectile to be stopped before it penetrates into the inner layer of the textile. To reduce blunt trauma injuries to wearers after being struck by a bullet or stabbed, the best fiber should have a high level of strain energy storage. Specifically, these fiber textiles are required to absorb and disperse the ballistic impact energy that is transmitted to the textile and then causes fiber fibrillation, fiber elongation, breakage, and disintegration of fabric structure [1,2]. Carbon nanotube fiber (CNTF) is an ideal alternative fiber due to its excellent combinations of extremely high elastic modulus, high yield strain, low density, good toughness and flexibility [3–6]. Therefore, CNTF presents enormous potentials for the fabrication of thinner, lighter and flexible bullet-resistant vests [5,7]. Several methods, including wet spinning [8], CVD forest spinning [9,10], CVD aerogel spinning [11], and electro-spinning [12], have been reported to produce the ‘‘super” CNTF characterized as raw carbon nanotubes (CNTs) with a large aspect ratio that has been spun into yarn-like textiles. Especially in densified dry-spun CNTF, CNTs are bundled into many sub-bundles and stacked to obtain both good CNT alignment and superior CNT volume fraction.
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The tensile properties of dry-spun CNTF are now comparable to those reported for top fibers [13]. It is worth noting that a bullet’s impact energy can be additionally dissipated through the CNT fibrillation within CNTF and through the disintegration of the yarn-like structure of the CNTF. It is most likely that, under ballistic impact, CNTF would result in a great number of interface interactions between CNTs. Since each CNTF has a very large interface area per unit volume and is composed of billions of CNTs (Fig. 1), the CNTF promises greater absorption of ballistic energy than other solid fibers. The basic components of CNTF are CNT bundles, within which CNTs adhere to each other through van der Waals attraction. The two-dimensional hexagonal structure of sp2-bonded carbon atoms forms the basis of graphene and CNT. Molecular dynamic (MD) simulations have shown that longitudinal and transverse waves travel at speeds of about 20 km/s and 3.4 km/s respectively on monolayer graphene [14,15]. Thus, we expect that CNT bundles might also be able to spread waves at high speeds that are beneficial to the diffusion of balletic impact. Two situations are often encountered for CNTs within CNTF. One occurs when CNTs lap with each other to form long bundles within the CNTF, resulting in many gaps between these lap-joint CNT bundles. The other is the presence of local buckling in CNTs, usually introduced during spinning densification of CNTF. The influences of lap-joint bundles and local buckling on the propagation of impact-induced waves have not yet been clarified. If lap joints and local buckling slow or block the spreading of impact energy through blocking the passage of longitudinal and transverse waves, then the efficiency of impact diffusion would be jeopardized. This would result in early failure of the CNTF textile at the instant of impact as the energy absorption capacity is exceeded. Therefore, detailed analyses are significant in gauging the capacity of the energy absorption and diffusion of the CNTF. Research in this aspect is beneficial to the design and modification of the manufacture of CNTF for bullet-resistant uses [16,17]. In bullet-resistant applications, efficient diffusion of a bullet’s impact over a wide area requires the propagation of both longitudinal and transverse waves through CNT bundles. Because the flexibility of CNTF is an important feature for the transport of transverse waves along CNT bundles, in comparison with multilayer CNTs, CNTF made from single-walled CNTs (SWCNTs) characterized by lower bending rigidity due to their smaller diameter is more suitable for the fabrication of bullet-resistant vests. In-depth understanding of the impact resistance of SWCNT bundles should enhance this fabrication process. MD simulation represents an elementary brick of a throughprocess modeling approach that has wide applications in study of the mechanical properties of graphene and CNTs [14,15,18–23]. Various mechanical properties of carbon nanotubes were evaluated using MD simulations [24–27]. The main subjects in these
1µm Fig. 1. Scanning electron microscopy image of dry-spun CNT fibers.
studies were analyzing the influences of different processing conditions, such as tensioning [24], rotating nanotubes in uniform liquid argon flow [25], water interaction [26], compression [27] on the mechanical properties. However, it should be noted that mechanical behavior of carbon nanotubes in response to external impact still needs to be investigated. It would be useful to understand the impact resistance of carbon nanotubes while interacting with a high-speed project. Hence, in the present study, MD simulations are performed with the maximum allowed bond-force criterion to investigate impact tests of a high-speed nanoprojectile on suspended SWCNT bundles. Impacts are inflicted on SWCNT bundles of three types: continuous, lap jointed, and featuring local buckling. The formation and propagation of the impact-induced shock waves are simulated at the atomic scale. The effectiveness in absorption of a high-speed nanoprojectile’s kinetic energy by SWCNT bundles of various thicknesses is analyzed. The thresholds of the initial kinetic energy of the high-speed nanoprojectile for determining the failure of SWCNT bundles are calculated. Through monitoring variation in the kinetic energy of SWCNT bundles after impact, the acoustic vibrations of SWCNT bundles during shock waves propagation are revealed. Acoustic vibrations of CNT bundles can generate acoustic noise and heat and should be an effective way of damping impact energy. To reveal the influences of lap joint and local buckling on the spread of impact energy, two further simulations of impact bundles with lap joint and local buckling are conducted. We show that both a lap joint and local buckling can block the passage of shock wave energy and limit the capability of the CNTF to diffuse impact energy. Finally, we propose that polymers may be an ideal matrix for infiltration in CNTF via capillary forces to increase crosslinks between adjacent CNTs to reinforce wave spreading.
2. Methodology For impact tests, a nanoscale cubic diamond (termed ‘‘n-bullet” in this study) is chosen as a projectile in order to minimize the impact-induced elastic deformation energy stored by the projectile, because diamond is known as the hardest material. The projectile is non-rigid. Normally, reactive force field simulations present plastic deformation of CNTs, characterized by the appearance and spreading of topological defects via bond breaking and reforming [28–30] that can theoretically occur at room temperature at very high strains (>20%). Scanning electron microscopy and transmission electron microscopy evidence shows that the fracture surfaces of broken CNTs are typically sharp and flat, indicating that CNTs break in a brittle manner at room temperature [23,31–34]. This means that the bond breakage and SWCNT breakage can be determined when a maximum allowed bond force is exceeded. The maximum allowed bond force is selected as 10 nN in the current study. Here, we use molecular dynamics (MD) with a maximum allowed bond force criterion to detect the bond breakage which evolves into a crack that propagates until complete failure. In this study, MD simulations are executed using the LAMMPS MD simulator [18] with the nonreactive COMPASS (‘Condensedphase Optimized Molecular Potentials for Atomistic Simulation Studies’) force field [22]. The COMPASS force field is widely used in commercial software Materials Studio and has been validated in simulating the variations in potential arising from small elastic deformations [35–37], thereby enabling accurate and simultaneous predictions of SWCNT structural deformation. The tensile force on each atom is computed using a symmetric per-atom stress tensor [14,18,23]. Atomic-resolution color maps are constructed to depict force distribution throughout SWCNT bundles. Based on the characteristics of force fields, the amount of energy required to break a covalent carbon-carbon bond is
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calculated. The simulated bond energy can be evaluated against the bond dissociation energy to detect bond failure and brittle failure in SWCNTs [38,39]. Derived from the bond dissociation energy (about 100 kcal/mol), a maximum allowed bond force of 10 nN (corresponding to a tensile stress of about 200 GPa) is used as a bond failure criterion to determine whether the bond strength is exceeded [18,39]. Continuous CNT bundles with different SWCNT numbers (two tubes, four tubes, and six tubes) are built into molecular models (Fig. 2a). Each SWCNT tube is 600 nm (6000 Å) in length. A lapjoint SWCNT bundle molecular model is built to simulate the effects of a lap joint (Fig. 2b). Three continuous SWCNTs in the bundle have the same length of 600 nm. A single gap (0.4 nm) is introduced between two coaxial SWCNTs with lengths of 450 nm
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and 150 nm, respectively. Another four-tube bundle model is built containing one SWCNT with a local buckling or a semi-loop (Fig. 2c). The four tubes are contiguous and have the same length of 600 nm. One of those tubes is locally buckled. The arch height and width are 12.5 nm and 43.3 nm respectively. For all the molecular models, the diameter of (6, 6) SWCNT is 0.804 nm. The wall thickness is 0.34 nm that represents the equilibrium spacing between two graphite layers [18]. The distance between neighboring SWCNTs is 0.34 nm. The axis to axis distance between neighboring SWCNT is 1.144 nm. The n-bullet contains 8628 carbon atoms and is imposed vertically above the CNT bundle at a distance of 0.5 nm. Impacts are simulated by applying an initial speed to the n-bullet [14,15,19,20]. Fixed boundary conditions are used at both ends of all SWCNT bundles over a small region (less than 0.3 nm).
Fig. 2. Simulation models of SWCNT bundle under impact. (a) Three continuous SWCNT bundles under impact from a diamond. The three continuous SWCNT bundles are a two-tube bundle, a four-tube bundle, and a six-tube bundle. (b) A SWCNT bundle with a lap joint under impact from a diamond. It consists of three continuous tubes and two coaxial tubes with a gap between them. The lap-joint region is marked out by a dashed box. (c) A SWCNT bundle with a local buckling under impact from a diamond. It consists of three continuous straight tubes and one locally-buckled tube. A magnified view of the local buckling in the dashed box is illustrated.
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The origin coordinates (0, 0, 0) are located at the middle of the SWCNT bundles. The n-bullet moves at the initial speeds of 1.5 km/s (0.015 Å/fs), 1.2 km/s, 0.9 km/s, 0.6 km/s, and 0.3 km/s. To precisely simulate the kinetic energy conversion from the n-bullet to SWCNT bundles, simulations are conducted in the microcanonical (NVE) ensemble (constant-energy and constantvolume) [14]. The fast inertial relaxation engine (FIRE) algorithm and the NVE ensemble relaxation engine (NVERE) are applied to determine the equilibrium state of the models. In the current simulations, the time step is 2 1015 s (2 fs) [40,41]. Equilibrium is achieved after 20,000 steps (40,000 fs) of the FIRE algorithm. To avoid interactions among neighboring boxes, the length of the simulation box is greater than that of SWCNT bundles to ensure enough space between simulation boxes. Both the stress field and molecular configuration over a SWCNT bundle during impact are mapped to show how the generation and expansion of longitudinal and transverse waves result in an irreversible energy transfer from the moving n-bullet to the SWCNT bundles. 3. Results and discussion 3.1. Continuous four-tube bundle under impact from n-bullet at 1.5 km/s The continuous SWCNT bundle consisting of four tubes (Fig. 2a) under impact from the n-bullet with the initial speed of 1.5 km/s is simulated. The n-bullet moves at the initial speed carrying an initial kinetic energy of 27,865 kcal/mol. Bond stresses must be continuously monitored [14,18,38,42]. The simulated results in Fig. 3 depict the axial stress distributions at three times (1 nN corresponding to a tensile stress of about 20 GPa) [18]. At the beginning of impact, 340 fs, tensile stresses are created, with the maximum stress concentrated on the lower surface of each SWCNT at the impact point and on the upper surface of each SWCNT on either side of the impact point (blue atoms). Then, the axial tensile stresses expand (1340 fs and 2340 fs). The longitudinal shock waves (green atoms) are continually monitored to measure the speed of the longitudinal wave. The measured longitudinal wave speed is not a constant and ranges from 18 to 20 km/s, a finding that is in fair agreement with the theoretically predicted value of 20 km/s [14,15]. Elongation of each hexagonal structure of sp2-bonded carbon atoms of the SWCNTs was monitored during the longitudinal shock waves (green atoms) passing through. The propagation of longitudinal waves results in about 1.3% tensile strain on the tubes. The impacts also generate shear waves (transverse waves) as shown in Fig. 4. The wave front is also continually monitored to obtain the transverse wave speed. The measured transverse wave speed, ranging from 1.5 to 1.7 km/s, is lower than that propagating on monolayer graphene, 3.4 km/s [14]. We attribute the difference to the higher bending stiffness of SWCNT than that of monolayer graphene [42–47], as monolayer graphene under pure bending pressure does not involve any in-plane tension or compression. Because the transverse waves propagate in the SWCNT bundle at such a relatively low speed, the capability of the SWCNT bundle to diffuse ballistic
Fig. 4. Spontaneous shear wave (transverse wave) patterns under impact from the n-bullet with the speed of 1.5 km/s.
impacts over a wider area through transverse waves could be jeopardized. The transformation of the n-bullet’s kinetic energy into the bundle’s kinetic energy and potential energy is shown in Fig. 5. After impact, almost all the n-bullet’s kinetic energy is transferred into the bundle’s wave energy. It is worth noting that accompanying the wave propagation, the bundle’s kinetic energy and potential energy begin to periodically exchange with each other (Fig. 5). This indicates that wave propagation induces longitudinal and bending acoustic vibration of the reactive bundle. Acoustic vibration modes provide a dissipation of impact energy. We speculate that the impact-induced shock waves propagating on the CNT bundles may be effectively dampened by way of generating acoustic noise and heat. The speed difference between longitudinal and transverse shock waves also enables us to separately calculate kinetic energy carried by the longitudinal and transverse waves. Before the initiation of the bundle’s acoustic vibration, the kinetic energy carried respectively by the transverse and longitudinal waves is calculated. The kinetic energy of the transverse wave is about 1.5 104 kcal/mol that accounts for about 53% of the nanoprojectile’s initial kinetic energy (27,865 kcal/mol). The kinetic energy of the longitudinal wave is about 4000 kcal/mol that accounts for 14% of the nanoprojectile’s initial kinetic energy. These figures indicate that most of the impact energy dissipates in the manner of transverse waves rather than longitudinal waves on the bundle. The increment of potential energy of the SWCNT bundle is about 7000 kcal/mol, which accounts for 25% of the nanoprojectile’s initial kinetic energy.
30000
Kinetic energy of the n-bullet Kinetic energy of the SWCNT bundle Potential energy of the SWCNT bundle
25000
Energy (Kcal/mol)
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20000 15000 10000 5000 0
Fig. 3. Distribution of axial tensile stress in the four-tube bundle at three times (i) 340 fs, (ii) 1340 fs, and (iii) 2340 fs, under impact from the n-bullet with the speed of 1.5 km/s. The most highly stressed atoms are colored blue. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
0
20000
40000
60000
80000
100000
Time (fs) Fig. 5. The n-bullet’s kinetic energy transforms into the four-tube bundle’s kinetic energy and potential energy under impact from the n-bullet with the initial speed of 1.5 km/s.
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This part of energy is transformed into the CNT bundle’s elastic strain energy. Under strong impact, the elastic strain causes the CNT to exceed its strength and then destroys the CNT. 3.2. Impact energy absorption After impacts, the conversion of energy from the n-bullet to the SWCNT bundle is expressed as:
K ni ¼ K nb þ U g þ K g
ð1Þ
where K ni is the initial kinetic energy of the n-bullet, K nb is the kinetic energy of the n-bullet after it bounces off, U g is the increment of potential energy of the SWCNT bundle, and K g is the increment of kinetic energy of the SWCNT bundle that includes two parts, transverse-wave energy and longitudinal-wave energy. For the three continuous SWCNT bundles in Fig. 2a, the percentage of initial kinetic energy loss due to the impact of the n-bullet at five initial speeds is calculated (Fig. 6). This percentage is defined as a (K ni K nb ) to K ni ratio. In all SWCNT bundles, the initial kinetic energy of the n-bullet is totally lost at the speed of 0.3 km/s. It is worth noting that after impact, the n-bullet with the lowest initial speed attaches to the bundles, due to the van der Waals attraction between them. For the other four impacting velocities, the n-bullet bounces off after impact and loses approximately 98–99% of its initial kinetic energy. Monitoring of the potential energy of the nbullet indicates that the bounciness of the n-bullet mainly comes from its impact-induced release of compressive strain energy [14]. The lost energy is transmitted mainly to the wave energy (kinetic and potential) of the SWCNT bundle. In the case of the four-tube bundle, the percentage of potential energy (U g ) and kinetic energy (K g ) carried by waves in the nbullet’s initial kinetic energy (K ni ) is calculated for impacts of the n-bullet with five initial speeds (Fig. 7) after the n-bullet bounces off. The percentage of kinetic energy is much higher than that of potential energy. Impacts with higher initial speeds of the n-bullet increase the proportion of impact energy converted to potential energy. The performance of the two-tube and six-tube bundles under impacts is similar to that of the four-tube bundle. 3.3. Threshold of n-bullet’s initial kinetic energy In each SWCNT bundle, there should be a threshold for the n-bullet’s initial kinetic energy K nip , beyond which penetration by the nanoprojectile occurs [14,18]. The bond breakage and SWCNT breakage can be determined when a maximum allowed bond force is exceeded. The maximum allowed bond force is selected as 10nN
Percentage of energy (U g/Kni , K g/Kni )
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100
100
Potential energy
80
80
60
60
40
40
20
20
0 0.0 0.3 0.6 0.9 1.2 1.5 1.8
Kinetic energy
0 0.0 0.3 0.6 0.9 1.2 1.5 1.8
Velocity (km / s) Fig. 7. Simulated percentage of potential energy and kinetic energy in the n-bullet’s initial kinetic energy. The case of a four-tube bundle is considered.
in the current study, close to that used in Ref. [38]. Impact tests of the n-bullet are simulated to obtain the thresholds. For the two-tube, four-tube, and six-tube bundles, the values of K nip are 2.1 105, 2.3 105, and 2.4 105 kcal/mol, respectively. All three bundle types can withstand an impact from an n-bullet with a hypersonic speed no greater than 4 km/s. The thicker bundles may be able to withstand impacts from an n-bullet at relatively higher speeds. 3.4. Lap-joint SWCNT bundle under impact Normally, longer SWCNT bundles within CNTF are formed through connecting SWCNTs by lap joints. MD simulations are performed for a lap-joint SWCNT bundle under impact (Fig. 2b), to determine whether longitudinal and transverse waves can effectively pass through the lap joint. In the bundle, three tubes are continuous and a gap is imposed between two coaxial tubes. The n-bullet is aimed at the middle of the bundle. There is some distance between the impact point and the lap joint. Only one initial n-bullet speed, 1.5 km/s, is simulated. As in the cases of continuous SWCNT bundles, the impact also generates longitudinal and transverse waves that spread along the axial direction of the bundle. The simulations show that there is less longitudinal wave emission to the right end of the SWCNT bundle with a lap joint. The longitudinal waves cannot pass directly through the gap. The propagation of longitudinal waves leads to about 1.3% tensile strain on the tubes. When the longitudinal waves reach the gap, the tensile strain causes the free end of SWCNT to move towards the impact point, resulting in expansion of the gap (Fig. 8). The gap does not affect the energy absorption of the bundle but constrains the diffusion of bullet’s impact via the spreading of impact-induced waves. Therefore, the capability of CNT fibertextile to spread impact-induced waves over a large portion of the textile is also jeopardized. 0.4 nm
8.78 nm
Fig. 6. Simulated percentage of initial kinetic energy loss of the n-bullet at five initial speeds.
Fig. 8. Expansion of the gap induced by longitudinal wave during impact.
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The kinetic energy of the longitudinal waves propagating to the right end of the bundle with the gap is about 60% of that propagating to the left end of the bundle without a gap. It is worth noting that the transverse waves successfully propagate through the gap without any obvious decrease in the kinetic energy. Because of the transverse waves, the three continuous SWCNTs in the SWCNT bundle oscillate in a direction perpendicular to the axial direction. When the transverse waves meet the gap, the three continuous SWCNTs fluctuate, forcing the SWCNT with the lap joint to oscillate with them. Also, the transverse waves passing through the gap do not lead to a decrease in the potential energy of the whole tube. Thus, the transverse waves propagate through the gap without losing the kinetic and potential energy attributed to van der Waals attraction. Compared to bundles that consist only of continuous tubes, the lap joint has a noticeable influence on the impact energy absorption of the bundle. 3.5. Local-buckling SWCNT bundle under impact MD simulations are conducted for the case of a local-buckling SWCNT bundle under impact to reveal whether the longitudinal and transverse waves can effectively propagate through the locally buckled SWCNT within the bundle. This bundle consists of four
continuous tubes, one of which has local buckling (Fig. 2c). The n-bullet is aimed at the middle of the bundle. There is a distance between the impact point and the local buckling. Only one initial speed of the n-bullet, 1.5 km/s, is simulated. The impact generates longitudinal and transverse waves that spread along the axial direction of the bundle. When the longitudinal waves pass the buckling, it gradually disappears (Fig. 9). This is because the axial tensile stresses leading to the left end of the buckling move towards the impact point. This observation indicates that local buckling can dampen the passage of longitudinal waves. Because of the buckling, the kinetic energy of the longitudinal wave propagating to the left end of the bundle is about 60% of that propagating to the right end. The localized buckling also impedes the transverse wave propagating through it. Fig. 10 provides plots of the distributions of axial tensile stress over the corresponding region when longitudinal and transverse waves pass through local buckling. In the buckled SWCNT, no wave-induced axial tensile stresses are observed, because the atoms colored red correspond to a force value of zero. This observation means that the wave-induced axial tensile stresses cannot pass through the deformed SWCNT. Therefore, as bullet-resistant material, CNTF containing SWCNTs with local buckling are considered harmful. Infiltration of polymer matrix within SWCNT fibers can fill the buckling-induced void spaces between SWCNTs and facilitate the passage of longitudinal and transverse waves through the buckling.
4. Conclusions
Fig. 9. Disappearing process of local buckling under impact from the n-bullet with the speed of 1.5 km/s. The buckling indicated by the dashed box is used to study stress distribution when waves pass through the tube.
The large dynamic deflection responses (longitudinal and transverse shock waves and acoustic vibrations) of SWCNT bundles subjected to impacts from a hypersonic n-bullet are revealed. The MD simulations showed that the longitudinal and transverse shock waves propagate at different speeds and consequently result in the n-bullet’s initial kinetic energy being transmitted to the atoms in bundles. More than 99% of n-bullet’s initial kinetic energy is absorbed by the suspended SWCNT bundles through impact. The impact-induced stress singularity at the impact point disappears as soon as the n-bullet bounces off. SWCNT bundles have the ability to absorb impacts from nanoprojectiles, a feature that is promising for bullet-resistance applications because this absorption meets the requirement for decelerating hypersonic bullets in order to stop them.
Fig. 10. Wave-induced axial-tensile-stress distributions. (a) Axial tensile stress distribution in the locally buckled region during the passage of longitudinal waves. (b) Axial tensile stress distribution in the locally buckled region during the passage of transverse waves. The lowest stressed atoms are colored red. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Acoustic vibrations of the SWCNT bundle caused by impactinduced longitudinal and transverse waves propagating should be effectively dampened in a manner of generating acoustic noise and heat. The impact-induced longitudinal and transverse wave propagating on the SWCNT bundles can be blocked by lap joints and local buckling within the bundles. We propose that crosslinks between lap-joint SWCNTs are desirable to promote the spreading of longitudinal wave along CNTF textile. We suggest that the buckling-induced void space between SWCNTs be fully filled, to promote longitudinal and transverse wave propagation along CNTF. Polymers can be ideal material for the infiltration of the yarn-like structure of CNTF to link lap-joint SWCNTs and to fill harmful void space. This infiltration is simply driven by capillary force due to the fiber’s yarn-like structure. The infiltration of polymer into CNTF is indispensable for bullet-resistance applications to spread impact energy over large area. Acknowledgement The authors gratefully acknowledge the financial supports from Harbin Institute of Technology and from Natural Science Foundation of Heilongjiang Province (Grants No. 2017054). L.Y. is indebted to D.W. from the Weizmann Institute of Science and L.T. from the University of Sydney for their support and guidance. References [1] R. Marissen, Mater. Sci. App. 2 (2011) 319–330. [2] L. Wang, S. Kanesalingam, R. Nayak, R. Padhye, Text. L. Ind. Sci. Tech. 3 (2014) 37–47. [3] M.F.L. De Volder, S.H. Tawfick, R.H. Baughman, A.J. Hart, Science 339 (2013) 535–539. [4] R. Mirzaeifar, Z. Qin, M.J. Buehler, Nanoscale 7 (2015) 5435–5445. [5] A.B. Dalton, S. Collins, E. Munoz, J.M. Razal, V.H. Ebron, J.P. Ferraris, J.N. Coleman, B.G. Kim, R.H. Baughman, Nature 423 (2003) 703. [6] Y. He, H. Li, Y. Li, H. Yu, Y. Jiang, Nanoscale 4 (2012) 269–277. [7] V.R. Coluci, S.O. Dantas, A. Jorio, D.S. Galvao, Phys. Rev. B 75 (2007) 075417. [8] P. Pötschke, T. Andres, T. Villmow, S. Pegel, H. Brünig, K. Kobashi, D. Fischer, L. Häussler, Compos. Sci. Technol. 70 (2010) 343–349. [9] K. Jiang, Q. Li, S. Fan, Nature 419 (2002) 801. [10] P. Miaudet, S. Badaire, M. Maugey, A. Derré, V. Pichot, P. Launois, P. Poulin, C. Zakri, Nano Lett. 5 (2005) 2212–2215.
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Atomistic-scale simulations of mechanical behavior of suspended single-walled carbon nanotube bundles under nanoprojectile impact Dongrong Liu a,1, Lin Yang b,c,⇑,1, Xiaodong He b, Rongguo Wang b, Quantian Luo c a
School of Materials Science and Engineering, Harbin University of Science and Technology, Harbin 150040, China Centre for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, China c School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia b
a r t i c l e
i n f o
Article history: Received 10 July 2017 Received in revised form 1 October 2017 Accepted 9 October 2017
Keywords: Mechanical behavior Carbon nanotube Molecular dynamic simulation
a b s t r a c t Carbon nanotube fiber (CNTF) is generally considered a strong candidate for the fabrication of bulletresistant vests due to its excellent combination of extremely high elastic modulus, high yield strain, low density, super toughness, as well as good flexibility. CNTF may also provide effective dissipation of impact energy through fibrillation within the CNTF and through disintegration of the CNTF. In this study, molecular dynamic (MD) simulations are performed to investigate the nanoprojectile impact on suspended single-walled carbon nanotube (SWCNT) bundles. The simulated results show that the fronts of impact-induced longitudinal and transverse waves travel at speeds ranging from 18 to 20 km/s and 1.5 to 1.7 km/s in the bundles that absorb most of the nanoprojectile’s initial kinetic energy. The manner in which ballistic impact energy spreads within the CNTF is predicted to be mainly through transverse waves. Acoustic vibrations of the SWCNT bundle caused by the impact-induced longitudinal and transverse waves are revealed. We propose that impact energy can be effectively dampened in a manner of generating acoustic noise and heat. The threshold of the nanoprojectile’s incidental kinetic energy is calculated and is used to evaluate the breaking of SWCNT bundle. The destructive role of a lap joint within the SWCNT bundle is demonstrated, as well as the role of local buckling in blocking the propagation of transverse and longitudinal waves. To facilitate the spreading of impact energy over a long distance, we propose that polymers may form an ideal matrix that should be infiltrated in the CNTF through capillary forces to increase the impact strength and to reinforce the wave spreading to release. Ó 2017 Elsevier B.V. All rights reserved.
1. Introduction Desirable features for bullet-resistant vests are that they be lightweight, air-permeable and soft. These features make bulletresistant vests more comfortable to wear and more applicable in various occasions and circumstances. Inspired by these requirements, today’s generation of soft bullet-resistant vests are developed using tightly woven layers, such as woven Kevlar and Dyneema fibers, to protect the wearer from gun bullets and stab attacks [1,2]. When a bullet strikes fiber-textile body armor, the tightly woven layers of fiber textile can diffuse its impact through spreading impact-induced plane and shear waves over a large portion of the vest to resist the ballistic impact. The kinetic energy of the projectile is absorbed by the fiber textile, allowing the
⇑ Corresponding author at: Centre for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, China. E-mail address: [email protected] (L. Yang). 1 These authors contributed equally to this work. https://doi.org/10.1016/j.commatsci.2017.10.018 0927-0256/Ó 2017 Elsevier B.V. All rights reserved.
projectile to be stopped before it penetrates into the inner layer of the textile. To reduce blunt trauma injuries to wearers after being struck by a bullet or stabbed, the best fiber should have a high level of strain energy storage. Specifically, these fiber textiles are required to absorb and disperse the ballistic impact energy that is transmitted to the textile and then causes fiber fibrillation, fiber elongation, breakage, and disintegration of fabric structure [1,2]. Carbon nanotube fiber (CNTF) is an ideal alternative fiber due to its excellent combinations of extremely high elastic modulus, high yield strain, low density, good toughness and flexibility [3–6]. Therefore, CNTF presents enormous potentials for the fabrication of thinner, lighter and flexible bullet-resistant vests [5,7]. Several methods, including wet spinning [8], CVD forest spinning [9,10], CVD aerogel spinning [11], and electro-spinning [12], have been reported to produce the ‘‘super” CNTF characterized as raw carbon nanotubes (CNTs) with a large aspect ratio that has been spun into yarn-like textiles. Especially in densified dry-spun CNTF, CNTs are bundled into many sub-bundles and stacked to obtain both good CNT alignment and superior CNT volume fraction.
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The tensile properties of dry-spun CNTF are now comparable to those reported for top fibers [13]. It is worth noting that a bullet’s impact energy can be additionally dissipated through the CNT fibrillation within CNTF and through the disintegration of the yarn-like structure of the CNTF. It is most likely that, under ballistic impact, CNTF would result in a great number of interface interactions between CNTs. Since each CNTF has a very large interface area per unit volume and is composed of billions of CNTs (Fig. 1), the CNTF promises greater absorption of ballistic energy than other solid fibers. The basic components of CNTF are CNT bundles, within which CNTs adhere to each other through van der Waals attraction. The two-dimensional hexagonal structure of sp2-bonded carbon atoms forms the basis of graphene and CNT. Molecular dynamic (MD) simulations have shown that longitudinal and transverse waves travel at speeds of about 20 km/s and 3.4 km/s respectively on monolayer graphene [14,15]. Thus, we expect that CNT bundles might also be able to spread waves at high speeds that are beneficial to the diffusion of balletic impact. Two situations are often encountered for CNTs within CNTF. One occurs when CNTs lap with each other to form long bundles within the CNTF, resulting in many gaps between these lap-joint CNT bundles. The other is the presence of local buckling in CNTs, usually introduced during spinning densification of CNTF. The influences of lap-joint bundles and local buckling on the propagation of impact-induced waves have not yet been clarified. If lap joints and local buckling slow or block the spreading of impact energy through blocking the passage of longitudinal and transverse waves, then the efficiency of impact diffusion would be jeopardized. This would result in early failure of the CNTF textile at the instant of impact as the energy absorption capacity is exceeded. Therefore, detailed analyses are significant in gauging the capacity of the energy absorption and diffusion of the CNTF. Research in this aspect is beneficial to the design and modification of the manufacture of CNTF for bullet-resistant uses [16,17]. In bullet-resistant applications, efficient diffusion of a bullet’s impact over a wide area requires the propagation of both longitudinal and transverse waves through CNT bundles. Because the flexibility of CNTF is an important feature for the transport of transverse waves along CNT bundles, in comparison with multilayer CNTs, CNTF made from single-walled CNTs (SWCNTs) characterized by lower bending rigidity due to their smaller diameter is more suitable for the fabrication of bullet-resistant vests. In-depth understanding of the impact resistance of SWCNT bundles should enhance this fabrication process. MD simulation represents an elementary brick of a throughprocess modeling approach that has wide applications in study of the mechanical properties of graphene and CNTs [14,15,18–23]. Various mechanical properties of carbon nanotubes were evaluated using MD simulations [24–27]. The main subjects in these
1µm Fig. 1. Scanning electron microscopy image of dry-spun CNT fibers.
studies were analyzing the influences of different processing conditions, such as tensioning [24], rotating nanotubes in uniform liquid argon flow [25], water interaction [26], compression [27] on the mechanical properties. However, it should be noted that mechanical behavior of carbon nanotubes in response to external impact still needs to be investigated. It would be useful to understand the impact resistance of carbon nanotubes while interacting with a high-speed project. Hence, in the present study, MD simulations are performed with the maximum allowed bond-force criterion to investigate impact tests of a high-speed nanoprojectile on suspended SWCNT bundles. Impacts are inflicted on SWCNT bundles of three types: continuous, lap jointed, and featuring local buckling. The formation and propagation of the impact-induced shock waves are simulated at the atomic scale. The effectiveness in absorption of a high-speed nanoprojectile’s kinetic energy by SWCNT bundles of various thicknesses is analyzed. The thresholds of the initial kinetic energy of the high-speed nanoprojectile for determining the failure of SWCNT bundles are calculated. Through monitoring variation in the kinetic energy of SWCNT bundles after impact, the acoustic vibrations of SWCNT bundles during shock waves propagation are revealed. Acoustic vibrations of CNT bundles can generate acoustic noise and heat and should be an effective way of damping impact energy. To reveal the influences of lap joint and local buckling on the spread of impact energy, two further simulations of impact bundles with lap joint and local buckling are conducted. We show that both a lap joint and local buckling can block the passage of shock wave energy and limit the capability of the CNTF to diffuse impact energy. Finally, we propose that polymers may be an ideal matrix for infiltration in CNTF via capillary forces to increase crosslinks between adjacent CNTs to reinforce wave spreading.
2. Methodology For impact tests, a nanoscale cubic diamond (termed ‘‘n-bullet” in this study) is chosen as a projectile in order to minimize the impact-induced elastic deformation energy stored by the projectile, because diamond is known as the hardest material. The projectile is non-rigid. Normally, reactive force field simulations present plastic deformation of CNTs, characterized by the appearance and spreading of topological defects via bond breaking and reforming [28–30] that can theoretically occur at room temperature at very high strains (>20%). Scanning electron microscopy and transmission electron microscopy evidence shows that the fracture surfaces of broken CNTs are typically sharp and flat, indicating that CNTs break in a brittle manner at room temperature [23,31–34]. This means that the bond breakage and SWCNT breakage can be determined when a maximum allowed bond force is exceeded. The maximum allowed bond force is selected as 10 nN in the current study. Here, we use molecular dynamics (MD) with a maximum allowed bond force criterion to detect the bond breakage which evolves into a crack that propagates until complete failure. In this study, MD simulations are executed using the LAMMPS MD simulator [18] with the nonreactive COMPASS (‘Condensedphase Optimized Molecular Potentials for Atomistic Simulation Studies’) force field [22]. The COMPASS force field is widely used in commercial software Materials Studio and has been validated in simulating the variations in potential arising from small elastic deformations [35–37], thereby enabling accurate and simultaneous predictions of SWCNT structural deformation. The tensile force on each atom is computed using a symmetric per-atom stress tensor [14,18,23]. Atomic-resolution color maps are constructed to depict force distribution throughout SWCNT bundles. Based on the characteristics of force fields, the amount of energy required to break a covalent carbon-carbon bond is
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calculated. The simulated bond energy can be evaluated against the bond dissociation energy to detect bond failure and brittle failure in SWCNTs [38,39]. Derived from the bond dissociation energy (about 100 kcal/mol), a maximum allowed bond force of 10 nN (corresponding to a tensile stress of about 200 GPa) is used as a bond failure criterion to determine whether the bond strength is exceeded [18,39]. Continuous CNT bundles with different SWCNT numbers (two tubes, four tubes, and six tubes) are built into molecular models (Fig. 2a). Each SWCNT tube is 600 nm (6000 Å) in length. A lapjoint SWCNT bundle molecular model is built to simulate the effects of a lap joint (Fig. 2b). Three continuous SWCNTs in the bundle have the same length of 600 nm. A single gap (0.4 nm) is introduced between two coaxial SWCNTs with lengths of 450 nm
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and 150 nm, respectively. Another four-tube bundle model is built containing one SWCNT with a local buckling or a semi-loop (Fig. 2c). The four tubes are contiguous and have the same length of 600 nm. One of those tubes is locally buckled. The arch height and width are 12.5 nm and 43.3 nm respectively. For all the molecular models, the diameter of (6, 6) SWCNT is 0.804 nm. The wall thickness is 0.34 nm that represents the equilibrium spacing between two graphite layers [18]. The distance between neighboring SWCNTs is 0.34 nm. The axis to axis distance between neighboring SWCNT is 1.144 nm. The n-bullet contains 8628 carbon atoms and is imposed vertically above the CNT bundle at a distance of 0.5 nm. Impacts are simulated by applying an initial speed to the n-bullet [14,15,19,20]. Fixed boundary conditions are used at both ends of all SWCNT bundles over a small region (less than 0.3 nm).
Fig. 2. Simulation models of SWCNT bundle under impact. (a) Three continuous SWCNT bundles under impact from a diamond. The three continuous SWCNT bundles are a two-tube bundle, a four-tube bundle, and a six-tube bundle. (b) A SWCNT bundle with a lap joint under impact from a diamond. It consists of three continuous tubes and two coaxial tubes with a gap between them. The lap-joint region is marked out by a dashed box. (c) A SWCNT bundle with a local buckling under impact from a diamond. It consists of three continuous straight tubes and one locally-buckled tube. A magnified view of the local buckling in the dashed box is illustrated.
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The origin coordinates (0, 0, 0) are located at the middle of the SWCNT bundles. The n-bullet moves at the initial speeds of 1.5 km/s (0.015 Å/fs), 1.2 km/s, 0.9 km/s, 0.6 km/s, and 0.3 km/s. To precisely simulate the kinetic energy conversion from the n-bullet to SWCNT bundles, simulations are conducted in the microcanonical (NVE) ensemble (constant-energy and constantvolume) [14]. The fast inertial relaxation engine (FIRE) algorithm and the NVE ensemble relaxation engine (NVERE) are applied to determine the equilibrium state of the models. In the current simulations, the time step is 2 1015 s (2 fs) [40,41]. Equilibrium is achieved after 20,000 steps (40,000 fs) of the FIRE algorithm. To avoid interactions among neighboring boxes, the length of the simulation box is greater than that of SWCNT bundles to ensure enough space between simulation boxes. Both the stress field and molecular configuration over a SWCNT bundle during impact are mapped to show how the generation and expansion of longitudinal and transverse waves result in an irreversible energy transfer from the moving n-bullet to the SWCNT bundles. 3. Results and discussion 3.1. Continuous four-tube bundle under impact from n-bullet at 1.5 km/s The continuous SWCNT bundle consisting of four tubes (Fig. 2a) under impact from the n-bullet with the initial speed of 1.5 km/s is simulated. The n-bullet moves at the initial speed carrying an initial kinetic energy of 27,865 kcal/mol. Bond stresses must be continuously monitored [14,18,38,42]. The simulated results in Fig. 3 depict the axial stress distributions at three times (1 nN corresponding to a tensile stress of about 20 GPa) [18]. At the beginning of impact, 340 fs, tensile stresses are created, with the maximum stress concentrated on the lower surface of each SWCNT at the impact point and on the upper surface of each SWCNT on either side of the impact point (blue atoms). Then, the axial tensile stresses expand (1340 fs and 2340 fs). The longitudinal shock waves (green atoms) are continually monitored to measure the speed of the longitudinal wave. The measured longitudinal wave speed is not a constant and ranges from 18 to 20 km/s, a finding that is in fair agreement with the theoretically predicted value of 20 km/s [14,15]. Elongation of each hexagonal structure of sp2-bonded carbon atoms of the SWCNTs was monitored during the longitudinal shock waves (green atoms) passing through. The propagation of longitudinal waves results in about 1.3% tensile strain on the tubes. The impacts also generate shear waves (transverse waves) as shown in Fig. 4. The wave front is also continually monitored to obtain the transverse wave speed. The measured transverse wave speed, ranging from 1.5 to 1.7 km/s, is lower than that propagating on monolayer graphene, 3.4 km/s [14]. We attribute the difference to the higher bending stiffness of SWCNT than that of monolayer graphene [42–47], as monolayer graphene under pure bending pressure does not involve any in-plane tension or compression. Because the transverse waves propagate in the SWCNT bundle at such a relatively low speed, the capability of the SWCNT bundle to diffuse ballistic
Fig. 4. Spontaneous shear wave (transverse wave) patterns under impact from the n-bullet with the speed of 1.5 km/s.
impacts over a wider area through transverse waves could be jeopardized. The transformation of the n-bullet’s kinetic energy into the bundle’s kinetic energy and potential energy is shown in Fig. 5. After impact, almost all the n-bullet’s kinetic energy is transferred into the bundle’s wave energy. It is worth noting that accompanying the wave propagation, the bundle’s kinetic energy and potential energy begin to periodically exchange with each other (Fig. 5). This indicates that wave propagation induces longitudinal and bending acoustic vibration of the reactive bundle. Acoustic vibration modes provide a dissipation of impact energy. We speculate that the impact-induced shock waves propagating on the CNT bundles may be effectively dampened by way of generating acoustic noise and heat. The speed difference between longitudinal and transverse shock waves also enables us to separately calculate kinetic energy carried by the longitudinal and transverse waves. Before the initiation of the bundle’s acoustic vibration, the kinetic energy carried respectively by the transverse and longitudinal waves is calculated. The kinetic energy of the transverse wave is about 1.5 104 kcal/mol that accounts for about 53% of the nanoprojectile’s initial kinetic energy (27,865 kcal/mol). The kinetic energy of the longitudinal wave is about 4000 kcal/mol that accounts for 14% of the nanoprojectile’s initial kinetic energy. These figures indicate that most of the impact energy dissipates in the manner of transverse waves rather than longitudinal waves on the bundle. The increment of potential energy of the SWCNT bundle is about 7000 kcal/mol, which accounts for 25% of the nanoprojectile’s initial kinetic energy.
30000
Kinetic energy of the n-bullet Kinetic energy of the SWCNT bundle Potential energy of the SWCNT bundle
25000
Energy (Kcal/mol)
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20000 15000 10000 5000 0
Fig. 3. Distribution of axial tensile stress in the four-tube bundle at three times (i) 340 fs, (ii) 1340 fs, and (iii) 2340 fs, under impact from the n-bullet with the speed of 1.5 km/s. The most highly stressed atoms are colored blue. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
0
20000
40000
60000
80000
100000
Time (fs) Fig. 5. The n-bullet’s kinetic energy transforms into the four-tube bundle’s kinetic energy and potential energy under impact from the n-bullet with the initial speed of 1.5 km/s.
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This part of energy is transformed into the CNT bundle’s elastic strain energy. Under strong impact, the elastic strain causes the CNT to exceed its strength and then destroys the CNT. 3.2. Impact energy absorption After impacts, the conversion of energy from the n-bullet to the SWCNT bundle is expressed as:
K ni ¼ K nb þ U g þ K g
ð1Þ
where K ni is the initial kinetic energy of the n-bullet, K nb is the kinetic energy of the n-bullet after it bounces off, U g is the increment of potential energy of the SWCNT bundle, and K g is the increment of kinetic energy of the SWCNT bundle that includes two parts, transverse-wave energy and longitudinal-wave energy. For the three continuous SWCNT bundles in Fig. 2a, the percentage of initial kinetic energy loss due to the impact of the n-bullet at five initial speeds is calculated (Fig. 6). This percentage is defined as a (K ni K nb ) to K ni ratio. In all SWCNT bundles, the initial kinetic energy of the n-bullet is totally lost at the speed of 0.3 km/s. It is worth noting that after impact, the n-bullet with the lowest initial speed attaches to the bundles, due to the van der Waals attraction between them. For the other four impacting velocities, the n-bullet bounces off after impact and loses approximately 98–99% of its initial kinetic energy. Monitoring of the potential energy of the nbullet indicates that the bounciness of the n-bullet mainly comes from its impact-induced release of compressive strain energy [14]. The lost energy is transmitted mainly to the wave energy (kinetic and potential) of the SWCNT bundle. In the case of the four-tube bundle, the percentage of potential energy (U g ) and kinetic energy (K g ) carried by waves in the nbullet’s initial kinetic energy (K ni ) is calculated for impacts of the n-bullet with five initial speeds (Fig. 7) after the n-bullet bounces off. The percentage of kinetic energy is much higher than that of potential energy. Impacts with higher initial speeds of the n-bullet increase the proportion of impact energy converted to potential energy. The performance of the two-tube and six-tube bundles under impacts is similar to that of the four-tube bundle. 3.3. Threshold of n-bullet’s initial kinetic energy In each SWCNT bundle, there should be a threshold for the n-bullet’s initial kinetic energy K nip , beyond which penetration by the nanoprojectile occurs [14,18]. The bond breakage and SWCNT breakage can be determined when a maximum allowed bond force is exceeded. The maximum allowed bond force is selected as 10nN
Percentage of energy (U g/Kni , K g/Kni )
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100
100
Potential energy
80
80
60
60
40
40
20
20
0 0.0 0.3 0.6 0.9 1.2 1.5 1.8
Kinetic energy
0 0.0 0.3 0.6 0.9 1.2 1.5 1.8
Velocity (km / s) Fig. 7. Simulated percentage of potential energy and kinetic energy in the n-bullet’s initial kinetic energy. The case of a four-tube bundle is considered.
in the current study, close to that used in Ref. [38]. Impact tests of the n-bullet are simulated to obtain the thresholds. For the two-tube, four-tube, and six-tube bundles, the values of K nip are 2.1 105, 2.3 105, and 2.4 105 kcal/mol, respectively. All three bundle types can withstand an impact from an n-bullet with a hypersonic speed no greater than 4 km/s. The thicker bundles may be able to withstand impacts from an n-bullet at relatively higher speeds. 3.4. Lap-joint SWCNT bundle under impact Normally, longer SWCNT bundles within CNTF are formed through connecting SWCNTs by lap joints. MD simulations are performed for a lap-joint SWCNT bundle under impact (Fig. 2b), to determine whether longitudinal and transverse waves can effectively pass through the lap joint. In the bundle, three tubes are continuous and a gap is imposed between two coaxial tubes. The n-bullet is aimed at the middle of the bundle. There is some distance between the impact point and the lap joint. Only one initial n-bullet speed, 1.5 km/s, is simulated. As in the cases of continuous SWCNT bundles, the impact also generates longitudinal and transverse waves that spread along the axial direction of the bundle. The simulations show that there is less longitudinal wave emission to the right end of the SWCNT bundle with a lap joint. The longitudinal waves cannot pass directly through the gap. The propagation of longitudinal waves leads to about 1.3% tensile strain on the tubes. When the longitudinal waves reach the gap, the tensile strain causes the free end of SWCNT to move towards the impact point, resulting in expansion of the gap (Fig. 8). The gap does not affect the energy absorption of the bundle but constrains the diffusion of bullet’s impact via the spreading of impact-induced waves. Therefore, the capability of CNT fibertextile to spread impact-induced waves over a large portion of the textile is also jeopardized. 0.4 nm
8.78 nm
Fig. 6. Simulated percentage of initial kinetic energy loss of the n-bullet at five initial speeds.
Fig. 8. Expansion of the gap induced by longitudinal wave during impact.
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The kinetic energy of the longitudinal waves propagating to the right end of the bundle with the gap is about 60% of that propagating to the left end of the bundle without a gap. It is worth noting that the transverse waves successfully propagate through the gap without any obvious decrease in the kinetic energy. Because of the transverse waves, the three continuous SWCNTs in the SWCNT bundle oscillate in a direction perpendicular to the axial direction. When the transverse waves meet the gap, the three continuous SWCNTs fluctuate, forcing the SWCNT with the lap joint to oscillate with them. Also, the transverse waves passing through the gap do not lead to a decrease in the potential energy of the whole tube. Thus, the transverse waves propagate through the gap without losing the kinetic and potential energy attributed to van der Waals attraction. Compared to bundles that consist only of continuous tubes, the lap joint has a noticeable influence on the impact energy absorption of the bundle. 3.5. Local-buckling SWCNT bundle under impact MD simulations are conducted for the case of a local-buckling SWCNT bundle under impact to reveal whether the longitudinal and transverse waves can effectively propagate through the locally buckled SWCNT within the bundle. This bundle consists of four
continuous tubes, one of which has local buckling (Fig. 2c). The n-bullet is aimed at the middle of the bundle. There is a distance between the impact point and the local buckling. Only one initial speed of the n-bullet, 1.5 km/s, is simulated. The impact generates longitudinal and transverse waves that spread along the axial direction of the bundle. When the longitudinal waves pass the buckling, it gradually disappears (Fig. 9). This is because the axial tensile stresses leading to the left end of the buckling move towards the impact point. This observation indicates that local buckling can dampen the passage of longitudinal waves. Because of the buckling, the kinetic energy of the longitudinal wave propagating to the left end of the bundle is about 60% of that propagating to the right end. The localized buckling also impedes the transverse wave propagating through it. Fig. 10 provides plots of the distributions of axial tensile stress over the corresponding region when longitudinal and transverse waves pass through local buckling. In the buckled SWCNT, no wave-induced axial tensile stresses are observed, because the atoms colored red correspond to a force value of zero. This observation means that the wave-induced axial tensile stresses cannot pass through the deformed SWCNT. Therefore, as bullet-resistant material, CNTF containing SWCNTs with local buckling are considered harmful. Infiltration of polymer matrix within SWCNT fibers can fill the buckling-induced void spaces between SWCNTs and facilitate the passage of longitudinal and transverse waves through the buckling.
4. Conclusions
Fig. 9. Disappearing process of local buckling under impact from the n-bullet with the speed of 1.5 km/s. The buckling indicated by the dashed box is used to study stress distribution when waves pass through the tube.
The large dynamic deflection responses (longitudinal and transverse shock waves and acoustic vibrations) of SWCNT bundles subjected to impacts from a hypersonic n-bullet are revealed. The MD simulations showed that the longitudinal and transverse shock waves propagate at different speeds and consequently result in the n-bullet’s initial kinetic energy being transmitted to the atoms in bundles. More than 99% of n-bullet’s initial kinetic energy is absorbed by the suspended SWCNT bundles through impact. The impact-induced stress singularity at the impact point disappears as soon as the n-bullet bounces off. SWCNT bundles have the ability to absorb impacts from nanoprojectiles, a feature that is promising for bullet-resistance applications because this absorption meets the requirement for decelerating hypersonic bullets in order to stop them.
Fig. 10. Wave-induced axial-tensile-stress distributions. (a) Axial tensile stress distribution in the locally buckled region during the passage of longitudinal waves. (b) Axial tensile stress distribution in the locally buckled region during the passage of transverse waves. The lowest stressed atoms are colored red. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Acoustic vibrations of the SWCNT bundle caused by impactinduced longitudinal and transverse waves propagating should be effectively dampened in a manner of generating acoustic noise and heat. The impact-induced longitudinal and transverse wave propagating on the SWCNT bundles can be blocked by lap joints and local buckling within the bundles. We propose that crosslinks between lap-joint SWCNTs are desirable to promote the spreading of longitudinal wave along CNTF textile. We suggest that the buckling-induced void space between SWCNTs be fully filled, to promote longitudinal and transverse wave propagation along CNTF. Polymers can be ideal material for the infiltration of the yarn-like structure of CNTF to link lap-joint SWCNTs and to fill harmful void space. This infiltration is simply driven by capillary force due to the fiber’s yarn-like structure. The infiltration of polymer into CNTF is indispensable for bullet-resistance applications to spread impact energy over large area. Acknowledgement The authors gratefully acknowledge the financial supports from Harbin Institute of Technology and from Natural Science Foundation of Heilongjiang Province (Grants No. 2017054). L.Y. is indebted to D.W. from the Weizmann Institute of Science and L.T. from the University of Sydney for their support and guidance. References [1] R. Marissen, Mater. Sci. App. 2 (2011) 319–330. [2] L. Wang, S. Kanesalingam, R. Nayak, R. Padhye, Text. L. Ind. Sci. Tech. 3 (2014) 37–47. [3] M.F.L. De Volder, S.H. Tawfick, R.H. Baughman, A.J. Hart, Science 339 (2013) 535–539. [4] R. Mirzaeifar, Z. Qin, M.J. Buehler, Nanoscale 7 (2015) 5435–5445. [5] A.B. Dalton, S. Collins, E. Munoz, J.M. Razal, V.H. Ebron, J.P. Ferraris, J.N. Coleman, B.G. Kim, R.H. Baughman, Nature 423 (2003) 703. [6] Y. He, H. Li, Y. Li, H. Yu, Y. Jiang, Nanoscale 4 (2012) 269–277. [7] V.R. Coluci, S.O. Dantas, A. Jorio, D.S. Galvao, Phys. Rev. B 75 (2007) 075417. [8] P. Pötschke, T. Andres, T. Villmow, S. Pegel, H. Brünig, K. Kobashi, D. Fischer, L. Häussler, Compos. Sci. Technol. 70 (2010) 343–349. [9] K. Jiang, Q. Li, S. Fan, Nature 419 (2002) 801. [10] P. Miaudet, S. Badaire, M. Maugey, A. Derré, V. Pichot, P. Launois, P. Poulin, C. Zakri, Nano Lett. 5 (2005) 2212–2215.
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