Energy absorption ability of buckyball C720 at low impact speed: a numerical study based on molecular dynamics
© Xu et al.; licensee Springer. 2013
Received: 7 December 2012
Accepted: 16 January 2013
Published: 29 January 2013
The dynamic impact response of giant buckyball C720 is investigated by using molecular dynamics simulations. The non-recoverable deformation of C720 makes it an ideal candidate for high-performance energy absorption. Firstly, mechanical behaviors under dynamic impact and low-speed crushing are simulated and modeled, which clarifies the buckling-related energy absorption mechanism. One-dimensional C720 arrays (both vertical and horizontal alignments) are studied at various impact speeds, which show that the energy absorption ability is dominated by the impact energy per buckyball and less sensitive to the number and arrangement direction of buckyballs. Three-dimensional stacking of buckyballs in simple cubic, body-centered cubic, hexagonal, and face-centered cubic forms are investigated. Stacking form with higher occupation density yields higher energy absorption. The present study may shed lights on employing C720 assembly as an advanced energy absorption system against low-speed impacts.
KeywordsImpact Energy absorption Buckyball Buckling
Absorption of external impact energy has long been a research topic with the pressing need from civil[1, 2] to military needs[3, 4]. In particular, effective absorption of mechanical energy at low-impact speed, i.e., below 100 m/s is of great interest[5, 6]. As one of the major branches of fullerene family, the carbon nanotube (CNT) has demonstrated an outstanding mechanical energy dissipation ability through water-filled CNT, CNT forest and bundle, CNT/epoxy nanocomposites, CNT immersed in nonaqueous liquid, intercalating vertical alignment with aligned existing layered compounds, and sponge-like material containing self-assembled interconnected CNT skeletons, among others. The advantage lies within the CNTs’ intriguing mechanical properties, i.e., ultra-strong (Young’s modulus of 0.9 to 5.5 TPa[12–14] and tensile strength of 60 GPa) and ultra-light, as well as the tube structure which buckles upon external loadings. Both theoretical modeling[16–18] and experiments[19–21] have proposed that the energy dissipation density of CNTs could be on the order of 200 J/cm3, about 1-2 order of magnitudes over traditional engineering material.
Naturally, another branch of fullerene family with a spherical shape, i.e., the buckyball, also possesses excellent mechanical properties similar to CNTs. Man et al. examined a C60 in collision with a graphite surface and found that the C60 would first deform into a disk-like structure and then recover to its original shape. It is also known that C60 has a decent damping ability by transferring impact energy to internal energy[23, 24]. This large deformation ability under compressive strain of C60 was also verified by Kaur et al.. For higher impact energy, Zhang employed C60/C320 to collide with mono/double layer graphene, and the penetration of graphene and the dissociation of buckyball were observed. Furthermore, Wang and Lee observed a novel phenomenon of heat wave propagation driven by impact loading between C60 and graphene which was responsible for the mechanical deformation of the buckyball. Meanwhile, giant buckyballs, such as C720, have smaller system rigidity as well as non-recoverable morphology upon impact, and thus they are expected to have higher capabilities for energy dissipation. However, to the best knowledge of the authors, currently, only few studies about the mechanical behavior of giant buckyball are available[29–31].
To understand the mechanical behavior of C720 and investigate its energy absorption potential in this paper, the dynamic response of C720 is studied at various impact speeds below 100 m/s by employing molecular dynamics (MD) simulations. Firstly, the buckling behaviors under both low-speed crushing and impact are discussed and described using classical thin shell models. Next, 1-D alignment of C720 system is investigated to identify the influence of packing of the buckyball on unit energy absorption. Finally, 3-D stacking of C720 system is considered, where four types of packing forms are introduced and the relationship between unit energy absorption and stacking density are elucidated by an empirical model.
Computational model and method
where ɛCC is the depth of the potential well between carbon-carbon atoms, σCC is the finite distance where the carbon-carbon potential is zero, r ij is the distance between the two carbon atoms. Here, L-J parameters for the carbon atoms of the buckyball and εCC = 0.27647 kJ/mol as used in the original parametrization of Girifalco and van der Waals interaction govern in the plate-buckyball interaction. A time integration step of 1 fs is used, and periodical boundary conditions are applied in the x y plane to eliminated the boundary effect.
Single buckyball mechanical behavior
Atomistic simulation result
The entire compression process could be divided into four phases according to the FR/Eh3 ~ W/D curve, i.e., buckling (W/D < 10%), post-buckling (10% ≤ W/D < 30%), densification (30% ≤ W/D < 40%), and inverted-cap-forming phase (W/D > 40%). Upon the ricochet of the plate, the deformation remains as a bowl shape with great volume shrinkage. The stabilization of such a buckled morphology is owing to a lower system potential energy in the buckled configuration due to van der Waals interaction; similar energy dissipation mechanism in CNT network is also revealed by.
The derivative of curve undergoes a sudden change at the same W/D value but in two completely different loading rates, suggesting that the sudden force-drop points are highly dependent on the buckyball deformation rather than the loading rate. And theoretical insights may be obtained from the four-phase deformation.
Phenomenological mechanical models
Note that due to the property of FR/Eh3 ~ W/D curve, among the phases of compression process, those with significant reduction of force (Figure 2) are relatively unimportant for energy absorption and not included in the modeling effort. A three-phase model for low-speed crushing and a two-phase model for impact loading are proposed separately in the following sections.
Three-phase model for low-speed crushing (quasi-static loading)
Phase I. Buckling phase
Phase II. Post-buckling phase
where. This nonlinear deformation behavior extends until it reaches the densification critical normalized strain Wb2. The value of Wb2 could be fitted from the simulation data for C720 where Wb2 ≈ 11h.
Phase III. Densification phase
Therefore, Equations 3, 5, and 10 together serve as the normalized force-displacement model which may be used to describe the mechanical behavior of the buckyball under quasi-static loading condition from small to large deformation.
Two-phase model for impact
The mechanical behaviors of buckyball during the first phase at both low-speed crushing and impact loadings are similar. Thus, Equation 2 is still valid in phase I with a different f* ≈ 4.30. The characteristic buckling time, the time it takes from contact to buckle, is on the order of τ ≈ 10− 1 ~ 100 ns ~ T ≈ 2.5R/c1 ≈ 5.71 × 10− 5ns, where ρ is the density of C720 and. It is much longer than the wave traveling time; thus, the enhancement of f* should be caused by the inertia effect.
Therefore, Equations 3 and 12 together provide a model to describe the mechanical behavior of the buckyball under dynamic loadings.
Results and discussion
In practice, buckyballs need to be assembled (shown in Figure 1) so as to protect materials/devices. Various stacking arrays are investigated as follows.
1-D alignment buckyball system
3-D stacking buckyball system
The packing density of a 3-D stacking system can be different than that of the 1-D system, and thus the performance is expected to vary. Four types of 3-D stacking forms are investigated, i.e., simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC) (a basic crystal structure of buckyball), and hexagonal-closed packing (HCP). The occupation density η SC = π/6 ≈ 0.52,, for SC, BCC, FCC, and HCP, respectively. Convergence study indicates that the profiles of force-displacement curves as well as the energy absorption rate at increasing buckyball numbers at one computational cell keep the same. In this case, a fundamental unit, such as containing 2 × 2 × 3 buckyballs for SC arrangement is shown in Figure 1c.
where A = 0.46, B = −1.94, C = 0.21, and D = 187.9 with fitting correlation coefficient of 0.96. These equations are valid for low-speed impact speed (below 100 m/s) on stacked C720 buckyballs. When the impact speed is fixed, the unit energy absorption linearly increases with the occupation density; under a particular spatial arrangement, the energy absorption ability increases nonlinearly with the impact speed.
C720 as a representative giant buckyball has the distinctive property of non-recovery deformation after crushing or impact, which makes it capable of absorbing a large amount of energy. The mechanical behaviors of a single C720 under quasi-static (low-speed crushing) and dynamic impact are investigated via MD simulation and analytical modeling. By understanding the mechanism of mechanical behavior of individual C720, the energy absorption ability of a 1-D array of buckyball system is studied. It is found that regardless of the direction of alignment and number of buckyballs, the unit energy absorption density is almost the same for low-speed impact. In addition, different 3-D stacking at various impact speeds and stacking forms are investigated. Explicit empirical models are suggested where packing density and impact speed may pose a positive effect on the unit energy absorption. This study may shed lights on the buckyball dynamic mechanical behavior and its application in energy absorption devices and inspire the related experimental work.
JX is a Ph.D. candidate in Department of Earth and Environmental Engineering at Columbia University, supported by the Presidential Distinguished Fellowship. His research interests are nanomechanics and energy-related materials. YL is a Professor in Department of Automotive Engineering at Tsinghua University. He has been awarded by the National Science and Technology Advancement Award (second prize) for twice. His major research interests are advanced energy absorption material. YX is a Professor in School of Energy Science and Engineering at University of Electronic Science and Technology of China. His research is focused on combinatorial materials research with emphasis on energy applications, particularly on thin film materials and devices, printed electronics, and power electronics. He has authored and co-authored more than 40 articles, with an h-index of 12. XC is an Associate Professor in Department of Earth and Environmental Engineering at Columbia University. He uses multiscale theoretical, experimental, and numerical approaches to investigate various research frontiers in materials addressing challenges in energy and environment, nanomechanics, and mechanobiology. He has published over 200 journal papers with an h-index over 30.
The work is supported by National Natural Science Foundation of China (11172231 and 11102099), DARPA (W91CRB-11-C-0112), National Science Foundation (CMMI-0643726), International joint research project sponsored by Tsinghua University (20121080050), Individual-research founding State Key Laboratory of Automotive Safety and Energy, Tsinghua University (ZZ2011-112), and World Class University program through the National Research Foundation of Korea (R32-2008-000-20042-0).
- Sun LY, Gibson RF, Gordaninejad F, Suhr J: Energy absorption capability of nanocomposites: a review. Compos Sci Technol 2009, 69: 2392–2409. 10.1016/j.compscitech.2009.06.020View ArticleGoogle Scholar
- Barnat W, Dziewulski P, Niezgoda T, Panowicz R: Application of composites to impact energy absorption. Comp Mater Sci 2011, 50: 1233–1237. 10.1016/j.commatsci.2010.05.030View ArticleGoogle Scholar
- Deka LJ, Bartus SD, Vaidya UK: Damage evolution and energy absorption of E-glass/polypropylene laminates subjected to ballistic impact. J Mater Sci 2008, 43: 4399–4410. 10.1007/s10853-008-2595-0View ArticleGoogle Scholar
- Mylvaganam K, Zhang LC: Energy absorption capacity of carbon nanotubes under ballistic impact. Appl Phys Lett 2006, 89: 123–127.View ArticleGoogle Scholar
- Xu J, Li YB, Chen X, Ge DY, Liu BH, Zhu MY, Park TH: Automotive windshield - pedestrian head impact: energy absorption capability of interlayer material. Int J Auto Tech-Kor 2011, 12: 687–695. 10.1007/s12239-011-0080-2View ArticleGoogle Scholar
- Wang DM: Impact behavior and energy absorption of paper honeycomb sandwich panels. Int J Impact Eng 2009, 36: 110–114. 10.1016/j.ijimpeng.2008.03.002View ArticleGoogle Scholar
- Xu J, Xu B, Sun Y, Li Y, Chen X: Mechanical energy absorption characteristics of hollow and water-filled carbon nanotubes upon low speed crushing. J Nanomechanics Micromechanics 2012, 2: 65–70. 10.1061/(ASCE)NM.2153-5477.0000049View ArticleGoogle Scholar
- Weidt D, Figiel L, Buggy M: Prediction of energy absorption characteristics of aligned carbon nanotube/epoxy nanocomposites. IOP Conf Ser Mater Sci Eng 2012, 40(1):012028.View ArticleGoogle Scholar
- Lu W, Punyamurtula VK, Qiao Y: An energy absorption system based on carbon nanotubes and nonaqueous liquid. Int J Mat Res 2011, 102: 587–590. 10.3139/146.110377View ArticleGoogle Scholar
- Zhang Q, Zhao MQ, Liu Y, Cao AY, Qian WZ, Lu YF, Wei F: Energy-absorbing hybrid composites based on alternate carbon-nanotube and inorganic layers. Adv Mater 2009, 21: 2876-+.View ArticleGoogle Scholar
- Gui XC, Wei JQ, Wang KL, Cao AY, Zhu HW, Jia Y, Shu QK, Wu DH: Carbon nanotube sponges. Adv Mater 2010, 22: 617-+.View ArticleGoogle Scholar
- Wang CM, Zhang YY, Xiang Y, Reddy JN: Recent studies on buckling of carbon nanotubes. Appl Mech Rev 2010, 63: 030804. 10.1115/1.4001936View ArticleGoogle Scholar
- Chandraseker K, Mukherjee S: Atomistic-continuum and ab initio estimation of the elastic moduli of single-walled carbon nanotubes. Comp Mater Sci 2007, 40: 147–158. 10.1016/j.commatsci.2006.11.014View ArticleGoogle Scholar
- Yakobson BI, Brabec CJ, Bernholc J: Nanomechanics of carbon tubes: instabilities beyond linear response. Phys Rev Lett 1996, 76: 2511–2514. 10.1103/PhysRevLett.76.2511View ArticleGoogle Scholar
- Cao GX, Chen X: Buckling behavior of single-walled carbon nanotubes and a targeted molecular mechanics approach. Phys Rev B 2006, 74: 165422.View ArticleGoogle Scholar
- Chesnokov SA, Nalimova VA, Rinzler AG, Smalley RE, Fischer JE: Mechanical energy storage in carbon nanotube springs. Phys Rev Lett 1999, 82: 343–346. 10.1103/PhysRevLett.82.343View ArticleGoogle Scholar
- Huhtala M, Krasheninnikov AV, Aittoniemi J, Stuart SJ, Nordlund K, Kaski K: Improved mechanical load transfer between shells of multiwalled carbon nanotubes. Phys Rev B 2004, 70: 045404.View ArticleGoogle Scholar
- Liu C, Li F, Ma L-P, Cheng H-M: Advanced materials for energy storage. Adv Mater 2010, 22: E28-+.View ArticleGoogle Scholar
- Coluci VR, Fonseca AF, Galvao DS, Daraio C: Entanglement and the nonlinear elastic behavior of forests of coiled carbon nanotubes. Phys Rev Lett 2008, 100: 086807.View ArticleGoogle Scholar
- Daraio C, Nesterenko VF, Jin S, Wang W, Rao AM: Impact response by a foamlike forest of coiled carbon nanotubes. J Appl Phys 2006, 100: 064309. 10.1063/1.2345609View ArticleGoogle Scholar
- Daraio C, Nesterenko VF, Jin SH: Highly nonlinear contact interaction and dynamic energy dissipation by forest of carbon nanotubes. Appl Phys Lett 2004, 85: 5724–5726. 10.1063/1.1829778View ArticleGoogle Scholar
- Zhenyong M, Zhengying P, Lei L, Rongwu L: Molecular dynamics simulation of low-energy C60 in collision with a graphite (0001) surface. Chinese Phys Lett 1995, 12: 751. 10.1088/0256-307X/12/12/013View ArticleGoogle Scholar
- Man ZY, Pan ZY, Ho YK: The rebounding of C60 on graphite surface: a molecular dynamics simulation. Phys Lett A 1995, 209: 53–56. 10.1016/0375-9601(95)00768-7View ArticleGoogle Scholar
- Pan ZY, Man ZY, Ho YK, Xie J, Yue Y: Energy dependence of C60-graphite surface collisions. J Appl Phys 1998, 83: 4963–4967. 10.1063/1.367298View ArticleGoogle Scholar
- Kaur N, Gupta S, Dharamvir K, Jindal VK: Behaviour of a bucky-ball under extreme internal and external pressures. In 26th International Symposium on Shock Waves: July 15–20 2007; Gottingen. Edited by: Hannemann K, Seiler F. Gottingen: Springer; 2009.Google Scholar
- Zhanga Z, Wanga X, Lia J: Simulation of collisions between buckyballs and graphene sheets. Int J Smart Nano Mat 2012, 3: 14–22. 10.1080/19475411.2011.637993View ArticleGoogle Scholar
- Wang X, Lee JD: Heat wave driven by nanoscale mechanical impact between and graphene. J Nanomechanics Micromechanics 2012, 2: 23–27. 10.1061/(ASCE)NM.2153-5477.0000044View ArticleGoogle Scholar
- Xu J, Sun Y, Li Y, Xiang Y, Chen X: Molecular dynamics simulation of impact response of buckyballs. Mech Res Commun In press In press
- Zope RR, Baruah T, Pederson MR, Dunlap BI: Static dielectric response of icosahedral fullerenes from C(60) to C(2160) characterized by an all-electron density functional theory. Phys Rev B 2008, 77: 115452.View ArticleGoogle Scholar
- Zope RR, Baruah T: Dipole polarizability of isovalent carbon and boron cages and fullerenes. Phys Rev B 2009, 80: 033410.View ArticleGoogle Scholar
- Dunlap BI, Zope RR: Efficient quantum-chemical geometry optimization and the structure of large icosahedral fullerenes. Chem Phys Lett 2006, 422: 451–454. 10.1016/j.cplett.2006.02.100View ArticleGoogle Scholar
- Plimpton S: Fast parallel algorithms for short-range molecular-dynamics. J Comput Phys 1995, 117: 1–19. 10.1006/jcph.1995.1039View ArticleGoogle Scholar
- Girifalco LA, Hodak M: Van der Waals binding energies in graphitic structures. Phys Rev B 2002, 65: 125404.View ArticleGoogle Scholar
- Chen X, Huang YG: Nanomechanics modeling and simulation of carbon nanotubes. J Eng Mech-Asce 2008, 134: 211–216. 10.1061/(ASCE)0733-9399(2008)134:3(211)View ArticleGoogle Scholar
- Huang Y, Wu J, Hwang KC: Thickness of graphene and single-wall carbon nanotubes. Phys Rev B 2006, 74: 245413.View ArticleGoogle Scholar
- Yang XD, He PF, Gao HJ: Modeling frequency- and temperature-invariant dissipative behaviors of randomly entangled carbon nanotube networks under cyclic loading. Nano Res 2011, 4: 1191–1198. 10.1007/s12274-011-0169-yView ArticleGoogle Scholar
- Updike DP, Kalnins A: Axisymmetric postbuckling and nonsymmetric buckling of a spherical shell compressed between rigid plates. J Appl Mech 1972, 39: 172–178. 10.1115/1.3422607View ArticleGoogle Scholar
- Updike DP, Kalnins A: Axisymmetric behavior of an elastic spherical shell compressed between rigid plates. J Appl Mech 1970, 37: 635–640. 10.1115/1.3408592View ArticleGoogle Scholar
- Reissner E: On the theory of thin, elastic shells. In Contributions to Applied Mechanics (the H. Reissner Anniversary Volume). Ann Arbor: J. W. Edwards; 1949:231–247.Google Scholar
- Pauchard L, Rica S: Contact and compression of elastic spherical shells: the physics of a ‘ping-pong’ ball. Philos Mag B 1998, 78: 225–233. 10.1080/13642819808202945View ArticleGoogle Scholar
- Hubbard M, Stronge WJ: Bounce of hollow balls on flat surfaces. Sports Engineering 2001, 4: 49–61. 10.1046/j.1460-2687.2001.00073.xView ArticleGoogle Scholar
- Steele CR: Impact of shells. In Fourth Conference on Non-linear Vibrations, Stability, and Dynamics of Structures and Mechanisms: June 1, 1988; Blacksburg. Edited by: Nayfey AH, Mook DT. Blacksburg: Virginia Polytechnic Institute; 1988.Google Scholar
- Lu G, Yu TX: Energy Absorption of Structures and Materials. Cambridge: Woodhead; 2003.View ArticleGoogle Scholar
- Koh ASJ, Lee HP: Shock-induced localized amorphization in metallic nanorods with strain-rate-dependent characteristics. Nano Lett 2006, 6: 2260–2267. 10.1021/nl061640oView ArticleGoogle Scholar
- Yi LJ, Yin ZN, Zhang YY, Chang TC: A theoretical evaluation of the temperature and strain-rate dependent fracture strength of tilt grain boundaries in graphene. Carbon 2013, 51: 373–380.View ArticleGoogle Scholar
- Zhao H, Aluru NR: Temperature and strain-rate dependent fracture strength of graphene. J Appl Phys 2010, 108: 064321. 10.1063/1.3488620View ArticleGoogle Scholar
- Ganin AY, Takabayashi Y, Khimyak YZ, Margadonna S, Tamai A, Rosseinsky MJ, Prassides K: Bulk superconductivity at 38 K in a molecular system. Nat Mater 2008, 7: 367–371. 10.1038/nmat2179View ArticleGoogle Scholar
- Hilbert D, Cohn-Vossen S: Geometry and the Imagination. New York: Chelsea; 1983.Google Scholar
- Ruoff RS, Ruoff AL: The bulk modulus of C60 molecules and crystals - a molecular mechanics approach. Appl Phys Lett 1991, 59: 1553–1555. 10.1063/1.106280View ArticleGoogle Scholar
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