Probabilistic mechanical properties and reliability of carbon nanotubes

• Autorzy: Esbati A. H. , Irani S.

Identyfikatory

DOI

10.1016/j.acme.2017.05.001

• Języki publikacji: EN

Abstrakty

EN

Carbon nanotubes (CNTs) and their products such as polymer nanocomposite (PNC) are an undeniable part of future materials. To use such future materials, it is necessary to have an accurate evaluation of their properties. Several uncertainties such as structural defects and their distributions cause change in the properties of CNTs that could be considered probabilistic variables. A novel procedure is presented for evaluating CNTs’ probabilistic fracture properties and structural reliability using stochastic finite element methods. By employing two dimensionless parameters, both types of Stone–Wales 5-7-7-5 defects are randomly applied to CNTs. Section defect density and critical section defect density are defined and used to manage the distribution and geometrical configuration of CNTs’ structural defects. A probabilistic method is used to evaluate the effect of defects’ distribution on Young's modulus, ultimate strain, and ultimate stress. It has been observed that normal and Weibull distribution functions are suitable for describing Young's modulus distribution and ultimate stress distribution, respectively. Defect density ratio is defined and, using this parameter, the effect of aggregated defects on mechanical properties is evaluated. It is demonstrated that the defects out of critical section have an unavoidable effect on Young's modulus and ultimate strain; but they have an insignificant effect on ultimate stress. A reliability analysis is performed on armchair (15,15) CNTs and it is investigated that the reliability of CNTs depends on critical defect density significantly. In addition, the reliability is equal to one for the stress of less than 50 GPa and this value is equal to zero for the stress of higher than 100 GPa, independent from the changes of critical defect density. Eventually, a procedure is described to estimate the reliability of armchair CNTs using critical defect density and the results’ accuracy is discussed and evaluated.

Słowa kluczowe

EN

single wall carbon nanotubes; probabilistic mechanical properties; Stone–Wales defects; stochastic finite element method; structural reliability

PL

nanorurki węglowe; właściwości mechaniczne; metoda elementów skończonych; niezawodność konstrukcji

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2018
• Tom: Vol. 18, no. 2
• Strony: 532--545
• Opis fizyczny: Bibliogr. 55 poz., rys., tab., wykr.

Twórcy

autor

Esbati A. H.

• Aerospace Faculty, K. N. Toosi University of Technology, University Blvd., East Vafadar, 4th Tehranpars Sq., Tehran, Iran

autor

Irani S.

• Aerospace Faculty, K. N. Toosi University of Technology, University Blvd., East Vafadar, 4th Tehranpars Sq., Tehran, Iran

Bibliografia

• [1] S. Iijima, Helical microtubules of graphitic carbon, Nature 354 (1991) 56–58.
• [2] M.S. Dresselhaus, G. Dresselhaus, P.C. Eklund, Science of Fullerenes and Carbon Nanotubes: Their Properties and Applications, Academic Press, 1996.
• [3] Q. Jiang, X. Wang, Y. Zhu, D. Hui, Y. Qiu, Mechanical, electrical and thermal properties of aligned carbon nanotube/polyimide composites, Composites Part B: Engineering 56 (2014) 408–412.
• [4] H.-E. Schaefer, Nanoscience: The Science of the Small in Physics, Engineering, Chemistry, Biology and Medicine, Springer Science & Business Media, 2010.
• [5] J.C. Burgos, E. Jones, P.B. Balbuena, Dynamics of topological defects in single-walled carbon nanotubes during catalytic growth, The Journal of Physical Chemistry C 118 (2014) 4808– 4817.
• [6] S. Zhang, S.L. Mielke, R. Khare, D. Troya, R.S. Ruoff, G.C. Schatz, T. Belytschko, Mechanics of defects in carbon nanotubes: atomistic and multiscale simulations, Physical Review B 71 (2005) 115403.
• [7] P.C. Watts, W.-K. Hsu, H.W. Kroto, D.R. Walton, Are bulk defective carbon nanotubes less electrically conducting? Nano Letters 3 (2003) 549–553.
• [8] M. Buongiorno Nardelli, J.-L. Fattebert, D. Orlikowski, C. Roland, Q. Zhao, J. Bernholc, Mechanical properties, defects and electronic behavior of carbon nanotubes, Carbon 38 (2000) 1703–1711.
• [9] Z. Spitalsky, D. Tasis, K. Papagelis, C. Galiotis, Carbon nanotube–polymer composites: chemistry, processing, mechanical and electrical properties, Progress in Polymer Science 35 (2010) 357–401.
• [10] Y. Kim, H. Kim, Structural modifications of multiwalled carbon nanotubes and their effects on optical properties, Journal of Nanoparticle Research 16 (2013) 1–11.
• [11] A.H. Esbati, S. Irani, Mechanical properties and fracture analysis of functionalized carbon nanotube embedded by polymer matrix, Aerospace Science and Technology 55 (2016) 120–130.
• [12] M.B. Nardelli, B. Yakobson, J. Bernholc, Mechanism of strain release in carbon nanotubes, Physical Review B 57 (1998) R4277.
• [13] M. Sammalkorpi, A. Krasheninnikov, A. Kuronen, K. Nordlund, K. Kaski, Mechanical properties of carbon nanotubes with vacancies and related defects, Physical Review B 70 (2004) 245416.
• [14] J. Xiao, S. Lopatnikov, B. Gama, J. Gillespie Jr., Nanomechanics on the deformation of single- and multi-walled carbon nanotubes under radial pressure, Materials Science and Engineering A 416 (2006) 192–204.
• [15] G.M. Odegard, T.S. Gates, L.M. Nicholson, K.E. Wise, Equivalent-continuum modeling with application to carbon nanotubes, Citeseer (2002).
• [16] T. Chang, H. Gao, Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model, Journal of the Mechanics and Physics of Solids 51 (2003) 1059–1074.
• [17] M. Meo, M. Rossi, A molecular-mechanics based finite element model for strength prediction of single wall carbon nanotubes, Materials Science and Engineering A 454 (2007) 170–177.
• [18] R. Merli, C. Lázaro, S. Monleón, A. Domingo, Geometrical nonlinear formulation of a molecular mechanics model applied to the structural analysis of single-walled carbon nanotubes, International Journal of Solids and Structures 58 (2015) 157–177.
• [19] S.-J. Guo, Q.-S. Yang, X.-Q. He, K.-M. Liew, Design of 3D carbon nanotube-based nanostructures and prediction of their extra- strong mechanical properties under tension and compression, Computational Materials Science 85 (2014) 324–331.
• [20] T. Belytschko, S. Xiao, G. Schatz, R. Ruoff, Atomistic simulations of nanotube fracture, Physical Review B 65 (2002) 235430.
• [21] J. Xiao, J. Staniszewski, J. Gillespie Jr., Fracture and progressive failure of defective graphene sheets and carbon nanotubes, Composite Structures 88 (2009) 602–609.
• [22] X. Wang, K. Wang, Q. Meng, D. Wang, Reactivity of the interior surface of (5,5) single-walled carbon nanotubes with and without a Stone–Wales defect, Computational and Theoretical Chemistry 1027 (2014) 160–164.
• [23] Q.-S. Yang, B.-Q. Li, X.-Q. He, Y.-W. Mai, Modeling the mechanical properties of functionalized carbon nanotubes and their composites: design at the atomic level, Advances in Condensed Matter Physics (2013).
• [24] J. Decklever, P. Spanos, Nanocomposite material properties estimation and fracture analysis via peridynamics and Monte Carlo simulation, Probabilistic Engineering Mechanics (2015).
• [25] M.B. Whiteside, S.T. Pinho, P. Robinson, Stochastic failure modelling of unidirectional composite ply failure, Reliability Engineering & System Safety 108 (2012) 1–9.
• [26] A. Kontsos, J.A. Cuadra, Multiscale stochastic finite elements modeling of polymer nanocomposites, in: Modeling and Prediction of Polymer Nanocomposite Properties, Wiley- VCH Verlag GmbH & Co. KGaA, 2013, pp. 143–168.
• [27] S.C. Baxter, B.J. Burrows, B.S. Fralick, Mechanical percolation in nanocomposites: microstructure and micromechanics, Probabilistic Engineering Mechanics (2015).
• [28] A. Kontsos, P. Spanos, Modeling of nanoindentation data and characterization of polymer nanocomposites by a multiscale stochastic finite element method, Journal of Computational and Theoretical Nanoscience 6 (2009) 2273–2282.
• [29] A. Esbati, S. Irani, Multiscale modeling of fracture in polymer nanocomposite reinforced by intact and functionalized CNTs, Journal of Science and Technology and Composites (2016).
• [30] K.-t. Lau, C. Gu, D. Hui, A critical review on nanotube and nanotube/nanoclay related polymer composite materials, Composites Part B: Engineering 37 (2006) 425–436.
• [31] E.T. Thostenson, Z. Ren, T.-W. Chou, Advances in the science and technology of carbon nanotubes and their composites: a review, Composites Science and Technology 61 (2001) 1899– 1912.
• [32] F.H. Gojny, J. Nastalczyk, Z. Roslaniec, K. Schulte, Surface modified multi-walled carbon nanotubes in CNT/epoxy- composites, Chemical Physics Letters 370 (2003) 820–824.
• [33] R. Ansari, S. Rouhi, M. Mirnezhad, M. Aryayi, Stability characteristics of single-walled boron nitride nanotubes, Archives of Civil and Mechanical Engineering 15 (2015) 162–170.
• [34] H. Jiang, P. Zhang, B. Liu, Y. Huang, P. Geubelle, H. Gao, K. Hwang, The effect of nanotube radius on the constitutive model for carbon nanotubes, Computational Materials Science 28 (2003) 429–442.
• [35] X. Lu, Z. Hu, Mechanical property evaluation of single-walled carbon nanotubes by finite element modeling, Composites Part B: Engineering 43 (2012) 1902–1913.
• [36] A.H. Esbati, S. Irani, H. Moosazadeh, Instability characteristics of a free-free multi-stepped Timoshenko beam with concentrated masses subjected to follower force, Transactions of the Japan Society for Aeronautical and Space Sciences 55 (2012) 12–20.
• [37] K.P. Saffar, N. JamilPour, A.R. Najafi, G. Rouhi, A.R. Arshi, A. Fereidoon, A finite element model for estimating Young's modulus of carbon nanotube reinforced composites incorporating elastic cross-links, Matrix 1 (2008) 9–11.
• [38] K.I. Tserpes, P. Papanikos, Finite element modeling of single- walled carbon nanotubes, Composites Part B: Engineering 36 (2005) 468–477.
• [39] M. Meo, M. Rossi, Prediction of Young's modulus of single wall carbon nanotubes by molecular-mechanics based finite element modelling, Composites Science and Technology 66 (2006) 1597–1605.
• [40] R. Maleki Moghadam, S.A. Hosseini, M. Salehi, The influence of Stone–Thrower–Wales defect on vibrational characteristics of single-walled carbon nanotubes incorporating Timoshenko beam element, Physica E: Low-dimensional Systems and Nanostructures 62 (2014) 80–89.
• [41] K. Tserpes, P. Papanikos, The effect of Stone–Wales defect on the tensile behavior and fracture of single-walled carbon nanotubes, Composite Structures 79 (2007) 581–589.
• [42] L. He, S. Guo, J. Lei, Z. Sha, Z. Liu, The effect of Stone–Thrower– Wales defects on mechanical properties of graphene sheets – a molecular dynamics study, Carbon 75 (2014) 124–132.
• [43] J. Xiao, J. Staniszewski, J. Gillespie, Tensile behaviors of graphene sheets and carbon nanotubes with multiple Stone– Wales defects, Materials Science and Engineering A 527 (2010) 715–723.
• [44] M.M.S. Fakhrabadi, N. Khani, S. Pedrammehr, M.M. Mashhadi, Prediction of buckling instability of perfect and defective carbon nanotubes, Journal of Computational and Theoretical Nanoscience 11 (2014) 2356–2369.
• [45] Q. Lu, B. Bhattacharya, Effect of randomly occurring Stone– Wales defects on mechanical properties of carbon nanotubes using atomistic simulation, Nanotechnology 16 (2005) 555.
• [46] W. Hou, S. Xiao, Mechanical behaviors of carbon nanotubes with randomly located vacancy defects, Journal of Nanoscience and Nanotechnology 7 (2007) 4478–4485.
• [47] R. Rafiee, R. Pourazizi, Evaluating the influence of defects on the Young's modulus of carbon nanotubes using stochastic modeling, Materials Research 17 (2014) 758–766.
• [48] J.R. Xiao, B.A. Gama, J.W. Gillespie Jr., An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes, International Journal of Solids and Structures 42 (2005) 3075–3092.
• [49] Q. Lu, B. Bhattacharya, Fracture resistance of zigzag single walled carbon nanotubes, Nanotechnology 17 (2006) 1323.
• [50] J. Zhu, M. He, F. Qiu, Effect of vacancy defects on the Young's modulus and fracture strength of graphene: a molecular dynamics study, Chinese Journal of Chemistry 30 (2012) 1399–1404.
• [51] C. Baykasoglu, M. Kirca, A. Mugan, Nonlinear failure analysis of carbon nanotubes by using molecular- mechanics based models, Composites Part B: Engineering 50 (2013) 150–157.
• [52] M. Rossi, M. Meo, On the estimation of mechanical properties of single-walled carbon nanotubes by using a molecular-mechanics based FE approach, Composites Science and Technology 69 (2009) 1394–1398.
• [53] A.H. Esbati, S. Irani, Failure analysis of CNTs with Stone- Wales defect using nonlinear finite element method, Mechanics of Composite Materials, in press.
• [54] P.D. Gosling, Faimun, O. Polit, A high-fidelity first-order reliability analysis for shear deformable laminated composite plates, Composite Structures 115 (2014) 12–28.
• [55] M. Chiachio, J. Chiachio, G. Rus, Reliability in composites – a selective review and survey of current development, Composites Part B: Engineering 43 (2012) 902–913.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018)