Studying buckling of composite rods made of hybrid carbon fiber/carbon nanotube-reinforced polyimide using multi-scale FEM

Document Type : Article


1 Department of Mechanical Engineering, University of Guilan, Rasht, P.O. Box 3756, Iran.

2 Department of Engineering Science, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran.


In this paper, the buckling behavior of rods made of carbon fiber/carbon nanotube-reinforced polyimide (CF/CNT-RP) under the action of axial load is investigated based on a multiscale finite element method. A dual-step procedure is first adopted to couple the influences of micro- and nano-scale in order to obtain the equivalent elastic properties of CF/CNT-RP for various volume fractions of CF and CNT. The interphase effect between CNTs and the polymer matrix is taken into consideration. Also, dispersion of CF/CNT into the polymer matrix is assumed to be random. Then, rods with square and circular cross sections are considered whose stability characteristics are analyzed. The finite element modeling is performed using two models including a 3D brick model and a 2D beam model. Selected numerical results are given to study the effects of volume fraction of CNT/CF, interphase and geometrical properties on the axial buckling response of multiscale composite rods.


Main Subjects

[1] Bekyarova, E., Thostenson, E. T., Yu, A., Kim, H., Gao, J., Tang, J., Hahn, H. T., Chou, T. W., Itkis, M. E., and Haddon, R. C., “Multiscale Carbon Nanotube−Carbon Fiber Reinforcement for Advanced Epoxy Composites,” Langmuir, 23, pp. 3970–3974 (2007).
[2] Kepple, K. L., Sanborn, G. P., Lacasse, P. A., Gruenberg, K. M., and Ready, W. J., “Improved fracture toughness of carbon fiber composite functionalized with multi walled carbon nanotubes,” Carbon, 46, pp. 2026–2033 (2008).
[3] Sawi, I. E., Olivier, P. A., Demont, P., and Bougherara, H.., “Processing and electrical character-ization of a unidirectional CFRP compositefilled with double walled carbon nano-tubes,” Compos. Sci. Technol., 73, pp. 19–26 (2012).
[4] Tehrani, M., Safdari, M., Boroujeni, A. Y., Razavi, Z., Case, S. W., Dahmen, K., Garmestani, H., and Al-Haik, M. S., “Hybrid carbon fiber/carbon nanotube composites for structural damping applications,” Nanotechnology, 24, 155704 (2013).
[5] Alipour Skandani, A., and Al-Haik, M., “Viscoplastic characterization and modeling of hybrid carbon fiber/carbon nanotubes reinforced composites,” Compos. Part B, 99, pp. 63–74 (2016).
[6] Pal, G., and Kumar, S., “Multiscale modeling of effective electrical conductivity of short carbon fiber-carbon nanotube-polymer matrix hybrid composites,” Mater. Des., 89, pp. 129–136 (2016).
[7] Zhou, H. W., Mishnaevsky Jr., L., Yi, H. Y., Liu, Y. Q., Hua, X., Warrier, A., and Dai, G. M., “Carbon fiber/carbon nanotube reinforced hierarchical composites: Effect of CNT distribution on shearing strength,” Compos. Part B, 88, pp. 201–211 (2016).
[8] Mittal, G., Dhand, V., Rhee, K. Y., Park, S.-J., and Lee, W. R., “A review on carbon nanotubes and graphene as fillers in reinforced polymer nanocomposites,” J. Indust. Eng. Chem., 21, pp. 11-25 (2015).
[9] Seidel, G. D., and Lagoudas, D. C., “Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites,” Mech. Mater., 38, pp. 884–907 (2006).
[10] Giannopoulos, G. I., Georgantzinos, S. K., and Anifantis, N. K., “A Semi-Continuum Finite Element Approach to Evaluate the Young’s Modulus of Single-Walled Carbon Nanotube Reinforced Composites,” Compos. Part B, 41, pp. 594-601 (2010).
[11] Loos, M. R., and Manas-Zloczower, I., “Micromechanical models for carbon nanotube and cellulose nanowhisker reinforced composites,” Polymer Eng. Sci., 53, pp. 882–887 (2013).
[12] Ansari, R., and Hassanzadeh Aghdam, M. K., “Micromechanics-based viscoelastic analysis of carbon nanotube-reinforced composites subjected to uniaxial and biaxial loading,” Compos. Part B, 90, pp. 512-522 (2016).
[13] Ansari, R., and Hassanzadeh Aghdam, M. K., “Micromechanical characterizing elastic, thermoelastic and viscoelastic properties of functionally graded carbon nanotube reinforced polymer nanocomposites,” Meccanica, 52, pp. 1625-1640 (2017).
[14] Alva, A., Bhagat, A., and Raja, S., “Effective Moduli Evaluation of Carbon Nanotube Reinforced Polymers Using Micromechanics,” Mech. Adv. Mater. Struct., 22, pp. 819-828 (2015).
[15] Ansari, R., Hassanzadeh Aghdam, M. K., and Mahmoodi, M. J., “Three-dimensional micromechanical analysis of the CNT waviness influence on the mechanical properties of polymer nanocomposites,” Acta Mech., 227, pp. 3475–3495 (2016).
[16] Wattanasakulpong, N., and Ungbhakorn, V., “Analytical Solutions for Bending, Buckling and Vibration Responses of Carbon Nanotube-Reinforced Composite Beams Resting on Elastic Foundation,” Comput. Mater. Sci., 71, pp. 201-208 (2013).
[17] Lin, F., and Xiang, Y., “Vibration Analysis of Carbon Nanotube Reinforced Composite Plates,” Appl. Mech. Mater., 553, pp. 681-686 (2014).
[18] Abdollahzadeh Shahrbabaki, E., and Alibeigloo, A., “Three-Dimensional Free Vibration of Carbon Nanotube-Reinforced Composite Plates with Various Boundary Conditions Using Ritz Method,” Compos. Struct., 111, pp. 362-370 (2014).
[19] Ansari, R., Faghih Shojaei, M., Mohammadi, V., and Sadeghi, F., “Nonlinear forced vibration analysis of functionally graded carbon nanotube-reinforced composite Timoshenko beams,” Compos. Struct., 113, pp. 316–327 (2014).
[20] Ansari, R., Hasrati, E., Faghih Shojaei, M., Gholami, R., and Shahabodini, A., “Forced vibration analysis of functionally graded carbon nanotube-reinforced composite plates using a numerical strategy,” Physica E, 69, pp. 294–305 (2015).
[21] Wu, H. L., Yang, J., and Kitipornchai, S., “Imperfection sensitivity of postbuckling behaviour of functionally graded carbon nanotube-reinforced composite beams,” Thin-Walled Struct., 108, pp. 225–233 (2016).
[22] Ansari, R., Shahabodini, A., and Faghih Shojaei, M., “Vibrational analysis of carbon nanotube-reinforced composite quadrilateral plates subjected to thermal environments using a weak formulation of elasticity,” Compos. Struct., 139, pp. 167–187 (2016).
[23] Mirzaei, M., and Kiani, Y., “Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout,” Beilstein J. Nanotechnol., 7, pp. 511–523 (2016).
[24] Ansari, R., Pourashraf, T., Gholami, R., and Shahabodini, A., “Analytical solution for nonlinear postbuckling of functionally graded carbon nanotube-reinforced composite shells with piezoelectric layers,” Compos. Part B, 90, pp. 267–277 (2016).
[25] Ghorbani Shenas, A., Malekzadeh, P., and Ziaee, S., “Vibration analysis of pre-twisted functionally graded carbon nanotube reinforced composite beams in thermal environment,” Compos. Struct., 162, pp. 325–340 (2017).
[26] Gholami, R., Ansari, R., and Gholami, Y., “Nonlinear resonant dynamics of geometrically imperfect higher-order shear deformable functionally graded carbon-nanotube reinforced composite beams,” Compos. Struct., 174, pp. 45-58 (2017).
[27] Gholami, R., and Ansari, R., “The effect of initial geometric imperfection on the nonlinear resonance of functionally graded carbon nanotube-reinforced composite rectangular plates,” Appl. Math. Mech., 39, pp. 1219–1238 (2018).
[28] Gholami, R., and Ansari, R., “Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates,” Eng. Struct., 156, pp. 197-209 (2018).
[29] Gholami, R., and Ansari, R., “Large deflection geometrically nonlinear analysis of functionally graded multilayer graphene platelet-reinforced polymer composite rectangular plates,” Compos. Struct., 180, pp. 760-771 (2018).
[30] Gholami, R., Ansari, R., and Gholami, Y., “Numerical study on the nonlinear resonant dynamics of carbon nanotube/fiber/polymer multiscale laminated composite rectangular plates with various boundary conditions,” Aerosp. Sci. Technol., 78, pp. 118-129 (2018).
[31] Gholami, R., and Ansari, R., “Nonlinear bending of third-order shear deformable carbon nanotube/fiber/polymer multiscale laminated composite rectangular plates with different edge supports,” Eur. Phys. J. Plus, 133, p. 282 (2018).
[32] Gholami, R., and Ansari, R., “Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading,” Eur. Phys. J. Plus, 133, p. 56 (2018).
[33] Odegard, G. M., Gates, T. S., Wise, K. E., Park, C., and Siochi, E. J., “Constitutive modeling of nanotube-reinforced polymer composites,” Compos. Sci. Technol., 63, pp. 1671–87 (2003).
[34] Tsai, J. L., Tzeng, S. H., and Chiu, Y. T., “Characterizing elastic properties of carbon nanotubes/polyimide nanocomposites using multi-scale simulation,” Compos. Part B, 41, pp. 106–115 (2010).
[35] Shokrieh, M. M., and Rafiee, R., “Stochastic multi-scale modeling of CNT/polymer composites,” Comput. Mater. Sci., 50, pp. 437–446 (2010).
[36] Joshi, U. A., Sharma, S. C., and Harsha, S. P., “A multiscale approach for estimating the chirality effects in carbon nanotube reinforced composites,” Physica E, 45, pp. 28–35 (2012).
[37] Vu-Bac, N., Rafiee, R., Zhuang, X., Lahmer, T., and Rabczuk, T., “Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters,” Compos. Part B, 68, pp. 446–464 (2015).
[38] Ahmadi, M., Ansari, R., and Rouhi, H., “Multi-scale bending, buckling and vibration analyses of carbon fiber/carbon nanotube-reinforced polymer nanocomposite plates with various shapes,” Physica E, 93, pp. 17–25 (2017). 
[39] Ahmadi, M., Ansari, R., and Hassanzadeh-Aghdam, M. K., “Low velocity impact analysis of beams made of short carbon fiber/carbon nanotube-polymer composite: A hierarchical finite element approach,” Mech. Adv. Mater. Struct., (2018).
[40] Ahmadi, M., Ansari, R., and Rouhi, H., “Free and forced vibration analysis of rectangular/circular/annular plates made of carbon fiber-carbon nanotube-polymer hybrid composites,” Sci. Eng. Compos. Mater., (2018).
[41] Ahmadi, M., Ansari, R., and Rouhi, H., “On the free vibrations of piezoelectric carbon nanotube-reinforced microbeams: a multiscale finite element approach,” Iranian J. Sci. Technol. Trans. Mech. Eng., (2018).
[42] Ahmadi, M., Ansari, R., and Rouhi, S., “Fracture behavior of the carbon nanotube/carbon fiber/polymer multiscale composites under bending test – A stochastic finite element method,” Mech. Adv. Mater. Struct., (2018).
[43] Ahmadi, M., Ansari, R., and Rouhi, H., “Free vibration analysis of carbon fiber-carbon nanotube-polymer matrix composite plates by a finite element-based multi-scale modeling approach,” J. Multiscale Model., 9, 1850002 (2018).
[44] Civalek, Ö., and Demir, Ç., “A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method,” Appl. Math. Comput., 289, pp. 335-352 (2016).
[45] Mercan, K., and Civalek, Ö., “DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix,” Compos. Struct., 143, pp. 300–309 (2016).
[46] Refaeinejad, V., Rahmani, O., and Hosseini, S. A. H., “An analytical solution for bending, buckling, and free vibration of FG nanobeam lying on Winkler-Pasternak elastic foundation using different nonlocal higher order shear deformation beam theories,” Scientia Iranica F, 24, pp. 1635-1653 (2017).
[47] Norouzzadeh, A., Ansari, R., and Rouhi, H., “Isogeometric vibration analysis of small-scale Timoshenko beams based on the most comprehensive size-dependent theory,” Scientia Iranica F, 25, pp. 1864-1878 (2018).
[48] Akgöz, B., and Civalek, Ö., “Buckling analysis of cantilever carbon nanotubes using the strain gradient elasticity and modified couple stress theories,” J. Comput. Theor. Nanosci., 8, pp. 1821-1827 (2011).
[49] Chen, W. J., and Li, X. P., “Size-dependent free vibration analysis of composite laminated Timoshenko beam based on new modified couple stress theory,” Arch. Appl. Mech., 83, pp. 431–444 (2013).
[50] Akgoz, B., and Civalek, Ö., “Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory,” Acta Astronautica, 119, pp. 1–12 (2016).
[51] Karimzadeh, A., and Ahmadian, M. T., “Vibrational characteristics of size dependent vibrating ring gyroscope,” Scientia Iranica B, DOI: 10.24200/SCI.2018.20495 (2018).
[52] Jafari-Talookolaei, R. -A., Ebrahimzade, N., Rashidi-Juybari, S., and Teimoori, K., “Bending and vibration analysis of delaminated Bernoulli-Euler microbeams using the modified couple stress,” Scientia Iranica B, 25, pp. 675-688 (2018).
[53] Shen, L., and Li, J., “Transversely isotropic elastic properties of single-walled carbon nanotubes,” Phys. Rev. B, 69, 045414 (2004).
[54] Shen, L., and Li, J., “Transversely isotropic elastic properties of multiwalled carbon nanotubes,” Phys. Rev. B, 71, 035412 (2005).
[55] Selmi, A., Friebel, C., Doghri, I., and Hassis, H., “Prediction of the elastic properties of single walled carbon nanotube reinforced polymers: A comparative study of several micromechanical models,” Compos. Sci. Technol., 67, pp. 2071–2084 (2007).
[56] Kulkarni, M., Carnahan, D., Kulkarni,K., Qian, D., and Abot, J. L., “Elastic response of a carbon nanotube fiber reinforced polymeric composite: A numerical and experimental study,” Compos. Part B, 41, pp. 414–421 (2010).
[57] Odegard, G. M., Clancy, T. C., and Gates, T. S., “Modeling of the mechanical properties of nanoparticle/polymer composites,” Polymer, 46, pp. 553–562 (2005).