DOI QR코드

DOI QR Code

Low-velocity impact response of laminated FG-CNT reinforced composite plates in thermal environment

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Habibi, Sajjad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
  • Received : 2016.11.26
  • Accepted : 2017.02.05
  • Published : 2017.06.25

Abstract

In this study, nonlinear response of laminated functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate under low-velocity impact based on the Eshelby-Mori-Tanaka approach in thermal conditions is studied. The governing equations are derived based on higher-order shear deformation plate theory (HSDT) under von $K\acute{a}rm\acute{a}n$ geometrical nonlinearity assumptions. The finite element method with 15 DOF at each node and Newmark's numerical integration method is applied to solve the governing equations. Four types of distributions of the uniaxially aligned reinforcement material through the thickness of the plates are considered. Material properties of the CNT and matrix are assumed to be temperature dependent. Contact force between the impactor and the laminated plate is obtained with the aid of the modified nonlinear Hertzian contact law models. In the numerical example, the effect of layup (stacking sequence) and lamination angle as well as the effect of temperature variations, distribution of CNTs, volume fraction of the CNTs, the mass and the velocity of the impactor in a constant energy level and boundary conditions on the impact response of the CNTRC laminated plates are investigated in details.

Keywords

References

  1. Alibeigloo, A. and Liew, K. (2013), "Thermoelastic analysis of functionally graded carbon nanotubereinforced composite plate using theory of elasticity", Compos. Struct., 106, 873-881. https://doi.org/10.1016/j.compstruct.2013.07.002
  2. Aragh, B.S., Barati, A.N. and Hedayati, H. (2012), "Eshelby-Mori-Tanaka approach for vibrational behavior of continuously graded carbon nanotube-reinforced cylindrical panels", Compos. Part B: Eng., 43(4), 1943-1954. https://doi.org/10.1016/j.compositesb.2012.01.004
  3. Arani, A.G., Maghamikia, S., Momammadimehr, M. and Arefmanesh, A. (2011), "Buckling analysis of laminated composite rectangular plates reinforced by SWCNTs using analytical and finite element methods", J. Mech. Sci. Technol., 25(3), 809-820. https://doi.org/10.1007/s12206-011-0127-3
  4. Benveniste, Y. (1987), "A new approach to the application of Mori-Tanaka's theory in composite materials", Mech. Mater., 6(2), 147-157. https://doi.org/10.1016/0167-6636(87)90005-6
  5. Delfosse, D., Vaziri, R., Pierson, M. and Poursartip, A. (1993), "Analysis of the non-penetrating impact behaviour of CFRP laminates", ICCM/9. Composite Behaviour, 5, 366-373.
  6. Ebrahimi, F. and Habibi, S. (2016), "Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate", Steel Compos. Struct., Int. J., 20(1), 205-225. https://doi.org/10.12989/scs.2016.20.1.205
  7. Ebrahimi, F. and Barati, M.R. (2016a), "Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams", Eur. Phys. J. Plus, 131(9), 346. https://doi.org/10.1140/epjp/i2016-16346-5
  8. Ebrahimi, F. and Barati, M.R. (2016b), "Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory", Smart Mater. Struct., 25(10), 105014. https://doi.org/10.1088/0964-1726/25/10/105014
  9. Ebrahimi, F. and Barati, M.R. (2016c), "Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory", Int. J. Smart Nano Mater., 7(3), 119-143. https://doi.org/10.1080/19475411.2016.1223203
  10. Ebrahimi, F. and Barati, M.R. (2016d), "An exact solution for buckling analysis of embedded piezo-electromagnetically actuated nanoscale beams", Adv. Nano Res., Int. J., 4(2), 65-84. https://doi.org/10.12989/anr.2016.4.2.065
  11. Ebrahimi, F. and Barati, M.R. (2016e), "Buckling analysis of smart size-dependent higher order magnetoelectro-thermo-elastic functionally graded nanosize beams", J. Mech., 1-11.
  12. Ebrahimi, F. and Barati, M.R. (2016f), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazil. Soc. Mech. Sci. Eng., 1-16.
  13. Ebrahimi, F. and Barati, M.R. (2016g), "Magnetic field effects on buckling behavior of smart sizedependent graded nanoscale beams", Eur. Phys. J. Plus, 131(7), 1-14. https://doi.org/10.1140/epjp/i2016-16001-3
  14. Ebrahimi, F. and Barati, M.R. (2016h), "Vibration analysis of nonlocal beams made of functionally graded material in thermal environment", Eur. Phys. J. Plus, 131(8), 279. https://doi.org/10.1140/epjp/i2016-16279-y
  15. Ebrahimi, F. and Barati, M.R. (2016i), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vib. Control, 1077546316646239.
  16. Ebrahimi, F. and Barati, M.R. (2016j), "A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures", Int. J. Eng. Sci., 107, 183-196. https://doi.org/10.1016/j.ijengsci.2016.08.001
  17. Ebrahimi, F. and Barati, M.R. (2016k), "Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., 1-13.
  18. Ebrahimi, F. and Barati, M.R. (2016l), "A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment", Applied Physics A, 122(9), 792. https://doi.org/10.1007/s00339-016-0322-2
  19. Ebrahimi, F. and Barati, M.R. (2016m), "Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment", Int. J. Smart Nano Mater., 7(2), 69-90. https://doi.org/10.1080/19475411.2016.1191556
  20. Ebrahimi, F. and Barati, M.R. (2016n), "Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory", Appl. Phys. A, 122(9), 843. https://doi.org/10.1007/s00339-016-0368-1
  21. Ebrahimi, F. and Barati, M.R. (2016o), "Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory", Arab. J. Sci. Eng., 1-12.
  22. Ebrahimi, F. and Barati, M.R. (2016p), "Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field", J. Intell. Mater. Syst. Struct., 1045389X16672569.
  23. Ebrahimi, F. and Barati, M.R. (2016q), Size-dependent thermal stability analysis of graded piezomagnetic nanoplates on elastic medium subjected to various thermal environments. Applied Physics A, 122(10), 910. https://doi.org/10.1007/s00339-016-0441-9
  24. Ebrahimi, F. and Barati, M.R. (2016r), "Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory", Smart Mater. Struct., 25(10), 105014. https://doi.org/10.1088/0964-1726/25/10/105014
  25. Eshelby, J.D. (1957), "The determination of the elastic field of an ellipsoidal inclusion, and related problems", Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, pp. 376-396.
  26. Esawi, A.M. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: potential and current challenges", Mater. Design, 28(9), 2394-2401. https://doi.org/10.1016/j.matdes.2006.09.022
  27. Formica, G., Lacarbonara, W. and Alessi, R. (2010), "Vibrations of carbon nanotube-reinforced composites", J. Sound Vib., 329 (10), 1875-1889. https://doi.org/10.1016/j.jsv.2009.11.020
  28. Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Computat. Mater. Sci., 39(2), 315-323. https://doi.org/10.1016/j.commatsci.2006.06.011
  29. Heydarpour, Y., Aghdam, M. and Malekzadeh, P. (2014), "Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells", Compos. Struct., 117, 187-200. https://doi.org/10.1016/j.compstruct.2014.06.023
  30. Jam, J. and Kiani, Y. (2015), "Low velocity impact response of functionally graded carbon nanotube reinforced composite beams in thermal environment", Compos. Struct., 132, 35-43. https://doi.org/10.1016/j.compstruct.2015.04.045
  31. Jooybar, N., Malekzadeh, P. and Fiouz, A. (2016), "Vibration of functionally graded carbon nanotubes reinforced composite truncated conical panels with elastically restrained against rotation edges in thermal environment", Compos. Part B: Eng., 106, 242-261. https://doi.org/10.1016/j.compositesb.2016.09.030
  32. Kim, M., Park, Y.-B., Okoli, O.I. and Zhang, C. (2009), "Processing, characterization, and modeling of carbon nanotube-reinforced multiscale composites", Compos. Sci. Technol., 69 (3), 335-342. https://doi.org/10.1016/j.compscitech.2008.10.019
  33. Lei, Z., Liew, K.M. and Yu, J. (2013), "Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method", Compos. Struct., 98, 160-168. https://doi.org/10.1016/j.compstruct.2012.11.006
  34. Lei, Z., Zhang, L. and Liew, K. (2015), "Free vibration analysis of laminated FG-CNT reinforced composite rectangular plates using the kp-Ritz method", Compos. Struct., 127, 245-259. https://doi.org/10.1016/j.compstruct.2015.03.019
  35. Li, X., Gao, H., Scrivens, W.A., Fei, D., Xu, X., Sutton, M.A., Reynolds, A.P. and Myrick, M.L. (2007), "Reinforcing mechanisms of single-walled carbon nanotube-reinforced polymer composites", J. Nanosci. Nanotech., 7(7), 2309-2317. https://doi.org/10.1166/jnn.2007.410
  36. Liew, K., Lei, Z. and Zhang, L. (2015), "Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review", Compos. Struct., 120, 90-97. https://doi.org/10.1016/j.compstruct.2014.09.041
  37. Malekzadeh, P. and Dehbozorgi, M. (2016), "Low velocity impact analysis of functionally graded carbon nanotubes reinforced composite skew plates", Compos. Struct., 140, 728-748. https://doi.org/10.1016/j.compstruct.2016.01.045
  38. Malekzadeh, P. and Shojaee, M. (2013), "Buckling analysis of quadrilateral laminated plates with carbon nanotubes reinforced composite layers", Thin-Wall. Struct., 71, 108-118. https://doi.org/10.1016/j.tws.2013.05.008
  39. Malekzadeh, P. and Zarei, A. (2014), "Free vibration of quadrilateral laminated plates with carbon nanotube reinforced composite layers", Thin-Wall. Struct., 82, 221-232. https://doi.org/10.1016/j.tws.2014.04.016
  40. Mura, T. (2013), Micromechanics of Defects in Solids, Springer Science & Business Media.
  41. Qian, D., Dickey, E.C., Andrews, R. and Rantell, T. (2000), "Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites", Appl. Phys. Lett., 76(20), 2868-2870. https://doi.org/10.1063/1.126500
  42. Rafiee, R. and Moghadam, R.M. (2012), "Simulation of impact and post-impact behavior of carbon nanotube reinforced polymer using multi-scale finite element modeling", Computat. Mater. Sci., 63, 261-268. https://doi.org/10.1016/j.commatsci.2012.06.010
  43. Rafiee, M., Liu, X., He, X. and Kitipornchai, S. (2014), "Geometrically nonlinear free vibration of shear deformable piezoelectric carbon nanotube/fiber/polymer multiscale laminated composite plates", J. Sound Vib., 333(14), 3236-3251. https://doi.org/10.1016/j.jsv.2014.02.033
  44. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press.
  45. Sahoo, N.G., Rana, S., Cho, J.W., Li, L. and Chan, S.H. (2010), "Polymer nanocomposites based on functionalized carbon nanotubes", Progress Polym. Sci., 35(7), 837-867. https://doi.org/10.1016/j.progpolymsci.2010.03.002
  46. Seidel, G.D. and Lagoudas, D.C. (2006), "Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites", Mech. Mater., 38(8), 884-907. https://doi.org/10.1016/j.mechmat.2005.06.029
  47. Shen, H.-S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91(1), 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026
  48. Shen, H.-S. (2011), "Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells", Compos. Struct., 93(8), 2096-2108. https://doi.org/10.1016/j.compstruct.2011.02.011
  49. Shen, H.-S. and Zhang, C.-L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates", Mater. Des., 31(7), 3403-3411. https://doi.org/10.1016/j.matdes.2010.01.048
  50. Shen, H.-S. and Zhang, C.-L. (2012a), "Non-linear analysis of functionally graded fiber reinforced composite laminated plates, Part I: Theory and solutions", Int. J. Non-Linear Mech., 47(9), 1045-1054. https://doi.org/10.1016/j.ijnonlinmec.2012.05.005
  51. Shen, H.-S. and Zhang, C.-L. (2012b), "Non-linear analysis of functionally graded fiber reinforced composite laminated plates, Part II: Numerical results", Int. J. Non-Linear Mech., 47(9), 1055-1064. https://doi.org/10.1016/j.ijnonlinmec.2012.03.003
  52. Shenas, A.G., Malekzadeh, P. and Ziaee, S. (2017), "Vibration analysis of pre-twisted functionally graded carbon nanotube reinforced composite beams in thermal environment", Compos. Struct., 162, 325-340. https://doi.org/10.1016/j.compstruct.2016.12.009
  53. Shu, X. and Sun, L. (1994), "Thermomechanical buckling of laminated composite plates with higher-order transverse shear deformation", Comput. Struct., 53(1), 1-7. https://doi.org/10.1016/0045-7949(94)90123-6
  54. Spitalsky, Z., Ttasis D., Papagelis, K. and Galiotis, C. (2010), "Carbon nanotube-polymer composites: chemistry, processing, mechanical and electrical properties", Progress Polym. Sci., 35(3), 357-401. https://doi.org/10.1016/j.progpolymsci.2009.09.003
  55. Sun, C. and Chen, J. (1985), "On the impact of initially stressed composite laminates", J. Compos. Mater., 19(6), 490-504. https://doi.org/10.1177/002199838501900601
  56. Vaziri, R., Quan, X. and Olson, M. (1996), "Impact analysis of laminated composite plates and shells by super finite elements", Int. J. Impact Eng., 18(7), 765-782. https://doi.org/10.1016/S0734-743X(96)00030-9
  57. Wang, J. and Pyrz, R. (2004), "Prediction of the overall moduli of layered silicate-reinforced nanocomposites-part I: basic theory and formulas", Compos. Sci. Technol., 64(7), 925-934. https://doi.org/10.1016/S0266-3538(03)00024-1
  58. Wang, Z.-X. and Shen, H.-S. (2011), "Nonlinear vibration of nanotube-reinforced composite plates in thermal environments", Computat. Mater. Sci., 50(8), 2319-2330. https://doi.org/10.1016/j.commatsci.2011.03.005
  59. Wang, Z.-X. and Shen, H.-S. (2012a), "Nonlinear dynamic response of nanotube-reinforced composite plates resting on elastic foundations in thermal environments", Nonlinear Dyn., 70(1), 735-754. https://doi.org/10.1007/s11071-012-0491-2
  60. Wang, Z.-X. and Shen, H.-S. (2012b), "Nonlinear vibration and bending of sandwich plates with nanotubereinforced composite face sheets", Compos. Part B: Eng., 43(2), 411-421. https://doi.org/10.1016/j.compositesb.2011.04.040
  61. Wang, C. and Zhang, L. (2008), "A critical assessment of the elastic properties and effective wall thickness of single-walled carbon nanotubes", Nanotechnology, 19(7), 075705. https://doi.org/10.1088/0957-4484/19/7/075705
  62. Wang, Z.-X., Xu, J. and Qiao, P. (2014), "Nonlinear low-velocity impact analysis of temperature-dependent nanotube-reinforced composite plates", Compos. Struct., 108, 423-434. https://doi.org/10.1016/j.compstruct.2013.09.024
  63. Yang, S. and Sun, C. (1982), "Indentation law for composite laminates", Proceedings of the 6th Conference on Composite Materials: Testing and Design, ASTM International.
  64. Yas, M. and Heshmati, M. (2012), "Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load", Appl. Math. Model., 36(4), 1371-1394. https://doi.org/10.1016/j.apm.2011.08.037
  65. Zhang, L., Lei, Z., Liew, K. and Yu, J. (2014), "Large deflection geometrically nonlinear analysis of carbon nanotube-reinforced functionally graded cylindrical panels", Comput. Method. Appl. Mech. Eng., 273, 1-18. https://doi.org/10.1016/j.cma.2014.01.024
  66. Zhu, P., Lei, Z. and Liew, K.M. (2012), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94(4), 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010
  67. Zienkiewicz, O.C. and Taylor, R.L. (2005), The Finite Element Method for Solid and Structural Mechanics, Butterworth-heinemann.