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Meccanica

, Volume 54, Issue 14, pp 2263–2279 | Cite as

Buckling of non-uniformly distributed graphene and fibre reinforced multiscale angle-ply laminates

  • Isaac Sfiso Radebe
  • Georgios A. DrosopoulosEmail author
  • Sarp Adali
Article
  • 76 Downloads

Abstract

Present work investigates the biaxial buckling of three-phase, angle-ply laminates reinforced with graphene platelets and carbon or glass fibres. The analysis is based on Classical Plate Theory with the shear effect neglected. The laminate is defined as a three-ply symmetric laminate with simply supported boundary conditions and with different graphene and fibre contents in the surface and middle layers. As such, the laminate has a non-uniform distribution of the reinforcements in the surface and middle layers. Thicknesses of surface and middle layers are also non-uniform, but symmetrical. The objective is to investigate the effect of having a higher content of graphene and fibre in the surface layers as compared to the middle layer and also the effect of the relative thicknesses of the surface and middle layers on the buckling load. The main idea is to produce a cost effective design by concentrating the reinforcements in the surface layers where they are most effective. Thickness of the surface layers can be specified as the minimum required for a given buckling load to reduce the cost and to keep the volume content of the expensive reinforcements to a minimum. Effective properties of the three-phase composite are determined via micromechanical relations. Cost-effective designs using the minimum amount of reinforcements for a given buckling load can be determined from the graphs in the numerical results section. It is observed that relative graphene and fibre contents and thickness ratios of surface and middle layers affect the buckling load at different degrees. It is also observed that higher fibre contents can lead to lower buckling loads if the graphene content exceeds a critical value.

Keywords

Graphene nanoplatelets Buckling Three-phase laminate Non-uniformly distributed reinforcement 

Notes

Funding

This study was funded by Grants from the University of KwaZulu-Natal (UKZN) and from National Research Foundation (NRF) of South Africa.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Zandiatashbar A, Picu C, Koratkar N (2012) Mechanical behavior of epoxy-graphene platelets nanocomposites. J Eng Mater Technol 134:031011-1–031011-6CrossRefGoogle Scholar
  2. 2.
    King KA, Klimek DR, Miskioglu I, Odegard GM (2013) Mechanical properties of graphene nanoplatelet/epoxy composites. J Appl Polym Sci 128:4217–23CrossRefGoogle Scholar
  3. 3.
    Atif R, Shyha I, Inam F (2016a) Mechanical, thermal, and electrical properties of graphene-epoxy nanocomposites—a review. Polymers 8:281.  https://doi.org/10.3390/polym8080281 CrossRefGoogle Scholar
  4. 4.
    Papageorgiou DG, Kinloch IGIA, Young RJ (2017) Mechanical properties of graphene and graphene-based nanocomposites. Prog Mater Sci 90:75–127CrossRefGoogle Scholar
  5. 5.
    Nikfar M, Asghari M (2018) A novel model for analysis of multilayer graphene sheets taking into account the interlayer shear effect. Meccanica 53:3061–3082CrossRefMathSciNetGoogle Scholar
  6. 6.
    Hassanpour S, Mehralian F, Firouz-Abadi RD, Borhan-Panah MR, Rahmanian M (2019) Prediction of in-plane elastic properties of graphene in the framework of first strain gradient theory. Meccanica 54:299–310CrossRefMathSciNetGoogle Scholar
  7. 7.
    Das TK, Prusty S (2013) Graphene-based polymer composites and their applications. J Polym Plast Technol Eng 52:319–331CrossRefGoogle Scholar
  8. 8.
    Singh K, Ohlan A, Dhawan SK (2012) Polymer-graphene nanocomposites: preparation, characterization, properties, and applications, nanocomposites—new trends and developments. In: Ebrahimi F (ed) InTech, RijekaGoogle Scholar
  9. 9.
    Parveen S, Rana S, Fangueiro R (2017) Advanced carbon nanotube reinforced multi-scale composites, advanced composite materials: properties and applications. De Gruyter Open, WarsawGoogle Scholar
  10. 10.
    Rafiee M, Nitzsche F, Labrosse MR (2018a) Modeling and mechanical analysis of multiscale fiber-reinforced graphene composites: nonlinear bending, thermal post-buckling and large amplitude vibration. Int J Non-Linear Mech 103:104–112CrossRefGoogle Scholar
  11. 11.
    Bekyarova E, Thostenson ET, Yu A, Kim H, Gao J, Tang J, Hahn HT, Chou TW, Itkis ME, Haddon RC (2007) Multiscale carbon nanotube-carbon fiber reinforcement for advanced epoxy composites. Langmuir 23:3970–3974CrossRefGoogle Scholar
  12. 12.
    Rafiee M, He XQ, Mareishi S, Liew KM (2014b) Modeling and stress analysis of smart cnts/fiber/polymer multiscale composite plates. Int J Appl Mech 6:1450025CrossRefGoogle Scholar
  13. 13.
    Ahmadi M, Ansari R, Rouhi H (2017) Multi-scale bending, buckling and vibration analyses of carbon fiber/carbon nanotube-reinforced polymer nanocomposite plates with various shapes. Physica E 93:17–25CrossRefADSGoogle Scholar
  14. 14.
    Huang X, Qi X, Boey F, Zhang H (2012) Graphene-based composites. Chem Soc Rev 41:666–86CrossRefGoogle Scholar
  15. 15.
    Rafiee MA, Rafiee J, Wang Z, Song H, Yu ZZ, Koratkar N (2009) Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano 3:3884–90CrossRefGoogle Scholar
  16. 16.
    Atif R, Inam F (2016b) Modeling and simulation of graphene based polymer nanocomposites: advances in the last decade. Graphene 5:96–142CrossRefGoogle Scholar
  17. 17.
    Fang M, Wang K, Lu H, Yang Y, Nutt S (2009) Covalent polymer functionalization of graphene nanosheets and mechanical properties of composites. J Mater Chem 19:7098–105CrossRefGoogle Scholar
  18. 18.
    Park OK, Kim SG, You NH, Ku BC, Hui D, Lee JH (2014) Synthesis and properties of iodo functionalized graphene oxide/polyimide nanocomposites. Compos Part B Eng 56:364–71CrossRefGoogle Scholar
  19. 19.
    Wang H, Xie G, Fang M, Ying Z, Tong Y, Zeng Y (2015b) Electrical and mechanical properties of antistatic PVC films containing multi-layer graphene. Compos Part B Eng 79:444–50CrossRefGoogle Scholar
  20. 20.
    Shokrieh MM, Esmkhani M, Shokrieh Z, Zhao ZZ (2014) Stiffness prediction of graphene nanoplatelet/epoxy nanocomposites by a combined molecular dynamics-micromechanics method. Comput Mater Sci 92:444–450CrossRefGoogle Scholar
  21. 21.
    Song M, Yang J, Kitipornchai S, Zhu W (2017a) Buckling and postbuckling of biaxially compressed functionally graded multilayer graphene nanoplatelet-reinforced polymer composite plates. Int J Mech Sci 131–132:345–355CrossRefGoogle Scholar
  22. 22.
    Song M, Kitipornchai S, Yang J (2017b) Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets. Compos Struct 159:579–588CrossRefGoogle Scholar
  23. 23.
    Feng C, Kitipornchai S, Yang J (2017a) Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLS). Compos Part B Eng 110:132–140CrossRefGoogle Scholar
  24. 24.
    Barati MR, Zenkour AM (2017) Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection. Compos Struct 181:194–202CrossRefGoogle Scholar
  25. 25.
    Gholami R, Ansari R (2017) Large deflection geometrically nonlinear analysis of functionally graded multilayer graphene platelet-reinforced polymer composite rectangular plates. Compos Struct 180:760–771CrossRefGoogle Scholar
  26. 26.
    Yang J, Chen D, Kitipornchai S (2018) Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev–Ritz method. Compos Struct 193:281–294CrossRefGoogle Scholar
  27. 27.
    Wang Y, Feng C, Zhao Z, Yang J (2018a) Eigenvalue buckling of functionally graded cylindrical shells reinforced with graphene platelets (GPL). Compos Struct 202:38–46CrossRefGoogle Scholar
  28. 28.
    Wang Y, Feng C, Zhao Z, Yang J (2018b) Buckling of graphene platelet reinforced composite cylindrical shell with cutout. Int J Struct Stab Dyn 18:1850040CrossRefGoogle Scholar
  29. 29.
    Song M, Yang J, Kitipornchai S (2018) Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets. Compos Part B Eng 134:106–113CrossRefGoogle Scholar
  30. 30.
    Rafiee M, Nitzsche F, Labrosse MR (2019) Processing, manufacturing, and characterization of vibration damping in epoxy composites modified with graphene nanoplatelets. Polym Compos 40:1–9CrossRefGoogle Scholar
  31. 31.
    Rafiee M, Nitzsche F, Laliberte J, Thibault J, Labrosse MR (2019) Simultaneous reinforcement of matrix and fibers for enhancement of mechanical properties of graphene-modified laminated composites. Polym Compos 40:E1732–E1745CrossRefGoogle Scholar
  32. 32.
    Rafiee M, Nitzsche F, Labrosse MR (2019) Fabrication and experimental evaluation of vibration and damping in multiscale graphene/fiberglass/epoxy composites. J Compos Mater 53:2105–2118CrossRefGoogle Scholar
  33. 33.
    Khan SU, Li CY, Siddiqui NA, Kim JK (2011) Vibration damping characteristics of carbon fiber-reinforced composites containing multi-walled carbon nanotubes. Compos Sci Technol 71:1486–1494CrossRefGoogle Scholar
  34. 34.
    Yang B, Yang J, Kitipornchai S (2017) Thermoelastic analysis of functionally graded graphene reinforced rectangular plates based on 3D elasticity. Meccanica 52:2275–2292CrossRefMathSciNetzbMATHGoogle Scholar
  35. 35.
    Zhao Z, Feng C, Wang Y, Yang J (2017) Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLS). Compos Struct 180:799–808CrossRefGoogle Scholar
  36. 36.
    García-Macías E, Rodríguez-Tembleque L, Sáez A (2018) Bending and free vibration analysis of functionally graded graphene vs. carbon nanotube reinforced composite plates. Compos Struct 186:123–38CrossRefGoogle Scholar
  37. 37.
    Shen HS, Xiang Y, Fan Y, Hui D (2018b) Nonlinear bending analysis of FG–GRC laminated cylindrical panels on elastic foundations in thermal environments. Compos Part B Eng 141:148–157CrossRefGoogle Scholar
  38. 38.
    Kitipornchai S, Chen D, Yang J (2017) Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Mater Des 116:656–65CrossRefGoogle Scholar
  39. 39.
    Wu H, Yang J, Kitipornchai S (2017) Dynamic instability of functionally graded multilayer graphene nanocomposite beams in thermal environment. Compos Struct 162:244–254CrossRefGoogle Scholar
  40. 40.
    Yang J, Wu H, Kitipornchai S (2017) Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams. Compos Struct 161:111–118CrossRefGoogle Scholar
  41. 41.
    Kiani Y, Mirzaei M (2018) Enhancement of non-linear thermal stability of temperature dependent laminated beams with graphene reinforcements. Compos Struct 186:114–22CrossRefGoogle Scholar
  42. 42.
    Huang Y, Yang Z, Liu A, Fu J (2018) Nonlinear buckling analysis of functionally graded graphene reinforced composite shallow arches with elastic rotational constraints under uniform radial load. Materials 11:910.  https://doi.org/10.3390/ma11060910 ADSCrossRefGoogle Scholar
  43. 43.
    Shen HS, Xiang Y, Lin F, Hui D (2017) Buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates in thermal environments. Compos Part B Eng 119:67–78CrossRefGoogle Scholar
  44. 44.
    Shen HS, Xiang Y (2019) Thermal buckling and postbuckling behavior of FG–GRC laminated cylindrical shells with temperature-dependent material properties. Meccanica 54:283–297CrossRefMathSciNetGoogle Scholar
  45. 45.
    Feng C, Kitipornchai S, Yang J (2017b) Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLS). Eng Struct 140:110–119CrossRefGoogle Scholar
  46. 46.
    Barati MR, Zenkour AM (2018) Vibration analysis of functionally graded graphene platelet reinforced cylindrical shells with different porosity distributions. Mech Adv Mater Struct 26:1–9Google Scholar
  47. 47.
    Shen HS, Xiang Y, Fan Y, Hui D (2018a) Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical panels resting on elastic foundations in thermal environments. Compos Part B Eng 136:177–86CrossRefGoogle Scholar
  48. 48.
    Thostenson ET, Li WZ, Wang DZ, Ren ZF, Choua TW (2002) Carbon nanotube-carbon fibre hybrid multiscale composites. J Appl Phys 91:6034–6037CrossRefADSGoogle Scholar
  49. 49.
    Inam F, Wong DWY, Kuwata M, Peijs T (2010) Multiscale hybrid micro-nanocomposites based on carbon nanotubes and carbon fibers. J Nanomater Article ID 453420:12 PagesGoogle Scholar
  50. 50.
    Ashrafi B, Guan J, Mirjalili V, Zhang Y, Chun L, Hubert P, Simard B, Kingston CT, Bourne O, Johnston A (2011) Enhancement of mechanical performance of epoxy/carbon fiber laminate composites using single-walled carbon nanotubes. Compos Sci Technol 71:1569–1578CrossRefGoogle Scholar
  51. 51.
    Seidi J, Kamarian S (2017) Free vibrations of non-uniform CNT/fiber/polymer nanocomposite beams. Curved Layer Struct 4:21–30Google Scholar
  52. 52.
    Gholami R, Ansari R, Gholami Y (2018) Numerical study on the nonlinear resonant dynamics of carbon nanotube/fiber/polymer multiscale laminated composite rectangular plates with various boundary conditions. Aerosp Sci Technol 78:118–129CrossRefGoogle Scholar
  53. 53.
    Jamal-Omidi M, ShayanMehr M (2018) An experimental study on the nonlinear free vibration response of epoxy and carbon fiber-reinforced composite containing single-walled carbon nanotubes. J Vib Control 24:4529–4540CrossRefGoogle Scholar
  54. 54.
    Kamarian S, Shakeri M, Yas MH (2018) Natural frequency analysis and optimal design of CNT/fiber/polymer hybrid composites plates using Mori–Tanaka approach, GDQ technique, and firefly algorithm. Polym Compos 39:1433–1446CrossRefGoogle Scholar
  55. 55.
    Rafiee M, Liu XF, He XQ, Kitipornchai S (2014a) Geometrically nonlinear free vibration of shear deformable piezoelectric carbon nanotube/fiber/polymer multiscale laminated composite plates. J Sound Vib 333:3236–3251CrossRefADSGoogle Scholar
  56. 56.
    Rafiee M, Nitzsche F, Labrosse MR (2018b) Cross-sectional design and analysis of multiscale carbon nanotubes-reinforced composite beams and blades. Int J Appl Mech 10:1850032CrossRefGoogle Scholar
  57. 57.
    Rafiee MA, Rafiee J, Yu ZZ, Koratkar N (2009) Buckling resistant graphene nanocomposites. Appl Phys Lett 95:223103CrossRefADSGoogle Scholar
  58. 58.
    Liu S, Hou Y, Sun X, Zhang Y (2012) A two-step optimization scheme for maximum stiffness design of laminated plates based on lamination parameters. Compos Struct 94:3529–3537CrossRefGoogle Scholar
  59. 59.
    Liu Q (2015) Analytical sensitivity analysis of eigenvalues and lightweight design of composite laminated beams. Compos Struct 134:918–926CrossRefGoogle Scholar
  60. 60.
    Liu Q, Paavola J (2016) Lightweight design of composite laminated structures with frequency constraint. Compos Struct 156:356–360CrossRefGoogle Scholar
  61. 61.
    Vo-Duy T, Ho-Huu V, Do-Thi TD, Dang-Trung H, Nguyen-Thoi T (2017) A global numerical approach for lightweight design optimization of laminated composite plates subjected to frequency constraints. Compos Struct 159:646–655CrossRefGoogle Scholar
  62. 62.
    Kassapoglou C (2013) Design and analysis of composite structures: with applications to aerospace structures, 2nd edn. Wiley, New YorkCrossRefGoogle Scholar
  63. 63.
    Reddy JN (2004) Mechanics of laminated composite plates and shells: theory and analysis, 2nd edn. CRC Press, Boca RatonCrossRefzbMATHGoogle Scholar
  64. 64.
    Reddy JN (2007) Theory and analysis of elastic plates and shells, 2nd edn. CRC Press, Boca RatonGoogle Scholar
  65. 65.
    Banerjee S, Sankar BV (2014) Mechanical properties of hybrid composites using finite element method based micromechanics. Compos Part B Eng 58:318–327CrossRefGoogle Scholar
  66. 66.
    Choi S, Sankar BV (2006) Micromechanical analysis of composite laminates at cryogenic temperatures. J Compos Mater 40:1077–1091CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringDurban University of TechnologyDurbanSouth Africa
  2. 2.Discipline of Civil Engineering, Howard CollegeUniversity of KwaZulu-NatalDurbanSouth Africa
  3. 3.Discipline of Mechanical Engineering, Howard CollegeUniversity of KwaZulu-NatalDurbanSouth Africa

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