In the present work, the elastic modulus of two series of polymer/hybrid nanocomposites, with a combination of graphene oxide (GO) either with multi walled carbon nanotubes (MWCNTs) or carbon nanofibers (CNFs) at an equal ratio and varying the total loading, was studied by a 3D finite element method. The two polymers employed as matrices were linear low-density polyethylene (mLLDPE) and poly-lactic acid (PLA) and comparison with the experimental data has been performed. The different degree of the mechanical enhancement between the two series of the polymer nanocomposites at comparable nanofiller loadings was analyzed. Given the importance of the geometrical features, the assumptions of straight and curved CNTs/CNFs, agglomeration and a combination of agglomeration and curvature, four representative volume elements (RVEs) were generated within the frame of Digimat-FE. A closer approximation to the experimental data was achieved under the assumption of both agglomeration and curvature. The lowest deviation was detected for the PLA/GO/CNF hybrid nanocomposites at the three nanofiller loadings. It was revealed that considering the coexistence of agglomerates formation and the curvature of CNTs/CNFs is an important condition for predicting the Young’s modulus.
SirajSAl-MarzouqiAIqbalM, et al.Impact of micro silica filler particle size on mechanical properties of polymeric based composite material. Polymers2022; 14: 4830.
2.
ChenYHanLDongL. Effect of silica particle size on the microstructure and physical properties of microporous poly(L-lactic acid) produced by uniaxial stretching. Polym Test2019; 79: 106051.
3.
SattlerK. Scanning tunneling microscopy of carbon nanotubes and nanocones. Carbon1995; 33: 915–920.
4.
FilleterTBernalRLiS, et al.Ultrahigh strength and stiffness in crosslinked hierarchical carbon nanotube bundles. Adv Mater2011; 23: 2855–2860.
5.
DikinDAStankovichSZimneyEJ, et al.Preparation and characterization of graphene oxide paper. Nature2007; 448: 457–460.
6.
RuoffRSLorentsDC. Mechanical and thermal properties of carbon nanotubes. Carbon1995; 33: 925–930.
7.
RostamiAMoosavMI. High-performance thermoplastic polyurethane nanocomposites induced by hybrid application of functionalized graphene and carbon nanotubes. J Appl Polym Sci2020; 137; 48520. DOI: 10.1002/APP.48520.
8.
CanalesJFernándezMPeñaJJ, et al.Rheological methods to investigate graphene/amorphous polyamide nanocomposites: aspect ratio, processing, and crystallization. Polym Eng Sci2015; 55: 1142–1151. DOI: 10.1002/pen.2398.
9.
FisherFTBradshawRDBrinsonLC. Fiber waviness in nanotube-reinforced polymer composites—I: modulus predictions using effective nanotube properties. Compos Sci Technol2003; 63: 1689–1703. DOI: 10.1016/S0266-3538(03)00069-1.
10.
BradshawRDFisherFTBrinsonLC. Fiber waviness in nanotube-reinforced polymer composites—II: modeling via numerical approximation of the dilute strain concentration tensor. Compos Sci Technol2003; 63: 1705–1722. DOI: 10.1016/S0266-3538(03)00070-8.
11.
BhattacharyaM. Polymer nanocomposites—a comparison between carbon nanotubes, graphene, and clay as nanofillers. Materials2016; 9: 262. DOI: 10.3390/ma9040262.
12.
GeorgousisGCharitosIKontouE, et al.Thermomechanical-electrical properties and micromechanics modeling of linear low density polyethylene reinforced with multi-walled carbon nanotubes. Polym Compos2018; 39: 1118–1128. DOI: 10.1002/pc.24584.
13.
CharitosIGeorgousisGKontouE. Preparation and thermomechanical Characterization of metallocene linear low-density polyethylene/carbon nanotube nanocomposites. Polym Compos2019; 40: 1263–1273. DOI: 10.1002/pc.24961.
14.
WuYGuZChenM, et al.Effect of functionalization of multi-walled carbon nanotube on mechanical and viscoelastic properties of polysulfide-modified epoxy nanocomposites. High Perform Polym2017; 29: 151–160.
15.
LiuYChenX. Evaluations of the effective material properties of carbon nanotubebased composites using a nanoscale representative volume element. Mech Mater2003; 35(1): 69–81.
16.
LinXLiuXJiaJ, et al.Electrical and mechanical properties of carbon nanofiber/graphene oxide hybrid papers. Compos Sci Technol2014; 100: 166–173. DOI: 10.1016/j.compscitech.2014.06.012.
17.
LeeCWeiXKysarJW, et al.Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science2008; 321: 385–388.
18.
HoepfnerJCLoosMRPezzinSH. Evaluation of thermomechanical properties of polyvinyl butyral nanocomposites reinforced with graphene nanoplatelets synthesized by in situ polymerization. J Appl Polym Sci2018; 135: 46157. DOI: 10.1002/app.46157.
19.
AbrishamMPanahi-SarmadMMir Mohamad SadeghiG, et al.Microstructural design for enhanced mechanical property and shape memory behavior of polyurethane nanocomposites: role of carbon nanotube, montmorillonite, and their hybrid fillers. Polym Test2020; 89: 106642. DOI: 10.1016/j.polymertesting.2020.106642.
20.
PeretsYAleksandrovychLMelnychenkoM, et al.The electrical properties of hybrid composites based on multiwall carbon nanotubes with graphite nanoplatelets. Nanoscale Res Lett2017; 12: 406. DOI: 10.1186/s11671-017-2168-8.
21.
CharitosIGeorgousisGKlonosPA, et al.The synergistic effect on the thermomechanical and electrical properties of carbonaceous hybrid polymer nanocomposites. Polym Test2021; 95: 107102. DOI: 10.1016/j.polymertesting.2021.107102.
22.
CharitosIKlonosPAKyritsisA, et al.Thermomechanical performance of biodegradable poly(lactic acid)/carbonaceous hybrid nanocomposites: comparative study. Polym Compos2022; 43: 1900–1915. DOI: 10.1002/pc.26506.
23.
JoshiUAJoshiPHarshaSP, et al.Evaluation of the mechanical properties of carbon nanotube based composites by finite element analysis. Int J Eng Sci Technol2010; 2(5): 1098–1107.
24.
MeisamOHossein RokniDTMilaniAS, et al.Prediction of the mechanical characteristics of multi-walled carbon nanotube/epoxy composites using a new form of the rule of mixtures. Carbon2010; 48: 3218–3228. DOI: 10.1016/j.carbon.2010.05.007.
25.
AnsariRRouhiSEghbalianM. On the elastic properties of curved carbon nanotubes/polymer nanocomposites: a modified rule of mixture. J Reinforc Plast Compos2017; 36(14): 991–1008.
ArmbristerCEEOkoliOIShanbhagS. Micromechanics predictions for two-phased nanocomposites and three-phased multiscale composites: a review. J Reinforc Plast Compos2015; 34(8): 605–623. DOI: 10.1177/0731684415574297.
28.
García-MacíasEFelipe GuzmánCFloresEIS, et al.Multiscale modeling of the elastic moduli of CNT- reinforced polymers and fitting of efficiency parameters for the use of the extended rule-of-mixtures. Composites Part B2019; 159: 114–131. DOI: 10.1016/j.compositesb.2018.09.057.
29.
CharitosIDrougkasAKontouE. Prediction of the elastic modulus of LLDPE/CNT nanocomposites by analytical modeling and finite element analysis. Mater Today Commun2020; 24: 101070. DOI: 10.1016/j.mtcomm.2020.101070.
30.
MaghsoudlouMABarbaz IsfahaniRSaber-SamandariS, et al.Effect of interphase, curvature and agglomeration of SWCNTs on mechanical properties of polymer-based nanocomposites: experimental and numerical investigations. Composites Part B2019; 175: 107119. DOI: 10.1016/j.compositesb.2019.107119.
31.
LiYSeidelGD. Multiscale modeling of the interface effects in CNT-epoxy nanocomposites. Comput Mater Sci2018; 153: 363–381. DOI: 10.1016/j.commatsci.2018.07.015.
32.
PoorsolhjouyAHassan NaeiM. Effects of carbon nanotubes’ dispersion on effective mechanical properties of nanocomposites: a finite element study. J Reinforc Plast Compos2015; 34(16): 1315–1328. DOI: 10.1177/0731684415590676.
33.
RafieeREskandariyunA. Predicting Young’s modulus of agglomerated graphene/polymer using multi-scale modeling. Compos Struct2020; 245: 112324. DOI: 10.1016/j.compstruct.2020.112324.
34.
RafieeRFirouzbakhtV. Multi-scale modeling of carbon nanotube reinforced Polymers using irregular tessellation technique. Mech Mater2014; 78: 74–84. DOI: 10.1016/j.mechmat.2014.07.021.
35.
RafieeRShahzadiR. Predicting mechanical properties of nanoclay/polymer composites using stochastic approach. Composites Part B2018; 152: 31–42. DOI: 10.1016/j.compositesb.2018.06.033.
36.
RafieeRGhorbanhosseiniA. Predicting mechanical properties of fuzzy fiber reinforced composites: radially grown carbon nanotubes on the carbon fiber. Int J Mech Mater Des2018; 14: 37–50.
37.
RafieeREskandariyunA. Estimating Young’s modulus of graphene/polymer composites using stochastic multi-scale modeling. Composites Part B2019; 173: 106842. DOI: 10.1016/j.compositesb.2019.05.053.
38.
EyupCDBenkaddourAAldrichDR, et al.A predictive model towards Understanding the effect of reinforcement agglomeration on the stiffness of nanocomposites. J Compos Mater2022; 56(10): 1591–1604. DOI: 10.1177/00219983221076639.
39.
ThorvaldsenTJohnsenBBOlsen TT, et al.Investigation of theoretical models for the elastic stiffness of nanoparticle-modified polymer composites. Hindawi Publishing Corporation Journal of Nanomaterials2015; 2015: 17. DOI: 10.1155/2015/281308.
40.
VattathurvalappilSHHaqM. Thermomechanical characterization of Nano-Fe3O4 reinforced thermoplastic adhesives and single lap-joints. Composites Part B2019; 175: 107162. DOI: 10.1016/j.compositesb.2019.107162.
41.
RohamRAbdolhosseinFHeidarhaeiM. Influence of non- bonded interphase on crack driving force in carbon nanotube reinforced polymer. Comput Mater Sci2012; 56: 25–28. DOI: 10.1016/j.commatsci.2011.12.025.
42.
ShokriehMMRafieeR. Development of a full range multi-scale model to obtain elastic properties of CNT/polymer composites. Iran Polym J (Engl Ed)2012; 21: 397–402.
43.
RohamRAminG. Stochastic multi-scale modeling of randomly grown CNTs on carbon fiber. Mech Mater2017; 106: 1–7.
44.
RafieeRSahraeiM. Characterizing delamination toughness of laminated composites containing carbon nanotubes: experimental study and stochastic multi-scale modeling. Compos Sci Technol2021; 201: 108487.
45.
RafieeRZehtabzadehHAminiMR. Predicting mechanical properties of 3D printed nanocomposites using multi-scale modeling. Addit Manuf2024; 83: 104055. DOI: 10.1016/j.addma.2024.104055.
46.
RafieeRRabczukTPouraziziR, et al.Challenges of the modeling methods for investigating the interaction between the CNT and the surrounding polymer. Adv Mater Sci Eng2013; 2013: 1–10. DOI: 10.1155/2013/183026.
47.
RohamRMahdaviM. Characterizing nanotube–polymer interaction using molecular dynamics simulation. Comput Mater Sci2016; 112: 356–363. DOI: 10.1016/j.commatsci.2015.10.041.
48.
Hyder VattathurvalappilSHaqMKundurthS. Hybrid nanocomposites—an efficient representative volume element formulation with interface properties. Polym Polym Compos2022; 30: 1–13. DOI: 10.1177/09673911221084651.
49.
BataklievTGeorgievVAngelovV, et al.Synergistic effect of graphene nanoplatelets and multiwall carbon nanotubes incorporated in PLA matrix: nanoindentation of composites with improved mechanical properties. J Mater Eng Perform2021; 30: 3822–3830.
50.
SantoJPenumakalaPKAdusumalliRB. Mechanical and electrical properties of three-dimensional printed polylactic acid–graphene–carbon nanofiber composites. Polym Compos2021; 42: 3231–3242. DOI: 10.1002/pc.26053.
51.
GeorgantzinosSKMarkolefasSIMavrommatisSA, et al.Finite element modelling of carbon fiber – carbon nanostructure - polymer hybrid composite structures. MATEC Web Conf2020; 314: 02004. ICSC-ISATECH 2019. DOI: 10.1051/matecconf/202031402004.
52.
SuhasAUDhamalNAShindeDK, et al.Polymeric hybrid nanocomposites processing and finite element modeling: an overview. Sci Prog2021; 104(3): 1–44. DOI: 10.1177/00368504211029471.
53.
KilikevičiusSKvietkaitėSŽukienėK, et al.Numerical investigation of the mechanical properties of a novel hybrid polymer composite reinforced with graphene and MXene nanosheets. Comput Mater Sci2020; 174: 109497. DOI: 10.1016/j.commatsci.2019.109497.
54.
DulSEccoLGPegorettiA, et al.Graphene/carbon nanotube hybrid nanocomposites: effect of compression molding and fused filament fabrication on properties. Polymer2020; 12: 101.
55.
CharitosIMouzakisDKontouE. Comparing the rheological and reinforcing effects of graphene oxide on glassy and semicrystalline polymers. Polym Eng Sci2019; 59: 1933–1947. DOI: 10.1002/pen.25195.
56.
AroraGPathakH. Modeling of transversely isotropic properties of CNT-polymer composites using meso-scale FEM approach. Composites Part B2019; 166: 588–597. DOI: 10.1016/j.compositesb.2019.02.061.
