Studies on Effective Elastic Properties of CNT/Nano-Clay Reinforced Polymer Hybrid Composite

Transcription

1 IOP onference Series: Materials Science and Engineering PAPER OPEN AESS Studies on Effective Elastic Properties of NT/Nano-lay Reinforced Polyer Hybrid oposite To cite this article: Arvind Kuar Thakur et al 6 IOP onf. Ser.: Mater. Sci. Eng. 5 7 View the article online for updates and enhanceents. Related content - orrigendu: Effective elastic properties of two diensional ultiplanar hexagonal nanostructures (7 D Mater. 4 56) T Mukhopadhyay, A Mahata, S Adhikari et al. - Deterination of effective elastic properties of etal atrix coposites with daage particulates using hoogenization ethod S Z Hali, K S Basaruddin, I Ibrahi et al. - The influence of defects on the effective Young's odulus of a defective solid Shen Wei, Fan Qun-Bo, Wang Fu-hi et al. Recent citations - Elastic behavior of NT-reinforced polyer coposites with discontinuities in NT configurations Puneet Kuar and Dr. J. Srinivas This content was downloaded fro IP address on //8 at 3:5

2 IOP onf. Series: Materials Science and Engineering 5 (6) 7 doi:.88/ x/5//7 Studies on Effective Elastic Properties of NT/Nano-lay Reinforced Polyer Hybrid oposite Arvind Kuar Thakur, Puneet Kuar,J. Srinivas 3 Master student, Research scholar, 3 Associate Professor Departent of Mechanical Engineering, National Institute of Technology Rourkela, Rourkela-7698, Odisha, India * E-ail: srin7@yahoo.co.in, Phone: Abstract.This paper presents a coputational approach to predict elastic propertiesof hybrid nanocoposite aterial prepared by adding nano-clayplatelets to conventional NT-reinforced epoxy syste. In coparison to polyers alone/single-fiber reinforced polyers, if an additional fiber is added to the coposite structure, it was found a drastic iproveent in resultant properties. In this regard, effective elastic oduli of a hybrid nano coposite are deterined by using finite eleent (FE) odel with square representative volue eleent (RVE). ontinuu echanics based hoogenization of the nano-filler reinforced coposite is considered for evaluating the voluetric average of the stresses and the strains under different periodic boundary conditions.a three phase Halpin-Tsai approach is selected to obtain the analytical result based on icroechanical odeling. The effect of the volue fractions of NTs and nano-clay platelets on the echanical behavior is studied. Two different RVEs of nano-clay platelets were used to investigate the influence of nano-filler geoetry on coposite properties. The cobination of high aspect ratio of NTs and larger surface area of clay platelets contribute to the stiffening effect of the hybrid saples. Results of analysis are validated with Halpin-Tsai epirical forulae. Keywords:Nano-clay, NT, Hybrid coposite, FEM, Halpin-Tsai, RVE.. Introduction Polyers with suitable and proper nano filler have eerged as an advanced polyeric coposites syste which shows prospective applications in the field of autootive, aerospace, packaging and construction industries []. opared to conventional and icro fillers, carbon nanotubes (NTs) reinforced polyers have gained increased interest in both industrial and acadeic fields, specifically utilizing their high aspect ratio and treendous echanical strength of NTs [-4]. But practical point of view NT reinforced polyer coposite aterials have liited applications because of poor load transfer through interfacial region and aggloerations of NTs [5-6]. Surface treatent and cheical functionalization are few effective techniques to enhance the interfacial adhesion and dispersion ability of NTs [7-8]. Siilarly, polyer aterials reinforced with Nano fillers such as layered silicates (clay) [9] are proinent substitute for conventional coposite aterials. Intuitively, polyer/clay Nano coposite provide best perforance with high degree of clay exfoliation. With the tie, rapid advanceent have taken place in aterial science and technology and developed new generation ulti-scale, ultifunctional nanostructured hybrid polyer coposite reinforced by NTs and other nano reinforceents. Therefore, it becoes necessary to investigate the reinforcing echanis of hybrid polyer coposite which provides basic foundation for odeling and design of these high perforances coposite. lay- NT/polyer atrix hybrid coposite [-4] is one of the ost widely used aterials due to their light weight, long durability, high strength, cheical resistant, and so forth. Great deals of analytical and ontent fro this work ay be used under the ters of the reative oons Attribution 3. licence. Any further distribution of this work ust aintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by Ltd

3 IOP onf. Series: Materials Science and Engineering 5 (6) 7 doi:.88/ x/5//7 nuerical works have been carried out to investigate the echanical properties of NTs reinforced polyer [5-6] and clay reinforced polyer [7] coposite separately. Aong the analytical techniques eployed to obtain effective properties of coposite, ost of the researchers used the rule of ixture and Halpin-Tsai equations to odeling nanocoposite. However, few odifications have been eployed to traditional theories to account the irregular geoetry and distribution of nanostructured reinforceent at nano-scale for hybrid coposite. Till to date no work found in literature related to odeling of clay- NTs/polyer hybrid coposite, however few articles are investigated nuerical analysis of silica nanoparticle-mwnt hybrid coposite [8]. Jia eta al. [9] prepared a novel nanostructure hybrid (SiO-MWNTs) polyer coposite, in which nano silica particle are grown over NTs. Rahanian et al.[] deonstrate the FE odeling of carbon nanotube silica reinforced epoxy coposite considering that NTs are grown over icro silica particle. In ost of work related to hybrid coposite finite eleent ethod is an efficient and preferable nuerical approach for investigating the reinforcing effect of different nano fillers on polyer coposite. This ethod deonstrates the continuu representation of nano filler structure and polyer atrix. Since NTs/nano-clay hybrid showed proinent reinforceent on polyer atrix than pure NTs as reported in previous work, there is a great potential in preparing new generation high perforance coposite. In present work, finite eleent ethod is used to predict the elastic behavior of epoxy coposite reinforce by NTs and nano-clay platelets. Specifically, to accurately describe geoetry and reinforcing echanis of NTs and nano-clay platelets, the traditional theories of the rule of ixtures and Halpin Tsai equations were properly corrected and a finite eleent approach based on nano-scale representative volue eleent (RVE) odel was built up. To better understand the stiffening effect of NTs and nano-clay nanoparticles in hybrid polyer coposite, the tensile odulus for NT/nanoclay/epoxy coposites predicted by three phase Halpin Tsai equations, were copared with FEM outcoes.. Modeling of hybrid coposite Modelling of NT and nano clay reinforced hybrid coposite is presented in two steps. In first part illustrate the icroechanical odelling and second one nuerical odelling (FEM)...Microechanical odeling To predict the echanical properties of three phase polyer coposite, Halpin-Tsai odel and theory of icroechanics were applied in hierarchy. The rule of ixture are used to obtained the effective elastic odulus of effective clay particle and effective NT fiber (as shown in figure ) which include clay, NT and interphase as follow, EP Eclay Eint ( ) () EF Ecnt Eint ( ) () Where E P and E F are the effective elastic odulus of clay particle and NT fiber. E clay, E cnt, α, β are the elastic odulus and volue fractions of clay and NT respectively.

4 IOP onf. Series: Materials Science and Engineering 5 (6) 7 doi:.88/ x/5//7 t t d c d I d I Interphase lay Interphase Effective clay particle d p Interphase r i r Effective NT r o r int NT fiber Fig. :- Representation of effective lay particle and effective NT fiber To evaluate the elastic odulus of hybrid coposite by cobining effective particle and polyer (epoxy) by using odified Halpin-Tsai odel as follow. P P ( PVP FVF ) (3) ( V V ) P P F F Where, P is the elastic property of hybrid coposite and P is elastic properties of polyer atrix. P F ( P ( P P P ( P ( P F F / P / P / P / P ) ) ) ) (4) (5) V V V (6) P F Where V, V P, and V F are the volue fraction of polyer atrix, clay particle and NT fiber respectively. ε, ε are the reinforceent efficiency paraeters for clay particle and NT fiber. For, longitudinal elastic odulus (l/d p ), (l/d) and for transverse elastic odulus 3 log(l/d p ),. Where d p =d c +*d I, d=r are total thickness of effective clay particle and diaeter of effective NT fiber respectively. Figure deonstrate the overall odeling procedure of NT/nano-clay reinforced hybrid coposite using icroechanical odeling. 3

5 IOP onf. Series: Materials Science and Engineering 5 (6) 7 doi:.88/ x/5//7 NT NT/Polyer Interphase Nano-lay Nano-lay/Polyer Interphase NT Fiber + Polyer + Nano-lay Particle Hybrid oposite Fig. :- Modeling procedure of NT/nano-clay reinforced hybrid coposite..onstitutive relations and RVE odel For a transversely isotropic coposite, the aterial behavior is based on only five independent constants. This concept is particularly ensured for regular fiber arrangeent. In this work arbitrary fiber distributions are considered which results in transversely isotropic properties. By considering effective stiffness coefficient and average stress-strain value, the constitutive equations for the hoogenized coposite can be expressed as (7) A representative volue eleent odel can be used for the calculation of effective elastic coefficients by applying the appropriate periodic boundary conditions under the assuption of periodicity of fiber arrangeent. Figure 3 shows the RVE odel for NT/nano-clay reinforced polyer coposite. 4

6 IOP onf. Series: Materials Science and Engineering 5 (6) 7 doi:.88/ x/5//7 Fig. 3:- RVE of NT/nano-clay reinforced polyer The ain advantage of the ethod is to replace the original coposite with globally hoogenized equivalent ediu with sae strain energy stored. To find out effective elastic coefficients such load cases with different boundary conditions ust be applied that for a particular load case only one value in the strain field vector is non-zero and all other becoes zero. Then fro corresponding colun, the effective coefficients can be deterined using calculated average stress value corresponding to unit strain..3.finite eleent odeling A three diensional ulti-field eleents is used for finite eleent calculations using FE package ANSYS. ANSYS Paraetric Design Language (APDL) coding is used for odeling and applying the constraint equations. An algorith was written in APDL for autoated generation of RVE with aligns NT and clay inside the polyer atrix. First -D odel is generated in X -X 3 plane with circle as NT and rectangle as clay and eshed with PLANE8 eleent. Further FE esh is extruded in X direction with SOLID85, 3-D eleent for eshing of RVE. Fibers surfaces are connected by Boolean operation with the ai of predicting the odulus of resin atrix reinforced with periodic nano-reinforceent of clay-nts. An interphase region is also considered here between NT/polyer and clay/polyer to deonstrate the iperfect load transfer phenoenon at interfaces. The interphase region is eshed with rando aterial properties lies between fiber and polyer atric properties. The generation of RVE can be controlled by soe input paraeters like size of RVE, NT and nano-clay diaeters for desired voluefraction. A certain iniu distance ust be ensuring to generate suitable eshing of each part of odel. Fro the nuerical analysis, the effective elastic paraeters of copositional aterial were estiated by relating boundary conditions.the calculation of effective coefficients in order to evaluate the overall stiffness atrix [] of hybrid coposite, RVE is subjected to an average strain. The six coponents of strain are applied by iposing the following boundary conditions on the displaceent coponents. a x a ui ( a, x, x3 ) ui ( a, x, x3 ) a i a3 x3 a3 a x a u x, a, x ) u ( x, a, x ) a a x a i ( 3 i 3 i

7 IOP onf. Series: Materials Science and Engineering 5 (6) 7 doi:.88/ x/5//7 u a x a i ( x, x, a3 ) ui ( x, x, a3 ) a3 i3 a x a (8) Here a j ε ij represents the applied displaceent necessary to enforce a strain ε ij over a distance a j. The strain applied on boundary results in coplex state of strain inside the RVE. So, volue average strain in the RVE equals to the applied strain, i.e. ij ijdv ij V V (9) onsidering hybrid coposite as hoogeneous aterial, the average stress-strain relationship can be written as () By choosing a unit applied strain in one direction and iposing periodic boundary conditions on other directions, stress field can be coputed. Whose average value over the volue gives the required coponents of stiffness atrix, one colun at a tie; x x x dv V,, 3 V () Where α, β are varying to 3. Gauss-Legendre quadrature can be used for evaluating the volue integrals of a finite eleent. oercial ANSYS have such type of capability to evaluate the average stress over the volue, eleent by eleent. Three loading cases are iposed to evaluate the all elastic coefficient of [] for transversely isotropic coposite. Figure 4 shows the eshing of RVEs used in finite eleent analysis. (a) (b) Fig. 4:- Meshing of (a) NT and 4 clay based RVE (b) clay and 4 NT based RVE 3. Results and discussion By considering interphase paraeters, elastic behavior of nanocoposite reinforced by NTs and nanoclay plateletsis first analyzed. The advantages of nano-clay in NT- reinforced polyer coposite can be explained with reduction of interfacial reinforcing area of NTs and enhancing the interfacial adhesion and dispersion of NTs in polyer. In Fig.5 stress and strain distributionswere shown to explain the elastic behavior of NT/nano-clay reinforced hybrid coposite. 6

8 IOP onf. Series: Materials Science and Engineering 5 (6) 7 doi:.88/ x/5//7 (a) (b) Fig. 5:- (a) Stress and (b) strain distribution across cross-section of a RVE The elastic and geoetric property of each phase of RVE is listed in table. For siplification of calculation RVE length is considered as 5 n. Table Material property of all phases in RVE Material Elastic Modulus Poisson s ratio Geoetry (GPa) ( ) Epoxy.6.4 5x5 n NT 54.5 r i =.35 n, r o =.65 lay (MMT) 78.8 t=4 n, d c = n NT/polyer 6..4 r int =.44 n interphase lay/polyer interphase 6..4 d I =3 n A case study has been illustrated to reveal the iportance of nano-clay reinforceent in NT reinforced coposite. Table shows the elastic properties of NT/clay hybrid coposite considering four types RVE. The finite eleent odeling results are validated with icroechanical odeling results. Table Elastic properties of hybrid coposite with variation of nuber of clay platelet RVE with E L E T G T υ L υ T NT NT + lay NT + lay NT + 3 lay NT +4 lay Three phase Halpin-Tsai

9 IOP onf. Series: Materials Science and Engineering 5 (6) 7 doi:.88/ x/5//7 In Table 3, elastic oduli are investigated considering constant volue fraction of NTs inside hybrid coposite. It can be concluded fro predicted results that four NTs with one clay based RVE gives better results as copared to one NT with four-clay RVE. Table 3 Elastic properties of hybrid coposite with variation of Nuber of NTs RVE with E L E T G T υ L υ T lay lay + NT lay + NT lay + 3 NT lay +4 NT onclusions A nano structured hybrid coposite coposed of clay nano particle and carbon nanotubes were studied using finite eleent odeling. For nuerical investigations through finite eleent approach, a square RVE was selected to deonstrate the hybrid coposite structure. Predicted values fro FE odeling were copared with three-phase Halpin-Tsai odel. It was found that the elastic odulus fro nuerical odelling is in close agreeent with icroechanics based results. This work provides basic overview of odeling of hybrid coposite; furtherore studies have to be done by considering the variation of interphase properties and rando distribution of nano-clay and NTs. It is also planned to prepare NT/nano clay polyer coposite specien and perfor tensile and copressive test to validate the predicted nuerical data. References []. K. Lau,. Gu, D. Hui, A critical review on nanotube and nanotube/nanoclay related polyer coposite aterials, oposites: Part B 37 (6) []. T. Hayashi, M.Endo, arbon nanotubes as structural aterial and their application in coposites, oposites: Part B 4() [3]. M.T. Ki, K.Y. Rhee, J.H. Lee, D. Hui, A. K.T. Lau, Property enhanceent of a carbon fiber/epoxy coposite by using carbon nanotubes, oposites: Part B4 () [4]. J. Srinivas P. Kuar,Analysis of elastic properties of transversely isotropic NT-reinforced polyers, Nano Science and Nano Technology8 (4) [5]. M.S.P. Shaffer, X. Fan, A.H. Windle, Dispersion and packing of carbon nanotubes, arbon 36 (998) [6]. S. Wang, R.Liang, B.Wang,. Zhang, Load-transfer in functionalized carbon nanotubes/polyer coposites, heical Physics Letters 457 (8) [7]. S.W. Ki, T. Ki, Y.S. Ki, H.S.hoi, H.J.Li, S.J.Yang,.R.Park, Surface odifications for the effective dispersion of carbon nanotubes in solvents and polyers,arbon 5 () [8]. P.. Ma, J.K.Ki, B.Z. Tang, Effects of silane functionalization on the properties of carbon nanotube/epoxy nanocoposites, oposite Science and Technology67 (7)

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