Thermomechanical modeling of polymer ...

Thermomechanical modeling of polymer nanocomposites by the asymptotic homogenization method Yasser M. Shabana & Gong-Tao Wang

Acta Mechanica ISSN 0001-5970 Volume 224 Number 6 Acta Mech (2013) 224:1213-1224 DOI 10.1007/s00707-013-0868-4

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Author's personal copy Acta Mech 224, 1213–1224 (2013) DOI 10.1007/s00707-013-0868-4

Yasser M. Shabana · Gong-Tao Wang

Thermomechanical modeling of polymer nanocomposites by the asymptotic homogenization method

Received: 27 November 2012 / Published online: 6 April 2013 © Springer-Verlag Wien 2013

Abstract There is much current interest to incorporate nano-scale fillers into polymer matrices to achieve potentially unique properties. Compared with traditional microcomposites, a nanocomposite has a significant large ratio of interface area to volume that results in improved thermomechanical properties. Desired thermomechanical properties of polymer nanocomposites, to achieve the ever-increasing performance requirements, can be obtained by tailoring their microstructures. To this end, computational analyses of the relations between the thermomechanical properties, e.g., Young’s modulus, shear modulus, Poisson’s ratio, yield strength, coefficient of thermal expansion and coefficient of thermal conductivity, in different directions and the microstructures of polymer nanocomposites are performed. The asymptotic homogenization method based on the finite element analysis is used to model the thermomechanical behaviors of different polymer nanocomposites with periodic microstructures. The effects of adding silica, rubber, and clay nanoparticles to epoxy resin as a polymer matrix are analyzed. Mixtures of the nano-particles which differ in volume fraction, material type, size and/or geometry are considered. Some predictions of the thermomechanical properties are compared with experimental data in order to verify the applied modeling technique as an effective design tool to tailor optimal microstructures of polymer nanocomposites. 1 Introduction Polymer nanocomposites have, in recent years, received much attention as a class of multi-functional engineering materials. The incorporation of nano-fillers in polymer matrices results in significant improvements of their thermomechanical properties as the microstructures can be suitably tailored. Hence, good understanding of the microstructure-property relationships of these polymer nanocomposites is of great importance. From the experimental perspective, Kwon et al. [1] investigated the mechanical properties of silica/epoxy composites containing a mixture of micro-sized (1.56 µm) and nano-sized (240 nm) silicas in the epoxy matrix. Strength and toughness were strongly dependent on the ratio of micro to nano-fillers. Asma and Isaac [2] examined both mechanical and thermal properties of graphite platelet/epoxy composites for enhanced storage modulus, glass transition temperature, thermal expansion coefficient, and thermal stability. Uddin and Sun [3] showed that the strength of unidirectional glass/epoxy composite could be improved by enhancing the matrix properties with nano-particles. Sanchez and Ince [4] studied the microstructural, physical, and mechanical (compressive and splitting tensile strengths) properties of hybrid composites. Y. M. Shabana (B) Mechanical Design Department, Faculty of Engineering, Helwan University, El-Mataria, P. O. Box 11718, Cairo, Egypt E-mail: [email protected] G.-T. Wang Centre for Advanced Materials Technology (CAMT), School of Aerospace, Mechanical and Mechatronic Engineering J07, University of Sydney, Sydney, NSW 2006, Australia

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Y. M. Shabana, G.-T. Wang

From the theoretical perspective, Gusev [5] predicted the linear-response and properties of whisker- and platelet-filled polymers with tailored elastic, thermal, and dielectric properties using a generic finite elementbased multi-inclusion RVE approach. The applicability of such a model was validated by comparison with other analytical predictions such as those of Halpin–Tsai [6] and Hashin–Shtrikman [7]. Boutaleb et al. [8] proposed a micromechanical analytical model to predict the stiffness and yield stress of nanocomposites consisting of silica nanoparticles embedded in an interphase with graded modulus embedded in the matrix. It took into account an interphase corresponding to a perturbed region of the matrix around the nanoparticles, while its modulus was continuously graded from that of the nanoparticle to that of the matrix. Kalamkarov et al. [9] gave two different approaches to model the behavior of carbon nanotubes. One approach considers carbon nanotubes as an inhomogeneous cylindrical network shell by the asymptotic homogenization method. Another approach used a FE model with beam and spring elements to represent inter-atomic bonds. The FE predictions correlated well with typical existing literature values with explicit formulae in terms of pertinent material and geometric parameters. Pierard et al. [10] dealt with mean-field Eshelby-based homogenization techniques for two- and multi-phase composites by including the properties, aspect ratio, and orientation of the inclusions. A large number of numerical mean-field predictions and comparisons with FE simulations and experiments were shown for several (metal and polymer) matrix composites. Abdul Rashid et al. [11] optimized the composition of α-alumina (1–6 µm) in polymer composites for best overall mechanical performance including mechanical and morphological properties. Sanada et al. [12] investigated numerically and experimentally the thermal conductivity of polymer composites with both nano- and micro-fillers. An FE model with specially devised closed-packing structure cell yielded good agreement with test results. In this paper, the asymptotic homogenization method (AHM) based on finite element analysis (FEA) is employed to investigate the effects of adding silica, rubber, and clay nano-fillers to an epoxy matrix on the effective thermomechanical properties. These effects include nanoparticle volume/weight fraction, material type, distribution, and shape. The effective Young moduli and yield strengths are compared with test results. Coefficients of thermal expansions (CTEs) are evaluated and compared with experimental data and other published analytical results. These comparisons show that the proposed modeling technique can be used as an effective design tool to tailor the optimal microstructures of polymer nanocomposites to achieve desired thermomechanical properties.

2 Material and characterization It is important to mention that a brief overview of the experimental work and samples preparation is given here and more details can be found in [13]. Araldite-F epoxy, a kind of diglycidyl ether of bisphenol A (DGEBA), and Piperidine hardener were obtained from Sigma Aldrich, Australia. Nanoparticles from suppliers were 40 wt% nano-silica (Nanopox F400, nanoresins AG, Germany) and 25 wt% nano-rubber in bisphenol A (Kaneka Corporation, Japan) master batches, respectively. The resin, silica, and/or rubber were mixed using stirring and degassing processes with details given elsewhere [13]. Sample curing at 120 ◦ C was performed in a preheated rigid open mold for 16–24 h and cooled down naturally to ambient in the oven. For comparison, neat resin was agitated, degassed, and cured with the same procedure. Surface grinding and polishing were used to prepare specimen surfaces, and 2 h annealing at 100 ◦ C was applied in order to remove residual stresses. Finally, before testing, all specimens were also conditioned at ambient for 2 weeks. Monotonic tests were conducted on an Instron 5567 machine with a strain rate 1.4 × 10−5 /s using ASTM D638-99 with type IV geometry. Tests are performed on five samples at least for each material composition under ambient temperature. Engineering stress and strain were obtained, and the Young’s modulus was taken as the linear slope of the stress-strain curve before 0.5 % strain and 0.2 % offset stress was taken as the yield strength of the material. Dispersions of nano-silica and nano-rubber were examined on a Philips CM120 biofilter transmission electron microscope at 120 kV following standard cryo-microtoming. Typical micrographs are shown in Fig. 1, from which spherical particles of (a) silica ∼20 nm and (b) rubber ∼100 nm in epoxy can be seen. These micrographs represent the in-plane projection of the nanoparticle distributions. For ternary nanocomposites shown in Figs. 1c, d, rubber particles are circled in yellow and silica in red. It is clear that every 100 nm rubber particle is surrounded by several smaller 20 nm silica particles, which validates an assumption, for numerical modeling, of the unit cell structure with rubber at the centre and silica at cell apexes. In Fig. 1c, each rubber particle on average is grouped with 4 silica particles. With increasing particle weight fractions, the inter-particle distance between rubber and silica becomes smaller and the ratio of silica/rubber in an average unit cell may be larger than 4.

Author's personal copy Thermomechanical modeling of polymer nanocomposites

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Fig. 1 TEM photos showing the microstructure of nanocomposites filled by a 10 wt% nano-rubber; b 10 wt% nano-silica; c 6 wt% nano-rubber and 10 wt% nano-silica; and d 10 wt% nano-rubber and 10 wt% nano-silica. Note that the typical unit cells have been marked in ternary nanocomposites (c) and (d), with yellow circles for nano-rubber and red circles for nano-silica particles (color figure online)

3 Modeling of thermomechanical properties Analytical approaches, such as by Mori-Tanaka [14], to some extent are able to model composites and consume less computing time and hence are cheaper than numerical solutions. However, the AHM based on FEA approach is a much more powerful tool to simulate a broad range of different behaviors including the thermomechanical properties of heterogeneous materials. This is most promising especially for composites with complicated geometries, complex microstructures, and morphologies of nano-fillers, and not simple boundary conditions [15,16]. Also, the AHM enables both microscopic and macroscopic stresses to be obtained, which is a distinct advantage over other homogenizing techniques, e.g., rule of mixtures. However, the AHM used in this work, like other AHMs, has a common shortcoming that it cannot quantify the interactions between neighboring heterogeneities in the microstructures of composites; hence, its validity is limited to dilute concentrations. The AHM is based on creating a unit cell (UC) that captures major features of the underlying microstructure, such as a regular pattern in the microstructure, i.e., periodic microstructure that is sometimes a reasonable approximation or an idealization. This requires applying periodic boundary conditions to the UC. Detailed analysis and explanations of AHM and corresponding periodic boundary conditions can be found in [17– 20]. The set of partial differential equations resulting from the AHM can be solved numerically by applying FEA [15].



Based on the AHM and FEA, the homogenized elastic tensor CiHjkl , the CTE αiHj , and the homogenized thermal conductivity tensor K iHj are derived as follows: CiHjkl αiHj K iHj

∂χmkl Ci jkl − Ci jmn dY, ∂ yn Y ∂φk 1 H = Si j pq C pqkl αkl − dY, |Y | ∂ yl 1 = |Y |

1 = |Y |

Y

Ki j − Ki p Y

∂φ j ∂yp

(1)

(2)

dY,

(3)

where |Y | is the volume of the UC and SiHj pq is the homogenized compliance tensor, which is the inverse of the homogenized elastic tensor. χ and φ are characteristic displacements due to the mismatch of the elastic tensor and the CTE of the constituents, respectively. After evaluating the compliance matrix coefficients under plane stress conditions and based on the hypothesis that the composite is an orthotropic material, it may be written in its 2-D general form as ⎡ ⎤ S11 S12 S13 ⎢ ⎥ (4) [S] = ⎣ S21 S22 S23 ⎦ . S31 S32 S33 Then, the longitudinal and transverse Young’s moduli, shear modulus, and Poisson’s ratios, for the equivalent homogenized material, in different directions of the x − y plane, can be evaluated by Ex Ey G νx y ν yx

= 1/S11 , = 1/S22 , = 1/S33 , = −S12 /S11 , = −S12 /S22 .

(5)

The effective yield strength is an important property of a nanocomposite as a heterogeneous medium. The ensemble volume averaged elastoplastic constitutive equations proposed by Ju and Sun [21] are used for evaluating the yield strength. Based on these constitutive equations, which are emanating from the eigen strain concept of micromechanics and the macroscopic homogenization, the effective yield function of twophase composites containing randomly located yet unidirectionally aligned spheroidal inhomogeneities under uniaxial loading is given by [22] 2 (1) (2) p ¯ ¯ ¯ F(σ¯ 11 ,e¯ ) = (1 − f ) T11 + 2T11 σ¯ 11 − σ y + h(e¯ p )q , (6) 3 where f denotes the volume fraction of particles, σ y signifies the initial yield stress of the matrix, h and q designate the linear and exponential isotropic hardening parameters, respectively, and e¯ p defines the effective (1) (2) equivalent plastic strain. In addition, T¯11 and T¯11 are defined in [21]. 4 Results and discussion Thermomechanical properties (e.g., elastic and shear moduli, Poisson ratio, yield strength, CTE and thermal conductivity) and microstructures of polymer nanocomposites are computed and compared with test results to proof the applicability of the used modeling technique as an effective design tool to tailor optimal microstructures of polymer nanocomposites. Then, the modeling technique is used to predict the thermomechanical properties of different microstructures and/or different constituents. The isotropic constituents of these nanocomposites are epoxy, rubber, silica, and clay. The thermomechanical and physical properties of these constituents are listed in Table 1. The tabulated density values can be used to convert the volume fractions of


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Table 1 Properties of constituent materials Property (×10−6 /◦ C)

Thermal expansion coefficient Young’s modulus (GPa) Poisson’s ratio Yield strength (MPa) Density (g/cm3 ) Thermal conductivity (W/m. ◦ C)

Epoxy

Rubber

Silica

Clay

55 2.86 0.35 42.1 1.164 0.59

77 0.6 0.49 – 1.02 0.16

0.42 70 0.17 – 2.201 1.4

5.0 175 0.2 – 1.98 0.15

y

Y

x

X R = X/Y

(a)

(b)

Fig. 2 Unit cells: a one-filler type and b two-filler type (color figure online)

the constituents into weight fractions and vice versa. The interfaces between different constituents are assumed as perfectly bonded at all times, and linear elastic behavior of the nanocomposite systems and plane stress conditions is considered. For the FEA, the generated meshes of the UCs have the same adaptivity as that in [15]. Also, the four-node element is used and the minimum numbers of elements and nodes are 10,000 and 11,200, respectively.

4.1 Nanocomposites with spherical nanoparticles based on silica and rubber Numerical results are obtained showing the variations of Young’s modulus with weight fraction of spherical (aspect ratio λ = 1) silica and rubber in silica/epoxy, rubber/epoxy and silica/rubber/epoxy nanocomposites. These nanocomposites are idealized by considering unit cells of aspect ratio R = 1 as shown in Fig. 2. The particle is put at the center of the UC in the case of only one type of filler, Fig. 2a. For silica/rubber/epoxy nanocomposites, rubber and silica particles are considered to be at the center and the corners, respectively, of the UC as shown in Fig. 2b. As the constituent materials are assumed isotropic, the generated FE meshes are symmetric and the reinforcements are spherical, it is found from the numerical results that the compliance matrix is symmetric and satisfies the isotropic elasticity hypothesis. Thus, S12 = S21 , S11 = S22 , S33 = 2(S11 − S12 ) and S13 , S23 , S31 and S32 are very small and tend to zero compared to the other terms. Figure 3a shows that when rubber nano-particles are added to neat epoxy, the elastic modulus of the matrix is reduced due to the much lower rubber stiffness. As silica is the stiffest, in contrast, increasing its loading in neat epoxy results in a stiffer material, Fig. 3b. When silica or rubber is added as second filler to the matrix, experiments show that it affects the elastic moduli by almost the same amount independent of the first filler loading. This means only an additive effect is obtained on elastic moduli of the ternary composites. Hence, the data agree nicely with the numerical results of the model which assumes no nanoparticle interaction as seen in Fig. 3. Thus, the AHM model can be used to predict the elastic modulus properties. The yield strengths of the binary and ternary nanocomposites are plotted in Fig. 4. In the binary systems, as expected, rubber decreases but silica increases the yield strength. In ternary systems, adding 6 wt% rubber to silica/epoxy composites reduces the yield strength at all silica loading. Numerical results agree well with



Fig. 3 Variation of Young’s modulus with weight fraction of nano-particles (color figure online)

Fig. 4 Variation of yield strength with weight fraction of nano-particles (color figure online)

test data of rubber (6 wt%)/silica/epoxy and silica/epoxy systems except at high silica loading (≥10 wt%) for the latter, where the difference can be as much as 17 %. These errors might be caused by departures from the ideal assumption of perfectly bonded interfaces of nanoparticles such as due to debonding of silica and cavitation of rubber and their interactions. Hence, for accurate estimations of yield strength, the precise yielding mechanisms must be incorporated in the model. Nonetheless, the maximum difference is less than 17 %. Judging from Figs. 3 and 4, it seems that the proposed modeling technique is a reliable tool for the prediction of elastic moduli, but is less accurate for yield strengths, of polymer nanocomposites with one or more nanoparticles provided there are no strong interactions between them. Figure 5 shows the experimental effective CTEs of a cyanate ester matrix filled with fumed silica nanoparticles of average particle diameters 12 and 40 nm. The results obtained from (a) the rule of mixtures, (b)


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CTE (x10-6/ oC)

40 nm exp. data 12 nm exp. data Rule of mixtures Schapery (upper) Schapery (lower) Turner Shi – 40 nm Shi – 12 nm AHM

CTE (x10-6/ oC)

Fig. 5 Variation of CTE with volume fraction of nano-particles adapted from Ref. [24] (color figure online)

Fig. 6 Variation of CTE with weight fraction of nano-particles (color figure online)

Schapery [23] which is based on energy principles, (c) Turner [24], who assumed equal dimensional changes with temperature for all phases, and (d) Shi [25] are all taken from Goertzen and Kessler [26]. For comparison, the AHM results are also superposed in Fig. 5. It can be seen that the rule of mixtures overestimates the CTEs, but Schapery’s lower limit and Turner’s model underestimate them substantially for all volume fractions. Although the UC model used in the present homogenization method considers the periodicity of nanoparticle arrangement, the predictions by the AHM, Schapery’s upper limit, and Shi’s model agree well with experimental measurements. It is therefore concluded that the quantitative accuracy of the present AHM and FEA approach is satisfactory and applicable for predicting the thermomechanical properties of the considered binary and ternary polymer nanocomposites. The predicted CTEs of silica/epoxy, rubber/epoxy, and silica/rubber/epoxy nanocomposites are displayed in Fig. 6. Computational estimates from the numerical approach show that αx = α y and αx y = 0. It is seen from these plots that, for the binary nanocomposites, increasing the silica loading reduces more significantly the CTE owing to its lower thermal expansion coefficient. However, increasing the rubber loading increases the CTE only slightly. Now, for the ternary nanocomposites, increasing the silica content to rubber/epoxy system decreases the CTE as expected and the CTE varies almost linearly for different silica loadings. However, adding 15 wt% rubber to silica/epoxy system has little effect on the CTE. The variations of the thermal conductivity, which is needed for solving most of the thermal problems, for binary and ternary nanocomposites are shown in Fig. 7. It can be seen that the thermal conductivity of the nanocomposites increases with the increase in the silica loading while rubber nanoparticles have stronger opposite effect due to the much lower conductivity of the rubber.



Fig. 7 Variation of the thermal conductivity with the nano-particle volume fraction for the epoxy/rubber/silica composites

Since the thermal residual stresses, which are induced due to the thermal contraction mismatch of the constituents, alter the strength of nanocomposites, it is important to have some insight about the developed thermal residual stresses during the cooling (curing) process from the molding temperature. Following Chawla [27], the residual radial and tangential thermal stresses are σr p = σθ p = −P ⎧ ⎨ σr m = P a33 − 1− f r a3 ⎩ σθ m = − P 1− f 2r 3 where P=

(in the particle) f (in the matrix) + f

αm − α p T 0.5(1+νm )+(1−2νm ) f E m (1− f )

+

1−2ν p Ep

.

(7) (8)

(9)

For the binary silica/epoxy composite with particle radius a, Fig. 8 shows the variations of the induced thermal residual stresses with the distance (r ) from the center of the particle for different volume fractions of the silica nano-particles ( f = 0.05, 0.1 and 0.15). Since CTE of the particle is lower than that of the matrix, the particle is under uniform pressure while the matrix has radial compressive and tangential tensile stress components. It can be noticed that the matrix thermal stresses follow the cubic order of variation. Also, the radial compressive thermal stresses in both the matrix and the particle are decreasing with the increase in the nano-particle volume fraction, while the tangential stress in the matrix has an opposite behavior. Also, the finite element analysis is used to model these thermal stresses and it is found that the steady-state numerical results meet the theoretical results with minor error that can be neglected. 4.2 Nanocomposites with hybrid nanoparticles Since the previous figures show an acceptable agreement between the theoretical and experimental results, nanocomposites with different microstructures and different constituents are analyzed and discussed based on the above mentioned modeling technique. Consider a system of hybrid nanocomposites containing two widely different particles in shape and aspect ratio. Figure 9 shows the variations of Young modulus, shear modulus and Poisson’s ratio of clay/rubber/epoxy nanocomposites in which the total volume fraction of nanoparticles is ( fr + f c =) 0.25 at all times. The clay nanoparticles are assumed to align in the x-direction and have an aspect ratio λc = 25 while the rubber particles are spheres with λr = 1. The aspect ratio of the unit cell, which shown in the figure, is R = X/Y = 2.5. In this example, the compliance matrix is found to be symmetric and S13 , S23 , S31 and S32 are very small and tend to zero compared with the other terms. This means that the material satisfies the hypothesis of orthotropic elasticity under the current analyses. As expected, reducing clay loading with more rubber decreases the Young’s moduli in both longitudinal and transverse directions, E x and E y , and shear moduli G x y . It is seen that


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f

m

Matrix

Particle

f r

Fig. 8 Thermal stress distributions of the epoxy/silica composites with the radial distance for different particle volume fractions of f = 0.05, 0.1 and 0.15 (color figure online)

y

(a)

Y

x

R = X/Y X

(b) Ex Ey

(c)

Gxy v xy v yx

Fig. 9 Variation of mechanical properties with nano-particle volume fraction for the epoxy/rubber/clay composites (color figure online)



E ( = 1) Ex ( = 3) Ex ( = 5) Ex ( = 7) Ey ( = 3) Ey ( = 5) Ey ( = 7)

Gxy ( = 1) Gxy ( = 3) Gxy ( = 5) Gxy ( = 7)

v ( = 1) v xy ( = 3) v xy ( = 5) v xy ( = 7) v yx ( = 3) v yx ( = 5) v yx ( = 7)

Fig. 10 Variation of mechanical properties with nano-particle aspect ratio for the epoxy/silica/silica composites (color figure online)

there is no hybrid effect on E y since it varies almost linearly with increasing rubber or decreasing clay loading obeying an additive law. However, E x shows a strong negative hybrid effect at intermediate loadings of the two nanofillers in that its value is lower than the additive law given by a straight line joining the two end points. A less prominent negative hybrid effect is found for G x y . The Poisson ratio νi j is the induced contraction strain ε

νi j = − εij . Hence, as E x is much higher than E y for low fr , ε j due to an imposed extensional strain εi the induced strain ε y by a unit applied strain εx will be larger than the induced strain εx due to a unit applied strain ε y . Therefore, νx y is larger than ν yx as shown in the figure. When fr increases, since E x decreases more rapidly than E y , this yields an increase of ν yx that eventually overtakes νx y when fr > 0.20. Figure 10 shows a square unit cell for a polymer nanocomposite with two types of silica nanoparticles. The first type is spherical at the center of the UC and the other type is ellipsoidal at the corners, and the two types share equally the total weight fraction of the reinforcements. The effects of the silica content and the second type aspect ratio are explored in Fig. 10. As the reinforcements are stiffer than the epoxy matrix, E x , E y and shear modulus are increasing with the increase in the silica content. It can be seen that E x increases by increasing the aspect ratio of the second type nano-silica. This is because the reinforcement effective length along the longitudinal direction is getting larger by the increase in the aspect ratio at the same volume fraction. The transverse modulus E y and shear modulus are slightly affected by the aspect ratio. Since the resistance to deformation is getting higher in the longitudinal direction than that in the transverse one, the Poisson’s ratio ν yx is affected more than νx y and decreases with the increase of the aspect ratio. In Fig. 11, a polymer nanocomposite with two different types of nano-fillers is shown. The first type is spherical silica (λs = 1) at the center of the UC with volume fraction 0.15 and the other type like


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Fig. 11 Variation of mechanical properties with nano-particle modulus E 2 (color figure online)

clay, with volume fraction 0.1, aspect ratio λc = 25 and has a variable Young’s modulus (E 2 ) in order to envisage its effect on the behavior of the polymer nanocomposite. However, E x , E y and shear modulus are increasing with E 2 , and the composite is stiffer in the longitudinal direction than in the transverse one due to the orientation of the second type reinforcements. Also, the Poisson’s ratio νx y is increasing while ν yx is decreasing. Referring to Figs. 10 and 11, the behaviors of polymer nanocomposites are affected largely by the microstructure including the reinforcement shape, material, and weight fraction. Therefore, it may be worthy to include these effects for an optimum microstructure when designing mechanical parts made of polymer nanocomposites.

5 Conclusion In this paper, we have reported numerical analyses to study the effects of adding different nano-fillers (e.g., silica, rubber, and clay) on the thermomechanical properties of polymer matrices (e.g., epoxy and cyanate ester resins). The influences of particle volume/weight fraction, shape, and distribution as well as material type are critically examined in terms of Young’s modulus, shear modulus, Poisson’s ratio, yield strength, coefficient of thermal expansion, and coefficient and thermal conductivity. Numerical results obtained from the AHM and FEA compared very well with experimental data for elastic modulus and thermal expansion coefficient. It is expected that this modeling technique can be used as an effective design tool to tailor optimal structures of polymer composites containing single or hybrid nanoparticles of different shapes and sizes especially when the experiments and test specimens are prohibitively expensive.



Acknowledgments This research work is financially supported by the University of Sydney through an International Visiting Research Fellowship awarded to YMS. GTW acknowledges a Faculty Scholarship from the School of AMME at the University of Sydney.

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