Size-dependent effective dynamic properties of unidirectional nanocomposites with interface energy effects

This article studies the size effect on wave propagation characteristics of plane longitudinal and transverse elastic waves in a two-phase nanocomposite consisting of transversely isotropic and unidirectionally oriented identical cylindrical nanofibers embedded in a transversely isotropic homogeneous matrix. The surface elasticity theory is employed to incorporate the interfacial stress effects. The effect of random distribution of nanofibers in the composite medium is taken into account via a generalized self-consistent multiple scattering model. The phase velocities and attenuations of longitudinal and shear waves along with the associated dynamic effective elastic constants are calculated for a wide range of frequencies and fiber concentrations. The numerical results reveal that interface elasticity at nanometer length scales can significantly alter the overall dynamic mechanical properties of nanofiber-reinforced composites. Limiting cases are considered and excellent agreements with solutions available in the literature have been obtained.     

Effect of nanotube geometry on the elastic properties of nanocomposites

Many analytical models replace carbon nanotubes with “effective fibers” to bridge the gap between the nano and micro-scales and allow for the calculation of the elastic properties of nanocomposites using micromechanics. Although curvature of nanotubes can have a direct impact on these properties, it is typically ignored. In this work, the nanotube geometry in 3D is included in the calculation of the elastic properties of a modified effective fiber. The strain energy of the nanotube and the effective fiber are calculated using Castligiano’s theorem and constraints imposed by the matrix on the deformation are taken into consideration. Model results are compared to results from archived literature, and a reasonable agreement is observed. Results show that the effect of nanotube curvature on reducing the modulus of the effective fiber is not limited to in-plane curvature but also to curvature in 3D. The impact of the nanotube curvature on the elastic properties of nanocomposites is studied utilizing the modified fiber model and the approach developed by Mori–Tanaka. Analytical results show that for a low weight fraction of nanotubes the effect of curvature seems to be minor and as the weight fraction increases, the effect of nanotube curvature becomes critical.     

Numerical characterisation of fullerene based polymer nanocomposites considering interface effects

In this investigation, the effective mechanical properties of fullerene nanocomposites considering interface effects were characterised. Load transfer in nanocomposite materials is achieved through the fullerene/matrix interface. Thus, to determine nanocomposite mechanical properties, the interface behaviour must be determined. A single fullerene and the surrounding polymer matrix are modelled. Two cases of perfect bonding and an elastic interface are considered. Two models are suggested for elastic interface. The first elastic interface model consists of a thin layer of an elastic material surrounding the fullerene. In the second elastic interface model, a series of spring elements are used as the fullerene/matrix interface. The results of numerical models indicate the importance of adequate interface bonding for a more effective strengthening of polymer matrix by fullerene. Also, Young’s modulus prediction for fullerene in epoxy matrix is compared to experimental data investigated by Rafiee et al. (2011), and good agreement is observed.     

A study on the prediction of the mechanical properties of nanoparticulate composites using the homogenization method with the effective interface concept

A sequential multi‐scale homogenization method combined with molecular dynamics (MD) simulation is developed for the mechanical characterization of nanoparticulate composites. In order to characterize the particle‐size effect of nanocomposites, the effective interface, which has been adopted in continuum micromechanics approaches, is considered as the characteristic phase. Owing to the existence of the interface and the size‐dependent elastic modulus that is observed from MD simulations, an analysis of the mechanical properties of nanocomposites with continuum micromechanics requires careful consideration of the particle‐concentration effect. Therefore, this study focuses on hierarchical information transfer from the molecular model to the continuum model through the homogenization method in lieu of an analytical micromechanics bridging method. Using the present multi‐scale homogenization method, the elastic properties of the effective interface are numerically evaluated and compared with the analytically obtained micromechanics solutions. In addition, the overall elastic modulus of nanocomposites is obtained from the present model and compared with the results of MD simulation, the micromechanics bridging model, and finite‐element analysis (FEA). Copyright © 2010 John Wiley & Sons, Ltd.     

Micromechanical analysis of nanocomposites using 3D voxel based material model

A computational study on the effect of nanocomposite structures on the elastic properties is carried out with the use of the 3D voxel based model of materials and the combined Voigt–Reuss method. A hierarchical voxel based model of a material reinforced by an array of exfoliated and intercalated nanoclay platelets surrounded by interphase layers is developed. With this model, the elastic properties of the interphase layer are estimated using the inverse analysis. The effects of aspect ratio, intercalation and orientation of nanoparticles on the elastic properties of the nanocomposites are analyzed. For modeling the damage in nanocomposites with intercalated structures, “four phase” model is suggested, in which the strength of “intrastack interphase” is lower than that of “outer” interphase around the nanoplatelets. Analyzing the effect of nanoreinforcement in the matrix on the failure probability of glass fibers in hybrid (hierarchical) composites, using the micromechanical voxel-based model of nanocomposites, it was observed that the nanoreinforcement in the matrix leads to slightly lower fiber failure probability.     

Mathematical investigation of interfacial property in fiber reinforced model composites

In the current paper, we have investigated the dependence of the effective elastic properties of a composite material on the fiber/matrix interface elastic property. The model composite consists of a single cylindrical fiber embedded in a concentric cylindrical matrix material. A three dimensional mathematical method has been developed connecting the interface properties with the effective axial Young’s modulus of the composite structure. Special effort has been devoted to decode information about the quality of the interface by exploiting the information provided by the elastic effective parameters. In particular, the effective modulus vs. stiffness coefficient curves have been generated for Ti/SiC composites. The aforementioned curves reveal the characteristics of the transition from the regime of perfect interface to the realm of complete debonding.     

Mechanical and thermal behavior of nanoclay based polymer nanocomposites using statistical homogenization approach

In the present study, the effects of nanoclay additives on the effective mechanical and thermal properties of polymer/nanoclay composites have been investigated using experimental and simulation analyzes. In this research, we propose the use of strong contrast statistical continuum theory to predict the effective elastic and thermal properties. To validate our modeling approach, we conducted experimental measurements of these properties for polyamide/nanoclay nanocomposites with concentrations of 1, 3 and 5 wt.% of nanoclay particles. Three-dimensional isotropic nanocomposite samples with randomly oriented monolayer nanoclays were computer generated and used to calculate the statistical correlation functions of the realized model. These correlation functions have been exploited to calculate effective thermal and elastic properties of the nanocomposite. The simulation results have shown that effective stiffness can be increased significantly with small amounts of particle concentration for the exfoliated clay monolayers. The predicted effective conductivity and elastic modulus have been compared to our experimental results. Effective thermal conductivity shows satisfactory agreement with experimental data. However, the predicted results for the elastic modulus overestimate the experimental data, which might be due to the increasing intercalated structure for high concentration of nanofiller and to anisotropic properties of the nanoclay.     

Effect of Interface Energy on Size-Dependent Effective Dynamic Properties of Nanocomposites with Coated Nano-Fibers

In nanocomposites, coated nano-fibers are often used to obtain good performance, and the high interface-to-volume ratio shows great effect on the macroscopic effective properties of nanocomposites. In this study, the effect of interface energy around the unidirectional coated nanofibers on the effective dynamic effective properties is explicitly addressed by effective medium method and wave function expansion method. The multiple scattering resulting from the series coating nano-fibers is reduced to the problem of one typical nano-fiber in the effective medium. The dynamic effective shear modulus is obtained on the basis of the derived imperfect interface conditions. Analyses show that the effect of the interface properties on the dynamic effective shear modulus is significantly related to the coating layer, the nano-fiber, and the wave frequency. Due to the existence of softer coating layers, the effect of the interfaces around the layers increases greatly. Comparison with the existing results is also illustrated in the numerical examples.     

Analysis of effect of fiber orientation on Young’s modulus for unidirectional fiber reinforced composites

Young’s modulus of unidirectional glass fiber reinforced polymer (GFRP) composites for wind energy applications were studied using analytical, numerical and experimental methods. In order to explore the effect of fiber orientation angle on the Young’s modulus of composites, from the basic theory of elastic mechanics, a procedure which can be applied to evaluate the elastic stiffness matrix of GFRP composite as an analytical function of fiber orientation angle (from 0° to 90°), was developed. At the same time, different finite element models with inclined glass fiber were developed via the ABAQUS Scripting Interface. Results indicate that Young’s modulus of the composites strongly depends on the fiber orientation angles. A U-shaped dependency of the Young’s modulus of composites on the inclined angle of fiber is found, which agree well with the experimental results. The shear modulus is found to have significant effect on the composites’ Young’s modulus, too. The effect of volume content of glass fiber on the Young’s modulus of composites was investigated. Results indicate the relation between them is nearly linear. The results of the investigation are expected to provide some design guideline for the microstructural optimization of the glass fiber reinforced composites.     

Scattering of antiplane shear waves in a fiber-reinforced composite medium with interfacial layers

Summary This paper deals with the scattering of antiplane shear waves in a metal matrix composite reinforced by fibers with interfacial layers. We assume same-size cylindrical inclusions and same-thickness interface layers with nonhomogeneous elastic properties. The effective complex wave numbers follow from the coherent wave equation which depends only upon the scattering amplitude of the single scattering problem. Effective elastic constants can be obtained from phase velocities of coherent waves. Numerical calculations for an SiC-fiber-reinforced Al composite are carried out, and the effect of interface properties on scattering cross section, phase velocity, attenuation of coherent plane wave, and effective elastic constant is shown graphically.     

Pseudo-percolation: Critical volume fractions and mechanical percolation in polymer nanocomposites

Polymer nanocomposites offer a basis for the design and manufacture composite materials with greatly enhanced properties at relatively low volume fractions of the included phase. One underlying mechanism, thought to contribute to these properties is the presence of an interfacial region, ∼15 nm thick, between the polymer matrix and included particles. The size of the interface makes relatively little contribution to the effective properties of composites with micro-sized particles but, because its thickness is comparable to the size of the nanoscaled included phase, its potential impact within nanocomposites is much greater. In particular, percolated nano-microstructures may result at volume fractions below theoretical thresholds, due to connectivity achieved through rod-interface-rod, or ‘pseudo-percolation’, contact. In this work the influence of the interface layer is incorporated into estimates of critical volume fraction through an excluded volume model. Results show a significant reduction in the range of critical volume fractions. These values are incorporated into a mean-field micromechanics model to illustrate mechanical percolation through changes in predicted effective elastic composite properties.     

Effect of the stochastic nature of the constituents parameters on the predictability of the elastic properties of fibrous nano-composites

The stochastic nature and the variability of the constituents of nano-composites materials affect the predictability of their properties. The few studies that dealt with the probabilistic nature of the micromechanics of fibrous nano-composites, focused on the effect of statistical variation of individual parameters. This study presents a systematic analysis of the influence of parameter randomness on the theoretical predictions of the elastic properties of nano-composites. To this end, Monte-Carlo simulations are performed using a modified version of the Mori–Tanaka Mean-Field theory under different combinations of parameter randomness. The results indicate that the randomness in interface imperfection, fibre orientation and length, and fibre stiffness have a significant influence on the variability of the composite properties. The analysis provided an insight into the sensitivity of the predictions of the elastic tensor to the probabilistic variations of the aforementioned parameters. A probabilistic model for the effective properties is called for in place of deterministic models.     

On the overall elastic moduli of polymer-clay nanocomposite materials using a self-consistent approach. Part II: Experimental verification

Polyamide-6 (PA6) based nanocomposites were prepared using a modified montmorillonite (MMT) Cloisite 20A as nanofillers. The silicate weight fraction of the prepared nanocomposites, determined by burning off the PA6 matrix, was ranged from 0.2 wt% up to 7.5 wt%. The thermomechanical properties of both the neat PA6 and the PA6 filled with MMT nanoclay were measured by means of uniaxial tension tests and dynamic mechanical thermoanalysis, their crystallinity analyzed by differential scanning calorimetry and their morphology observed by transmission electron microscopy. The elastic stiffness of PA6-clay nanocomposites was examined under two moisture levels and was analyzed with the theory formulated in the Part I of this work. Predicted results are found in good agreement with our experiments. The model capabilities are also critically discussed by comparisons with both experiments issued from the literature and the Mori-Tanaka approach widely used in recent literature. It is demonstrated that the proposed micromechanical model is more efficient than the Mori-Tanaka approach. Moreover, the obtained results support the idea that the elastic stiffness of polymer-clay nanocomposites is governed by the same mechanisms as microcomposites, the effects of particle dimension or constrained region being of a second order.     

Modeling the effective elastic properties of nanocomposites with circular straight CNT fibers reinforced in the epoxy matrix

In the present study, the consistent effective elastic properties of straight, circular carbon nanotube epoxy composites are derived using the micromechanics theory. The CNT composites are known to provide high stiffness and elastic properties when the shape of the fibers is cylindrical and straight. Accordingly, in the present work, the effective elastic moduli of composite are newly obtained for straight, circular CNTs aligned in the specified direction as well as distributed randomly in the matrix. In this direction, novel analytical expressions are proposed for four cases of fiber property. First, aligned, and straight CNTs are considered with transverse isotropy in fiber coordinates, and the composite properties are also transversely isotropic in global coordinates. The short comings in the earlier developments are effectively addressed by deriving the consistent form of the strain tensor and the stiffness tensor of the CNT nanocomposite. Subsequently, effective relations for composites reinforced with aligned, straight CNTs but fibers isotropic in local coordinates are newly developed under hydrostatic loading. The effect of the unsymmetric Eshelby tensor for cylindrical fibers on the overall properties of the nanocomposite is included by deriving the strain concentration tensors. Next, the random distribution of CNT fibers in the matrix is studied with fibers being transversely isotropic as well as isotropic when CNT nanocomposites are subjected to uniform loading. The corresponding relations for the effective elastic properties are newly derived. The modeling technique is validated with results reported, and the variations in the effective properties for different CNT volume fractions are presented.     

On the overall elastic moduli of polymer-clay nanocomposite materials using a self-consistent approach. Part I: Theory

Although few investigations recently proposed to describe the overall elastic response of polymer-clay nanocomposite materials using micromechanical-based models, the applicability of such models for nanocomposites is far from being fully established. The main point of criticism to mention is the shelving of crucial physical phenomena, such as interactions and length scale effects, generally associated by material scientists, in addition to the nanofiller aspect ratio, to the remarkable mechanical property enhancement of polymer-clay nanocomposites. In this Part I of two-part paper, we present a micromechanical approach for the prediction of the overall moduli of polymer-clay nanocomposites using a self-consistent scheme based on the double-inclusion model. This approach is used to account for the inter-inclusion and inclusion-matrix interactions. Although neglected in the models presented in the literature, the active interaction between the nanofillers should play a key role in the reinforcing effect of nano-objects dispersed in a polymer matrix. The present micromechanical model incorporates the nanostructure of clay stacks, modeled as transversely isotropic spheroids, and the so-called constrained region, modeled as an interphase around reinforcements. This latter is linked to the interfacial interaction between matrix and reinforcements that forms a region where the polymer chain mobility is reduced. To account for length scale effects, interphase thickness and particle dimensions are taken as explicit model parameters. Instead of solving iteratively the basic homogenization equation of the self-consistent scheme, our formulation yields to a pair of equations that can be solved simultaneously for the overall elastic moduli of composite materials. When the interphase is disregarded for spheroids with zero aspect ratio, our formulation coincides with the Walpole solution (J Mech Phys Solids 1969;17:235-251). Using the proposed general form, a parametric study is presented to analyze the respective influence of aspect ratio, number of silicate layers, interlayer spacing and nanoscopic size of the transversely isotropic spheroids on the overall elastic moduli of nanocomposite materials.     

Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters

We propose a stochastic multiscale method to quantify the correlated key-input parameters influencing the mechanical properties of polymer nanocomposites (PNCs). The variations of parameters at nano-, micro-, meso- and macro-scales are connected by a hierarchical multiscale approach. The first-order and total-effect sensitivity indices are determined first. The input parameters include the single-walled carbon nanotube (SWNT) length, the SWNT waviness, the agglomeration and volume fraction of SWNTs. Stochastic methods consistently predict that the key parameters for the Young’s modulus of the composite are the volume fraction followed by the averaged longitudinal modulus of equivalent fiber (EF), the SWNT length, and the averaged transverse modulus of the EF, respectively. The averaged longitudinal modulus of the EF is estimated to be the most important parameter with respect to the Poisson’s ratio followed by the volume fraction, the SWNT length, and the averaged transverse modulus of the EF, respectively. On the other hand, the agglomeration parameters have insignificant effect on both Young’s modulus and Poisson’s ratio compared to other parameters. The sensitivity analysis (SA) also reveals the correlation between the input parameters and its effect on the mechanical properties.     

A simulation study on the effect of spring-shaped fillers on the viscoelasticity of rubber nanocomposite

Background/PurposeRubber nanocomposites have been widely used in many engineering fields due to their unique properties such as high elasticity and viscoelasticity. Much attention has been paid to the viscoelasticity of rubbers because it directly relates to the performance of the rubber products.MethodsBased on the micromechanical theory, the finite element method is used to analyze the effect of elastic modulus and volume content of spring-shape nanofillers on the dynamic viscosity of composites.ResultsThe simulation results show that there is an optimal elastic modulus of spring-shape nanofillers to make the loss factor a minimum. There is a threshold value of spring-shape nanofiller content for the dissipation energy density of composite.ConclusionThe elastic modulus of spring-shape nanofillers has a large effect on the loss factor of composites. The selection of elastic modulus of spring-shape nanofillers is critical for applications of composites. The efficiency of spring-shape nanofillers in reducing the dynamic viscosity of composites is so high that volume content of spring-shape nanofillers as low as 0.1% can greatly reduce the loss factor of composites with bonding interface.     

Mechanical properties of carbon nanotube reinforced polymer nanocomposites: A coarse-grained model

In this work, a coarse-grained (CG) model of carbon nanotube (CNT) reinforced polymer matrix composites is developed. A distinguishing feature of the CG model is the ability to capture interactions between polymer chains and nanotubes. The CG potentials for nanotubes and polymer chains are calibrated using the strain energy conservation between CG models and full atomistic systems. The applicability and efficiency of the CG model in predicting the elastic properties of CNT/polymer composites are evaluated through verification processes with molecular simulations. The simulation results reveal that the CG model is able to estimate the mechanical properties of the nanocomposites with high accuracy and low computational cost. The effect of the volume fraction of CNT reinforcements on the Young's modulus of the nanocomposites is investigated. The application of the method in the modeling of large unit cells with randomly distributed CNT reinforcements is examined. The established CG model will enable the simulation of reinforced polymer matrix composites across a wide range of length scales from nano to mesoscale.     

Analysis of elastic properties of carbon nanotube reinforced nanocomposites with pinhole defects

Due to their unique molecular structure, carbon nanotubes exhibit outstanding properties. They are regarded as ideal reinforcements of composites. In this paper, the effects of pinhole defects on mechanical properties are investigated for wavy carbon nanotubes based nanocomposites using 3-D Representative Volume Element with long carbon nanotubes. The carbon nanotubes are modeled as continuum hollow cylindrical shape elastic material with pinholes, having some curvature in its shape. These defects are considered on the single walled carbon nanotubes. The mechanical properties like Young’s modulus of elasticity are evaluated for various values of waviness index, as well as type and number of pinhole defects. The effects of interactions between both defects as well as their influence on the nanocomposites are studied under an axial loading condition. Numerical equations are used to extract the effective material properties for the different geometries of Representative Volume Elements with non-defective carbon nanotubes. The finite element method results obtained for non-defective carbon nanotubes are consistent with analytical results for cylindrical Representative Volume Elements, which validate the proposed model. It is observed that the presence of pinhole defects as well as waviness, can significantly reduces the effective reinforcement, when compared with nanotubes without pinhole defects and this reinforcement decreases with the increase of the number of pinhole defects.