Nanoscale Representative Volume Element Research Articles

An efficient nanoscale representative volume element simulation including graded interphase for tensile behavior of epoxy/silica nanocomposites

AbstractThe behavior of interphase‐particle adhesion and interphase region around the nanoparticles can significantly affect the stress distribution and mechanical properties of polymeric nanocomposites. In this study, the elastic modulus of epoxy/silica nanocomposites is analyzed using the finite element method and different mathematical models. A nanoscale representative volume element including graded interphase, homogenous interphase, and no interphase model is implemented. Furthermore, the effect of interfacial adhesion is also considered. The final elastic modulus was clearly affected by the interphase modulus, especially at higher nanoparticle content. Under imperfect interfacial bonding, the existence of an interphase region leads to a slight increase in modulus, and in the absence of that area, the elastic modulus decreases to 3.28 GPa. In perfect bonding models, stress transferred from the matrix to interphase and, then, to nanoparticle, which led to a significant increase in elastic modulus. Unlike the imperfect bonding, the maximum stress was located in the elements along to the loading direction. A maximum 26% increase in elastic modulus for perfect bonding/graded interphase model with 6.54 vol% of nanosilica particles compared to bulk epoxy was achieved. Finally, on comparing the FEM analysis and theoretical results with the experimental data, good agreement between obtained results was found.

Investigating the elastic behavior of carbon nanocone reinforced nanocomposites

This paper deals with the evaluation of the effective mechanical properties of carbon nanocone centered composites using a 3D nanoscale representative volume element based on continuum mechanics. For extracting the effective material constants, the authors have taken the basis of theories of elasticity. The results constituting the effective Young's modulus of the composite and Poisson's ratio for different parameters stated above have been presented and validated with rule of mixtures. It can be clearly visualized from the results that the load-carrying capacities of carbon nanocones in the representative volume elements are quite significant and the same has been demonstrated with subsequent cases. Simulation-based modeling can show a considerable part in the improvement of carbon nanocone-based composites by providing results that help in appreciative of the performance of composites. Moreover, for a volume fraction of the CNC as 2.33% in a cylindrical representative volume element and a 19.2° apex angle of the cone, the stiffness of the composite can increase as many as 4.9 times of the matrix. Similarly for hexagonal and square, the increase is in terms of 4.3 and 3.01 times respectively. Cylindrical representative volume element is the best as it provides the maximum reinforcement in terms of effective Young's modulus of the composite. Carbon nanocone-based composites provide results that help in understanding the elastic behavior of composites.

Multiscale modeling of strength and failure behavior of carbon nanostructure reinforced epoxy composite adhesives in bonded systems

In this study, atomistic based continuum (ABC) multiscale modeling approach is presented for strength and failure prediction of carbon nanotube (CNT) reinforced epoxy composite adhesives in bonded systems. Assuming that the CNTs are uniformly dispersed in the epoxy matrix, the mechanical properties of the nanocomposite adhesive are determined utilizing a two-step sequential homogenization procedure. In the first step, effective mechanical properties of a nanoscale representative volume element (RVE) are determined. The RVE comprises a CNT embedded in the epoxy matrix separated by an interphase. The structure-property relationship at the nanoscale is captured through ABC modeling approach wherein a CNT is modeled as a space-frame structure with beam elements and the epoxy is modeled using solid elements. The interphase between the CNT and the epoxy is modeled using non-linear spring elements to account for non-bonded van-der Waals interactions. In the second step, CNT inclusions with random orientations in the matrix are considered to create a microscale RVE of the nanocomposite. In both the steps, different boundary conditions were applied on the RVEs, and finite element (FE) analyses were conducted to estimate the effective mechanical properties through numerical homogenization. Furthermore, the strength of CNT/epoxy composite is estimated using modified Kelly-Tyson theory. Finally, modeling scheme proposed here is utilized to assess the load carrying capacity and failure behavior of a single lap-joint (SLJ) comprising composite adherends and CNT/epoxy nanocomposite adhesive by conducting continuum scale FE analyses. Results show over 30% improvement in strength for the SLJ with CNT/epoxy bondlayer comprising 2 vol% CNT. The findings of the study indicate that both strength and damage tolerance of the bonded joints can be significantly optimized utilizing nanoreinforced bondlayer.

Mechanical characterization and postbuckling behavior of carbon nanotube–carbon fiber reinforced nanocomposite laminate

The aim of this study is to investigate the effect of carbon nanotube reinforcement in conventional carbon fiber reinforced composite on the buckling and postbuckling behavior of the laminated nanocomposite plate made of carbon nanotube and carbon fiber reinforcements in a matrix material. The method of representative volume element is utilized to perform the multiscale modeling of the problem. Initially, Boolean-based random sequential adsorption algorithm is utilized to model a nanoscale representative volume element of nanocomposite material to mimic the effect of randomly distributed (i.e. having random orientation and position) carbon nanotubes in a matrix material. After estimating the elastic properties of the nanocomposite material using representative volume element, another microscale representative volume element of carbon fiber reinforced in the nanocomposite (i.e. carbon nanotube reinforced matrix material) is modeled to evaluate the stiffness properties of the lamina formed of carbon nanotube–carbon fiber reinforced nanocomposite. The laminae are further stacked in the sequence of (45°/−45°/−45°/45°) to model a laminate. Thereafter, the evaluated stiffness properties of the lamina are employed to predict the effect of carbon nanotube reinforcement on buckling and postbuckling behavior of the laminated plates through nonlinear finite element method formulation based on the first-order shear deformation theory and von Karman’s assumptions. It is established that carbon nanotube reinforcement in carbon fiber reinforced composite lamina results in the enhancement of stiffness properties of the resulting carbon nanotube–fiber nanocomposite lamina, with more prevalent effect on the matrix-dominated properties—transverse and shear moduli—than the axial modulus. The increased stiffness properties result in the substantial improvement in the buckling load and postbuckling strength of the laminated plate made of carbon nanotube–carbon fiber nanocomposite material, for all volume fractions of carbon nanotube, loading and boundary conditions, geometric parameters (i.e. aspect ratio and width-to-thickness ratio), and matrix materials.

Elastic properties of CNT- and graphene-reinforced nanocomposites using RVE

The present paper is aimed to evaluate and compare the effective elastic properties of CNT- and graphene-based nanocomposites using 3-D nanoscale representative volume element (RVE) based on continuum mechanics using finite element method (FEM). Different periodic displacement boundary conditions are applied to the FEM model of the RVE to evaluate various elastic constants. The effects of the matrix material, the volume fraction and the length of reinforcements on the elastic properties are also studied. Results predicted are validated with the analytical and/or semiempirical results and the available results in the literature. Although all elastic stiffness properties of CNT- and graphene-based nanocomposites are found to be improved compared to the matrix material, but out-of-plane and in-plane stiffness properties are better improved in CNT- and graphene-based nanocomposites, respectively. It is also concluded that long nanofillers (graphene as well as CNT) are more effective in increasing the normal elastic moduli of the resulting nanocomposites as compared to the short length, but the values of shear moduli, except G23 of CNT nanocomposite, of nanocomposites are slightly improved in the case of short length nanofillers (i.e., CNT and graphene).

Electromechanical peridynamics modeling of piezoresistive response of carbon nanotube nanocomposites

In this work, a coupled electromechanical peridynamics formulation is presented which is used to study the electrical and piezoresistive response of a carbon nanotube (CNT) reinforced polymer nanocomposite material. CNT nanocomposites are multiscale materials which have unique piezoresistive properties arising from mechanisms operating from the nanoscale to the macroscale. The origin of piezoresistivity in CNT nanocomposites is a nanoscale phenomenon known as electron hopping or the electrical tunneling effect which allows an electric current to flow between neighboring CNTs even when not in contact, thereby forming a conductive network. A nanoscale representative volume element of a CNT bundle is chosen, i.e. a local region of high CNT volume fraction within the polymer matrix, wherein coupled electromechanical peridynamic equations are solved to evaluate the effective electrical and piezoresistive properties. The peridynamics formulation is used to introduce electron hopping in a unique way, through electron hopping bonds which have a horizon distance and conductivity dictated by the appropriate physics operating at the nanoscale. The effective electromechanical response depends on parameters such as CNT volume fraction, properties of the polymer matrix between CNTs and applied strain which are investigated in detail. Both quasistatic and dynamic loading conditions are considered where the effective electromechanical response is found to depend on variations in the local conductivity of intertube regions.

Role of Interphase in the Mechanical Behavior of Silica/Epoxy Resin Nanocomposites

A nanoscale representative volume element has been developed to investigate the effect of interphase geometry and property on the mechanical behavior of silica/epoxy resin nanocomposites. The role of interphase–matrix bonding was also examined. Results suggested that interphase modulus and interfacial bonding conditions had significant influence on the effective stiffness of nanocomposites, while its sensitivities with respect to both the thickness and the gradient property of the interphase was minimal. The stiffer interphase demonstrated a higher load-sharing capacity, which also increased the stress distribution uniformity within the resin nanocomposites. Under the condition of imperfect interfacial bonding, the effective stiffness of nanocomposites was much lower, which was in good agreement with the documented experimental observations. This work could shed some light on the design and manufacturing of resin nanocomposites.

Multiscale modeling of interface debonding effect on mechanical properties of nanocomposites

Mechanical behavior of SiO2 nanoparticle‐epoxy matrix composites was investigated via finite element analysis with an emphasis on the nanofiller‐interphase debonding effect using a three‐dimensional nanoscale representative volume element (RVE). The new model, in which a cohesive zone material (CZM) layer is considered as an inclusion‐interphase bonding, can be applied to polymer nanocomposites reinforced by inclusions of different forms, including spherical, cylindrical, and platelet shapes. Upon validation by experimental data, the model was used to study the effects of interphase properties, nanoparticle size, and inclusion volume fraction on the mechanical properties of nanocomposites. According to the results, taking into account the inclusion‐interphase debonding provides more precise results compared with perfect bonding, especially in nanocomposites with nanoparticles of smaller size. Moreover, the outcomes disclosed that the amount of changes in the elastic modulus by particle size variation is higher when the relative thickness (the interphase thickness to the particle diameter ratio) increases. For relative thicknesses lower than a critical value, the particle size and the interphase properties have negligible effect on the elastic modulus of the nanocomposite, and the elastic modulus of nanocomposite mostly depends on nanofiller content. POLYM. COMPOS., 38:789–796, 2017. © 2015 Society of Plastics Engineers

Effect of CNT waviness on the effective mechanical properties of long and short CNT reinforced composites

Carbon nanotubes (CNTs) possess extremely high stiffness, strength and resilience, and may provide ultimate reinforcing materials for the development of nanocomposites. CNT reinforced composite materials (CNTRC) can be effectively used in aircraft structures, due to their high strength to weight ratio. Accordingly, several experimental and analytical studies have been performed for evaluating effective mechanical properties of CNT-reinforced polymer matrix. However, several complex issues including sizes and forms of CNTs dispersed in a matrix, their distribution and orientation in the matrix make the simulations of the mechanical behaviour of these composites extremely complicated. One such issue is assessing the effect of nanotube curvature since embedded CNTs seldom remain straight inclusions. Nanotube curvature is often characterized by means of the waviness that accounts for the deviation from the straight particles assumption. In this paper, the effect of waviness of CNT is analyzed using a 3-D nanoscale representative volume element (RVE) based on continuum mechanics, and effective elastic modulus is calculated for two cases namely, a RVE with long CNT (CNT throughout the length of RVE) and a RVE with short CNT (CNT completely inside the RVE). Finite element method is used for the analysis. Further, a theoretical model based on the micromechanics of multi-phase composite and energy principles has also been developed to evaluate effective elastic constants of these RVEs. It is found that the reinforcing capacity of the CNTs reduces drastically even with a small waviness as compared to the straight CNTs. The effect of waviness is much more pronounced in case of long wavy CNT than short wavy CNT. The analysis is finally extended to predict the effective moduli of these composites embedded with completely randomly oriented CNTs of different waviness.

Multiscale micromechanical modeling of the constitutive response of carbon nanotube-reinforced structural adhesives

Appropriate formulations are developed to allow for the atomistic-based continuum modeling of nano-reinforced structural adhesives on the basis of a nanoscale representative volume element that accounts for the nonlinear behavior of its constituents; namely, the reinforcing carbon nanotube, the surrounding adhesive and their interface. The newly developed representative volume element is then used with analytical and computational micromechanical modeling techniques to investigate the homogeneous dispersion of the reinforcing element into the adhesive upon both the linear and nonlinear properties. Unlike our earlier work where the focus was on developing linear micromechanical models for the effective elastic properties of nanocomposites, the present approach extends these models by describing the development of a nonlinear hybrid Monte Carlo Finite Element model that allows for the prediction of the full constitutive response of the bulk composite under large deformations. The results indicate a substantial improvement in both the Young’s modulus and tensile strength of the nano-reinforced adhesives for the range of CNT concentrations considered.

Dynamic Analysis of Single Walled Boron Nitride Nanotube Reinforced Composite Based Nanomechanical Resonator

Boron nitride nanotubes (BNNTs) possess extremely high stiffness and strength and may provide the ultimate reinforcing materials for the development of nanocomposites. In this paper, the Young’s modulus of BNNT based composites are evaluated using a 3-D nanoscale representative volume element based on continuum mechanics (CM) and using the finite element method (FEM). Additionally, the suitability of the BNNTs reinforced polymeric composites as nanomechanical resonators, using CM based approach and FEM is illustrated in this paper. Analytical formulas based on CM are used to examine the mass sensitivity of single walled BNNT (SWBNNT) reinforced composite considered as a thin wall BNNT for different aspect ratios and volume fractions of BNNT in composites. The FEM analysis, considering SWBNNT as a transversely anisotropic material is performed and results are compared with the CM based approach. The results indicated that the mass sensitivity of SWBNNT reinforced composite based nanomechanical resonators can reach 10−3 fg and a logarithmically linear relationship exists between the resonant frequency and the attached mass, when mass is larger than 10−3 fg. The simulation results which have been obtained based on FEM are found to be in good agreement with the analytical approach used in this paper.

Evaluations of Young's Modulus of Boron Nitride Nanotube Reinforced Nano-composites

Boron Nitride Nanotubes (BNNTs) possess extremely high stiffness and strength and may provide the ultimate reinforcing materials for the development of nano-composites. In this paper, the Young's modulus of BNNT based composites are evaluated using a 3-D nanoscale representative volume element (RVE) based on continuum mechanics and using the finite element method (FEM). Formulas to extract the Young's modulus from solutions for the RVE are derived, based on the elasticity theory. An extended rule of mixtures, based on the strength of materials theory for estimating the effective Young's modulus in the axial direction of the RVE, is applied for comparisons with the numerical solutions based on the elasticity theory. It is observed that with additions of 5% of volume fraction of the BNNTs in a matrix of various materials, the strength of the composite can increases by an amount 20- 55% depending on material of matrix, suggesting possible use of BNNT as reinforcing material to strengthen the matrix material in composite.

Effective mechanical properties of nanocomposites reinforced with wavy carbon nanotubes

Carbon nanotubes (CNTs) possess exceptional mechanical properties and are therefore suitable reinforcements for composite materials. Nanotube efficiency in reinforcing the matrix depends on the CNT alignment, volume fraction and configuration, as well as matrix properties. In this investigation, finite element method (FEM) is used to investigate the effects of nanotube waviness ratio, volume fraction, and matrix modulus on properties of CNT based polymer nanocomposites. Nanocomposite mechanical properties are evaluated using a 3D nanoscale representative volume element. Models consisting of CNTs with different waviness ratios are created to investigate the effects of nanotube configuration on nanocomposite mechanical properties. Next, the effect of nanotube volume fraction on nanocomposite moduli of elasticity is investigated. Finally, the effects of matrix modulus are investigated by analysing models consisting of matrices with different moduli. The results of this investigation are compared with those found in the literature and good agreement is observed.

Numerical analysis of synergistic reinforcing effect of silica nanoparticle–MWCNT hybrid on epoxy-based composites

A novel nanostructural hybrid (SiO2–MWCNTs) composed of zero-dimensional silica nanoparticles (SiO2) and one-dimensional multi-walled carbon nanotubes (MWCNTs) were successfully prepared by multi-step functionalization. Synergistic reinforcing effect of SiO2–MWCNTs on epoxy-based composites was investigated using various theoretical methods. Specifically, a novel finite element method (FEM) based on nanoscale representative volume element (RVE) model was built up to describe the irregular geometry and reinforcing effect of SiO2–MWCNTs. In contrast with the corrected rule of mixtures and corrected Halpin–Tsai equations, the established FEM based on nanoscale RVE model was highly accurate and effective in predicting mechanical properties for polymer-based composites reinforced by SiO2–MWCNTs.

Micromechanical analysis of nanoparticle-reinforced dental composites

The mechanical behavior of TiO2 nanoparticle-reinforced resin-based dental composites was characterized in this work using a three-dimensional nanoscale representative volume element. The impacts of nanoparticle volume fraction, aspect ratio, stiffness and interphase zone between the resin matrix and nanoparticle on the bulk properties of the composite were characterized. Results clearly demonstrated the mechanical advantage of nanocomposites in comparison to microfiber reinforced composites. The bulk response of the nanocomposite could be further enhanced with the increased nanoparticle volume fraction, or aspect ratio, while the influence of nanoparticle stiffness was minimal. The effective Young’s modulus and yield strength of the composite was also significantly affected by the interphase stiffness. Results obtained in this work could provide insights for the optimization of nanoparticle-reinforced dental composites.

Effects of interface characteristics on mechanical properties of carbon nanotube reinforced polymer composites

Carbon nanotubes (CNTs) possess exceptional mechanical properties and are therefore suitable candidates for use as reinforcements in composite materials. To take full advantage of their exceptional properties, load sharing mechanisms needs to be understood in the composite materials. Load transfer in composites is achieved through the fibre/matrix interface. In the present paper, finite element method is used to investigate the effects of interface behaviour on carbon nanotube based composite mechanical properties. The effective nanocomposite mechanical properties are evaluated using a three-dimensional nanoscale representative volume element (RVE). In this RVE approach, a single nanotube and the surrounding polymer matrix are modelled. Two cases of perfect bonding and an elastic interface are considered. In addition, the rule of mixtures relations is used to validate the results of numerical models. The results indicate that mechanical properties of nanocomposite materials are significantly influenced by the interface strength.

Numerical characterization of CNT-based polymer composites considering interface effects

Carbon nanotubes (CNTs) possess exceptional mechanical properties and are therefore suitable candidates for use as reinforcements in composite materials. Load transfer in nanocomposite materials is achieved through the CNT/matrix interface. Thus, to determine nanocomposite mechanical properties, the interface behavior must be determined. In this investigation, finite element method is used to investigate the effects of interface strength on effective CNT-based composite mechanical properties. Nanocomposite mechanical properties are evaluated using a 3D nanoscale representative volume element (RVE). A single nanotube and the surrounding polymer matrix are modeled. Two cases of perfect bonding and an elastic interface are considered. For the perfect bonding interface, the no slip conditions are applied. To better investigate the elastic interface behavior, two models are proposed for this type of interface. The first elastic interface model consists of a thin layer of an elastic material surrounding the CNT. In the second elastic interface model, a series of spring elements are used as the nanotube/matrix interface. The results of numerical models indicate the importance of adequate interface bonding for a more effective strengthening of polymer matrix by CNT’s.

Effect of Fiber Diameter Waviness and Wavelength Ratio on the Effective Tensile Elastic Modulus of Carbon Nanotube-Based Polymer Composites

In this paper, the effects of nanotube diameter, waviness ratio and wavelength ratio on the tensile elastic modulus (TEM) of the carbon nanotube (CNT) reinforced polymer composites is investigated using a 3-D nanoscale representative volume element (RVE) based on continuum mechanics and using the finite element method (FEM). Formula to extract the effective material constant from solutions for the RVE under axial loading is derived based on the elasticity theory. Both long and short CNT embedded in the matrix are considered for investigating the effect of fiber diameter variation whereas only long wavy CNT is considered for investigating the effect of waviness and wavelength ratio variation, all at a volume fraction of 5%. First, the effects of CNT diameter on the TEM of the composite are investigated. Numerical results show that TEM of the polymer composite is influenced by tube diameter variation for both long and short CNT. Then the effects of waviness ratio and wavelength ratio on the TEM of polymer composite are investigated. Results show that both the waviness and wavelength ratio variation of CNT significantly influence the TEM of the polymer composite.

A Micromechanics Model for the Electrical Conductivity of Nanotube-Polymer Nanocomposites

The introduction of carbon nanotubes (CNTs) into nonconducting polymers has been observed to yield orders of magnitude increases in conductivity at very low concentrations of CNTs. These low percolation concentrations have been attributed to both the formation of conductive networks of CNTs within the polymer and to a nanoscale effect associated with the ability of electrons to transfer from one CNT to another known as electron hopping. In the present work, a micromechanics model is developed to assess the impact of the effects of electron hopping and the formation of conductive networks on the electrical conductivity of CNT-polymer nanocomposites. The micromechanics model uses the composite cylinders model as a nanoscale representative volume element where the effects of electron hopping are introduced in the form of a continuum interphase layer, resulting in a distinct percolation concentration associated with electron hopping. Changes in the aspect ratio of the nanoscale representative volume element are used to reflect the changes in nanocomposite conductivity associated with the formation of conductive networks due to the formation of nanotube bundles. The model results are compared with experimental data in the literature for both single- and multi-walled CNT nanocomposites where it is observed that the model developed is able to qualitatively explain the relative impact of electron hopping and nanotube bundling on the nanocomposite conductivity and percolation concentrations.

Heat Conduction Analysis in Bodies Containing Thin-Walled Structures by Means of Hybrid BNM with an Application to CNT-Based Composites

This paper discusses an implementation of Hybrid Boundary Node Method (Hybrid BNM) to the heat conduction analysis within bodies containing thin-walled structures. As an application, the thermal analysis in carbon nanotubes (CNT) based composites is presented. CNTs are predicted to possess superior heat conductivity and may, even with a small amount embedded, substantially improve heat conducting behavior of polymers. In this paper the equivalent heat conductivities of CNT-based nanocomposites are evaluated using a 3-D nanoscale representative volume element (RVE) model and the hybrid boundary node method (Hybrid BNM). The temperature distribution and heat flux concentration are studied. The equivalent heat conductivity of the RVE as a function of the nanotube length is calculated and discussed, and, moreover, an approximate formula for its evaluation for an RVE containing single nanotube is proposed. Computations indicate that addition of about 7.2% to 17% (volume fraction) of CNT to the polymer matrix may result in the increase of heat conductivity of the composite varying from 49% to 334% both for short and long CNT.