Fast HdBNM for large-scale thermal analysis of CNT-reinforced composites

Because of their high thermal conductivities, carbon nanotubes (CNT) have promising potential in development of fundamentally new composites. To study the influence of CNTs distribution on the overall properties of a composite, the modeling of a Representative Volume Element (RVE) including a large number of CNTs that are randomly distributed and oriented is necessary. However, analysis of such a RVE using standard numerical methods faces two severe difficulties, namely the discretization of the geometry and a very large computational scale. In this paper, the first difficulty is alleviated by employing the Hybrid Boundary Node Method (HdBNM), which is a form of the boundary type meshless methods. To overcome the second difficulty, the Fast Multipole Method (FMM) is combined with the HdBNM to solve a simplified mathematical model. RVEs containing various numbers of CNTs with different lengths, shapes and alignments have been analyzed, resulting in valuable insights gained into the thermal behavior of the composite material.     

Modeling the tensile stress–strain response of carbon nanotube/polypropylene nanocomposites using nonlinear representative volume element

This paper presents a finite element model for predicting the mechanical behavior of polypropylene (PP) composites reinforced with carbon nanotubes (CNTs) at large deformation scale. Existing numerical models cannot predict composite behavior at large strains due to using simplified material properties and inefficient interfaces between CNT and polymer. In this work, nonlinear representative volume elements (RVE) of composite are prepared. These RVEs consist of CNT, PP matrix and non-bonded interface. The nonlinear material properties for CNT and polymer are adopted to solid elements. For the first time, the interface between CNT and matrix is simulated using contact elements. This interfacial model is capable enough to simulate wide range of interactions between CNT and polymer in large strains. The influence of adding CNT with different aspect ratio into PP is studied. The mechanical behavior of composites with different interfacial shear strength (ISS) is discussed. The success of this new model was verified by comparing the simulation results for RVEs with conducted experimental results. The results shows that the length of CNT and ISS values significantly affect the reinforcement phenomenon.     

Effect of carbon nanotube orientation on the mechanical properties of nanocomposites

Carbon nanotubes (CNTs) have been regarded as ideal reinforcements of high-performance composites with enormous applications. In this paper, nano-structure is modeled as a linearly elastic composite medium, which consists of a homogeneous matrix having hexagonal representative volume elements (RVEs) and homogeneous cylindrical nanotubes with various inclination angles. Effects of inclined carbon nanotubes on mechanical properties are investigated for nano-composites using 3-D hexagonal representative volume element (RVE) with short and straight CNTs. The CNT is modeled as a continuum hollow cylindrical shape elastic material with different angles. The effect of the inclination of the CNT and its parameters is studied. Numerical equations are used to extract the effective material properties for the hexagonal RVE under axial as well as lateral loading conditions. The computational results indicated that elastic modulus of nano-composite is remarkably dependent on the orientation of the dispersed SWNTs. It is observed that the inclination significantly reduces the effective Young’s modulus of elasticity under an axial stretch. When compared with lateral loading case, effective reinforcement is found better in axial loading case. The effective moduli are very sensitive to the inclination and this sensitivity decreases with the increase of the waviness. In the case of short CNTs, increasing trend is observed up to a specific value of waviness index. It is also found from the simulation results that geometry of RVE does not have much significance on stiffness of nano-structures. The results obtained for straight CNTs are consistent with ERM results for hexagonal RVEs, which validate the proposed model results.     

Three Phase Composite Cylinder Assemblage Model for Analyzing the Elastic Behavior of MWCNT-Reinforced Polymers

Evolution of computational modeling and simulation has given more emphasis on the research activities related to carbon nanotube (CNT) reinforced polymer composites recently. This paper presents the composite cylinder assemblage (CCA) approach based on continuum mechanics for investigating the elastic properties of a polymer resin reinforced by multi-walled carbon nanotubes (MWCNTs). A three-phase cylindrical representative volume element (RVE) model is employed based on CCA technique to elucidate the effects of inter layers, chirality, interspacing, volume fraction of MWCNT, interphase properties and temperature conditions on the elastic modulus of the composite. The interface region between CNT and polymer matrix is modeled as the third phase with varying material properties. The constitutive relations for each material system have been derived based on solid mechanics and proper interfacial traction continuity conditions are imposed. The predicted results from the CCA approach are in well agreement with RVE-based finite element model. The outcomes reveal that temperature softening effect becomes more pronounced at higher volume fractions of CNTs.     

Fabrication and effective thermal conductivity of multi-walled carbon nanotubes reinforced Cu matrix composites for heat sink applications

A novel particles-compositing method was used for the first time to disperse different contents of multi-walled carbon nanotubes (CNTs) in micron sized copper powders, which were subsequently consolidated into CNT/Cu composites by spark plasma sintering (SPS). Microstructural observations showed that the homogeneous distribution of CNTs and dense composites could be obtained for 0–10 vol.% CNT contents. The CNT clusters were appeared in the powder mixture with 15 vol.% CNTs, which resulted in an insufficient densification of the composites. The effective thermal conductivity of the composites was analyzed both theoretically and experimentally. The addition of CNTs showed no enhancement in overall thermal conductivity of the composites due to the interface thermal resistance associated with the low phase contrast of CNT to copper and the random tube orientation. Besides, the composite containing 15 vol.% CNTs led to a rather low thermal conductivity due possiblely to the combined effect of unfavorable factors induced by the presence of CNT clusters, i.e. large porosity, lower effective conductivity of CNT clusters themselves and reduction of SPS cleaning effect. The CNT/Cu composites may be a promising thermal management material for heat sink applications.     

Thermal Analysis of CNT-Based Nano-Composites by Element Free Galerkin Method

This paper deals with the thermal analysis of carbon nanotube (CNT) based composites by meshless element free Galerkin method. Cylindrical representative volume element (cylindrical RVE) has been chosen to evaluate the thermal properties of nano-composites using multi-domain and simplified approaches. The values of temperature have been calculated at different points and plotted against RVE length and RVE radius. A sensitivity analysis of RVE as well as CNT dimensions has been carried out in detail. The present computations show that the equivalent thermal conductivity is a function of CNT length, CNT radius, RVE length and RVE radius. Based on present numerical simulations, an approximate formula is proposed to calculate the equivalent thermal conductivity of nano-composites. The results obtained by simplified approach have been found in good agreement with those obtained by multi-domain approach.     

Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element

Carbon nanotubes (CNTs) possess extremely high stiffness, strength and resilience, and may provide the ultimate reinforcing materials for the development of nanocomposites. In this paper, the effective mechanical properties of CNT-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 effective material constants from solutions for the RVE under three loading cases 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. Numerical examples using the FEM are presented, which demonstrate that the load carrying capacities of the CNTs in a matrix are significant. With additions of the CNTs in a matrix at volume fractions of only about 2% and 5%, the stiffness of the composite can increase as many as 0.7 and 9.7 times for the short and long CNT cases, respectively. These simulation results are consistent with the experimental ones reported in the literature.     

Mechanical properties of high density polyethylene/carbon nanotube composites

Carbon-nanotubes (CNTs) have been used with polymers from the date of their inception to make composites having remarkable properties. An attempt has been made in this direction, in order to enhance mechanical and tribological properties of the composite materials. The latter, were achieved through the injection molding of high density polyethylene (HDPE) reinforced with specific volume fraction of CNTs. A considerable improvement on mechanical properties of the material can be observed when the volume fraction of CNT is increased. The composite reinforcement shows a good load transfer effect and interface link between CNT and HDPE. The volumetric wear rate is calculated from the Wang’s model, Ratner’s correlation and reciprocal of toughness. The results obtained clearly show the linear relationship with CNT loading which supports the microscopic wear model. It is concluded that both Halpin–Tsai and modified series model can be used to predict Young’s modulus of CNT–HDPE composites. From thermal analysis study, it is found that melting point and oxidation temperature of the composites are not affected by the addition of CNTs, however its crystallinity seems to increase.     

Multi-scale modeling of carbon nanotube reinforced polymers using irregular tessellation technique

A multi-scale modeling approach to extract mechanical properties of CNTRP emphasizing on the effective parameters associated with meso- and micro-scale is developed. Investigated material region at macro scale is regularly tessellated into constitutive blocks. Assigning random CNT volume fractions to each block, non-uniform dispersion of CNT is modeled. Irregular tessellation technique based on Voronoi method and Bayes algorithm is employed to partition the RVE at meso scale into constitutive polygons containing one single aggregated CNTs. Mechanical properties of the tessellated regions are extracted by a modified micromechanics rules addressing local positions of aggregates in the material region. A bounding technique accounting for non-straight shape of CNT is utilized to consider any arbitrary shapes of wavy CNT. The obtained results of modeling are compared with experimental observations. A novel formulation is developed taking into account all inconsistencies attributed to CNTRPs.     

Carbon nanotubes dispersed polymer nanocomposites: mechanical,electrical, thermal properties and surface morphology

The various properties and surface morphology of the carbon nanotubes (CNTs) dispersed polydimethyl siloxane (PDMS) matrix were studied to determine their usefulness in various applications. The tensile strength, Young’s modulus and electrical breakdown strength of CNT/polymer composites were 0.35 MPa, 1.2 MPa and 8.1 kV, respectively. The thermal conductivity and dielectric constant for the material having 4.28 wt% CNT were 0.225 W m^?1 K^?1 and 2.329, respectively. The CNT/polymer composites are promising functional composites with improved mechanical and electrical properties. The scanning electron microscope analysis of surface morphology of PDMS/CNT composite showed that the rough surface texture on nanocomposite has large surface area with circular pores. The Fourier transform infrared spectroscopy showed the functional groups present in polymer nanocomposite.     

Mechanical,electrical and thermal properties of aligned carbon nanotube/polyimide composites

Carbon nanotubes (CNTs) have high strength and modulus, large aspect ratio, and good electrical and thermal conductivities, which make them attractive for fabricating composite. The poly(biphenyl dianhydride-p-phenylenediamine) (BPDA/PDA) polyimide has good mechanical and thermal performances and is herein used as matrix in unidirectional carbon nanotube composites for the first time. The strength and modulus of the composite increase by 2.73 and 12 times over pure BPDA–PDA polyimide, while its electrical conductivity reaches to 183 S/cm, which is 10¹⁸ times over pure polyimide. The composite has excellent high temperature resistance, and its thermal conductivity is beyond what has been achieved in previous studies. The improved properties of the composites are due to the long CNT length, high level of CNT alignment, high CNT volume fraction and good CNT dispersion in polyimide matrix. The composite is promising for applications that require high strength, lightweight, or high electrical and thermal conductivities.     

The effective properties and local aggregation effect of CNT/SMP composites

A micromechanics model of the thermomechanical constitutive behavior and micro-structural inhomogeneity of carbon nanotubes (CNTs)/shape memory polymer (SMP) composites is presented. It is assumed that the CNTs are elastic and the SMP obeys a thermomechanical constitutive law. The effective properties of CNT/SMP composites are examined using a micro-mechanics method. The effect of CNT aggregation in the composite, frequently encountered in real engineering situations, is studied. The degree of aggregation is described by an aggregation coefficient, and the effective properties of SMP composites with aggregated CNTs are calculated using a stepping scheme. It is shown that the degree of CNT aggregation dramatically influences the effective properties of the CNT/SMP composites. A homogeneous microstructure leads to maximum levels of effective composite properties.     

Enhanced thermal and mechanical properties of carbon nanotube composites through the use of functionalized CNT-reactive polymer linkages and three-roll milling

We report enhanced thermal and mechanical properties of carbon nanotube (CNT) composites achieved through the use of functionalized CNTs-reactive polymer linkages and three-roll milling. CNTs were functionalized with carboxyl groups and dispersed in a polymer containing an epoxide group resulting in a chemical reaction. To maximize CNT dispersion for practical usage, entangled CNTs are separated and then evenly dispersed within the polymer matrix using three horizontally positioned rotating rolls that apply a strong shear force to the composite. Consequently, accompanying with thermal stability, elastic modulus and storage modulus of such functionalized CNT/polymer composites were increased by 100% and 500% that of the untreated epoxy polymer.     

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.     

Two-dimensional distribution of carbon nanotubes in copper flake powders

We report an approach of flake powder metallurgy to the uniform, two-dimensional (2D) distribution of carbon nanotubes (CNTs) in Cu flake powders. It consists of the preparation of Cu flakes by ball milling in an imidazoline derivative (IMD) aqueous solution, surface modification of Cu flakes with polyvinyl alcohol (PVA) hydrosol and adsorption of CNTs from a CNT aqueous suspension. During ball milling, a hydrophobic monolayer of IMD is adsorbed on the surface of the Cu flakes, on top of which a hydrophilic PVA film is adsorbed subsequently. This PVA film could further interact with the carboxyl-group functionalized CNTs and act to lock the CNTs onto the surfaces of the Cu flakes. The CNT volume fraction is controlled easily by adjusting the concentration/volume of CNT aqueous suspension and Cu flake thickness. The as-prepared CNT/Cu composite flakes will serve as suitable building blocks for the self-assembly of CNT/Cu laminated composites that enable the full potential of 2D distributed CNTs to achieve high thermal conductivity.     

Hygro-Thermo-Electric Properties of Carbon Nanotube Epoxy Nanocomposites with Agglomeration Effects

In the present study, the effective electric, thermal, and moisture properties of carbon nanotube (CNT) epoxy composites are derived by considering the agglomeration effect of CNT concentrations in the epoxy matrix. In this direction, the Voigt and Reuss homogenization method is adopted in the derivations. It is well known from experiments that the CNT thermal and electrical conductivities and the epoxy hygro-thermal expansion coefficients have significant effects on the behavior of CNT nanocomposites. Moreover, it has been experimentally proved that the agglomeration of CNTs in the matrix with high and low concentrations of the CNTs certainly affects the resistivity and, hence, the thermal expansion properties. Therefore, the effective elastic, thermal, electrical, and moisture properties for the randomly distributed CNTs in the matrix has been derived in terms of the agglomeration volume fractions of CNTs. In the effective relations, a single agglomeration parameter is considered to be active for a given potential. The results of variation in the hygro-electro-thermal properties due to change in CNT volume fraction as well as agglomeration parameters have been presented. The results and observation show that CNT agglomeration has a strong influence on the effective hygro-thermo-electric properties of the nanocomposites.     

Effect of carbon nanotube (CNT) content on the mechanical properties of CNT-reinforced aluminium composites

The interest in carbon nanotubes (CNTs) as reinforcements for aluminium (Al) has been growing considerably. Efforts have been largely focused on investigating their contribution to the enhancement of the mechanical performance of the composites. The uniform dispersion of CNTs in the Al matrix has been identified as being critical to the pursuit of enhanced properties. Ball milling as a mechanical dispersion technique has proved its potential. In this work, we use ball milling to disperse up to 5 wt.% CNT in an Al matrix. The effect of CNT content on the mechanical properties of the composites was investigated. Cold compaction and hot extrusion were used to consolidate the ball-milled Al–CNT mixtures. Enhancements of up to 50% in tensile strength and 23% in stiffness compared to pure aluminium were observed. Some carbide formation was observed in the composite containing 5 wt.% CNT. In spite of the observed overall reinforcing effect, the large aspect ratio CNTs used in the present study were difficult to disperse at CNT wt.% greater than 2, and thus the expected improvements in mechanical properties with increase in CNT weight content were not fully realized.     

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.     

A novel approach to fabricate high volume fraction nanocomposites with long aligned carbon nanotubes

Conventional micro-fiber-reinforced composites provide insight into critical structural features needed for obtaining maximum composite strength and stiffness: the reinforcements should be long, well aligned in a unidirectional orientation, and should have a high reinforcement volume fraction. It has long been a challenge for researchers to process CNT composites with such structural features. Here we report a method to quickly produce macroscopic CNT composites with a high volume fraction of millimeter long, well aligned CNTs. Specifically, we use the novel method, shear pressing, to process tall, vertically aligned CNT arrays into dense aligned CNT preforms, which are subsequently processed into composites. Alignment was confirmed through SEM analysis while a CNT volume fraction in the composites was calculated to be 27%, based on thermogravimetric analysis data. Tensile testing of the preforms and composites showed promising mechanical properties with tensile strengths reaching 400 MPa.