Systematic study of thermal properties of CNT composites by the fast multipole hybrid boundary node method

Carbon nanotubes (CNTs) are predicted to possess superior heat conductivity, which makes the CNTs promising in development of fundamentally new composite material. With the current advancement in nanotechnology, it is possible to design materials with desired properties for specific applications. On the other hand, the overall properties of CNT composites are usually evaluated using a representative volume element (RVE) with a number of CNTs embedded. For realistic modeling, an RVE including a large number of CNTs, for example, tens or hundreds, is necessary. However, analysis of such an RVE using standard numerical methods faces two severe difficulties: discretization of the geometry into elements and the very large computational scale. In this paper, the first difficulty is alleviated by developing the hybrid boundary node method (HdBNM), which is a boundary-type meshless method. To overcome the second difficulty, a simplified mathematical model for thermal analysis of CNT analysis is first proposed, by which the size of the linear system can be reduced by nearly half. Then, the HdBNM is combined with the Fast Multipole Method (FMM) based on the model to further reduce the computational scale. A variety of RVEs containing different numbers of CNTs, from small to large scales, have been studied in an attempt to investigate the influence of CNT length, distribution, orientation and volume fraction on the overall thermal properties of the composites. Insights have been gained into the thermal behavior of the CNT composite material.     

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.     

固相纳米复合材料的导热系数预测

研究了分散剂和纳米颗粒对固相纳米复合材料导热系数的影响。假设纳米颗粒在纳米流体中均匀分布,构建了一个考虑纳米颗粒尺度和分散介质影响的物理分析模型;并由此利用最小热阻力法则和比等效导热系数相等法则,建立了一个固相纳米复合材料的导热系数理论模型。计算结果表明,颗粒的体积分数和导热系数、以及分散剂导热系数的增大,都会引起复合材料导热系数的增大。     

A homogenization technique for heat transfer in periodic granular materials

A homogenization technique is proposed to simulate the thermal conduction of periodic granular materials in vacuum. The effective thermal conductivity (ETC) and effective volumetric heat capacity (EVHC) can be obtained from the granular represent volume element (RVE) via average techniques: average heat flux and average temperature gradient can be formulated by the positions and heat flows of particles on the boundaries of the RVE as well as of the contact pairs within the RVE. With the thermal boundary condition imposed on the border region around the granular RVE, the ETC of the granular RVE can be computed from the average heat flux and average temperature gradient obtained from thermal discrete element method (DEM) simulations. The simulation results indicate that the ETC of the granular assembly consisting of simple-cubic arranged spheres coincides with the theoretical prediction. The homogenization technique is performed to obtain the ETC of the RVE consisting of random packed particles and the results exhibit the anisotropy of the thermal conduction properties of the RVE. Both the ETC and EVHC obtained are then employed to simulate the thermal conduction procedure in periodic granular materials with finite element analyses, which give the similar results of temperature profile and conduction properties as the DEM simulations.     

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.     

Geometry dependence of the electrostatic and thermal response of a carbon nanotube during field emission

In this paper we present an analysis to simulate heating within an isolated carbon nanotube (CNT) attached to an etched tungsten tip during field emission of an electron beam. The length, radius, wall thickness and shape of the tip (closed with a hemispherical shape or open and flat) of the CNT and its separation distance from the flat surface are considered as variables. Using a finite element method, we predict the field enhancement, emission current and temperature of the CNT as a function of these parameters. The electrostatic and transient thermal analyses are integrated with the field-emission models based on the Fowler-Nordheim approximation and heating/cooling due to emitting energetic electrons (the Nottingham effect). These simulations suggest that the main mechanism responsible for heating of the CNT is Joule heating, which is significantly larger than the Nottingham effect. Results also indicate that the electrostatic characteristics of CNTs are very sensitive to the considered parameters whereas the transient thermal response is only a function of the CNT radius and wall thickness. Further, the thermal response of the CNT is independent of its geometry, meaning that, as long as a given set of geometrical conditions are present that result in a given emission current, the maximum temperature a CNT attains will be the same.     

Stability and thermal conductivity enhancement of carbon nanotube nanofluid using gum arabic

This experimental study reports on the stability and thermal conductivity enhancement of carbon nanotubes (CNTs) nanofluids with and without gum arabic (GA). The stability of CNT in the presence of GA dispersant in water is systematically investigated by taking into account the combined effect of various parameters, such as sonication time, temperature, dispersant and particle concentration. The concentrations of CNT and GA have been varied from 0.01 to 0.1?wt% and from 0.25 to 5?wt%, respectively, and the sonication time has been varied in between 1 and 24?h. The stability of nanofluid is measured in terms of CNT concentration as a function of sediment time using UV-Vis spectrophotometer. Thermal conductivity of CNT nanofluids is measured using KD-2 prothermal conductivity meter from 25 to 60°C. Optimum GA concentration is obtained for the entire range of CNT concentration and 1–2.5?wt% of GA is found to be sufficient to stabilise all CNT range in water. Rapid sedimentation of CNTs is observed at higher GA concentration and sonication time. CNT in aqueous suspensions show strong tendency to aggregation and networking into clusters. Stability and thermal conductivity enhancement of CNT nanofluids have been presented to provide a heat transport medium capable of achieving high heat conductivity. Increase in CNT concentrations resulted in the non-linear thermal conductivity enhancement. More than 100–250% enhancement in thermal conductivity is observed for the range of CNT concentration and temperature.     

Multiscale modeling for mechanical properties of carbon nanotube reinforced nanocomposites subjected to different types of loading

Multiscale modeling was presented for the nonlinear properties of polymer/single wall carbon nanotube (SWNT) nanocomposite under tensile, bending and torsional loading conditions. To predict the mechanical properties of both armchair and zigzag SWNTs, a finite element (FE) model based on the theory of molecular mechanics was used. For reducing the computational efforts, an equivalent cylindrical beam element was proposed, which has the unique advantage of describing the mechanical properties of SWNTs considering the nonlinearity of SWNT behavior. For a direct evaluation of the rigidities of the proposed equivalent beam, the data obtained through atomistic FE analyses of SWNT were fitted to six different equations, covering the three types of loading for both armchair and zigzag configurations. The proposed equivalent beam element was then used to build a cylindrical representative volume element (RVE) using which the effects of the interphase between SWNT and the polymer on the mechanical properties of RVE could be studied. It was found that while the interphase has a small effect on the nanocomposite stiffness, the ratio of (SWNT length)/(RVE length) dramatically affects the nanocomposite stiffness.     

Thermal conductivity of carbon nanotube reinforced aluminum composites: A multi-scale study using object oriented finite element method

In this study, object oriented finite element method (OOF) has been utilized to compute the thermal conductivity of plasma sprayed Al-12 wt.% Si containing 10 wt.% multiwall carbon nanotubes (CNTs). The computations have been made at micro- and macro-length scales which highlight the effect of CNT dispersion on thermal conductivity. Experimentally measured values at 50 °C indicate that CNT addition reduced the thermal conductivity of Al–Si matrix from 73 W m⁻¹ K⁻¹ to 25.4 W m⁻¹ K⁻¹ which is attributed to the presence of CNT clusters. OOF calculations at micro-length scale predicted an 81% increase in the conductivity of Al–Si matrix due to presence of well dispersed CNTs inside the matrix. At larger lengths scale, the decrease in the overall conductivity is related to the extremely low conductivity of CNT clusters. Thermal conductivity of CNT clusters could be up to three orders of magnitude lower than individual CNTs. OOF computed values match well with experimental results. OOF compute thermal conductivity of Al–CNT composite is also compared with theoretical two-phase models for CNT-composites at different length scales.     

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.     

复合材料热传导系数均匀化计算的实现方法

均匀化理论可以有效预测周期性结构复合材料的等效热传导系数,然而其控制方程的载荷项形式特殊,通用有限元软件中没有对应的载荷形式,难以直接求解.提出一种本构关系及场变量的类比方法,证明了在此类比下等效热传导系数均匀化方程与等效弹性模量均匀化方程是等价的.根据求解等效弹性模量均匀化方程的热应变法,提出一种新的等效热传导系数均匀化方程数值求解方法.以ABAQUS为平台,预测单向纤维复合材料以及金属蜂窝夹芯板的等效热传导系数,计算结果与参考值吻合良好.该方法为基于通用有限元软件的复合材料等效热传导系数的均匀化计算提供了简便途径.     

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.     

Multiscale approach with RSM for stress–strain behaviour prediction of micro-void-considered metal alloy

This paper presents the concept of using a representative volume element (RVE) in a multiscale approach to predict the macroscopic stress–strain behaviour of a cast SS316L specimen under tension up to the point prior to necking. RVE models with various micro-void spatial configurations were built, and the effects of micro-voids and strain rate on the material properties (e.g., yield strength, ultimate tensile strength (UTS), ultimate tensile strain and strain hardening coefficient) were analysed. The spatial configuration of the micro-voids inside the cast SS316L specimen was acquired by the X-ray CT scanning system and each micro-void in the gauge length part was converted into a matching RVE model in the finite element (FE) analysis. Response surface methodology (RSM) was employed to investigate the effect of RVE configurations, i.e., the size of the RVE and the shape and spatial location of the micro-voids, on the material properties (yield strength and UTS) of the cast SS316L specimen at the macroscopic level, and then the optimal levels of the RVE configuration were determined. The stress–strain curve from the simulation did show a good agreement with the experimental results and hence the proposed concept was verified.     

Finite cluster model and effective conductivity of a composite with non-randomly oriented elliptic inclusions

The finite cluster model (FCM)-based homogenization scheme has been formulated in terms of the dipole moments of the representative volume element (RVE) of actual composite and equivalent inclusion. Provided the interactions between the inclusions were taken into account, this scheme is asymptotically exact in the sense that the effective properties converge to its exact value with increasing RVE size and thus can be regarded as a rigorous method of micromechanics. To demonstrate its potential, the conductivity problem for a composite with non-randomly oriented elliptic inclusions is considered. The convergence of the solution is illustrated, and an effect of the microstructure including the orientation factor on the effective conductivity of the composite has been explored. The methodological issues of FCM application are discussed including an appropriate shape of the composite cluster and equivalent inclusion. The practical importance of the FCM consists in its direct applicability to the image of the microstructure obtained by the instrumental methods which makes it a convenient tool for estimating the effective properties of a composite in situ.     

蜂窝芯体面外方向导热系数等效研究

利用商用有限元软件分析了高温阶段蜂窝芯体面外方向等效导热系数,分析结果与试验数据和半经验公式结果进行了对比,对比结果显示有限元软件可以用来预测蜂窝芯体面外方向等效导热系数。利用有限元软件分析了低温阶段蜂窝芯体面外方向等效导热系数,证明在0℃以下时辐射换热对蜂窝芯体面外方向导热系数的影响可以忽略,同时得到了铝合金蜂窝芯体在0℃以下时面外方向等效导热系数近似公式。     

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.     

Representative volume: Existence and size determination

The concept of the representative volume element (RVE) is analysed in the present paper. For elastic materials the RVE exists and one can determine the size of the RVE. However, for other applications, such as the case of softening materials, the RVE may not exist. In the present work the RVE has been investigated for different stages of the material response, including pre- and post-peak loading regimes. Results were based on a statistical analysis of numerical experiments, where tests have been performed on a random heterogeneous material.     

A numerical study on carbon nanotube pullout to understand its bridging effect in carbon nanotube reinforced composites

Carbon nanotube (CNT) reinforced polymeric composites provide a promising future in structural engineering. To understand the bridging effect of CNT in the events of the fracture of CNT reinforced composites, the finite element method was applied to simulate a single CNT pullout from a polymeric matrix using cohesive zone modelling. The numerical results indicate that the debonding force during the CNT pullout increases almost linearly with the interfacial crack initiation shear stress. Specific pullout energy increases with the CNT embedded length, while it is independent of the CNT radius. In addition, a saturated debonding force exists corresponding to a critical CNT embedded length. A parametric study shows that a higher saturated debonding force can be achieved if the CNT has a larger radius or if the CNT/matrix has a stronger interfacial bonding. The critical CNT embedded length decreases with the increase of the interfacial crack initiation shear stress.     

碳纳米管/聚丙烯腈基复合材料的热导率研究

采用原位聚合法制备了碳纳米管/聚丙烯腈(CNT/PAN)复合材料,用MDSC的测试方法研究了复合材料的热性能,并由此推导了复合材料的热导率.应用Cheng-Vachon、Nielsen-Lewis和Okamoto-Ishida 3种导热理论模型对CNT/PAN复合材料的热导率进行估算.对比实验测试与导热理论模型的计算结果,考虑到碳纳米管在聚合物基体中的分散和取向情况,得出Nielsen-Lewis理论在低填充含量及室温条件下可以较准确地估算无规分散的CNT/PAN复合材料体系的热导率.