Meshless method for nonlinear heat conduction analysis of nano-composites

Carbon nanotubes (CNTs) may become ideal reinforcing materials for high-performance nano-composites due their exceptional properties. Still, much work is needed to be done before the potentials of CNT based composites can be fully realized. The evaluation of effective material properties of nano-composites is one of many difficult tasks. Simulations using continuum mechanics approach can play a significant role in the analysis of these composites. In the present work, nonlinear heat conduction analysis of CNT based composites has been carried out using continuum mechanics approach. Element free Galerkin method has been applied as a numerical tool. Thermal conductivities of nanotube and polymer matrix are assumed to vary quadratically with temperature. Picard and quasi-linearization schemes have been utilized to obtain the solution of a system of nonlinear equations. Cylindrical representative volume element has been used to evaluate the thermal properties of nano-composites. Present simulations show that the temperature dependent matrix thermal conductivity has a significant effect on the equivalent thermal conductivity of the composite, whereas temperature dependent nanotube thermal conductivity has a small effect on the equivalent thermal conductivity of the composite. The results obtained by Picard method have been found almost similar with those obtained by quasi-linearization approach.     

Effect of dispersion method on thermal conductivity and stability of nanofluid

Preparing a stable nanofluid with high thermal conductivity is of a great concern. In order to find an optimum dispersion method to achieve a better performance, five different carbon nanotube (CNT) structures, namely SWNTs (single wall CNT), DWNTs (double wall CNT), FWNTs (few wall CNT) and two different MWNTs (multiwall nanotubes) were synthesized to prepare nanofluids with three different dispersion methods namely functionalization, SDS/ultrasonic probe and SDS/ultrasonic bath. The experiments reveal that the best stability and thermal conductivity are associated with the functionalized nanofluids. Specifically, for the times after 50 h, the functionalized profiles begin to level off due to their higher stability, while the other two paths continue their declining trend.     

Carbonate-salt-based composite materials for medium- and high-temperature thermal energy storage

This paper discusses composite materials based on inorganic salts for medium- and high-temperature thermal energy storage application. The composites consist of a phase change material （PCM）, a ceramic material, and a high thermal conductivity material. The ceramic material forms a microstructural skeleton for encapsulation of the PCM and structural stability of the composites; the high thermal conductivity material enhances the overall thermal conductivity of the composites. Using a eutectic salt of lithium and sodium carbonates as the PCM, magnesium oxide as the ceramic skeleton, and either graphite flakes or carbon nanotubes as the thermal conductivity enhancer, we produced composites with good physical and chemical stability and high thermal conductivity. We found that the wettability of the molten salt on the ceramic and carbon materials significantly affects the microstructure of the composites.     

Prediction of thermal conductivity of composites with spherical fillers by successive embedding

In this study, a new model to predict the thermal conductivity of composites with spherical fillers is proposed. The original Eshelby model is extended to a finite filler volume fraction by successively embedding small filler volume fraction. The predicted results by the present model are compared with bounds such as parallel, series, and Hashin–Shtrikman models, results by modified Eshelby model, generalized self-consistent model, and effective medium theory, and the experimental results from the literature. It is found that the present model always lies between the bounds and shows better agreement with the experimental results than the other models for various filler volume fractions and thermal conductivity ratios.     

A theory of plasticity for carbon nanotube reinforced composites

Carbon nanotubes (CNTs) possess exceptional mechanical properties, and when introduced into a metal matrix, it could significantly improve the elastic stiffness and plastic strength of the nanocomposite. But current processing techniques often lead to an agglomerated state for the CNTs, and the pristine CNT surface may not be able to fully transfer the load at the interface. These two conditions could have a significant impact on its strengthening capability. In this article we develop a two-scale micromechanical model to analyze the effect of CNT agglomeration and interface condition on the plastic strength of CNT/metal composites. The large scale involves the CNT-free matrix and the clustered CNT/matrix inclusions, and the small scale addresses the property of these clustered inclusions, each containing the randomly oriented, transversely isotropic CNTs and the matrix. In this development the concept of secant moduli and a field fluctuation technique have been adopted. The outcome is an explicit set of formulae that allows one to calculate the overall stress-strain relations of the CNT nanocomposite. It is shown that CNTs are indeed a very effective strengthening agent, but CNT agglomeration and imperfect interface condition can seriously reduce the effective stiffness and elastoplastic strength. The developed theory has also been applied to examine the size (diameter) effect of CNTs on the elastic and elastoplastic response of the composites, and it was found that, with a perfect interface contact, decreasing the CNT radius would enhance the overall stiffness and plastic strength, but with an imperfect interface the size effect is reversed. A comparison of the theory with some experiments on the CNT/Cu nanocomposite serves to verify the applicability of the theory, and it also points to the urgent need of eliminating all CNT agglomeration and improving the interface condition if the full potential of CNT reinforcement is to be realized.     

Anisotropic thermal conductivity in sheared polypropylene

We discuss the anisotropy of the thermal conductivity tensor in polymer flow in this paper. Isotactic polypropylene (iPP) specimens were deformed by injection moulding at high shear rates and by steady shear at low shear rates, and were then quenched. The thermal conductivities parallel and perpendicular to the shear direction were measured using modulated differential scanning calorimetry (MDSC) in accordance with the ASTM E1952-01. The measured results showed that the thermal conductivity of the sheared polymer was anisotropic with an increase in the shear direction. The thermal conductivity can be regarded as varying either with the strain or the stress, as suggested by Van den Brule (1989). In addition to the Van den Brule mechanism, crystallization during flow also changes the thermal conductivity and this effect may often be dominant. Suggestions for procedures in processing computations, based on both effects, are given.     

考虑碳纳米管非均匀分布的复合材料电导率计算

碳纳米管作为导电相在机敏复合材料中广泛应用,但碳纳米管为团簇材料,在基体中很难均匀分散。本文考虑碳纳米管的非均匀分布特性,提出了计算碳纳米管复合材料电导率的数值方法。通过引入随机谐和函数,建立了碳纳米管体积分数的三维随机场模型。基于细观力学的有效介质理论、Mori-Tanaka方法和H-S界限理论,考虑碳纳米管之间的隧穿效应,发展了复合材料微小体积单元的电导率计算方法。在此基础上,构建了考虑碳纳米管非均匀分布的复合材料等效电导率三维有限元计算模型。数值分析结果与试验值能够很好吻合,表明这一方法可以准确计算碳纳米管复合材料的电导率。本文进一步分析了碳纳米管非均匀分布对复合材料电导率的影响。     

Non-Linear Dynamic Response of a Single Wall Carbon Nanotube Subjected to Radial Impulse

This paper investigates non-linear dynamic response of a single wall carbon nanotube (CNT) based on a thin-walled shell mode. Following the subsequent motion of a single wall (CNT) under radial impulsive pressure, a nonlinear dynamic response may occur through interaction of circumferential membrane force with flexural curvature. The results carried out show that the initial deformation energy in the single wall CNT will be transferred, over a number of cycles, from the breathing mode to one or two high flexural modes, so that the nonlinear flexural stress of the single wall CNT is significantly higher than that given by linear theory. The principal point of interest are the conditions for significant interaction to occur and the increased flexural stress associated with the altered radial motion of a single wall CNT. An erratum to this article can be found at     

Analysis of the entanglements in carbon nanotube fibers using a self-folded nanotube model

Carbon nanotube (CNT) fibers have shown superb mechanical properties, and have high potential to be used as reinforcements in multifunctional composites. CNT entanglements always exist in CNT fibers and play a crucial role in affecting their mechanical properties. In this study, the CNT entanglement is modeled as two connecting self-folded CNTs (SFCNTs). At large aspect ratios, a CNT is energetically favorable to be self-folded due to the van der Waals interactions between different parts of the CNT. The geometrical characteristics of the SFCNTs, such as the critical length for self-folding as well as the critical effective width and length, are investigated by using both an exact theoretical model and an approximate theoretical model. The tensile properties of the SFCNTs have been examined by using both the approximate theoretical model and atomistic simulations. Good agreements are achieved in the results of these two approaches.     

An elastic model for bioinspired design of carbon nanotube bundles

Collagen fibers provide a good example of making strong micro-or mesoscale fibers from nanoscale tropocollagen molecules through a staggered and crosslinked organization in a bottom-up manner.Mimicking the architectural features of collagen fibers has been shown to be a promising approach to develop carbon nanotube(CNT)fibers of high performance.In the present work,an elastic model is developed to describe the load transfer and failure propagation within the bioinspired CNT bundles,and to establish the relations of the mechanical properties of the bundles with a number of geometrical and physical parameters such as the CNT aspect ratio and longitudinal gap,interface cross-link density,and the functionalizationinduced degradation in CNTs,etc.With the model,the stress distributions along the CNT-CNT interface as well as in every individual CNT are well captured,and the failure propagation along the interface and its effects on the mechanical properties of the CNT bundles are predicted.The work may provide useful guidelines for the design of novel CNT fibers in practice.     

Stiffness threshold of randomly distributed carbon nanotube networks

For carbon nanotube (CNT) networks, with increasing network density, there may be sudden changes in the properties, such as the sudden change in electrical conductivity at the electrical percolation threshold. In this paper, the change in stiffness of the CNT networks is studied and especially the existence of stiffness threshold is revealed. Two critical network densities are found to divide the stiffness behavior into three stages: zero stiffness, bending dominated and stretching dominated stages. The first critical network density is a criterion to judge whether or not the network is capable of carrying load, defined as the stiffness threshold. The second critical network density is a criterion to measure whether or not most of the CNTs in network are utilized effectively to carry load, defined as bending–stretching transitional threshold. Based on the geometric probability analysis, a theoretical methodology is set up to predict the two thresholds and explain their underlying mechanisms. The stiffness threshold is revealed to be determined by the statical determinacy of CNTs in the network, and can be estimated quantitatively by the stabilization fraction of network, a newly proposed parameter in this paper. The other threshold, bending–stretching transitional threshold, which signs the conversion of dominant deformation mode, is verified to be well evaluated by the proposed defect fraction of network. According to the theoretical analysis as well as the numerical simulation, the average intersection number on each CNT is revealed as the only dominant factor for the electrical percolation and the stiffness thresholds, it is approximately 3.7 for electrical percolation threshold, and 5.2 for the stiffness threshold of 2D networks. For 3D networks, they are 1.4 and 4.4. And it also affects the bending–stretching transitional threshold, together with the CNT aspect ratio. The average intersection number divided by the fourth root of CNT aspect ratio is found to be an invariant at the bending–stretching transitional threshold, which is 6.7 and 6.3 for 2D and 3D networks, respectively. Based on this study, a simple piecewise expression is summarized to describe the relative stiffness of CNT networks, in which the relative stiffness of networks depends on the relative network density as well as the CNT aspect ratio. This formula provides a solid theoretical foundation for the design optimization and property prediction of CNT networks.     

Model for predicting effective thermal conductivity of composites with aligned continuous fibers of graded conductivity

Governing differential equations in both transverse and longitudinal directions for predicting the effective thermal conductivities of composites with aligned, graded continuous fibers are derived. It is shown that the effective conductivities of composites with graded fibers are predicted by solving the equations. The results by the present approach are applicable to both dilute and non-dilute cases without additional procedures unlike other approaches. The results are compared with those in the literature, and the applicability of the present approach is justified. A solution by the present approach is obtained analytically or numerically as long as thermal conductivity profile of fibers is given.     

MOLECULAR DYNAMICS SIMULATION OF POLYMER/CARBON NANOTUBE COMPOSITES

In this paper, we present classical molecular dynamics(MD) simulations of model polymer/CNT composites constructed by embedding a single wall(10,10) CNT into two different amorphous polymer matrices: poly(methyl methacrylate) and poly{(m-phenylene-vinylene)-co-[(2,5-dioctoxy-p-phenylene) vinylene]}, respectively, with different volume fractions. The simulation results support the idea that it is possible to use CNTs to mechanically reinforce an appropriate polymer matrix, especially in the longitudinal direction of the nanotube. The comparison of the simulation results with the macroscopic rule-of-mixtures for composite systems showed that for strong interfacial interactions, there can be large deviations of the results from the rule-ofmixtures. In order to verify this study, results obtained have been compared with those given by Elliott and Han(2007).     

EFFECTS OF DIFFERENT FUNCTIONALIZATION SCHEMES ON THE INTERFACIAL STRENGTH OF CARBON NANOTUBE POLYETHYLENE COMPOSITE

The mechanical performance of carbon nanotube(CNT) reinforced polymer composites is primarily controlled by the dispersive capacity and interfacial shear strength of CNTs in polymer matrices. CNT functionalizations will improve dispersion and strengthen interfacial bonding of CNTs in matrices. To understand the effects of different functionalization schemes on the interfacial strength of CNT-polymer composites, pullout of the covalent, noncovalent, and mixed functionalized single-walled carbon nanotube(SWCNT) from polyethylene(PE) matrix was simulated by using molecular dynamics, respectively. The results show that the SWCNT-PE interfacial shear strength is significantly improved by SWCNT functionalizations, particularly by mixed functionalization.     

Flow of variable thermal conductivity fluid due to inclined stretching cylinder with viscous dissipation and thermal radiation

The aim of the present study is to investigate the flow of the Casson fluid by an inclined stretching cylinder. A heat transfer analysis is carried out in the presence of thermal radiation and viscous dissipation effects. The temperature dependent thermal conductivity of the Casson fluid is considered. The relevant equations are first simplified under usual boundary layer assumptions, and then transformed into ordinary differential equations by suitable transformations. The transformed ordinary differential equations are computed for the series solutions of velocity and temperature. A convergence analysis is shown explicitly. Velocity and temperature fields are discussed for different physical parameters by graphs and numerical values. It is found that the velocity decreases with the increase in the angle of inclination while increases with the increase in the mixed convection parameter. The enhancement in the thermal conductivity and radiation effects corresponds to a higher fluid temperature. It is also found that heat transfer is more pronounced in a cylinder when it is compared with a flat plate. The thermal boundary layer thickness increases with the increase in the Eckert number. The radiation and variable thermal conductivity decreases the heat transfer rate at the surface.     

Influence of Nonlinear Local Properties on Effective Transport

The assumption of constant local coefficients is one of the first restrictions in most of the smoothing theories for transport in porous media. In this paper we present a formal analysis of the effects produced by nonconstant local transport coefficients on the nonlinear behavior of the effective transport properties. In particular, we use the volume averaging method to study heat transport in a two-component system considering the local thermal conductivities as analytical functions of the temperature. Within this approach we obtain a general expression for the effective nonlinear thermal conductivity dependence on the averaged temperature gradient. The important result is that the effective conductivity is obtained by a linearly bounded problem (the closure problem), just as if the conductivities were constants, by replacing the constant conductivities by the actual temperature dependent ones. As an example, we model the porous medium as cylindrical inclusions in a periodic array and solve the closure problem for the case of the one-equation model. We analyze the values of the second derivative of the thermal conductivity with respect to the temperature to establish the range where the nonlinear corrections must be considered to correctly describe the effective transport.     

碳纳米管/碳纤维增强复合材料层合板低速冲击响应和破坏的数值模拟

碳纳米管/碳纤维增强复合材料（carbon nanotube/carbon fibre reinforced plastic,CNT/CFRP）是一种多尺度复合材料,比传统CFRP有更好的综合性能和更广阔的应用前景。对CNT/CFRP在低速冲击下的响应和破坏进行了数值模拟研究。首先,基于先前的研究通过引入基体增韧因子、残余强度因子并改进损伤耦合方程,建立了新的FRP动态渐进损伤模型;然后,利用新建立的本构模型并结合黏结层损伤模型,对4种碳纳米管含量的增韧碳纤维增强树脂基复合材料层合板在5个能量下的冲击实验进行了数值模拟;最后,将模拟结果与文献中的相关实验结果进行了比较,并讨论了冲击速度的影响。结果表明:新建立的FRP本构模型能够预测CNT/CFRP层合板在低速冲击载荷作用下的响应、破坏过程和分层形貌,模拟得到的载荷-位移曲线和破坏形貌与实验吻合较好;冲击速度会影响CNT/CFRP层合板拉伸和压缩破坏的比例,相同的冲击能量下,更大的冲击速度会造成更多的拉伸破坏。     

Two-fold enhancement in tensile strength of carbon nanotube–carbon fiber hybrid epoxy composites through combination of electrophoretic deposition and alternating electric field

A new carbon nanotube (CNT)–hybridized carbon fiber (CF) was introduced in an attempt to improve interfacial strength between CF and polymeric matrix. Amine-functionalized CNTs was radially deposited on the CF surface through a combination of alternating electric field with electrophoretic deposition process. Radial deposition of CNTs on CF formed a unique porous structure around CF that could significantly increase the interfacial adhesion through interlocking of polymeric matrix. Tensile properties and fatigue life of the reinforced composites were investigated in order to study the effect of interfacial adhesion on mechanical properties of reinforced composites. Results indicate that the radial deposition of CNT on CF can remarkably enhance the compatibility of polymeric matrix with CF. This improvement in compatibility of polymeric matrix with CNT–hybridized CF resulted in considerable enhancement in mechanical properties of composites. The interfacial reinforcing mechanism was explored through fractography of reinforced composites and possible failure modes have been precisely discussed.     

基于非局部效应和表面效应的输流碳纳米管稳定性分析简

应用非局部黏弹性夹层梁模型分析双参数弹性介质中输送脉动流碳纳米管的稳定性. 新模型中同时考虑了由管道内、外壁上的薄表面层引起的表面弹性效应和表面残余应力，经典的欧拉梁模型因此通过引入非局部参数和表面参数得到了改进. 用平均法对其控制方程进行求解，得到了管道稳定性区域. 数值算例揭示了纳米材料的非局部效应、表面效应及两个弹性介质参数对管道固有频率、临界流速和动态稳定性的复杂影响，结论可为纳米流体机械的结构设计和振动分析提供理论基础.