Effects of the carbon nanotube distribution on the macroscopic stiffness of composite materials

Having extremely high stiffness and low specific weight, carbon nanotubes (CNTs) have been known recently as perfect reinforcing fibers in nanotechnology. They can improve the stiffness and strength of nanocomposites by being used as reinforcing elements for example in polymer matrices. The corresponding properties of the fibers and matrix, such as volume fraction and aspect ratio are some of the significant factors in the characterization of mechanical properties of CNT reinforced composites. In recent years, the way in which fibers are distributed inside the matrix, in terms of randomness, has introduced another important factor in characterizing the mechanical properties of such composites. Based on this factor, composites can be classified into two types namely, aligned and randomly distributed. This research has studied the effect of random distribution of fibers in the matrix on the elastic modulus and initial yield stress of the nanocomposite. Therefore, several models of composites, with different distribution of fibers, were considered while holding the volume fractions and aspect ratio constant. As a result, the effect of randomness on the effective modulus of CNT reinforced composites was estimated. The finite element method (FEM), using the MSC.Marc software, was employed to predict the effective modulus of CNT reinforced composites and the results were successfully validated by comparison with the analytical Halpin-Tsai method.     

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.     

A study on the tensile response and fracture in carbon nanotube-based composites using molecular mechanics

A study on the mechanical properties of polyethylene and carbon nanotube (CNT) based composites is presented using molecular mechanics simulations. The systems being investigated consist of amorphous as well as crystalline polyethylene (PE) composites with embedded single-walled CNTs. All the systems are subjected to quasi-static tensile loading, with the assumption that no cross-link chemical bonds exist between the CNT and polyethylene matrix in the case of nanocomposites. Based on the numerical simulations, we report Young’s moduli (C₃₃) of 212–215 GPa for crystalline PE, which closely match the experimental measurement. Furthermore, elastic stiffness of 3.19–3.69 GPa and tensile strength of 0.21–0.25 GPa are obtained for amorphous PE. The tensile responses are found to be highly isotropic. In the case of crystalline PE reinforced by long through CNTs, moderate improvements in the tensile strength and elastic stiffness are observed. However, the results differ from the predictions using the rule of mixtures. On the other hand, although significant increase in the overall tensile properties is observed when amorphous PE is reinforced by long through CNTs, the load transfer at the nanotube/polymer interface has negligible effect. Finally, degradations in both tensile strength and elastic stiffness are reported when amorphous PE is reinforced by embedded CNTs. The study presented indicates the importance of specific CNT and polymer configurations on the overall properties of the nanocomposite.     

Effects of CNT diameter on mechanical properties of aligned CNT sheets and composites

Drawing, winding, and pressing techniques were used to produce horizontally aligned carbon nanotube (CNT) sheets from free-standing vertically aligned CNT arrays. The aligned CNT sheets were used to develop aligned CNT/epoxy composites through hot-melt prepreg processing with a vacuum-assisted system. Effects of CNT diameter change on the mechanical properties of aligned CNT sheets and their composites were examined. The reduction of the CNT diameter considerably increased the mechanical properties of the aligned CNT sheets and their composites. The decrease of the CNT diameter along with pressing CNT sheets drastically enhanced the mechanical properties of the CNT sheets and CNT/epoxy composites. Raman spectra measurements showed improvement of the CNT alignment in the pressed CNT/epoxy composites. Research results suggest that aligned CNT/epoxy composites with high strength and stiffness are producible using aligned CNT sheets with smaller-diameter CNTs.     

Mechanical property enhancement of aligned multi-walled carbon nanotube sheets and composites through press-drawing process

A solid-state drawing and winding process was done to create thin aligned carbon nanotube (CNT) sheets from CNT arrays. However, waviness and poor packing of CNTs in the sheets are two main weaknesses restricting their reinforcing efficiency in composites. This report proposes a simple press-drawing technique to reduce wavy CNTs and to enhance dense packing of CNTs in the sheets. Non-pressed and pressed CNT/epoxy composites were developed using prepreg processing with a vacuum-assisted system. Effects of pressing on the mechanical properties of the aligned CNT sheets and CNT/epoxy composites were examined. Pressing with distributed loads of 147, 221, and 294 N/m showed a substantial increase in the tensile strength and the elastic modulus of the aligned CNT sheets and their composites. The CNT sheets under a press load of 221 N/m exhibited the best mechanical properties found in this study. With a press load of 221 N/m, the pressed CNT sheet and its composite, respectively, enhanced the tensile strength by 139.1 and 141.9%, and the elastic modulus by 489 and 77.6% when compared with non-pressed ones. The pressed CNT/epoxy composites achieved high tensile strength (526.2 MPa) and elastic modulus (100.2 GPa). Results show that press-drawing is an important step to produce superior CNT sheets for development of high-performance CNT composites.     

The effects of carbon nanotube orientation and aggregation on vibrational behavior of functionally graded nanocomposite cylinders by a mesh-free method

In this paper, axisymmetric natural frequencies of nanocomposite cylinders reinforced by straight single-walled carbon nanotubes are presented based on a mesh-free method. The straight carbon nanotubes (CNTs) are oriented, aligned or randomly or locally aggregated into some clusters. Volume fractions of the CNTs and clusters are assumed to be functionally graded along the thickness, so material properties of the carbon nanotube reinforced composite cylinders are variable and are estimated based on the Eshelby–Mori–Tanaka approach. In the mesh-free analysis, moving least squares shape functions are used for an approximation of the displacement field in the weak form of motion equation, and the transformation method is used for the imposition of essential boundary conditions. The effects of orientation and aggregation of the functionally graded CNT are studied. It is observed that kind of distributions, aggregation or even randomly orientations of CNTs has significant effect on the effective stiffness and frequency parameter.     

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

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

Mechanical and electrical property improvement in CNT/Nylon composites through drawing and stretching

The excellent mechanical properties of carbon nanotubes (CNTs) make them the ideal reinforcements for high performance composites. The misalignment and waviness of CNTs within composites are two major issues that limit the reinforcing efficiency. We report an effective method to increase the strength and stiffness of high volume fraction, aligned CNT composites by reducing CNT waviness using a drawing and stretching approach. Stretching the composites after fabrication improved the ultimate strength by 50%, 150%, and 190% corresponding to stretch ratios of 2%, 4% and 7%, respectively. Improvement of the electrical conductivities exhibited a similar trend. These results demonstrate the importance of straightening and aligning CNTs in improving the composite strength and electrical conductivity.     

Two analytical models for the study of periodic fibrous elastic composite with different unit cells

In this work, the effective elastic moduli of two-phase fibrous periodic composites are obtained by means of the Asymptotic Homogenization Method (AHM) and eigenfunction expansion-variational method (EEVM), for different types of parallelogram cells. The constituents exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The behavior of the shear elastic coefficient for different geometry arrays of the cell related to the angle of the fibers is studied. Some numerical examples and comparisons with other theoretical results demonstrate that both methods (AHM and EEVM) are efficients for the analysis of composites with presence of rhombic cell. The effect of the configuration of the cells on the shear effective property is observed.     

Modulus–density negative correlation for CNT-reinforced polymer nanocomposites: Modeling and experiments

Mechanical and weight properties of polymer nanocomposites (PNCs) are measured and modeled at the interlaminar region, predicting the density and elastic modulus of individual carbon nanotubes (CNTs). A simple model of the CNTs density and elastic modulus within the PNC, accounting for fundamental material properties, geometry, and interactions, is developed, capable of predicting CNT contributions in the PNCs. Furthermore, the model is validated with experimental results that demonstrate enhancement of the elastic modulus, while reducing density in the presence of aligned CNTs. By establishing an inverse relation of density and elastic modulus (negative correlation), it is demonstrated the potential of increasing mechanical properties while reducing weight. Therefore, by introducing controlled nanoporosity through suitable CNT distributions within the interlayer of multi-lamina structures, it is possible to simultaneously control effective weight reduction and enhanced modulus, toward bio-inspired carbon fiber reinforced polymer composites.     

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.     

Modeling carbon nanotube reinforced composite materials with the cylindrical method of cells

Micromechanics modeling, utilizing a cylindrical method of cells (CMOC) model, is employed to obtain the effective mechanical properties of an elastic transversely isotropic, isothermal material system consisting of a hollow carbon nanotube (CNT) embedded in an isotropic polymeric material matrix. It is shown that weak interfacial bonding between the CNT and polymeric matrix, which is characteristic of this type of material system, can be modeled with the CMOC. Numerical solutions of the effective independent material constants are obtained, based upon appropriate values of the properties of the carbon nanotube and epoxy matrix. The numerical results are presented graphically and compared with corresponding classical closed‐form solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Effects of nanotube helical angle 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. The CNTs, however, form complicated shapes and do not usually appear as straight reinforcements when introduced in polymer matrices. This results in a decrease in nanotube effectiveness in enhancing the matrix mechanical properties. In this paper, theory of elasticity of anisotropic materials and finite element method (FEM) are used to investigate the effects of CNT helical angle on effective mechanical properties of nanocomposites. Helical nanotubes with different helical angles are modeled to investigate the effects of nanotube helical angle on nanocomposite effective mechanical properties. In addition, the results of models consisting of helical nanotubes are compared with the effective mechanical properties of nanocomposites reinforced with straight nanotubes. Ultimately, the effects of helical CNT volume fraction on nanocomposite longitudinal modulus are investigated.     

复合材料的等效弹性性能

用细观力学的分析方法研究了复合材料的宏观等效弹性性能。在严格满足组分相间界面的连续性条件下,正确反映了组分相间的相互作用, 考虑了弹性张量各分量之间的相互关系, 分析了层合介质的宏观等效弹性性能。进一步用统计平均的思想, 得到了总体横观各向同性及总体各向同性复合材料的等效弹性性能的解析表达式。与有关的理论及实验结果比较, 得到了非常满意的结果。      

The effects of surface elasticity and surface tension on the transverse overall elastic behavior of unidirectional nano-composites

The effects of surface elasticity and surface tension on the transverse overall behavior of unidirectional nano-scale fiber-reinforced composites are studied. The interfaces between the nano-fibers and the matrix are regarded as material surfaces described by the Gurtin and Murdoch model. The analysis is based on the equivalent inhomogeneity technique. In this technique, the effective elastic properties of the material are deduced from the analysis of a small cluster of fibers embedded into an infinite plane. All interactions between the inhomogeneities in the cluster are precisely accounted for. The results related to the effects of surface elasticity are compared with those provided by the modified generalized self-consistent method, which only indirectly accounts for the interactions between the inhomogeneities. New results related to the effects of surface tension are presented. Although the approach employed is applicable to all transversely isotropic composites, in this paper we consider only a hexagonal arrangement of circular cylindrical fibers.     

Cylindrical Bending and Vibration of Polar Material Laminates

This article considers a plane strain problem, which is known in conventional linear elasticity as cylindrical bending of simply supported plates and cross-ply laminates. By considering fibrous composites containing fibers resistant to bending, it formulates and solves corresponding polar elasticity equations governing the static and dynamic behavior of beam-like components made of a homogeneous or layered transversely isotropic material; each layer has embedded a single family of fibers. Fiber bending stiffness is accounted for through involvement of an extra elastic modulus, which, unlike its conventional elasticity counterparts that have dimensions of stress, has dimensions of force. Its involvement in the analysis implies existence of some intrinsic material area or length parameter, which may be associated, for instance, with fiber thickness of fiber spacing. A considerable amount of relevant numerical results are presented for thick beam components made of either homogeneous or two-layered transversely isotropic material. For the static bending problem, these include a detailed presentation of through-thickness distributions of displacements, stresses, as well as couple-stress. For the dynamic problem, attention is focused on the influence that fiber bending stiffness exerts on fundamental frequency parameters.     

Toughening by partial or full bridging of cracks in ceramics and fiber reinforced composites

A complete solution is given for a fully or partially bridged straight crack in transversely isotropic elastic materials which may correspond to unidirectionally fiber-reinforced ceramics or other brittle composites. The stiffness of the bridging materials may have an arbitrary variation along the crack, representing partially failed fibers or ligaments. The crack may have any orientation with respect to the axis of the material symmetry. The solution is explicit in terms of the Chebychev polynomials when the bridging-forces are linearly dependent on the crack-opening-displacement. In addition, uniformly valid asymptotic solutions are developed for fully or partially bridging cracks. For the case when the crack is short relative to a length scale which depends on the material properties, the method yields a complete asymptotic solution when the bridging forces are linearly or non-linearly dependent on the crack-opening-displacement (a square-root dependence, corresponding to continuous fibers, is used for illustration). For the case of long cracks, the proposed asymptotic is effective, but the results are not presented in this work.The mechanism of crack kinking is studied for an oblique partially or fully bridged, or unbridged crack in a macroscopically transversely isotropic elastic solid. The crack is assumed to grow in the matrix material (containing unbroken strong fibers) under local driving forces which are calculated on the basis of the overall anisotropic material response. The results of various fracture criteria are studied. It is illustrated that, under far-field tensile forces normal to the crack, the criterion of the maximum opening mode stress intensity factor in the homogenized anisotropic solid (i.e., the orientation for which the strength of the singularity associated with the tensile hoop stress is maximum) produces results which suggest crack growth more or less parallel to the fibers, whereas the results based on the maximum Mode I stress intensity factor in the isotropic matrix material and/or on the local symmetry criterion (again, for the isotropic matrix) predict crack extension more or less normal to the reinforcing fibers.     

任意荷载作用下层状横观各向同性弹性地基的直角坐标解

首次建立了在直角坐标系下层状地基力学问题的通用解法,改变了过去仅能在柱坐标系下进行求解此类的状况。首先将坐标系的原点选在荷载影响范围以外足够远处,从直角坐标系下的横观各向同性弹性问题的基本方程出发,利用Laplace变换及其微分性质,建立了单层横观各向同性弹性地基的状态控制方程,并利用状态空间理论给出了单层地基的解答。然后再利用传递矩阵技术,给出了任意荷载作用下的层状横观各向同性弹性地基的解析解。用提供的方法求解层状横观各向同性地基的非轴对称问题比在极坐标下求解简单、快捷。     

Maximum nanotube volume fraction and its effect on overall elastic properties of nanotube-reinforced composites

The potential capability of improving overall elastic modulus of nanotube-reinforced composites is a fundamental concern in nanotechnology applications. Based on geometric analysis and micromechanics estimation, this study reports that the ratio of surface-to-surface distance of adjacent carbon nanotubes (CNTs) to the CNT diameter plays a key role in improving the overall elastic modulus of the CNT-reinforced composites when the tubes are perfectly aligned, completely separated from other tubes, and ideally bonded with the composite matrix. With the decrease of this ratio, that is, decrease of the surface-to-surface distance of adjacent CNTs and/or increase CNT diameter, the improvement capability increases. However, theoretical and experimental results show that an increase of the CNT diameters degrades the elastic moduli of CNTs. This paper discusses the criterion of choosing CNTs with larger diameter and addresses the factors influencing the surface-to-surface distance of adjacent CNTs.