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The Effect of Nanotube Waviness and Agglomeration on the Elastic Property of Carbon Nanotube-Reinforced Composites
Abstract
Owing to their superior mechanical and physical properties, carbon nanotubes seem to hold a great promise as an ideal reinforcing material for composites of high-strength and low-density. In most of the experimental results up to date, however, only modest improvements in the strength and stiffness have been achieved by incorporating carbon nanotubes in polymers. In the present paper, the stiffening effect of carbon nanotubes is quantitatively investigated by micromechanics methods. Especially, the effects of the extensively observed waviness and agglomeration of carbon nanotubes are examined theoretically. The Mori-Tanaka effective-field method is first employed to calculate the effective elastic moduli of composites with aligned or randomly oriented straight nanotubes. Then, a novel micromechanics model is developed to consider the waviness or curviness effect of nanotubes, which are assumed to have a helical shape. Finally, the influence of nanotube agglomeration on the effective stiffness is analyzed. Analytical expressions are derived for the effective elastic stiffness of carbon nanotube-reinforced composites with the effects of waviness and agglomeration. It is found that these two mechanisms may reduce the stiffening effect of nanotubes significantly. The present study not only provides the relationship between the effective properties and the morphology of carbon nanotube-reinforced composites, but also may be useful for improving and tailoring the mechanical properties of nanotube composites.
... When these randomly oriented CNTs agglomerate, they tend to form clusters in finite areas, leading to notable variations in the material properties of CNTRCs compared to other regions. Thus, researchers have suggested diverse approaches to evaluate the mechanical characteristics of clustered CNTs, employing both experimental (Kuzumaki et al. 2000) and numerical methods (Shi et al. 2004). ...
... While the Mori-Tanaka technique (Mori and Tanaka 1973) offers comprehensive modeling, it may not account for nanotubes aggregation. To address this limitation, an equivalent micromechanics approach, based on Mori-Tanaka homogenization and the use of CNT Hill's elastic moduli, was first proposed by Shi et al. 2004. This micromechanics model, proposed as the foundation, has become the focus of certain studies aiming to predict the mechanical response of composite structures reinforced by agglomerated CNT particles (Yas and Heshmati 2012;Kamarian et al. 2016;Tornabene et al. 2017;Maurya et al. 2023;Mallek et al. 2023). ...
... Initially, the developed modeling approach allows us to simulate realistic representative volume elements (RVE) of a polymeric matrix reinforced with straight CNTs that are distributed with random orientation, different aspect ratios and volume fractions, as presented in Fig. 1. According to the literature, the Mori-Tanaka micromechanical technique (Shi et al. 2004) has been extensively adopted in studies to scale up the nanoscale properties of nanocomposites with high performance. Thus, it is used, in this work, the Mori-Tanaka homogenization scheme is used here in order to evaluate the effective bulk modulus K and shear modulus G of the reinforced composite as mentioned in Fig. 2. It should be noted that quantities of the matrix and the carbon fibers are symbolized, respectively, by the subscripts m and r. ...
The application of piezomagnetic layers on the external surfaces of passive sandwich shells has the potential to create multifunctional smart sandwich structures. This work introduces new, smart magnetoelectroelastic (MEE) shells and studies their geometrically nonlinear bending and transient behavior as a first endeavor. A High-order Shear Deformation Theory (HSDT) is adopted to develop the Finite-Element model of the smart MEE shells considering the multiphysics couplings, meanwhile the Lagrangian nonlinear strain–displacement relations are employed to account for the geometric nonlinearity. The developed FE is modeled with nodal degrees of freedom that include displacements, rotations, and electric and magnetic potentials. Moreover, the physical characteristics of aggregated CNTRC are evaluated based on a micromechanics model incorporating the two agglomeration parameters. Different agglomeration schemas are considered for CNTs in the nanocomposite core layer. The precision and reliability of the current FE model are confirmed through a comparison of the existing results in the open literature. The study explores the influence of parameters such as CNT volume fraction and their agglomeration phenomena and various geometrical parameters of the shell on the nonlinear bending and dynamic behavior of smart MEE sandwich structures. The findings provide valuable insights into the subject.
... When these randomly oriented CNTs agglomerate, they tend to form clusters in finite areas, leading to notable variations in the material properties of CNTRCs compared to other regions. Thus, researchers have suggested diverse approaches to evaluate the mechanical characteristics of clustered CNTs, employing both experimental (Kuzumaki et al., 2000) and numerical methods (Shi et al., 2004). ...
... While the Mori-Tanaka technique (Mori and Tanaka, 1973) offers comprehensive modeling, it may not account for nanotubes aggregation. To address this limitation, an equivalent micromechanics approach, based on Mori-Tanaka homogenization and the use of CNT Hill's elastic moduli, has been firstly proposed by Shi et al. 2004. This micromechanics model, proposed as the foundation, has been the focus of certain studies aiming to predict the mechanical response of composite structures reinforced by agglomerated CNT particles (Yas and Heshmati., 2012 ;Kamarian et al., 2016 ;Tornabene et al., 2017 ;Maurya et al., 2023 ;Mallek et al., 2023). ...
... Initially, the developed modeling approach allows us to simulate realistic representative volume elements (RVE) of polymeric matrix reinforced with straight CNTs which are distributed with random orientation, different aspect ratios and volume fractions, as presented in Fig. 1. According to the literature, the Mori-Tanka micromechanical technique (Shi et al., 2004) has been extensively adopted in researches to scale up the nanoscale properties of nanocomposites with high performance. Thus, it is used, in this work, the Mori-Tanka homogenization scheme in order to evaluate the effective bulk modulus K and shear modulus G of the reinforced composite as mentioned in Fig. 2. It should be mentioned that quantities of the matrix and the Carbon fibers are symbolized respectively by the subscripts m and r. ...
The application of piezomagnetic layers on the external surfaces of passive sandwich shells has the potential to create multifunctional smart sandwich structures. This work introduces new smart magneto–electro–elastic (MEE) shells and studies its geometrically nonlinear bending and transient behavior as a first endeavor. A High-order Shear Deformation Theory (HSDT) is adopted to develop the Finite Element model of the smart MEE shells considering the multiphysics couplings, meanwhile the Lagrangian nonlinear strain-displacement relations are employed to account the geometric nonlinearity. The developed FE is modeled with nodal degrees of freedom that include displacements, rotations, electric and magnetic potentials. Moreover, the physical characteristics of aggregated CNTRC are evaluated based on micromechanics model incorporating the two agglomeration parameters. Different agglomeration schemas are considered for CNTs in nanocomposite core layer. The precision and reliability of the current FE model are confirmed through a comparison of the existing results in the open literature. The study explores the influence of parameters such CNT volume fraction and their agglomeration phenomena and various geometrical parameters of the shell on the nonlinear bending and dynamic behavior of smart MEE sandwich structures. The findings provide valuable insights into the subject.
... High slenderness ratio, and low elastic stiffness normal to the CNT axis are also two key factors that result in a low bending stiffness (Ref. [26]). Accordingly, the aggregation of CNTs is approximately inevitable (Ref. ...
... Accordingly, the aggregation of CNTs is approximately inevitable (Ref. [26]). A micromechanical model was developed by Shi et al. [26] in order to specify the efficient elastic stiffness of an aggregated CNT nanocomposite, where the CNTs were distributed randomly or uniformly in the nanocomposite. ...
... [26]). A micromechanical model was developed by Shi et al. [26] in order to specify the efficient elastic stiffness of an aggregated CNT nanocomposite, where the CNTs were distributed randomly or uniformly in the nanocomposite. The procedure was on the basis of EMT method, while the waviness and straightness of CNTs were incorporated. ...
Large amplitude vibrations are inevitable in the life cycle of a composite structure. On the other hand, the large amplitude deflections may give rise to cracks and fractures in the composite structure. Consequently, in order to avoid such issues, in this study, the examination of nonlinear events including bifurcation analysis of a beam structure made of advanced materials exposed to superharmonic excitation is presented, for the first time. In this regard, an unshearable model is developed for an aggregated carbon nanotube-strengthened beam in line with the Eshelby–Mori–Tanaka hypothesis. Making use of the advantage of the direct method of multiple scales, the reduced order equations for the aggregated nanocomposite beam subjected to primary, and superharmonic excitations are disclosed. Some fascinating numerical simulations clarify nonlinear aspects of the aggregated beam under the alterations of agglomeration parameters as well as temperature. It is deduced that the increment of heterogeneity enlarges the maximum quantity of the steady-state response until, two more steady-state responses are generated. Thereafter, the heterogeneity increment reduces the gap between the two stable steady-state responses. After a catastrophic bifurcation, one stable steady-state response remains. The amplitude of the remained steady state response decreases as a consequence of the heterogeneity increment. The aggregation decreases the temperature at which the multi-valued steady-state response zone starts, when the nanocomposite beam is superharmonically excited. Moreover, the heterogeneity doesn’t change the maximum steady-state amplitude of the nanocomposite beam undergone superharmonic excitation at a given force frequency. On the other hand, the gap between the two steady state amplitudes of the nanocomposite beam subjected to primary resonance excitation extends as a consequence of the heterogeneity increment.
... Modified form of the Mori-Tanaka micromechanical model accounting for non-uniform dispersion of spherical inclusion is utilized [55]. The modified Mori-Tanaka model also takes into account random orientations of reinforcing agent. ...
... The improved Mori-Tanaka model developed by Shi et al. [55] evaluates the bulk modulus (K) and shear modulus (G) of meso-scale RVE depicted in Fig. 3 using reflected formulations in Appendix A. The procedure is briefly outlined here. First of all, based on the random selection of equivalent fiber length, stiffness matrix of the equivalent fiber is formed according to Eq. A15 in Appendix A. After that, the Hill constants of the equivalent fiber are obtained through Eqs. ...
... The improved Mori-Tanaka model [55] evaluates the bulk modulus (K) and shear modulus (G) of meso-scale RVE (Fig. 3) using below equations: ...
... The rule of mixture has a low accuracy in estimating the elastic constants of a CNT-reinforced polymer and cannot incorporate the CNTs agglomeration. Thus, in what follows the elastic constants are calculated utilizing the Eshelby-Mori-Tanaka approach, 31 and CNTs agglomeration is modeled via a two-parameter model proposed by Shi et al. 32 Because of the high values of the length-to-diameter of the CNTs, they suffer from a low bending stiffness. Due to this weakness and the interfacial bonding between the polymeric matrix and the CNTs, the CNTs have a propensity to aggregate as illustrated in Figure 4. ...
... This inevitable phenomenon is called CNTs agglomeration. 33 To consider the CNTs agglomeration, Shi et al. 32 proposed a two-parameter model. In this model, the intensity of the CNTs agglomeration is described via two parameters as ...
... Utilizing equations (1), (18), (24), (25), (32), and (33), the relation below can be achieved: ...
In the presented work, the free vibration analysis of a rotating truncated conical shell whose thickness varies in the meridional direction is examined. The material that the shell is made of is a polymeric matrix (epoxy) enriched with carbon nanotubes (CNTs) whose volume fraction varies in the meridional direction. CNTs agglomeration is considered and the density and elastic constants of such a two-phase nanocomposite are calculated sequentially based on the Eshelby-Mori-Tanaka approach alongside the rule of mixture. The conical shell is modeled using the first-order shear deformation theory (FSDT) including the relative acceleration, Coriolis acceleration, and centrifugal acceleration along with the initial hoop tension, and the governing equations are obtained utilizing Hamilton's principle. The solution of governing equations is performed via the combination of an analytical solution in the circumferential direction and a numerical one in the meridional direction via the differential quadrature method (DQM). The impacts of several parameters on the forward and backward natural frequencies of such a rotating shell are studied such as chirality, mass fraction and dispersion pattern of the CNTs, thickness variation parameters, and boundary conditions. It is observed that higher natural frequencies and critical rotational speeds can be achieved for CNT-reinforced conical shells when the volume fraction of the CNTs and the thickness of the shell increase from its small radius to the large one.
... The reinforcement of CNTs can significantly improve the strength (Qian et al. 2000;Ganguli, Aglan, and Dean 2005;Ciecierska et al. 2013;Korayem et al. 2015;Lin et al. 2022) agglomerations that significantly influence the effective material properties. The influences of CNT agglomeration in polymer composites were discussed by Shi et al. (2004). It is observed that CNTs agglomeration in polymer degrades the effective properties of polymer matrix and viceversa with an increment of mass fraction of CNTs. ...
... In both cases, the elastic properties decrease with an increase in agglomeration. The obtained elastic modulus is compared with the results of Shi et al. (2004). The results show a good agreement with the published results. ...
... However, the potential of other types of nanoparticles can also be studied in future. Moreover, CNTs are approximated as short straight fibers and neglected the waviness effect as discussed by Shi et al. (2004). For accurate prediction of stability of CNT-reinforced slender structures such waviness effect can be a significant parameter, which may be considered in future studies. ...
... To understand the agglomeration and orientation of CNT behavior, an equivalent continuum micromechanics model is developed by Shi et al. [26] based on MT scheme using the constitutive relations of the nanoparticles according to Hill's elastic moduli. It is proven that their predictions are in well concordance with the experimental observations. ...
... The effective bulk modulus K and shear modulus G of the composite can be evaluated via the Mori-Tanaka method [26] as ...
... Figure 2 shows three agglomeration states of CNT dispersed in the matrix. As mentioned by Shi et al. [26], the above-mentioned regions can be approximately defined as spherical and regarded as ''inclusions'' with distinct elastic properties from the surrounding material. Hence, a two-parameter agglomeration model is adopted in this research to model the mechanical behavior of clustered CNT-reinforced composites. ...
This work introduces a linear dynamic analysis of composite smart solid-shell structures reinforced with agglomerated Carbone Nanotubes and embedded at external faces with piezolayers. The coupled electro-mechanical governing equation of solid-shell structures under dynamic loads is obtained by the estimation of the displacement field with the First-Order Shear Deformation Theory (FSDT). In this proposed model, the shear and thickness locking were solved by the use of the Assumed Natural Strain (ANS) method as well as the Enhanced Assumed Strain (EAS) method is adopted for enhancing of the membrane and transversal strains. Each element of the structure is modeled by an eight-node hexahedron with four degrees of freedom: three displacements and an electrical potential. The middle part of the structure is made of a composite reinforced with agglomerated Carbone Nanotubes (CNTs) along the thickness. Different agglomeration schemes are investigated by means of a two-parameter agglomeration model. The external faces of the shell structure are made with piezoelectric material which accentuates the smart aspect of such structures. The mechanical properties of such a reinforced composite are evaluated using Mori–Tanaka (EMT)’s technique. An enhanced finite-element solid-shell model is implemented to investigate the effects of nanotubes agglomeration on the transient response of solid shells, such as the impact of various configurations of agglomerations, the volume fraction of CNTs, and some geometrical parameters of solid-shell structures. From deduced numerical results, it is exposed that the reinforcing fibers with different agglomeration schemes retain a significant impact on the dynamic performances of the solid-shell structure.
... The effects of the CNTs agglomeration on the elastic constants of the two-phase CNT-reinforced polymer can be incorporated through the following two-parameter micromechanics model [38]: ...
... in which G mr and K mr sequentially represent the shear and bulk moduli of the two-phase CNT-reinforced polymer. In accordance with the Eshelby-Mori-Tanaka approach, these elastic constants are presented in relations as follows [38]: in which the superscripts "in" and "out," respectively, imply the inside and outside of the clusters (agglomerated regions), and corresponding shear and bulk moduli are presented as follows [38]: ...
... in which G mr and K mr sequentially represent the shear and bulk moduli of the two-phase CNT-reinforced polymer. In accordance with the Eshelby-Mori-Tanaka approach, these elastic constants are presented in relations as follows [38]: in which the superscripts "in" and "out," respectively, imply the inside and outside of the clusters (agglomerated regions), and corresponding shear and bulk moduli are presented as follows [38]: ...
In the presented paper, the free vibration of a polymer/fiber/CNT laminated nanocomposite conical shell with nonuniform thickness and surrounded by an elastic two-parameter foundation is analyzed. The shell is made of a polymeric matrix enriched simultaneously with randomly oriented carbon nanotubes (CNTs) and aligned glass fibers. CNTs agglomeration is included and the density and elastic constants of such a three-phase nanocomposite are calculated using the rule of mixture and the Eshelby–Mori–Tanaka approach alongside Hanh’s homogenization method. The conical shell and the elastic foundation are modeled using the first-order shear deformation theory and the Pasternak foundation model, consecutively. The governing equations are derived using Hamilton’s principle and are solved numerically via the differential quadrature method. The impacts of several parameters on the natural frequencies of such a structure are discussed such as thickness variation parameters, mass fraction and chirality of the CNTs, mass fraction of the fibers, and boundary conditions. It is observed that by considering the specific value for the average thickness of the shell, the thickness variation parameters associated with the highest natural frequency are different in various vibrational modes. It is discovered that the natural frequencies grow by increasing the mass fraction of the CNTs, but the influences of the mass fraction of the fibers on the natural frequencies are strongly dependent on the vibration mode.
... The given equations enable the calculation of the effective bulk modulus "K" and shear modulus "G" for the CNTs/polymer composite. These moduli are essential in characterizing the mechanical properties of the composite material and understanding its overall behavior under stress and deformation (Shi et al. 2004): ...
... The remaining variables in the previously mentioned equations can be explained as follows (Shi et al. 2004): ...
... In the domain of nanocomposite structures, the aggregation and bundling of carbon nanotubes (CNTs) can lead to a substantial agglomeration effect, and as illustrated in Fig. 3, evaluating the effective material properties of a nanocomposite material reinforced with randomly oriented CNTs while accounting for the influence of agglomeration can be achieved using a two-parameter homogenization method introduced by Shi et al. (2004). In this micromechanical model, the total volume fraction of CNTs within the chosen representative volume element (RVE) is divided into two distinct parts, as illustrated below (Tornabene et al. 2016). ...
... The authors pointed out that the agglomeration/clustering of CNTs has a direct effect on the thermal, electrical, and mechanical properties of composites and reduces the physical properties. To predict the effective properties such as Young's modulus and Poisson's ratio of composites reinforced by agglomerated CNTs, Shi et al. [14] proposed a two-parameter micromechanical model that accounts for the influence of CNT agglomeration. The model in Ref. [14] was used in conjunction with Mori-Tanaka scheme by Heshmati and Yas [15] to derive elastic moduli of randomly oriented CNTRC in a free vibration analysis of functionally graded (FG)-CNTRC beams. ...
... To predict the effective properties such as Young's modulus and Poisson's ratio of composites reinforced by agglomerated CNTs, Shi et al. [14] proposed a two-parameter micromechanical model that accounts for the influence of CNT agglomeration. The model in Ref. [14] was used in conjunction with Mori-Tanaka scheme by Heshmati and Yas [15] to derive elastic moduli of randomly oriented CNTRC in a free vibration analysis of functionally graded (FG)-CNTRC beams. Finite element method was adopted in [15] to obtained the beam frequencies. ...
... The two-parameter micromechanical model of Shi et al. [14] is adopted herein to account for the CNT agglomeration. The model is developed by considering a representative volume element (RVE) with Eshelby cluster model of CNT agglomeration, as depicted in Figure 2. The total volume V r of CNTs in the RVE is divided into two parts as: ...
... Carbon nanotubes with outstanding mechanical, [1][2][3][4][5][6][7][8][9][10] . 10 CNTs tend to agglomerate due to their high aspect ra- 11 tio, low bending rigidity, and this causes the fabrica- the two parameters micromechanics model 11 was 20 adopted to account for the influence of CNT agglom-21 eration on elastic properties of randomly oriented 22 CNTRC, and the Mori-Tanaka (M-T) scheme was 23 adopted to estimate effective moduli of the composite. 24 Different CNT distributions in the beam thickness 25 have been considered in evaluating the frequencies of 26 the beam in reference 12 . ...
... Carbon nanotubes with outstanding mechanical, [1][2][3][4][5][6][7][8][9][10] . 10 CNTs tend to agglomerate due to their high aspect ra- 11 tio, low bending rigidity, and this causes the fabrica- the two parameters micromechanics model 11 was 20 adopted to account for the influence of CNT agglom-21 eration on elastic properties of randomly oriented 22 CNTRC, and the Mori-Tanaka (M-T) scheme was 23 adopted to estimate effective moduli of the composite. 24 Different CNT distributions in the beam thickness 25 have been considered in evaluating the frequencies of 26 the beam in reference 12 . ...
... Dev. J. -Engineering and Technology; 6(1): [1][2][3][4][5][6][7][8][9][10][11]. (1) in which V cluster r and V m r represent the CNT volumes 84 inside and outside the cluster, respectively. ...
In this paper, the dynamic behavior of carbon nanotube (CNT) reinforced composite sandwich beams under a moving mass taking into account the influence of the CNT agglomeration is investigated by the finite element method. The sandwich beams composed of a homogeneous core and two face layers made from carbon nanotube–reinforced composite (CNTRC) material. The two-parameter micromechanical model is adopted to describe the agglomeration of the CNTs, and the Eshelby–Mori–Tanaka approach is used to estimate the effective material properties of the composite face layers. Based on a third-order shear deformation beam theory, a beam element in which the transverse shear rotation, not the conventional section rotation, is employed as an independent variable is formulated and used to establish the discretized equation of motion for the beams. Using an implicit Newmark method, dynamic characteristics such as the time histories for mid-span deflections and the dynamic magnification factors are obtained for a sandwich beam with simply supported ends. The accuracy of the derived beam element is confirmed by comparing the results obtained in the present work with the published data. The numerical result reveals that the CNT volume fraction and the CNT agglomeration have a significant influence on the dynamic response of the sandwich beams. The dynamic magnification factor is found to be decreased with an increase of the CNT volume fraction, but it is higher for the case of the severse CNT agglomeration. A parametric study carried out to highlight the effects of the CNT reinforcement and the mass velocity on the dynamic behavior of the sandwich beams. The influence of the layer thickness ratio on the dynamic response of the composite sandwich beams is also studied and discussed.
... It was found that the formation of graphene agglomeration inside the polymer matrix is a serious undesirable phenomenon hindering the enhancement of nanocomposite effective properties. Similar to previous studies [44][45][46], a two-step micromechanical method can be employed to simulate the GNS agglomeration inside the polymer matrix. In this approach [44][45][46], a number of GNSs are homogeneously dispersed inside the polymer matrix forming a new matrix phase (NMP) and that other GNSs exist in a concentrated state forming the agglomeration phase (AP). ...
... Similar to previous studies [44][45][46], a two-step micromechanical method can be employed to simulate the GNS agglomeration inside the polymer matrix. In this approach [44][45][46], a number of GNSs are homogeneously dispersed inside the polymer matrix forming a new matrix phase (NMP) and that other GNSs exist in a concentrated state forming the agglomeration phase (AP). So, the entire volume of graphene in the composite system is divided into two portions, including the GNS volume within the AP (∀ g, AP ) and GNS volume in the NMP (∀ g, NMP ). ...
... in which ∀ signifies the composite volume and ∀ AP is the agglomeration phase volume. Following relations can be obtained in terms of ξ , ζ and V g to calculate the GNS volume fraction inside the AP and inside the NMP [44][45][46], respectively, ...
One mechanism that is expected to play a key role in the enhanced properties of fiber-reinforced composites is adding nano-scale fillers as the second reinforcing agents in the polymer matrix. In this paper, micromechanical analysis of a hybrid smart nanocomposite in which continuous BaTiO3 fibers are embedded into the graphene nanosheet (GNS)-contained epoxy matrix is performed. The Mori–Tanaka model is used at a multi-step procedure to predict the thermal expansion (TE), elastic stiffness and piezoelectric constants of BaTiO3 fiber/graphene hybrid nanocomposites. The micromechanical model has the ability to describe the non-uniform dispersion of GNSs into the epoxy matrix. Further, the effect of the interfacial interaction between the graphene nanoparticles and polymer is captured in the smart nanocomposite modeling through the inclusion of an equivalent solid interphase. Our results indicate that by adding GNSs into the epoxy resin, all stiffness constants, transverse coefficient of TE and piezoelectric constants \({e}_{31}\) and \({e}_{15}\) of the hybrid nanocomposite are significantly improved. However, non-uniform dispersion and agglomeration of GNSs can decrease the thermo-mechanical and piezoelectric performances of the BaTiO3 fiber/graphene hybrid nanocomposite. In addition, the dependence of effective properties on the interphase characteristics and alignment of GNSs is tested and discussed in details. Comparison studies are carried out in order to show the validity of the present model.
... in which Gmr and Kmr sequentially represent the shear and bulk moduli of the two-phase CNTreinforced polymer. In accordance with the Eshelby-Mori-Tanaka approach, these elastic constants are presented in relations below [26]: ...
... in which the superscripts "in" and "out" respectively imply the inside and outside of the clusters (agglomerated regions), and corresponding shear and bulk moduli are presented as follows [26]: In Eq. (14), αr, βr, δr, and ηr are presented in relations below [26]: ...
... in which the superscripts "in" and "out" respectively imply the inside and outside of the clusters (agglomerated regions), and corresponding shear and bulk moduli are presented as follows [26]: In Eq. (14), αr, βr, δr, and ηr are presented in relations below [26]: ...
In the presented paper, the free vibration of a polymer/fiber/CNT laminated nanocomposite conical shell with nonuniform thickness and surrounded by an elastic two-parameter foundation are analyzed. The shell is made of a polymeric matrix enriched simultaneously with randomly oriented carbon nanotubes (CNTs) and aligned glass fibers. CNTs agglomeration is included and the density and elastic constants of such a three-phase nanocomposite are calculated using the rule of mixture and the Eshelby–Mori–Tanaka approach alongside Hanh’s homogenization method. The conical shell and the elastic foundation are modeled using the first-order shear deformation theory (FSDT) and the Pasternak foundation model, consecutively. The governing equations are derived using Hamilton’s principle and are solved numerically via the differential quadrature method (DQM). The impacts of several parameters on the natural frequencies of such a structure are discussed such as thickness variation parameters, mass fraction and chirality of the CNTs, mass fraction of the fibers, and boundary conditions. It is observed that by considering the specific value for the average thickness of the shell, the thickness variation parameters associated with the highest natural frequency are different in various vibrational modes. It is discovered that, the natural frequencies grow by increasing mass fraction of the CNTs, but the influences of mass fraction of the fibers on the natural frequencies are strongly dependent on the vibration mode.
... When the non-uniformity exists in the nanofiller dispersion, some local domains take a higher nanofiller percentage as compared to the average percentage inside the polymer nanocomposite. Domains with concentrated nanofillers have a spherical configuration, and are defined as agglomeration part (Ji et al., 2010;Nafar Dastgerdi et al., 2013;Shi et al., 2004). Remaining domain in which hybrid nanofillers are uniformly dispersed, is defined as the enriched matrix. ...
... To begin with, the elastic properties of the agglomeration and the enriched matrix parts are determined using the H-T and ROM. Next, considering the agglomeration part as spherical inclusions embedded inside the enriched matrix, the M-T model is employed to predict the bulk modulus and shear modulus of the nanocomposites (Ji et al., 2010;Nafar Dastgerdi et al., 2013;Shi et al., 2004) as follows ...
This paper focuses on the prediction of piezoelectric coefficients, Young’s moduli and shear moduli of unidirectional piezoelectric fiber/carbon nanotube (CNT)/graphene nanoplatelet (GNP)-reinforced polymer composites using a novel micromechanics modeling technique. The multiphase composite configuration is that piezoelectric fibers are embedded within a polymer matrix filled by CNT/GNP hybrids. Agglomeration of hybrid nanofillers as a significant factor is identified and incorporated in the micromechanical calculation. Parametric studies are carried out to understand the effect of volume fraction, size and dispersion type of carbonous nanofillers as well as the piezoelectric fiber volume fraction on the effective material constants of multiphase composites. It is found that in comparison with the piezoelectric fibrous composite, the piezoelectric fiber multiphase composite containing CNT/GNP hybrids shows better elastic and piezoelectric properties. Also, further improvement in effective properties can be obtained by increasing the length and percentage of CNTs and GNPs. But, degradation in the elastic and piezoelectric constants is observed by the agglomeration of CNT/GNP hybrids. The current results are found to be in close proximity with the experimental data and other numerical results available in the literature.
... Despite the exceptional mechanical properties attributed to CNTs, experimental results have shown only modest improvements in the effective elastic moduli of nanocomposites, which could be attributed to CNT agglomeration. Shi et al. [23] proposed an analytical method to study the effects of CNT agglomeration on nanocomposite elastic properties using the MT method, suggesting that increased agglomeration could lead to a significant decrease in Young's modulus. While MD is a potent method for nanoscale material modeling and simulation, it is limited by its applicability to small sizes [24][25][26][27]. ...
Multiscale modeling (MM) has broadened its scope to encompass the calculation of mechanical properties, with a particular focus on investigating how the dimensions of single-walled carbon nanotubes (SWCNTs), specifically their diameters, affect the mechanical properties (Longitudinal and Transverse Young's modulus) of simulated nanocomposites through Molecular Dynamics (MD) simulations. The MD method was employed to construct nanocomposite models comprising five different SWCNTs chiralities: (5, 0), (10, 0), (15, 0), (20, 0), and (25, 0), serving as reinforcements within a common Polymethyl methacrylate (PMMA) matrix. The findings indicate a correlation between the SWCNT diameter increase and enhancements in mechanical and physical properties. Notably, as the diameter of SWCNTs increases, the density, Longitudinal Young's modulus, Transvers Young's Shear modulus, Poisson's ratio, and Bulk modulus of the simulated nanocomposite transition from (5, 0) to (25, 0) by approximately 1.54, 3, 2, 1.43, 1.11, and 1.75 times, respectively. To corroborate these results, stiffness matrices were derived using Materials Studio software.
... Due to their small diameter, low radial elastic modulus, and high aspect ratio, CNTs exhibit a tendency to agglomerate in polymer matrices. These characteristics contribute to reduced bending stiffness [7]. In this section to study the influence of the agglomeration of CNTs on the effective elastic moduli of CNT-reinforced composites. ...
: This study investigates the free vibration behavior of nanocomposite beams reinforced with agglomerated single-walled carbon nanotubes (SWCNTs) embedded in an epoxy matrix. The effective material properties of the reinforced composite are estimated using the Weng model, and the equation of motion for the beam is derived based on Euler-Bernoulli beam theory. A MATLAB code is developed to determine the natural frequencies and eigenmodes of the nanocomposite beams. The results demonstrate that the elastic modulus of the agglomerated CNT composite increases with the increasing volume fraction of CNTs, leading to an increase in natural frequencies.
... The uniform distribution (UD) and FG-V, FG-O, and FG-X are the FG distributions of CNTs in the thickness direction of the composite beams as shown in Fig. 1. The effective material properties of the two-phase nanocomposites, a mixture of CNTs and an isotropic polymer, can be expected according to the Eshelby-Mori-Tanaka plan (Shi et al. [2]) or the rule of mixture (Fidelus et al. [3], Esawi and Farag [4]). Because of its straightforwardness and comfort, the standard of the mixture is utilized in this study by presenting the CNTs proficiency boundaries and the viable material possessions of CNTRC pillars can hence be recorded (Shen [6], Bouazza and Zenkour [23]) ...
In this work, we are interested in studying bending, buckling stability, and dynamic behaviors of functionally graded nanobeams reinforced by carbon nanotubes (FG-CNTRC) by a novel shear deformation theory. This model is simple and efficient based on the new polynomial-exponential integral shear deformation theory including the effect of size taking into account the effects of the Winkler–Pasternak elastic foundations. The polynomial-exponential transverse shear function is incorporated to better represent a new displacement field that includes indeterminate integral terms. It is presumed that the material possessions of FG-CNTRC are diverse along the thickness direction employing distinct four distributions of carbon nanotubes (NT-CNTs). The nonlocal elasticity offered by Eringen is used to involve size effects in this approach. The impacts of numerous factors such as the volume fraction of CNTs, the nonlocality, and the impacts of the elastic foundation on the response of the FG-CNTRC beams are examined.
... Based on the Eshelby-Mori-Tanaka micro-mechanical model, the shear and bulk modulus of clusters can be written as [43,44]: ...
Nanocomposites have gained fame due to their characteristics and are used in many industries such as automotive, aerospace, and biomedical. Also, curled structures (arches) are deeply applicable in fields of engineering. So, in this paper, the influence of nanoparticles’ aggregation on the behavior of the dispersed elastic waves in the hybrid nanocomposite arches is evaluated for the first time. The arches are supposed to be made of hybrid multi-scale nanocomposite reinforced with single-walled carbon nanotubes and carbon fibers. The physical properties of arches are calculated in the framework of the rule of the mixture and the Eshelby–Mori–Tanaka homogenization model. The theoretical formulation of kinetic relations of the arches is presented based on the Euler–Bernoulli curved beam theory. Moreover, Hamilton’s principle is applied to obtain the partial differential governing equations of arches. In the next step, an analytical solution method is implemented to solve the derived partial differential equations, and then, the frequency and velocity of the dispersed waves will be calculated. Next, the impacts of different effective parameters on the change of wave dispersion of hybrid nanocomposite arches are comprehensively studied. Finally, the obtained outcomes are reported in detail namely the correlations between phase velocity, wave frequency, weight fraction, etc.
... In this scenario, the matrix seems to be situated in the lower portion of the structure, while the agglomerated carbon nanotubes are presumed to occupy the upper region. In order to get more insights into this matter, it is strongly recommended that scholars consult the work of Shi et al. [44]. The determination of effective material characteristics may be achieved by using the relationships established by the Eshelby-Mori-Tanaka micromechanical model. ...
The study explores the free vibration characteristics of hybrid laminated nanocomposite truncated conical shells and panels incorporating functionally graded graphene platelet-reinforced (FG-GPLs) and functionally graded carbon nanotube-reinforced (FG-CNTs) materials, advancing understanding in hybrid material applications. The structures are assumed to be supported by a two-parameter elastic foundation, and the study also considers the influence of CNT agglomeration. The estimation of CNT agglomeration effect is performed using a two-parameter agglomeration model based on the Mori–Tanaka approach, considering the random orientation of carbon nanotubes. By employing a combination of various control parameters, it becomes possible to determine the optimal mode for setting the natural frequency of the system. To ensure accurate calculations for both thin and thick shells, a third-order shear deformation theory is employed. The governing equations and boundary conditions are formulated based on Hamilton's principle. Numerical solutions are obtained through the systematic differential quadrature method, wherein the Kronecker delta function is employed. By introducing subtle adjustments to the governing equations, this method effectively minimizes computational volume and complexity, proving particularly advantageous for addressing problems characterized by higher degrees of freedom. To estimate the effective mechanical properties of the CNT-reinforced nanocomposite layers, the rule of mixtures is employed. Meanwhile, the Halpin–Tsai micromechanical model is utilized for calculating the properties of the GPL-reinforced nanocomposite layers. The presented study establishes convergence and accuracy through evaluation, considering various parameters such as CNTs volume fraction, GPLs mass fraction, different distribution patterns, different geometries under various boundary conditions, vertex angle of the cone, agglomeration characteristics of CNTs, and different stiffness of the elastic foundation.
... 50, respectively, favor the lesser development of agglomeration phenomena because, being that all OPEFB/vinyl acrylic composites were made with the same reinforcement load, the packing density of fiber collectives decreases as a result of a greater spatial allocation between the longer fibers with the shorter ones in vicinity. 58 As a last point for the first stage of analysis, statistically non-significant differences in the composite toughness were identified by the multi-factor categorical ANOVA, both between the materials processed at 75 C and 100 C, as well as between the materials reinforced with OPEFB fibers retained on mesh no. 30 and no. ...
The performance of natural fiber‐reinforced polymer composites (NFRPCs) can be markedly affected by fiber length, to the extent that a sole mean value and standard deviation fail to accurately represent its overall dispersion. Hence, measuring the variability of fiber length is crucial to comprehend its influence on the properties of the resulting composites. Unfortunately, few studies have been conducted on this topic. This work consisted of two research stages: the first related to the effect of both fiber length distribution and processing temperature on the properties of oil palm empty fruit bunch (OPEFB) fiber‐reinforced vinyl acrylic composites, while the second stage analyzed the influence of the fiber length distribution on the material performance under accelerated weathering tests. Broadly, composites were characterized by tensile mechanical testing, optical microscopy and SEM, FTIR spectroscopy, TGA, and microbiological analysis. The key results showed that processing the material at temperatures surpassing 75°C did not lead to a homogenous phase between the components, rendering it unworthy of consideration. Furthermore, composites containing the longest OPEFB fibers exhibited the lowest elongation‐at‐break values. Regarding the incidence of aging treatments, pronounced effects were observed in those composites exposed to UV radiation and salt fog. In detail, the elongation at break decreased by up to 34%, while the tensile strength increased by up to 1 MPa, and Young's modulus rose by up to 17%. Finally, two fungal genera, Fusarium sp. and Rhizophydium sp., were identified on the OPEFB fibers; nevertheless, no fungal growth was observed on the composites.
Highlights
Natural reinforcement/filler size measured as fiber length distribution.
Effect of fiber length distribution on composite performance.
Composite performance after accelerated weathering tests.
This work has analyzed the bending, free vibration and buckling performance of a three-phase (CNT/Polymer/Carbon fiber) composite plate as a function of the carbon fiber volume fraction and the CNT volume fraction, under several values of the plate aspect ratio (a/b) and the plate slenderness parameter (h/b), and considering the presence of defects due to the poor dispersion on the CNTs. Based on a two-steps homogenization technique, the mechanical properties of the carbon
fibers reinforced –CNT enriched– polymeric matrix are computed. Then, the mechanical response of the plate is computed according to the first-order shear deformation plate theory solutions presented in Reddy’s books. The numerical results have revealed the presence, in three-phase (CNT/Polymer/Carbon fiber) composite plates, of a CNT volume fraction threshold above which the bending, free vibration and buckling performance of the plate decay with the carbon fiber volume
fraction. URL: https://doi.org/10.1080/15376494.2024.2362417
Carbon nanotube (CNT) has fostered research as a promising nanomaterial for a variety of applications due to its exceptional mechanical, optical, and electrical characteristics. The present article proposes a novel and comprehensive micromechanical framework to assess the viscoelastic properties of a multiscale CNT-reinforced two-dimensional (2D) woven hybrid composite. It also focuses on demonstrating the utilisation of the proposed micromechanics in the dynamic analysis of shell structure. First, the detailed constructional attributes of the proposed trans-scale composite material system are described in detail. Then, according to the nature of the constructional feature, mathematical modelling of each constituent phase or building block’s material properties is established to evaluate the homogenised viscoelastic properties of the proposed composite material system. To highlight the novelty of this study, the viscoelastic characteristics of the modified matrix are developed using the micromechanics method of Mori–Tanaka (MT) in combination with the weak viscoelastic interphase (WI) theory. In the entire micromechanical framework, the CNTs are considered to be randomly oriented. The strength of the material (SOM) approach is used to establish mathematical frameworks for the viscoelastic characteristics of yarns, whereas the unit cell method (UCM) is used to determine the viscoelastic properties of the representative unit cell (RUC). Different numerical results have been obtained by varying the CNT composition, interface conditions, agglomeration, carbon fibre volume percentage, excitation frequency, and temperature. The influences of geometrical parameters like yarn thickness, width, and the gap length to yarn width ratio on the viscoelasticity of such composite material systems are also explored. The current study also addresses the issue of resultant anisotropic viscoelastic properties due to the use of dissimilar yarn thickness. The results of this micromechanical analysis provide valuable insights into the viscoelastic properties of the proposed composite material system and suggest its potential applications in vibration damping. To demonstrate the application of developed novel micromechanics in vibration analysis, as one of the main contributions, comprehensive numerical experiments are conducted on a shell panel. The results show a significant reduction in vibration amplitudes compared to traditional composite materials in the frequency response and transient response analyses. To focus on the aspect of micromechanical behaviour on dynamic response and for the purpose of brevity, only linear strain displacement relationships are considered for dynamic analysis. These insights could inform future research and development in the field of composite materials.
Shape memory polymers (SMPs) are known for their unique ability to withstand large deformations and revert to their original shape under specific external stimuli. However, their broader application in biomedical and structural applications is restricted by limited mechanical and thermal properties. Introducing multi-walled carbon nanotubes (MWCNTs) into SMPs has proven to significantly enhance these characteristics without affecting their inherent shape memory features. This study investigates shape memory nanocomposites (SMNCs) through dynamic and thermogravimetric analyses, along with tensile, flexural, and shape memory testing, and explores fracture interfaces using scanning electron microscopy. Findings indicate optimal shape memory, thermal, and mechanical properties with 0.6 wt% MWCNT content, showcasing a shape recovery ratio of 93.11%, storage modulus of 4127.63 MPa, tensile strength of 55 MPa, and flexural strength of 107.94 MPa. Moreover, incorporating MWCNTs into epoxy demonstrated a reduction in recovery times by up to 50% at 0.6 wt% concentration. Despite a slight decrease in shape fixity ratio from 98.77% to 92.11%, shape recoverability remained nearly consistent across all samples. The study also introduces a novel finite element (FE) method in ABAQUS for modeling the thermomechanical behaviour of SMNCs, incorporating viscoelasticity, validated by matching experimental results with FE simulations, highlighting its accuracy and practical applicability in engineering.
The small‐scale‐dependent nonlinear dynamical attributes of microplate‐type laminated piezoelectric systems of harvesting energy subjected to a triangular mechanical actuation are explored in the current exploration. The core of harvesting systems is supposed to be made of nanocomposites reinforced by randomly oriented carbon nanotubes (CNTs) having various degrees of agglomeration coated by piezoelectric layers. In this regard, the microplate‐type systems of harvesting energy are modeled via a quasi‐3D plate theory combined with the modified strain gradient elasticity in the presence of various microsize‐dependent strain gradient tensors. Thereafter, the solution of the developed coupled electromechanical size‐dependent nonlinear problem is obtained numerically by utilizing the meshless collocation approach employing incorporation of the polynomial and radial basis functions to remove any feasible singularity for the associated moment matrices. It comes to the conclusion that by elevating the quantity of CNTs disclosed within the clusters, the significance of the microsize dependency in the achieved voltage enhances from 22.06% to 22.73% toward the simply supported bridge‐type context, and from 33.00% to 33.92% toward the clamped bridge‐type context.
Highlights
Development of a microstructural‐dependent quasi‐3D shear flexible energy harvester model.
Incorporating the roles of various strain gradient tensors in the nonlinear dynamics of microharvesters.
Size‐dependent time‐histories of achieved voltage from triangular mechanical‐loaded microharvesters.
Influence of the CNT reinforcement clustering on the nonlinear dynamic performance.
Size dependency plays an important role in mechanical responses of structures at microscale. In this regard, within the framework of the modified strain gradient theory (SGT), the nonlinear dynamic characteristics of porous/piezoelectric laminated energy microharvesters under sinusoidal impulsive mechanical actuation are explored. The through-thickness porosity dispersion pattern relevant to the passive core of the considered laminated microharvesters is assumed based upon three different functions including a uniform and two graded ones satisfying the necessary requirements associated with the rule of Gaussian random field. In order to derive numerically the solution of the constructed microscale-dependent energy harvester model, the meshless collocation approach as an efficient subset of the meshfree technique is utilized possessing multiquadric radial basis function. It is indicated that by considering a higher value for the microstructural gradient parameters utilized in the SGT-based microharvester model leads to a more prominent effect of the strain gradient tensors which makes more decrement in the value of attained voltage. In this regard, for the laminated energy microharvester under simply edge condition, the value of attained voltage reduces from in the conventional case to the SGT-based value of ( decrement) associated with the microstructural gradient parameters equal to , to the SGT-based value of ( decrement) associated with the microstructural gradient parameters equal to , and to the SGT-based value of ( decrement) associated with the microstructural gradient parameters equal to . On the other hand, for the laminated energy microharvester under clamped edge condition, the value of attained voltage reduces from in the conventional case to the SGT-based value of ( decrement) associated with the microstructural gradient parameters equal to , to the SGT-based value of ( decrement) associated with the microstructural gradient parameters equal to , and to the SGT-based value of ( decrement) associated with the microstructural gradient parameters equal to .
This paper presents a semi-analytical approach for nonlinear vibration and dynamic response of ceramic–metal functionally graded doubly curved shallow shells reinforced by carbon nanotubes under three different types of boundary conditions. This approach utilizes a new sinusoidal shear deformation theory combined with von Kármán’s geometric nonlinearity. The proposed theory contains the sinusoidal distribution of transverse shear strains and satisfies the conditions of free transverse shear stress on both the top and bottom surfaces of the shell with only four unknown variables. The shells are made of a ceramic–metal matrix reinforced by carbon nanotubes with two types of distributions, both uniform distributions and functionally graded distributions. Equations of motion are derived from Hamilton’s principle and then solved by the Galerkin method and Airy’s stress function in which the closed-form solutions of the shells with fully simply supported edges, fully clamped edges, and two opposite simply supported and two opposite clamped edges are obtained. The study investigates the effects of boundary conditions, distribution types, volume fraction of carbon nanotubes, and geometrical parameters on the dynamic response, free and forced vibration of doubly curved shallow shells through numerical results.
This work introduces an analysis of the nonlinear buckling and free vibration behavior of polymer plates reinforced with aligned carbon nanotubes using Reddy's third-order shear deformation plate theory and incorporating Theodore von Kármán's geometric nonlinearity. The polymer plates were enhanced with single-walled carbon nanotubes assumed to exhibit either uniform distribution or functionally graded distribution across the thickness. The equations of motion were established through Hamilton’s principle and then solved by the Galerkin method and Airy’s stress function for the composite plates with fully simply supported edges. The investigation focused on assessing the effects of carbon nanotube distribution, volume fraction, and geometrical parameters on the buckling load and fundamental frequency parameters of composite plates through numerical results.
The applications of nanoelectromechanical systems integrating simultaneously the mechanical and electrical functionalities at nanoscale have been gotten wider in the last decade. The main objective of this exploration is to analyze the small scale‐dependent nonlinear dynamical feedback of multilayer energy nanoharvesters containing a graded porous passive core coated by piezoelectric facesheets under a sinusoidal impulsive external actuation. For this purpose, the technique of meshless collocation is constructed at the same time the nonlocal stress and strain gradient tensors without any necessary background meshes and integration procedure. It is found that by taking the nonlocal stress tensor into account, the average of extremum points of maximum lateral deflection increases from to , and from to for simply supported and clamped multilayer nanoharvesters, respectively. On the contrary, through considering the strain gradient tensor, the average of extremum values of the maximum lateral deflection reduces from to for the simply supported nanoharvester, and from to for the clamped one.
Highlights
Development a third‐order shear flexible nonlocal strain gradient (NSG)‐based plate‐type nanoharvester model
Incorporating the role of nonlocal stress and strain gradient tensors in nonlinear dynamics of nanoharvesters
Time‐histories of achieved voltage of sinusoidal impulsive loaded plate‐type nanoharvesters
Influence of porosity on the NSG‐based nonlinear dynamic performance.
The thermoelastic free vibrational characteristics of sandwich composite shell panels reinforced with carbon nanotubes (CNTs) and bonded with shape memory alloy (SMA) fibres have been analyzed numerically utilizing the higher-order shear deformation theory (HOSDT).
The sandwich face sheets are considered to be CNT-reinforced composites (single-walled). In which CNTs are randomly oriented in XY-plane and functionally graded along the thickness coordinate (Z-axis). Moreover, the SMA has been introduced as a foreign functional material to improve the structural strength due to its inherent recovery stress characteristics under constraint conditions. The system of equations for vibration analysis is acquired via Hamilton’s principle, and the finite element (FE) approach is executed to attain the solution.
The current numerical solutions are validated by comparing them with published results. The impact of diverse design parameters such as volume fraction of individual constituents, aspect ratios, thickness ratio, types of CNT reinforcement, temperature and SMA pre-strain value on the eigenvalues of SMA embedded CNT reinforced sandwich structure are examined.
The current outcomes suggest that using SMA at higher temperatures (active condition of SMA) is more effective in vibration control of the CNT-reinforced sandwich composite structure.
The nonlinear stability characteristics of doubly curved panels made of three-phase composites with randomly dispersed carbon nanotubes (RD-CNTRFC) subjected to practically-relevant non-uniform in-plane loads are investigated in this study. Carbon nanotubes, when mixed with resin polymer, may give rise to bundles, termed as agglomerations, which can have a profound impact on the effective material properties. There exists a strong rationale to investigate the influence of such agglomeration on the nonlinear equilibrium path of panels, which can subsequently be included in the structural stability design process to enhance operational safety. A multi-stage bottom-up numerical framework is developed here to probe the nonlinear stability characteristics. The effective material properties of RD-CNTRFC panels are determined using the Eshelby-Mori-Tanaka approach and the Chamis method of homogenization. By considering von-Kármán non-linearity and Reddy's higher-order shear deformation theory, strain-displacement relations are established for the non-linear stability analysis. The governing partial differential equations are simplified into nonlinear algebraic relations using Galerkin's method. Subsequently, by reducing the stiffness matrix neglecting the non-linear terms and solving the Eigenvalue problem, we obtain critical load and non-linear stability path of shell panels based on arc-length approach. In the present study, various shell geometries such as cylindrical, elliptical, spherical and hyperbolic shapes are modeled along with the flat plate-like geometry to investigate the non-linear equilibrium paths, wherein a geometry-dependent programmable softening and hardening behavior emerges.
Huge available scientific literature revealed that due to exceptional thermal, mechanical, electrical and optical characteristics, carbon nanotubes (CNTs) hold an eminent status in the panoply of composites and nanomaterials arena and explore extensive applications in numerous industries. The continuously growing interest in incorporating CNTs into various matrices has spurred sustained efforts to fabricate CNT-based nanocomposites. Furthermore, the development in the fabrication of novel CNT-reinforced polymers (engineering and natural) and polymer/fiber nanocomposites with exceptional characteristics, stands out as one of the most significant achievements for the materials, nanoscience, biomedical and aviation industries. This review article aims to highlight the most noteworthy and novel research work carried out in the recent era exploring the ultimate characteristics of Polymer/Fibre/CNT composites and hybrid composites. Moreover, advancements in experimental, numerical and analytical investigations of the thermo-mechanical, thermal, mechanical, vibrational and impact response characteristics of CNT-reinforced composites (CNTRCs) are thoroughly discussed. Also, the mechanical properties of the CNT-reinforced nanocomposites reported in the earlier literature are summarized in tabular form. This review demonstrates that the current research effort by the researchers is mainly devoted to fabricating lightweight novel CNTRC structures with exceptional characteristics.
Nano-constituent incorporation into composites has been extensively studied in the literature due to its improvement in static and dynamic mechanical properties, as well as its prevention from interlaminar crack initiation and propagation. This work introduces a detailed manufacturing process of nano-engineered composite laminates, from impregnation to consolidation, without damaging the initial morphology of carbon nanotubes transferred on prepreg interfaces. Based on prepreg and vertically aligned carbon nanotubes (VACNTs) synthesized on an aluminium alloy (Al) substrate, the impregnation step allows for the transfer of VACNTs onto the prepreg surface through partial resin-rising capillarity. The Al alloy substrate is then removed from the VACNTs through a separation step, ensuring highly effective and repeatable transfer with more than 80% VACNTs transferred onto the prepreg surface. This paper provides insight into the impregnation and transfer processes and guides the choice of process parameters to ensure minimal VACNTs buckling during the consolidation of the hybrid composites at high pressure in an autoclave.
Experimental observations of various deformation and fracture modes under compression of single multiwalled carbon nanotubes, obtained as a result of embedment within a polymeric film, are reported. Based on a combination of experimental measurements and the theory of elastic stability, the compressive strengths of thin- and thick-walled nanotubes are found to be about 2 orders of magnitude higher than the compressive strength of any known fiber.
Carbon nanotubes (CNTs) seem to hold a great promise as an ideal reinforcing material for composites of high-strength and low-density. In most experimental results to date, however, only modest improvements in the strength and stiffness have been achieved by incorporating CNTs in polymers. There are many factors that influence the mechanical properties of CNT-reinforced composites, e.g. the weak bonding between CNTs and matrix, the waviness and agglomeration of CNTs. In this paper, the effects of these factors on the stiffness of CNT-reinforced composites are examined. It is found that the waviness and agglomeration may significantly reduce the stiffening effect of CNTs, while the interface adhesion between the matrix and CNTs has little influence.
Well-aligned bundles of single-wall carbon nanotubes under tensile stresses were observed to fracture in real-time by transmission electron microscopy. The expansion of elliptical holes in the polymer matrix results in a tensile force in bridging nanotubes. The polymer matrix at both ends of the bundles deforms extensively under the tension force, and fracture of the nanotubes occurs in tension within the polymer hole region rather than in shear within the gripping polymer region at the ends of the bundles. This provides evidence of significant polymer-nanotube wetting and interfacial adhesion.
The tensile strengths of individual multiwalled carbon nanotubes (MWCNTs) were measured with a “nanostressing stage” located
within a scanning electron microscope. The tensile-loading experiment was prepared and observed entirely within the microscope
and was recorded on video. The MWCNTs broke in the outermost layer (“sword-in-sheath” failure), and the tensile strength of
this layer ranged from 11 to 63 gigapascals for the set of 19 MWCNTs that were loaded. Analysis of the stress-strain curves
for individual MWCNTs indicated that the Young's modulus E of the outermost layer varied from 270 to 950 gigapascals. Transmission electron microscopic examination of the broken nanotube
fragments revealed a variety of structures, such as a nanotube ribbon, a wave pattern, and partial radial collapse.
We report the observation of single nanotube fragmentation, under tensile stresses, using nanotube-containing thin polymeric films. Similar fragmentation tests with single fibers instead of nanotubes are routinely performed to study the fiber-matrix stress transfer ability in fiber composite materials, and thus the efficiency and quality of composite interfaces. The multiwall nanotube-matrix stress transfer efficiency is estimated to be at least one order of magnitude larger than in conventional fiber-based composites. © 1998 American Institute of Physics.
THE interest in carbon nanotubes has been greatly stimulated by theoretical predictions that their electronic properties are strongly modulated by small structural variations1–8. In particular, the diameter and the helicity of carbon atoms in the nanotube shell are believed to determine whether the nanotube is metallic or a semiconductor. Because of the enormous technical challenge of making measurements on individual nanotubes, however, experimental studies have been limited mainly to bulk measurements9, which indicate only that a fraction of the nanotubes are metallic or narrow-band semiconductors10. Recently, measurements of the magneto-conductance of a single multi-shell nanotube in a two-probe configuration showed that the transport is characterized by disorder and localization phenomena11. To avoid possible ambiguities due to poor sample contacts, four-probe measurements are needed. Here we report four-probe measurements on single nanotubes made by lithographic deposition of tungsten leads across the tubes. We find that each multi-shell nanotube has unique conductivity properties. Both metallic and non-metallic behaviour are observed, as well as abrupt jumps in conductivity as the temperature is varied. The differences between the electrical properties of different nanotubes are far greater than expected. Our results suggest that differences in geometry play a profound part in determining the electronic behaviour.
Recent experimental results demonstrate that substantial improvements in the mechanical behavior of polymers can be obtained using very small amounts of carbon nanotubes as a reinforcing phase. Here, a method is developed to incorporate the typically observed curvature of the embedded nanotubes into traditional micromechanical methods for determination of the effective modulus of the nanotube-reinforced polymer. Using a combined finite element and micromechanical approach, it was determined that the nanotube curvature significantly reduces the effective reinforcement when compared to straight nanotubes. This model suggests that nanotube waviness may be an additional mechanism limiting the modulus enhancement of nanotube-reinforced polymers. (C) 2002 American Institute of Physics.
This Letter describes the production of single-wall carbon nanotube (SWNT) – polymer composites with enhanced mechanical and electrical properties and exceptional nanotube alignment. A combination of solvent casting and melt mixing was used to disperse SWNT materials in poly(methyl methacrylate) (PMMA). Composite films showed higher conductivity along the flow direction than perpendicular to it. Composite fibers were melt spun to achieve draw ratios between 20 and 3600. The elastic modulus and yield strength of SWNT–PMMA composite fibers increased with nanotube loading and draw ratio. Polarized resonant Raman spectroscopy indicates that the nanotubes in the fibers are well aligned, with mosaic distribution FWHMs as small as 4°.
Carbon nanotubes show great promise for applications ranging from nanocomposites, nanoelectronic components, nanosensors, to nanoscale mechanical probes. These materials exhibit very attractive mechanical properties with extraordinarily high stiffness and strength, and are of great interest to researchers from both atomistic and continuum points of view. In this paper, we intend to develop a continuum theory of fracture nucleation in single-walled carbon nanotubes by incorporating interatomic potentials between carbon atoms into a continuum constitutive model for the nanotube wall. In this theory, the fracture nucleation is viewed as a bifurcation instability of a homogeneously deformed nanotube at a critical strain. An eigenvalue problem is set up to determine the onset of fracture, with results in good agreement with those from atomistic studies.
The mechanical response of 15 single wall carbon nanotube (SWCNT) ropes under tensile load was measured. For 8 of these ropes strain data were obtained and they broke at strain values of 5.3% or lower. The force-strain data are well fit by a model that assumes the load is carried by the SWCNTs on the perimeter of each rope. This model provides an average breaking strength of SWCNTs on the perimeter of each rope; the 15 values range from 13 to 52 GPa (mean 30 GPa). Based on the same model the 8 average Young's modulus values determined range from 320 to 1470 GPa (mean 1002 GPa).
A simple method was used to assemble single-walled carbon nanotubes into indefinitely long ribbons and fibers. The processing consists of dispersing the nanotubes in surfactant solutions, recondensing the nanotubes in the flow of a polymer solution to form a nanotube mesh, and then collating this mesh to a nanotube fiber. Flow-induced alignment may lead to a preferential orientation of the nanotubes in the mesh that has the form of a ribbon. Unlike classical carbon fibers, the nanotube fibers can be strongly bent without breaking. Their obtained elastic modulus is 10 times higher than the modulus of high-quality bucky paper.
This book stems from a course on Micromechanics that I started about fifteen years ago at Northwestern University. At that time, micromechanics was a rather unfamiliar subject. Although I repeated the course every year, I was never convinced that my notes have quite developed into a final manuscript because new topics emerged constantly requiring revisions, and additions. I finally came to realize that if this is continued, then I will never complete the book to my total satisfaction. Meanwhile, T. Mori and I had coauthored a book in Japanese, entitled Micromechanics, published by Baifu-kan, Tokyo, in 1975. It received an extremely favorable response from students and re searchers in Japan. This encouraged me to go ahead and publish my course notes in their latest version, as this book, which contains further development of the subject and is more comprehensive than the one published in Japanese. Micromechanics encompasses mechanics related to microstructures of materials. The method employed is a continuum theory of elasticity yet its applications cover a broad area relating to the mechanical behavior of materi als: plasticity, fracture and fatigue, constitutive equations, composite materi als, polycrystals, etc. These subjects are treated in this book by means of a powerful and unified method which is called the 'eigenstrain method. ' In particular, problems relating to inclusions and dislocations are most effectively analyzed by this method, and therefore, special emphasis is placed on these topics.
A simple method was used to assemble single-walled carbon nanotubes into indefinitely long ribbons and fibers. The processing consists of dispersing the nanotubes in surfactant solutions, recondensing the nanotubes in the flow of a polymer solution to form a nanotube mesh, and then collating this mesh to a nanotube fiber. Flow-induced alignment may lead to a preferential orientation of the nanotubes in the mesh that has the form of a ribbon. Unlike classical carbon fibers, the nanotube fibers can be strongly bent without breaking. Their obtained elastic modulus is 10 times higher than the modulus of high-quality bucky paper.
The tensile strengths of individual multiwalled carbon nanotubes (MWCNTs) were measured with a "nanostressing stage" located within a scanning electron microscope. The tensile-loading experiment was prepared and observed entirely within the microscope and was recorded on video. The MWCNTs broke in the outermost layer ("sword-in-sheath" failure), and the tensile strength of this layer ranged from 11 to 63 gigapascals for the set of 19 MWCNTs that were loaded. Analysis of the stress-strain curves for individual MWCNTs indicated that the Young's modulus E of the outermost layer varied from 270 to 950 gigapascals. Transmission electron microscopic examination of the broken nanotube fragments revealed a variety of structures, such as a nanotube ribbon, a wave pattern, and partial radial collapse.
The elastic constants, Young's and bulk moduli, and Poisson ratio of triangular close-packed crystal lattices of single-walled carbon nanotubes are calculated for various tube types using analytical expressions. Some of these quantities exhibit up to three different regimes of behavior which are due to the interplay of the intertube van der Waals forces and the elastic forces in the tubes. These regimes are most prominent in the case of the bulk modulus which has a maximal value of 38 GPa at tube radius R 6 A and decreases for larger radii.
Single walled carbon nanotubes (SWNTs) were dispersed in isotropic petroleum pitch matrices to form nanotube composite carbon fibers with enhanced mechanical and electrical properties. We find that the tensile strength, modulus, and electrical conductivity of a pitch composite fiber with 5 wt % loading of purified SWNTs are enhanced by ∼ 90%, ∼150%, and 340% respectively, as compared to the corresponding values in unmodified isotropic pitch fibers. These results serve to highlight the potential that exits for developing a spectrum of material properties through the selection of the matrix, nanotube dispersion, alignment, and interfacial bonding.
Quenched molecular dynamics simulations are used to investigate the elastic behavior of open-ended, free-standing, single wall, carbon nanotubes. Interatomic interactions are described by a Tersoff-Brenner potential. The tubes' response to axial compression is examined and typical failure modes as well as stress-strain curves for a number of tube radii are shown. Data collected are used to calculate Young's modulus for the tubes and to develop a simple formula that approximates this quantity over a wide range of tube radii.
Multiwall carbon nanotubes have been dispersed homogeneously throughout polystyrene matrices by a simple solution-evaporation method without destroying the integrity of the nanotubes. Tensile tests on composite films show that 1 wt % nanotube additions result in 36%-42% and ~25% increases in elastic modulus and break stress, respectively, indicating significant load transfer across the nanotube-matrix interface. In situ transmission electron microscopy studies provided information regarding composite deformation mechanisms and interfacial bonding between the multiwall nanotubes and polymer matrix.
Composites of uniaxially oriented multiwalled carbon nanotubes embedded in polymer matrices were fabricated and investigated by transmission electron microscopy. In strained composite films, buckling was ubiquitously observed in bent nanotubes with large curvatures. By analyses of a large number of bent nanotubes, the onset buckling strain and fracture strain were estimated to be ≈5% and ⩾18%, respectively. The buckling wavelengths are proportional to the dimensions of the nanotubes. Examination of the fracture surface showed adherence of the polymer to the nanotubes. © 1999 American Institute of Physics.
CARBON nanotubes are predicted to have interesting mechanical properties—in particular, high stiffness and axial strength—as a result of their seamless cylindrical graphitic structure1–5. Their mechanical properties have so far eluded direct measurement, however, because of the very small dimensions of nanotubes. Here we estimate the Young's modulus of isolated nanotubes by measuring, in the transmission electron microscope, the amplitude of their intrinsic thermal vibrations. We find that carbon nanotubes have exceptionally high Young's moduli, in the terapascal (TPa) range. Their high stiffness, coupled with their low density, implies that nanotubes might be useful as nanoscale fibres in strong, lightweight composite materials.
Are nanotubes ideally suited to a straightforward reinforcing role? Results reported here indicate that that may not be the case, but they could find application as a polymer modifier. A successful route is described for the fabrication of large composite films containing carbon nanotubes based on the formation of a stable colloidal intermediate, a route that should be broadly applicable to a range of nanotube materials and polymers. The resulting thermo-mechanical and electrical properties are discussed. While the stiffness of the composites at room temperature is rather low they show promise at high temperatures.
Soon after the discovery of carbon nanotubes, it was realized that the theoretically predicted mechanical properties of these interesting structures–including high strength, high stiffness, low density and structural perfection–could make them ideal for a wealth of technological applications. The experimental verification, and in some cases refutation, of these predictions, along with a number of computer simulation methods applied to their modeling, has led over the past decade to an improved but by no means complete understanding of the mechanics of carbon nanotubes. We review the theoretical predictions and discuss the experimental tech-niques that are most often used for the challenging tasks of visualizing and manipulating these tiny structures. We also outline the computational approaches that have been taken, including ab initio quantum mechanical simulations, classical molecular dynamics, and continuum mod-els. The development of multiscale and multiphysics models and simulation tools naturally arises as a result of the link between basic scientific research and engineering application; while this issue is still under intensive study, we present here some of the approaches to this topic. Our concentration throughout is on the exploration of mechanical properties such as Young's modulus, bending stiffness, buckling criteria, and tensile and compressive strengths. Finally, we discuss several examples of exciting applications that take advantage of these properties, including nanoropes, filled nanotubes, nanoelectromechanical systems, nanosensors, and nanotube-reinforced polymers. This review article cites 349 references.
The dispersion of nanotubes in polymer matrices has been investigated as a means of deriving new and advanced engineering materials. These composite materials have been formed into fibers and thin films and their mechanical and electrical properties determined. The nanotube concentration at which conductivity was initiated (the percolation threshold) varied with host polymer. In poly(propylene), this was as low as 0.05 vol.-%, while higher concentrations were required for polystyrene and particularly for ABS. There was a small increase in elastic modulus and decrease in tensile strength at low nanotube loading, but as the concentration was increased there was a progressive increase in both strength and stiffness.
Results in the literature demonstrate that substantial improvements in the mechanical behavior of polymers have been attained through the addition of small amounts of carbon nanotubes as a reinforcing phase. This suggests the possibility of new, extremely lightweight carbon nanotube-reinforced polymers with mechanical properties comparable to those of traditional carbon-fiber composites. Motivated by micrographs showing that embedded nanotubes often exhibit significant curvature within the polymer, we have developed a model combining finite element results and micromechanical methods to determine the effective reinforcing mod-ulus of a wavy embedded nanotube. This effective reinforcing modulus (ERM) is then used within a multiphase micromechanics model to predict the effective modulus of a polymer reinforced with a distribution of wavy nanotubes. We found that even slight nanotube curvature significantly reduces the effective reinforcement when compared to straight nanotubes. These results suggest that nanotube waviness may be an additional mechanism limiting the modulus enhancement of nanotube-reinforced polymers.
The rheological behavior of compression molded mixtures of polycarbonate containing between 0.5 and 15 wt% carbon nanotubes was investigated using oscillatory rheometry at 260 °C. The nanotubes have diameters between 10 and 15 nm and lengths ranging from 1 to 10 μm. The composites were obtained by diluting a masterbatch containing 15 wt% nanotubes using a twin-screw extruder. The increase in viscosity associated with the addition of nanotubes is much higher than viscosity changes reported for carbon nanofibers having larger diameters and for carbon black composites; this can be explained by the higher aspect ratio of the nanotubes. The viscosity increase is accompanied by an increase in the elastic melt properties, represented by the storage modulus G′, which is much higher than the increase in the loss modulus G″. The viscosity curves above 2 wt% nanotubes exhibit a larger decrease with frequency than samples containing lower nanotube loadings. Composites containing more than 2 wt% nanotubes exhibit non-Newtonian behavior at lower frequencies. A step increase at approximately 2 wt% nanotubes was observed in the viscosity–composition curves at low frequencies. This step change may be regarded as a rheological threshold. Ultimately, the rheological threshold coincides with the electrical conductivity percolation threshold which was found to be between 1 and 2 wt% nanotubes.
Thin films of poly(methyl methacrylate)-singlewalled nanotubes (PMMA-SWNTs) composite were produced by spin coating using different nanotubes concentrations. Characterization of these new materials was performed by scanning electron microscopy (SEM) and Raman spectroscopy in order to obtain information on the possible interactions between these two materials and especially, on the modifications of the nanotubes and their organization. It is found that in the composite films, the distance between the nanotubes in bundles increases because of the intercalation of polymer. For low nanotube concentrations, amorphous carbon is dispersed in the polymer matrix giving more uniform thin films.
Having noted an important role of image stress in work hardening of dispersion hardened materials, (1,3) the present paper discusses a method of calculating the average internal stress in the matrix of a material containing inclusions with transformation strain. It is shown that the average stress in the matrix is uniform throughout the material and independent of the position of the domain where the average treatment is carried out. It is also shown that the actual stress in the matrix is the average stress plus the locally fluctuating stress, the average of which vanishes in the matrix. Average elastic energy is also considered by taking into account the effects of the interaction among the inclusions and of the presence of the free boundary.
Themacroscopic elastic moduli of two-phase composites are estimated by a method that takes account of the inhomogeneity of stress and strain in a way similar to the Hershey-Kröner theory of crystalline aggregates. The phases may be arbitrarily aeolotropic and in any concentrations, but are required to have the character of a matrix and effectively ellipsoidal inclusions. Detailed results arc given for an isotropic dispersion of spheres.
A nanoscale continuum theory is established to directly incorporate interatomic potentials into a continuum analysis without any parameter fitting. The theory links interatomic potentials and atomic structure of a material to a constitutive model on the continuum level. The theory is applied to study the linear elastic modulus of a single-wall carbon nanotube. The Young's modulus predicted by this nanoscale continuum theory agrees well with prior experimental results and atomistic studies.
The mechanical properties of single-walled carbon nanotube (SWCNT) are computed and simulated by using molecular dynamics (MD) in this paper. From the MD simulation for an armchair SWCNT whose diameter is 1.2 nm and length is 4.7 nm, we get that its Young modulus is 3.62 TPa, and tensile strength is 9.6 GPa. It is shown that the Young modulus and tensile strength of armchair SWCNTs are 1∼2 order higher than those of ordinary metal materials. Therefore we can draw a conclusion that carbon nanotubes (CNT) belong to a particular material with excellent mechanical properties.
In this study, a technique is presented for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Because the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties can no longer be determined through traditional micromechanical approaches that are formulated by using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber by using an equivalent-continuum modeling method. The effective fiber serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube lengths, concentrations, and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/polyimide composite systems.
Using state-of-the-art classical and quantum simulations, we have studied the mechanical and electronic response of carbon nanotubes to external deformations, such as strain and bending. In strained nanotubes the spontaneous formation of double pentagon–heptagon defect pairs is observed. Tubes containing these defects are energetically preferred to uniformly stretched tubes at strains greater than 5%. These defects act as nucleation centers for the formation of dislocations in the originally ideal graphitic network and constitute the onset of further deformations of the carbon nanotube. In particular, plastic or brittle behaviors can occur depending upon the external conditions and tube symmetry. We have also investigated the effects that the presence of addimers has on strained carbon nanotubes. The main result is the formation of a new class of defects that wrap themselves about the circumference of the nanotube. These defects are shown to modify the geometrical structure and to induce the formation of nanotube-based quantum dots. Finally, we computed transport properties for various ideal and mechanically deformed carbon nanotubes. High defect densities are shown to greatly affect transport in individual nanotubes, while small diameter bent armchair nanotubes mantam thier basic electrical properties even in presence of large deformations with no defects involved.
Since their first observation nearly a decade ago by Iijima (Iijima S. Helical microtubules of graphitic carbon Nature. 1991; 354:56–8), carbon nanotubes have been the focus of considerable research. Numerous investigators have since reported remarkable physical and mechanical properties for this new form of carbon. From unique electronic properties and a thermal conductivity higher than diamond to mechanical properties where the stiffness, strength and resilience exceeds any current material, carbon nanotubes offer tremendous opportunities for the development of fundamentally new material systems. In particular, the exceptional mechanical properties of carbon nanotubes, combined with their low density, offer scope for the development of nanotube-reinforced composite materials. The potential for nanocomposites reinforced with carbon tubes having extraordinary specific stiffness and strength represent tremendous opportunity for application in the 21st century. This paper provides a concise review of recent advances in carbon nanotubes and their composites. We examine the research work reported in the literature on the structure and processing of carbon nanotubes, as well as characterization and property modeling of carbon nanotubes and their composites.
Nanotube-reinforced polymers offer significant potential improvements over the pure polymer with regard to mechanical, electrical and thermal properties. This article investigates the degree to which the characteristic waviness of nanotubes embedded in polymers can impact the effective stiffness of these materials. A 3D finite element model of a single infinitely long sinusoidal fiber within an infinite matrix is used to numerically compute the dilute strain concentration tensor. A Mori–Tanaka model utilizes this tensor to predict the effective modulus of the material with aligned or randomly oriented inclusions. This hybrid finite element-micromechanical modeling technique is a powerful extension of general micromechanics modeling and can be applied to any composite microstructure containing non-ellipsoidal inclusions. The results demonstrate that nanotube waviness results in a reduction of the effective modulus of the composite relative to straight nanotube reinforcement. The degree of reduction is dependent on the ratio of the sinusoidal wavelength to the nanotube diameter. As this wavelength ratio increases, the effective stiffness of a composite with randomly oriented wavy nanotubes converges to the result obtained with straight nanotube inclusions. The approach developed in this paper can also be utilized in the analysis of other problems involving nanotube-reinforced polymers, including alternate nanotube representations, viscoelastic response, assessing the effect of low matrix-NT bond strength and in the determination of thermal and electrical conductivity.
Carbon nanotubes (CNTs) can be used to compound poly (methyl methacrylate)/carbon nanotube (PMMA/CNT) composites by an in situ process. The experimental results show that CNTs can be initiated by AIBN to open their π-bonds, which imply that CNTs may participate in PMMA polymerization and form a strong combining interface between the CNTs and the PMMA matrix. Through the use of an improved in situ process, the mechanical properties and the heat deflection temperatures of composites rise with the increase of CNTs. The dispersion ratio of CNTs in the PMMA matrix is proportional to the reaction time of polymerizing MMA before CNTs are added into the PMMA mixture.
A dimensional model was set up to study the electronic and lattice property of single-walled carbon nanotubes. The calculations clearly confirmed the experimental results, which included that armchair-type nanotubes were metallic, zigzag-type semiconductive or metallic depending upon the charity and tube diameters. Our investigation revealed that the quasi-one dimension was the essential characteristic of carbon nanotubes.
The preparation of a new type of finite carbon structure consisting of
needlelike tubes is reported. Produced using an arc-discharge
evaporation method similar to that used for fullerene sythesis, the
needles grow at the negative end of the electrode used for the arc
discharge. Electron microscopy reveals that each needle comprises
coaxial tubes of graphitic sheets ranging in number from two up to about
50. On each tube the carbon-atom hexagons are arranged in a helical
fashion about the needle axis. The helical pitch varies from needle to
needle and from tube to tube within a single needle. It appears that
this helical structure may aid the growth process. The formation of
these needles, ranging from a few to a few tens of nanometers in
diameter, suggests that engineering of carbon structures should be
possible on scales considerably greater than those relevant to the
fullerenes.
Nanophase materials — metals or ceramics with very small grain sizes — have been fairly disappointing. It was thought that small grains should result in much harder metals. It turns out that they are harder but also more brittle. We also hoped that ceramics with very small grains would be much stronger but that hasn't really been demonstrated yet. Yet there is still reason to expect that nanometre-scale composite materials might turn out to be better than conventional composites, such as the carbon fibre-epoxy composites used in high-performance aircraft. For example, we could use nanometre-sized fibres to strengthen a polymer matrix, and carbon nanotubes are now available in sufficient quantities to test this idea. When researchers met at a conference in Alaska, to discuss the challenge of making nanocomposites, it became clear that inputs from several fields will be needed to make it work.
Carbon nanotubes subject to large deformations reversibly switch into different morphological patterns. Each shape change corresponds to an abrupt release of energy and a singularity in the stress-strain curve. These transformations, simulated using a realistic many-body potential, are explained by a continuum shell model. With properly chosen parameters, the model provides a remarkably accurate ``roadmap'' of nanotube behavior beyond Hooke's law.
- R Saito
- G Dresselhaus
- M S Dresselhaus
Saito, R., Dresselhaus, G., and Dresselhaus, M. S., 1998, Physical Properties
of Carbon Nanotubes, Imperial College Press, London.
Single-Walled Nanotube-Polymer Composites: Strength and Weaknesses
- P M Ajayan
- L S Schadler
- C Giannaris
- A Rubio