Wavy Carbon Nanotubes Research Articles

3D micromechanics assisted finite element approach for bending analysis of straight/wavy CNT-reinforced multi-scale hybrid composite plate

This study examines the micromechanical and structural behavior of straight and wavy carbon nanotube (CNT) reinforced multi-scale fiber-reinforced hybrid composite (MFRHC) plates. An important feature of MFRHC is the incorporation of nano-scale CNTs into two-phase carbon fiber-reinforced composites (CFRC), enhancing their micromechanical and macroscopic properties, particularly the bending and stress behaviors. In CNT fiber-reinforced composites, the fiber waviness can arise from manufacturing imperfections which demands in-depth analysis of MFRHC plates reinforced with both straight or wavy CNTs to characterize their relative influences. In this work, the CNTs are assumed to be continuous and distributed uniformly within the CFRC, and the waviness is considered to be sinusoidal spanning both longitudinal and transverse planes. A mathematical formulation is devised, based on a three-dimensional mechanics of materials (MOM) model, to analyze the micromechanical behavior of the hybrid composite and the model’s accuracy are compared with the multi-inclusion Mori-Tanaka method and the Voigt/Reuss rule of mixtures. The MOM model indicates that the waviness pattern of the CNTs significantly influences the effective stiffness properties of MFRHC in comparison to that of the straight CNTs. Following this, a finite element model is constructed to investigate the bending deflection and stress properties of a simply-supported symmetric cross-ply (0/90/0) MFRHC laminate under sinusoidal transverse loading, utilizing first-order shear deformation theory (FSDT). The results suggest that the bending deflection decreases for the MFRHC laminate when the waviness factor ( Ψ ) is ≤ 0.05 , but increases when Ψ > 0.05 . Finally, the bending stress behavior is examined for both straight and wavy CNT-reinforced MFRHC laminates considering their geometrical parameters ( a / h , z / h ), and the CNTs’ waviness factor ( Ψ ), respectively.

Combined analytical and numerical modelling of the electrical conductivity of 3D printed carbon nanotube-cementitious nanocomposites

This study explores the electrical properties of 3D-printed carbon nanotube (CNT)-cementitious nanocomposites using a dual modelling approach that integrates micromechanics with finite element (FE) analysis for self-sensing applications. 3D-printed cementitious structures are prone to early crack formation, and incorporating CNTs enhances the material’s electrical conductivity, enabling a built-in health monitoring system. Given the critical impact of CNT dispersion, waviness, and orientation on the electrical conductivity, a theoretical model was developed to incorporate these factors. Experimental tests were conducted to evaluate the material’s conductivity and mechanical performance, and to validate the model. The results show that CNTs align with the printing direction at a 3D-printed layer’s surface, while maintaining isotropic behaviour at the core. Additionally, although the CNTs aggregate, they do not entangle with each other, instead creating conductive networks within the bundles. Moreover, the CNTs are not straight but wavy, which affects the material’s electrical conductivity. Based on the experimental results and the analytical model, a finite element model was developed to predict the conductivity of printed layers, accounting for varying CNT orientations throughout the layer. The results indicate that the model overestimates 3D-printed materials’ conductivity, suggesting that further studies are needed to account for interlayer effects on the measurements.

Active damping of multiscale composite shells using Sinus theory incorporated with Murakami’s zig-zag function

This article is divided into two main sections, the focus of the first is to develop a finite element model using the in-house MATLAB codes, implementing the sinusoidal shear deformation theory incorporating Murakami’s zig-zag function to encounter the inherent zig-zag effects of the laminated structures. The focus of the second is to investigate the active damping behavior of laminated multiscale hybrid fiber-reinforced composite (HFRC) smart shells via active constrained layer damping (ACLD) treatment using the proposed theory. The ACLD treatment layers comprise a constrained layer of viscoelastic material and an advance constraining layer of 1–3 piezoelectric composite material with vertically/obliquely oriented piezo-fibers, responsible for the active control. The computed numerical results of the laminated HFRC shell are analyzed and compared with the laminated base composite shell for symmetric/anti-symmetric cross-ply and anti-symmetric angle-ply. Moreover, we investigated the effect of carbon nanotube waviness and piezo-fibers orientation on the damping performance of the laminated HFRC/ACLD smart shell system. The analysis shows that the damping behavior of laminated HFRC shells improved due to the waviness of carbon nanotubes and that the orientation of piezo-fibers greatly influenced the effectiveness of the ACLD treatment patches. The proposed laminated multiscale HFRC/ACLD shell system with straight and wavy carbon nanotubes can be extensively used in structural health monitoring applications to actively control the mechanical vibrations induced in structures.

Finite element modeling of the effective creep compliance of carbon nanotube-polymer nanocomposites: A critical microstructure-level investigation

A micromechanical model implemented with the finite element method (FEM) using the representative volume element (RVE) approach is developed to investigate the creep compliance behavior of carbon nanotube (CNT)-polymer nanocomposites. Effects of the CNT waviness, orientation, volume fraction and aspect ratio on the creep compliance of the nanocomposite are examined. Contribution of the interphase region formed due to the interaction between CNTs and matrix to the nanocomposite creep behavior is considered. The nanocomposite creep behavior is affiliate on the waviness and orientation of CNTs. Increasing the volume fraction and length of CNT and interphase thickness improves the nanocomposite creep performance.

Application of DQHFEM for free and forced vibration, energy absorption, and post-buckling analysis of a hybrid nanocomposite viscoelastic rhombic plate assuming CNTs’ waviness and agglomeration

Vibrations and stability responses are two mechanical characteristics of engineering materials that are highly important for designing new engineering structures. This numerical research deals with investigating the effects of reinforcing a hybrid nanocomposite viscoelastic rhombic plate with Carbon Nano-Tubes (CNTs) and Carbon Fibers (CFs) on the post-buckling behavior, free and forced vibration as well as energy absorption characteristics. The structure is located on a viscoelastic torsional fractional substrate. In addition, the influence of random distribution, waviness, and agglomeration of CNTs is analyzed using the Halpin-Tsai theory. The structural damping is based on the Kelvin-Voigt method and the structure model is created according to the first-order shear deformation theory. Four types of boundary conditions such as fixed, simply, and free-supported are considered for the structure model. To solve the governing equations, a novel approach known as the Differential Quadrature Hierarchical Finite Element Method (DQHFEM) is applied. The numerical achievements revealed that by reducing the skewness angle to 30°, decreasing the aspect ratio to 1, and increasing the CNTs weight percentage up to 0.4, dimensionless frequency improved by 101%. Application of FFFF boundary conditions has dramatically effect since the amplitudes of the dynamic deflection sharply raised (about 91.78% higher than CCCC rhombic plate) and led to deteriorated energy absorption. The dynamic deflection of the structure is increased by nearly 29.36% when both waviness and random distribution (agglomeration) parameters are considered for CNTs. Besides, the random distribution factor is more effective than waviness on post-buckling behavior, energy absorption, and stability of the rhombic plate. It is also worth mentioning that the weight percent of the CNTs affects the number of oscillations and changes the vibration pattern so that with increasing the CNTs content, the number of oscillations is enhanced.

Electrical Conductivity Modeling and Fabrication of Carbon Nanotubes/Silicone Rubber Composites for High Voltage Insulators in Regions With a Polluted Atmosphere

The condensation mechanism of the insulators’ surface, increase the surface electrical conductivity. The electrical conductivity of the insulator creates a high level of leakage current and causes the failure. Difference between the dew point and the surface temperature of the insulator which occur due to radiative cooling mechanism, is the major reason of the moisture condensation on the polluted insulator surface. To compensate for the temperature difference, carbon nanotubes (CNTs) are being added to the silicone rubber housing material. The main idea of this research is based on generating joule heating by reducing the surface resistance of high voltage insulators. For this purpose, a developed model based on Halpin–Tsai formulation for tensile modulus of nanocomposites is joined with the conventional power-law model for the effective electrical conductivity of silicone rubber matrix carbon nanotube composite (SMCNT). SMCNT samples are prepared with the addition of various CNT volume fractions to high temperature vulcanizing (HTV) silicone rubber by melt-blending method. The developed model reveals that the high fraction of thinner and longer CNT, thicker interphase, higher concentration of percolated CNT, lower waviness of CNT, and higher conductivity of CNT can make a higher effective conductivity for SMCNT.

Modelling the effects of carbon nanotube length non-uniformity and waviness on the electrical behavior of polymer composites

Carbon nanotube (CNT) length non-uniformity and waviness exist inevitably in practical CNT/polymer composites (CPCs) and are two major factors that have significant influences on the composite electrical behavior. However, these two factors have been rarely considered simultaneously in previous modellings. In this study, a numerical model is presented to predict the electrical behavior of CPCs by simultaneously taking into account the two factors besides other ones considered in existing modellings. The length non-uniformity of CNTs is represented by the Weibull distribution and each wavy CNT is modeled by a piecewise sequence of several line segments. Besides, the tunneling distance is reasonably defined to calculate the tunneling resistance between adjacent CNTs. The prediction results reveal that both the CNT length non-uniformity and waviness have significant effects on the electrical behavior of CPCs. It is shown that the percolation threshold evidently decreases with either increasing the CNT length non-uniformity or decreasing the CNT waviness degree. Furthermore, the predictions agree well with existing experimental data, indicating the validity of the present numerical model in predicting the electrical conductivity of CPCs. In particular, it should be emphasized that compared with the previous models without simultaneously considering the effects of these two factors, the present model provides better predictions of the electrical behavior of CPCs.

Energy dissipation of CFRP composites coated by wavy CNT with focus on the CNT maximum reachable volume fraction

Dynamic moduli and energy dissipation capability of polymer hybrid nanocomposite reinforced with carbon fiber (CF) coated by carbon nanotube (CNT) which makes a fuzzy fiber nanocomposite (FFNC) are estimated through a micromechanical model. An analytical expression is derived to extract the damping properties in the frequency domain. Then, a separate phase known as interphase whose properties vary gradually is taken into account to model the CNT/polymer interactions. The CNT waviness and random orientation are also included. Acceptable agreements in comparison with the molecular dynamics simulations and experiments prove the accuracy of the proposed model. Moreover, the maximum reachable volume fraction of CNTs is studied considering the radius of gyration of polymer chain, the CNT aspect ratio (CNTAR), radius, and waviness amplitude. The effects of the CNT inter-tube distance (CNTID), waviness, CNTAR, and the loading frequency are examined on the energy dissipation and storage capability, and hysteresis loop of FFNC. It is found that the FFNC effective dynamic moduli enhance by increasing the CNTAR, while the CNTAR becomes less influential as the CNTID increases. Furthermore, as the frequency increases, the area of the hysteresis loop is decreased. Whereas the hysteresis loop is converted to a straight line beyond the frequency of about 1e17 Hz.

Effect of orientation of CNTs and piezoelectric fibers on the damping performance of multiscale composite plate

The present work deals with the study of active constrained layer damping treatment of multiscale carbon nanotube-based hybrid carbon fiber-reinforced composite plates. The distinctive feature of novel multiscale hybrid carbon fiber-reinforced composites is that the wavy/straight carbon nanotubes are distributed uniformly in the matrix phase of hybrid carbon fiber-reinforced composites, and the waviness of carbon nanotubes is considered to be coplanar with two mutually orthogonal planes. Firstly, the effective elastic properties of hybrid carbon fiber-reinforced composites are estimated using the Mori-Tanaka method. The outcomes of the Mori-Tanaka method suggest that the transverse effective elastic properties of hybrid carbon fiber-reinforced composites containing wavy carbon nanotubes are better than those of hybrid carbon fiber-reinforced composites with straight carbon nanotubes. Secondly, a finite element model using the layer-wise first-order shear deformation theory is developed to study the damping performance of hybrid carbon fiber-reinforced composite plates integrated with the active constrained layer damping treatment. The constraining layer of active constrained layer damping treatment is a 1–3 piezoelectric composite layer with vertically/obliquely-oriented piezo-fibers. The piezo-fibers make an angle [Formula: see text] with the vertical plane of a layer coplanar with the xz- or yz-plane. The effect of the orientation of piezo-fibers angle on the control authority of active constrained layer damping treatment patches is investigated. Our results reveal that the performance of multiscale hybrid carbon fiber-reinforced composite plates has improved due to the incorporation of wavy carbon nanotubes, and the orientation angle of piezo-fibers has a major impact on the control authority of active constrained layer damping patches. The proposed multiscale composite with the combination of wavy carbon nanotubes and active constrained layer damping patches can be actively used in the aerospace and transport industries to control the mechanical vibrations of structures.

Finite element predictions on vibrations of laminated composite plates incorporating the random orientation, agglomeration, and waviness of carbon nanotubes

Finite element predictions on vibrations of laminated composite plates incorporating the random orientation, agglomeration, and waviness of carbon nanotubes

Microstructure-sensitive investigation on the mechanical behavior of CNT-reinforced composites considering debonding damage based on cohesive finite element method

In this paper, an analytical modeling and numerical approach based on the finite element (FE) method are introduced to study the influence of the real morphology (e.g., length and waviness) and distribution of carbon nanotubes (CNTs) on the mechanical behavior of the CNT-reinforced composites. The analytical model has considered the real morphology effect using the equivalent curved CNTs with perfect bonding. The equivalent chord length, diameter, and waviness have been computed using the abundance of different values of measured parameters in an actual microstructure of the CNTs in the matrix. In the FE method, a computational tool is used to map an actual composite microstructure onto a FE representative volume element (RVE) with the exact shape, size, distribution, and waviness of CNTs. FE analysis has been carried out in both well-bonded and interface-debonding conditions. The cohesive zone model (CZM) with bilinear traction-separation law for both opening and sliding modes has been utilized to capture the debonding at the CNT-matrix interface. Results indicate that in the presence of weak bonding, CNT waviness can enhance the composite stiffness rather than reduce it. A quite different conclusion to what can be obtained with the assumption of perfect adhesion. In the presence of poor bonding, the curvature has a positive effect on composite properties and improves the load transferring from the matrix. FE analysis for different RVEs highlights that the curvature and length of the CNTs are essential features of the microstructure, and they can effectively influence the mechanical properties of the material. Results demonstrate that the equivalent curved CNTs cannot appropriately represent the real microstructure.

Effects of polymer’s viscoelastic properties and curved shape of the CNTs on the dynamic response of hybrid nanocomposite beams

Carbon nanotube (CNT)-reinforced polymer nanocomposites have excellent stiffness, strength and viscoelastic nature due to the time-dependent properties of the polymers. Hence, adequate knowledge about their rheological behavior is required to use such nanomaterials in designing aerospace structures. The present paper gives an account of the time dependency of the polymer and curvy shape of the CNTs while tracking the vibrational responses of multiscale hybrid nanocomposites. A combination of the modified Halpin–Tsai model and mixture’s rule is used for the homogenization process. According to the dynamic form of the virtual work’s principle, the governing equations will be attained based on a refined shear deformable beam theorem. In addition, Galerkin’s analytical solution is implemented to extract the system’s natural frequency for supported and clamped beams. The findings of this paper indicate that vibration suppression in the nanocomposite structures can be delayed if a high value is assigned to the polymer’s relaxation time. Besides, it is illustrated that hybrid nanocomposites consisting of wavy CNTs cannot provide ideal frequencies related to the nanocomposites manufactured from straight CNTs.

3D waviness effect of carbon nanotubes on fundamental natural frequency and modeling of resonance of nanocomposite structure

Optimum waviness of carbon nanotubes (CNTs) inside a matrix composite beam and composite bridge is endeavor to obtain its utmost natural frequencies considering a volume fraction of CNTs. 3D FE model of the beam is generated via ABAQUS along with Python programming and thereafter to calculate an optimal waviness under encastre boundary conditions and different vibration modes. The effect of waviness and the number of waves on mode shapes, natural frequency, and corresponding stiffness of a beam are examined, and the outcomes are compared to those of a pure polymer beam, straight CNT-based composite beam and nanobridge value. It was decided to conduct a convergence analysis and the optimum value of the number of elements and nodes was studied and found that 19666 nodes are reliable to give correct results. The FE analysis results reveal that the waviness effect of CNTs significantly depends on mode shapes. The fundamental natural frequency, as well as other related vibrational properties, is observed to be enhanced. By decreasing the waviness from 50 to 25, there is an increment in natural frequency in the 3rd mode by 68.68, 5th mode by 44.6 and 6th mode by 62.4, but in other modes, there is negligible difference. When single-wave CNTs were compared, the sine wave produced more frequency in the third mode by 206.03, 4th mode by 199.8 and 6th mode by 478.6 Hz. After comparing the results of different waviness types, single sine waviness, multi-waved CNTs, straight CNTs and neat matrix, it is found that for the highest value of waviness of CNT fiber-based nanocomposites, the natural frequency of CNT-reinforced nanocomposite reaches the frequency of the neat matrix and further adding of CNTs does not increase the value of frequency. The result showed that the finite element model (FEM) is a good simulation of the vibratory system.

Aerodynamic Analysis of Temperature-Dependent FG-WCNTRC Nanoplates under a Moving Nanoparticle using Meshfree Finite Volume Method

Transporting of nanomachines using the nanoplates has been acknowledged as an emerging frontier of nanotechnology over recent years. This paper investigates the aerodynamic response of a temperature-dependent functionally-graded composite nanoplate reinforced by wavy carbon nanotubes (FG-WCNTRC nanoplate) under a nanoparticle moving in a straight path exposed by air drag. The meshfree finite volume (MFV) approach is implemented to develop the governing equations based on the Mindlin's plate and Eringen's non-local theories. Therefore, one uniform distribution and three linear distributions of wavy CNTs are considered through the thickness of the FG composite nanoplate. Moreover, a generalized rule of mixtures is employed to predict the mechanical properties of the nanoplate. In this sense, the material properties of the matrix and wavy CNTs are presumed to depend on temperature. A comprehensive investigation is then carried out for the first time to assess the effects of nanoplate elastic foundation coefficients, nanoparticle velocity, temperature dependency of material, volume fraction, waviness, distribution pattern, and orientation of the wavy CNTs on the amount of air drag effect. It is revealed that in the aerodynamic response of temperature-dependent FG-WCNTRC nanoplates under a moving nanoparticle, the air drag amount can be influenced considerably by the material properties of the nanoplate.

Elastic properties of cement-based composites reinforced by nano-tailored hybrid fiber

The elastic properties of cementitious composites reinforced by nano-tailored hybrid fibers are analyzed using a micromechanical method. The microstructural feature of the hybrid fiber is that uniformly aligned carbon nanotubes (CNTs) are grown radially on the circumferential surface of carbon fibers (CFs). The CNT waviness and CNT/cement interfacial region are considered. The predictions are compared with experiments, which guarantee the validity of the model. The mechanical properties of cementitious composites, especially in transverse direction, are enhanced due to the radial growth of CNTs on the CFs. The CNT/cement interfacial zone may have a significant effect on the elastic behavior of the nano-tailored hybrid fiber-cement composites. As the mechanical properties of interphase are higher than those of the cement matrix, increasing the interphase thickness causes an improvement in the elastic and shear moduli. The CNT non-straight shape decreases the transverse elastic modulus.

Effect of viscoelastic properties of polymer and wavy shape of the CNTs on the vibrational behaviors of CNT/glass fiber/polymer plates

Carbon nanotube (CNT)-reinforced polymer nanocomposites possess marvelous stiffness and strength as well as viscoelastic nature due to the time-dependent properties of the polymers. Hence, adequate knowledge about their rheological behavior is required if it is aimed at using such nanomaterials in design of aerospace structures. Present manuscript is arranged to account for the time-dependency of the polymer as well as wavy shape of the CNTs while tracking the vibrational responses of multi-scale hybrid nanocomposites for the first time. To this purpose, a mixture of the modified Halpin–Tsai model and mixture’s rule is used for the homogenization process. According to the dynamic form of the virtual work’s principle, the governing equations of the problem will be attained based on a higher-order shear deformable plate theorem to consider for thick structures. In addition, the Navier’s analytical solution is implemented to extract the system’s natural frequency for simply-supported plates. The findings of this paper indicate on the fact that the vibration suppression in the nanocomposite structures can be delayed if a high value is assigned to the characteristic relaxation time of the polymer. Besides, it is illustrated that hybrid nanocomposites consisted of wavy CNTs (i.e., corresponding with more realistic case) cannot provide ideal frequencies related to the nanocomposites manufactured from straight CNTs.

Conditions for Obtaining High-Modulus Polymer/Carbon Nanotube Nanocomposites

We consider physical foundations for the realization of high-modulus and high-strength polymer/carbon nanotube nanocomposites with mechanical characteristics comparable with those for steel. We have determined two main factors that make it possible to obtain such nanocomposites, i.e., the structure of the nanofiller in the polymer matrix and a quite high concentration of the nanofiller. The fractal dimension of such a structure must be close to that of the surrounding Euclidian space (i.e., 3). It is shown that additional stretching of the nanocomposite gives two positive effects: the reduction of waviness of carbon nanotubes and the increase of the elastic modulus of the polymer matrix due to alignment of its macromolecules.

A new analytical model for predicting the electrical conductivity of carbon nanotube nanocomposites

In predicting the electrical conductivity (EC) of carbon nanotube (CNT)/polymer nanocomposites (CPCs), previous analytical models did not simultaneously consider the effects of CNT waviness and dispersion state, which exist inevitably for real CPCs. In this work, an effective and comprehensive analytical model is developed to predict the percolation threshold and the EC of CPCs by taking into account the effects of CNT waviness and dispersion, etc. A detailed investigation of the effects of CNT content, conductivity, size, waviness and dispersion is conducted on the EC of CPCs. In particular, it is shown that both CNT waviness and dispersion play significant roles in determining the composite EC. Moreover, the predicted results agree well with the existing experimental results and display a higher prediction accuracy compared with the previous typical models for predicting the composite EC. Analytical results indicate that a high EC can be achieved for CPCs with CNTs of a high conductivity, a large aspect ratio (AR), a perfect dispersion state and a low degree of waviness.

Условия получения высокомодульных нанокомпозитов полимер/углеродные нанотрубки

The physical basis of realization of high-modulus and high-strength nanocomposites polymer/carbon nanotube, having mechanical characteristics comparable with the same ones for steel, were considered. Two main factors, allowing to create such nanocomposites, were defined – the structure of nanofiller in polymer matrix and large enough content of nanofiller. The indicated structure fractal dimension should be close to dimension of surrounding Euclidean space, i.e. three one. Besides, elastic modulus of nanofiller depends on stiffness of polymer matrix. Therefore additional drawing of nanocomposite gives two positive effects: reduction of waviness of carbon nanotubes and enhancement of elastic modulus of polymer matrix owing to orientation of its macromolecules.

Three-Dimensional Stochastic Modelling of Wavy Carbon Nanotube Reinforced Epoxy Nanocomposites

Carbon nanotubes (CNTs) are frequently used as the nanoscale filler materials. It has been observed that when they are added to the polymer matrix by a small fraction, they are able to form a strong yet light-weight multifunctional composite materials. Previous studies found these properties to be significantly influenced by the morphology of CNTs embedded in the matrix. In general, long CNTs become wavy and randomly oriented when dispersed in the matrix material. Collectively, they form an interconnected network. Over the past several decades, many theoretical and computational studies have been carried out to capture the mechanics of CNT-reinforced nanocomposites. In most of these models, CNTs are modeled as straight fibers. In addition, a perfect interphase between CNT and epoxy is generally assumed. As such, these models may not capture the realistic morphology of CNT reinforced composites. In the current study, we have developed a method to construct stochastic three-dimensional finite element models of wavy CNT reinforced epoxy nanocomposites. Both aligned type and randomly distributed type are considered. Uniform random distributions are assumed for both waviness and orientation angles of the dispersed CNTs. To study the effect of waviness on the elastic properties, finite element models with maximum CNT waviness angles of 0° (straight), 10° , 20° , and 30° are generated for CNT volume fractions ranging from 0.1 to 1%. A significant decrease in the properties is observed as the maximum allowable waviness angle (θmax) of the embedded CNTs in the epoxy is increased. The obtained values are compared with the theoretical models available in the literature. The three-phase model including CNTs, CNT/epoxy interphase and matrix is also studied to evaluate the effect of ‘soft’ (Ei = 10–75% Em) as well as ‘hard’ interphase (Ei = 110–175% Em) on the composite modulus. These results suggest that due to ineffective load transfer between CNT and epoxy in the presence of CNT waviness, the elastic modulus of the CNT composites is compromised by 4–8%. The modulus is further decreased by nearly 2.5% as the CNT/epoxy interphase modulus decreases by 90%. The ‘hard’ interphase model confirms an efficient load transfer from matrix to CNT fibers, leading to the increase in composite stiffness. It is found that the composite modulus is more sensitive to the ‘soft’ interphase.