Effects Of Carbon Nanotube Volume Fraction Research Articles

Bending analysis of carbon nanotube coated–fiber multi-scale composite beams using the refined zigzag theory

The present work aims to investigate the bending analysis of sandwich and laminated carbon nanotube coated–fiber multi-scale composite (CFMC) beams employing the Refined Zigzag Theory (RZT). The model encompasses core fiber, surrounding carbon nanotube (CNT) coating region, and polymer matrix covering all scales from nano to macro-scale. Hierarchical multi-scale modeling is utilized where information is only transmitted from the fine-scale to the next coarser scale. The CNT coating region (CCR) consists of CNT, matrix, and non-bonded interphase whose mechanical properties are determined employing the Eshelby–Mori–Tanaka method and the equivalent continuum fiber approach. Considering different configurations of grown CNTs around the core fiber, two CCRs are constructed, comprising axially aligned (ACCR) and randomly oriented CCRs (RNCCR). The mechanical properties of the core fiber coated with the surrounding CCR are then obtained through the composite cylinder assemblage (CCA) method. Consequently, four RZT kinematic variables are acquired for the CFMC beams, and the effects of CNT volume fraction, coating thickness, and coating types are thoroughly investigated for various laminated and sandwich beams. The results reveal a substantial reduction in the maximum transverse displacements of the CFMC beams compared to the conventional composite beams, considering the low volume fraction of the CNTs in the coating region. Moreover, by employing a combination of ACCR and RNCCR for the layers in the sandwich CFMC beams, a pronounced decline in the transverse shear stress of the core medium is demonstrated, which can postpone the core shear failure in the sandwich structures. A great agreement is observed between the obtained results and the outcomes predicted by finite element analysis.

Molecular dynamics simulation for interfacial properties of carbon nanotube reinforced aluminum composites

A molecular dynamics (MD) simulation method has been used to predict the interfacial behavior of single-wall carbon nanotube (CNT) reinforced aluminum (Al) composites. At the interface of the CNT and the Al, only van der Waals interaction was considered. The effect of CNT volume fraction and chirality on CNT pull-out has been studied for the first time with a proper distinction between them. The length of all the CNTs was kept constant throughout the study. The approach used in this work was validated with an earlier study. The present study revealed that the average pull-out load was found proportional to both the CNT volume fraction as well as the diameter. The smaller diameter CNTs improved the interfacial shear strength (ISS) at lower volume fraction significantly in comparison to that of the larger diameter CNTs. The highest improvement of 38.7% was observed in the ISS during pull-out of (6, 6) CNT at a CNT volume fraction of 3.17%. The average energy increment was found to be increasing with CNT volume fraction and was higher for larger diameter CNTs.

A molecular dynamics investigation for predicting the effect of various parameters on the mechanical properties of carbon nanotube-reinforced aluminum nanocomposites.

Carbon nanotube (CNT)-reinforced aluminum (Al) composites are being developed to replace the conventional materials due to the enhanced stiffness for more cost-effective engineering applications. In the present study, a qualitative analysis has been conducted on carbon nanotube aluminum (CNT-Al) composites to predict the effect of CNT volume fraction, diameter, and structure (zigzag, armchair) on elastic modulus, shear modulus, bulk modulus, and ultimate tensile strength (UTS) through molecular dynamics simulation. This study shows that the elastic modulus was improved by 105% compared with pure Al, for the CNT-Al composite reinforced with the (4, 4) armchair SWCNT at a volume fraction of 8.79%. The highest value of Young's modulus of 130.37GPa occurred at the volume fraction of 11.75% for zigzag SWCNT. The CNT-Al composites showed better UTS for the Al matrix reinforced with larger diameter CNT. An enhancement of 31.65% was observed in the UTS of CNT-Al composite from 4.74 to 6.24GPa with (6, 6) CNT at 0.51% volume fraction. Elastic and bulk moduli were found to improve with a higher volume fraction of CNTs. The CNT-Al composite reinforced with smaller diameter CNT's have better elastic modulus than those reinforced with larger diameter CNT for the same volume fraction. Graphical abstract Variation of Young's modulus with SWCNT volume fraction for a constant cell size of CNT-Al composite.

Thermal and thermomechanical buckling of shear deformable FG-CNTRC cylindrical shells and toroidal shell segments with tangentially restrained edges

This paper presents a simple and effective analytical approach to investigate buckling behavior of carbon nanotube-reinforced composite (CNTRC) cylindrical shells and toroidal shell segments surrounded by elastic media and subjected to elevated temperature, lateral pressure and thermomechanical load. The properties of constituents are assumed to be temperature-dependent, and effective properties of CNTRC are estimated according to extended rule of mixture. Carbon nanotubes (CNTs) are reinforced into matrix material such in a way that their volume fraction is varied in the thickness direction according to functional rules. Formulations are established within the framework of first-order shear deformation theory taking surrounding elastic media and tangential elasticity of edges into consideration. The solutions of deflection and stress function are assumed to satisfy simply supported boundary conditions, and Galerkin method is used to derive expressions of buckling loads. In thermal buckling analysis, an iteration algorithm is employed to evaluate critical temperatures. The effects of CNT volume fraction and distribution patterns, degree of in-plane edge constraints, geometrical parameters, preexisting loads and surrounding elastic foundations on the critical loads of nanocomposite shells are analyzed through a variety of numerical examples.

Shear buckling analysis of functionally graded (FG) carbon nanotube reinforced skew plates with different boundary conditions

In this paper, a four-nodded straight-sided geometric element is proposed for shear buckling problem of functionally graded material (FGM) composite and carbon nanotube (CNT) reinforced composite skew plate. By using the transformation rule, quadrilateral plate field is mapped into a square domain in the computational space using discrete singular convolution (DSC) method. Related governing equations of skew plate buckling and boundary conditions of the problem are transformed from the physical domain into a square computational domain by using the geometric transformation based singular convolution. The discretization process is achieved via the DSC method together with numerical differential and two-different regularized kernel such as regularized Shannon's delta (RSD) and Lagrange delta sequence (LDS) kernels. The accuracy of the present DSC results is first verified via exiting results in literature. Then, some parametric studies have been presented to show the effects of CNT volume fraction, CNT distribution pattern, geometry of skew plate and skew angle on the shear buckling responses of FG-CNTR composite skew plates with different boundary conditions. Some new results related to critical buckling of FGM and CNT reinforced composite skew plate have been presented which can serve as benchmark solutions for future investigations.

Nonlinear buckling of orthogonal carbon nanotube-reinforced composite cylindrical shells under axial compression surrounded by elastic foundation in thermal environment

Nonlinear buckling and postbuckling of orthogonal carbon nanotube-reinforced composite (Orthogonal CNTRC) cylindrical shells subjected to axial compression in thermal environments surrounded by elastic foundation are presented in this paper. Two layers of shell are reinforced by carbon nanotube (CNT) in two orthogonal directions (longitudinal and circumferential directions). Based on Donnell’s shell theory with von Karman’s nonlinearity and the Galerkin method, the governing equations are established to obtain the critical buckling loads and postbuckling load-deflection curves. The large effects of CNT volume fraction, temperature change, elastic foundation and geometrical parameters of cylindrical shells on the buckling load and postbuckling behavior of Orthogonal CNTRC cylindrical shells are obtained.

Compressive instability of open section nanocomposite struts using a layerwise theory

The application of carbon nanotubes (CNTs) to improve postbuckling characteristics of T-section nanocomposite strut is the subject of this research. A solution procedure according to the layerwise theory along with the first-order shear deformation theory (FSDT) by taking into account the von Karman geometrical nonlinearity is proposed. Nonlinear governing equations are developed in regard to the minimum total potential energy principle, and solved by the aid of the Rayleigh–Ritz method in conjunction with Newton–Raphson method. A comprehensive parametric study is conducted to provide an insight into effects of CNT volume fraction and dispersion, geometrical parameters and boundary conditions on the bifurcation points and paths, in-plane displacement, normal stress and strain, and bending moment of T-section nanocomposite struts. A three dimensional finite element analysis using the ABAQUS commercial software is carried out to verify the obtained results, which shows close agreement. Results indicate that dispersion of CNTs plays a dominant role in bifurcation behavior of nanocomposite struts. The results also show that volume fraction of CNTs has a significant effect on the load-carrying capacity of open section nanocomposite struts. The results of this research shed light into using ultra-high-strength and light-weight open section nanocomposite struts for civil and aerospace applications.

Thermal postbuckling behavior of CNT-reinforced composite sandwich plate models resting on elastic foundations with tangentially restrained edges and temperature-dependent properties

Buckling and postbuckling behaviors of sandwich plates reinforced by single-walled carbon nanotube (CNT), rested on elastic foundations and subjected to uniform temperature rise, are investigated in this article. CNT is embedded into matrix phase through uniform or functionally graded distributions. The properties of constituent materials are assumed to be temperature-dependent, and effective properties of nanocomposite are determined by extended rule of mixture. Two models of sandwich plates with face sheets and core layer reinforced by CNTs are presented. Formulations are based on the first-order shear deformation theory taking geometrical nonlinearity, initial geometrical imperfection, plate-foundation interaction, and elasticity of tangential edge constraints into consideration. Analytical solutions of deflection and stress function are assumed, and Galerkin method is applied to derive nonlinear temperature–deflection relation from which buckling temperatures and thermal postbuckling paths are obtained through an iteration algorithm. Numerical examples show the effects of CNT volume fraction, distribution patterns, in-plane edge constraint, elastic foundations, geometrical ratios, initial imperfection, and temperature dependence of properties on thermal postbuckling behavior of nanocomposite sandwich plates. The most important finding is that sandwich plate constructed from CNT-poor nanocomposite core layer and thin homogeneous face sheets with partially movable edges bring the best capacities of thermal buckling resistance and postbuckling load carrying.

Bending Behavior of Sandwich Plates with Aggregated CNT-Reinforced Face Sheets

The main aim of this paper is to investigate bending behavior in sandwich plates with functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets with considering the effects of carbon nanotube (CNT) aggregation. The sandwich plates are assumed resting on Winkler-Pasternak elastic foundation and a mesh-free method based on first order shear deformation theory (FSDT) is developed to analyze the deflection of sandwich plates. In the face sheets, volume fraction of CNTs and their clusters are considered to be changed along the thickness. To estimate the material properties of the nanocomposite, Eshelby-Mori-Tanaka approach is applied. In the mesh-free analysis, moving least squares (MLS) shape functions are employed to approximate the displacement field and transformation method is used for imposition of essential boundary conditions. The effects of CNT volume fraction, distribution and degree of aggregation, and also boundary conditions and geometric dimensions are investigated on the bending behavior of the sandwich plates. It is observed that in the same value of cluster volume, FG distribution of clusters leads to less deflection in these structures.

Buckling and postbuckling of axially-loaded CNT-reinforced composite cylindrical shell surrounded by an elastic medium in thermal environment

Buckling and postbuckling behaviors of nanocomposite cylindrical shells reinforced by single walled carbon nanotubes (SWCNTs), surrounded by an elastic medium, exposed to a thermal environment and subjected to uniform axial compression are investigated in this paper. Material properties of carbon nanotubes (CNTs) and isotropic matrix are assumed to be temperature dependent, and effective properties of nanocomposite are estimated by extended rule of mixture. The CNTs are embedded into matrix via uniform distribution (UD) or functionally graded (FG) distribution along the thickness direction. Governing equations are based on Donnell’s classical shell theory taking into account von Karman-Donnell nonlinear terms and interaction between the shell and surrounding elastic medium. Three-term form of deflection and stress function are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain load-deflection relation from which buckling and postbuckling behaviors are analyzed. Numerical examples are carried out to analyze the effects of CNT volume fraction and distribution types, geometrical ratios, environment temperature and surrounding elastic foundation on the buckling loads and postbuckling strength of CNTRC cylindrical shells.

Creep performance of CNT polymer nanocomposites -An emphasis on viscoelastic interphase and CNT agglomeration

The present work is aimed at presenting a multi-stage hierarchical micromechanical model to investigate creep response of polymer nanocomposites containing randomly dispersed carbon nanotubes (CNTs). Two frequently real situations-encountered fundamental aspects affecting the polymer nanocomposite mechanical behavior including the CNT/polymer interphase region and CNT agglomeration are taken into account. It is assumed that the CNT to be a transversely isotropic material and the polymer matrix obeys a viscoelastic constitutive law. The multi-stage procedure homogenizes the nanocomposite by exploiting a unit cell-based micromechanical model coupled with Eshelby method. Generally, an excellent agreement is found between the results of the current model and available experiment. The outcomes clearly prove that for a more realistic prediction in the case of creep performance of CNT-polymer nanocomposites, considering the (i) random dispersion and (ii) transversely isotropic behavior of CNTs as well as (iii) viscoelastic interphase region is essential. Moreover, when CNTs are not well-dispersed into the polymer nanocomposites, the three significant factors together with the CNTs agglomerated state must be precisely incorporated in the analysis to achieve a more accurate estimation of the creep response. It is shown that the CNT agglomeration dramatically influences and degrades the creep resistance of the CNT-polymer nanocomposites. Also, the effects of CNT volume fraction and interphase characteristics on the nanocomposites creep behavior are extensively examined.

Wave propagation in piezoelectric cylindrical composite shells reinforced with angled and randomly oriented carbon nanotubes

Wave propagation behavior in piezoelectric cylindrical composite shells reinforced with angled and randomly oriented, straight carbon nanotubes (CNTs) is analytically investigated for the first time via the first-order shear deformation shell theory including the transverse shear effects and rotary inertia. The Mori-Tanaka method is used for micromechanical modeling. Dispersion solutions are computed by solving an eigenvalue problem. The effects of CNT orientation, CNT volume fraction, and shell geometry on the dispersion solutions are examined. Various orientations of CNTs lead to different dispersion behaviors; the variation of wave phase velocities is more significant at lower axial wave numbers; and the effects of CNT volume fraction and shell geometry on wave dispersion behaviors are more obvious at higher circumferential wave numbers. The presented model and analytical results of this study can be utilized in the wave propagation analysis of piezoelectric shells reinforced with CNTs for the design of new smart structures used in structural health monitoring and/or energy harvesting applications.

Nonlinear buckling of CNT-reinforced composite toroidal shell segment surrounded by an elastic medium and subjected to uniform external pressure

Buckling and postbuckling behaviors of Toroidal Shell Segment (TSS) reinforced by single-walled carbon nanotubes (SWCNT), surrounded by an elastic medium and subjected to uniform external pressure are investigated in this paper. Carbon nanotubes (CNTs) are reinforced into matrix phase by uniform distribution (UD) or functionally graded (FG) distribution along the thickness direction. Effective properties of carbon nanotube reinforced composite (CNTRC) are estimated by an extended rule of mixture through a micromechanical model. Governing equations for TSSs are based on the classical thin shell theory taking into account geometrical nonlinearity and surrounding elastic medium. Three-term solution of deflection and stress function are assumed to satisfy simply supported boundary condition, and Galerkin method is applied to obtain nonlinear load-deflection relation from which buckling loads and postbuckling equilibrium paths are determined. The effects of CNT volume fraction, distribution types, geometrical ratios and elastic foundation on the buckling and postbuckling behaviors of CNTRC TSSs are analyzed and discussed.

Postbuckling behavior of CNT-reinforced composite cylindrical shell surrounded by an elastic medium and subjected to combined mechanical loads in thermal environments

Cylindrical shells are usually buckled under complex and combined loading conditions. This article presents an analytical approach to investigate the buckling and postbuckling behaviors of cylindrical shells reinforced by single-walled carbon nanotubes, surrounded by an elastic medium, exposed to thermal environments, and subjected to combined axial compression and lateral pressure loads. Carbon nanotubes (CNTs) are imbedded into matrix phase by uniform distribution or functionally graded distribution along the thickness direction. The properties of constituents are assumed to be temperature dependent, and effective properties of CNT-reinforced composite (CNTRC) are determined by an extended rule of mixture. Governing equations are based on the classical shell theory (CST) taking von Karman–Donnell nonlinearity and surrounding elastic foundations into consideration. Three-term form of deflection is assumed to satisfy simply supported boundary conditions, and Galerkin method is applied to obtain nonlinear load–deflection relations from which buckling loads and postbuckling equilibrium paths are determined. Numerical examples are carried out to show the effects of CNT volume fraction, distribution types, thermal environments, preexisting nondestabilizing lateral pressure and axial compression loads, and elastic medium on the buckling and postbuckling behaviors of CNTRC cylindrical shells.

Vibration analysis of CNT-reinforced thick laminated composite plates based on Reddy’s higher-order shear deformation theory

In this paper, free vibration behavior of carbon nanotube (CNT) reinforced functionally graded thick laminated composite plates utilizing Reddy’s higher-order shear deformation theory (HSDT) is studied. To the best of authors’ knowledge, this paper is the first to incorporate HSDT with one of the element-free approaches to investigate this issue. The element-free IMLS-Ritz method is employed and four types of CNT distributions are considered. The resulting effective material properties of the CNT-reinforced composite are estimated by a detailed and straightforward Mori–Tanaka approach. The numerical results have been compared with the literature showing excellent agreement. Considering various CNT orientation angles, a parametric study showing the effects of CNT volume fraction, plate aspect ratio, plate width-to-thickness ratio and number of plate’s layers on the non-dimensional natural frequencies is investigated. Finally, the influence of boundary conditions on the sequence of the first six mode shapes for various lamination arrangements is presented.

Effect of CNT volume fraction on wear properties of hybrid CNT+SiCsf/AS52 Mg matrix composites

The effect of the carbon nanotube (CNT) volume fraction on the wear properties of hybrid Mg composites was investigated. The hybrid x vol% CNT + 15 vol% SiCsf-reinforced Mg–5Al–2Si alloy (AS52) matrix composites (x=0, 5 and 10 vol%) were fabricated in two steps involving preform fabrication and squeeze infiltration. The wear rate of the hybrid CNT+SiCsf/AS52 Mg metal matrix composites (MMCs) was evaluated using ballon-disk wear testing, and the roughness was measured using confocal laser 3D microscopy. Additionally, the worn surfaces were examined using high-resolution transmission electron microscopy. The adhesive wear and worn surface roughness of the hybrid CNT+SiCsf/AS52 Mg MMCs were reduced with increasing CNT addition. The CNTs hindered pull-out or cracking of the SiCsfs and matrix deformation. The wear resistance of the hybrid CNT+SiCsf/AS52 Mg MMCs was improved by the CNT additions, causing self-lubricant and strengthening effects compared with the single SiCsf/AS52 Mg MMCs.

Biaxial buckling analysis of functionally graded nanocomposite sandwich plates reinforced by aggregated carbon nanotube using improved high-order theory

In this work, biaxial buckling analysis of sandwich plates with symmetric composite laminated core and two functionally graded nanocomposite face sheets is carried out by a new improved high-order theory. The nanocomposite face sheets are carbon nanotube (CNT)-reinforced nanocomposites and the material properties of the nanocomposites plates are graded along the thickness and are estimated though the Mori–Tanaka approach. CNTs are assumed randomly oriented and aggregated into some clusters. The same third order theory is used for modeling of core and the faces sheets. The theory has third and second orders of z for in-plane and normal displacements, respectively. The principle of minimum potential energy is used to derive the equations of motion and boundary conditions. Analytical solution for static analysis of simply supported sandwich plates under biaxial in-plane compressive loads is presented using Navier’s solution. The effects of CNT volume fraction, CNT aggregation states, CNT distribution, biaxial loads ratio, and geometric dimensions of sandwich plate are investigated on the overall buckling of functionally graded carbon nanotube-reinforced nanocomposite sandwich plates.

Elastodynamic analysis of quadrilateral CNT-reinforced functionally graded composite plates using FSDT element-free method

An elastodynamic analysis of quadrilateral carbon nanotube (CNT) reinforced functionally graded composite plates subjected to a transverse sudden dynamic load is studied. Based on the first-order shear deformation theory (FSDT), the element-free IMLS-Ritz method is extended to conduct a numerical simulation for this study. A numerical time integration for the dynamic problems is performed using the Newmark-β method. To verify the stability and accuracy of the element-free IMLS-Ritz method, convergence studies are carried out for an isotropic square plate with different support sizes and different numbers of nodes. Detailed numerical simulations are further carried out to investigate the effect of CNT volume fraction, CNT distribution type, side angles, area of quadrilateral plate, plate width-to-thickness ratio and boundary condition on the dynamic behaviors of quadrilateral CNT reinforced composite plates.

Three-dimensional free vibration of carbon nanotube-reinforced composite plates with various boundary conditions using Ritz method

In this paper, three-dimensional free vibration of carbon nanotube (CNT) reinforced composite rectangular plates with various boundary conditions is analyzed by developing a set of orthogonal admissible functions used in Ritz method. To validate the present analysis, numerical results were compared with those obtained in the open literature. Furthermore, the effect of CNT volume fraction, two cases of CNT distribution, boundary conditions and aspect ratio of plate on non-dimensional natural frequencies were studied. Modified rule of mixture is used to find material constants of the reinforced composite. This benchmark solution can be used to assess the accuracy of conventional two-dimensional theory.

The effect of CNT volume fraction on the magneto-thermo-electro-mechanical behavior of smart nanocomposite cylinder

In this article, using analytical approach, the stress analysis of a long piezoelectric polymeric hollow cylinder reinforced with carbon nanotube (CNT) under combined magneto-thermo-electro-mechanical loading is investigated. Considering three combined loading conditions such as pressure-electric, pressure-electric magnetic and pressure-electric thermal, the governing equation of the problem is obtained. The rule of mixture and modified multiscale bridging model are used to predict effective properties of nanocomposite. The magneto-thermo-electro-mechanical stresses in hollow cylinder are discussed in detail. It can be concluded that increasing CNT volume fraction enhances strength of the nanocomposite cylinder. The results of this work could be useful in view of optimum design of the smart nanocomposite cylinder under magneto-thermo-electro-mechanical loadings and could also be as a reference for future related works.