Volume Fraction Of Carbon Nanotubes Research Articles

Nonlinear vibration of a nanocomposite laminated piezoelectric trapezoidal actuator in subsonic airflow under combined electrical and forcing excitations

The nonlinear dynamic and vibration behaviors of a cantilevered carbon nanotube-reinforced composite trapezoidal plate with two surface-bonded piezoelectric layers as an actuator in micro air vehicles are considered in this article. The plate is reinforced by single-walled carbon nanotubes and is exposed to subsonic airflow under combined parametric and external excitations. The large deflection von Karman plate assumptions and the classical laminated plate theory are applied to derive the governing equations of the motion of the piezoelectric nanocomposite laminated trapezoidal plate by using Hamilton's principle. The geometry of the trapezoidal plate is mapped into a rectangular computational domain. The Galerkin's approach is used for transforming the nonlinear partial differential equations of motion into nonlinear two-degrees-of-freedom ordinary differential equations of cubic nonlinearities. The case of 1:3 internal resonance and primary resonance is considered, and the multiple scales method is employed. The aerodynamic pressure distribution formula is modeled by linear potential flow theory. The frequency and time history responses and phase portrait in free forced vibrations are obtained to analyze the nonlinear dynamic behavior of the plate. The effects of different parameters such as the plate geometry, volume fraction of carbon nanotubes, and different excitations on the nonlinear vibration of the thin laminated plate are also discussed. A complex softening nonlinearity with two peaks in the higher mode is observed in frequency response curves. The influence of electrical excitation with several amplitudes and frequencies on dynamic stability is investigated using time response curves.

Influence of Multiwall Carbon Nanotube on mechanical and wear properties of Copper – Iron composite

Multiwall Carbon nanotubes (MWCNTs) are frequently attractive due to their novel physical and chemical characteristics, as well as their larger aspect ratio and higher conductivity. Therefore, MWCNTs can allow tremendous possibilities for the improvement of the necessarily unique composite materials system. The present work deals with the fabrication of Cu-Fe/CNTs hybrid composites manufactured by powder metallurgy techniques. Copper powder with 10 vol. % of iron powder and different volume fractions of Multi-Wall Carbon Nanotubes (MWCNTs) were mixed to get hybrid composites. The hybrid composites were fabricated by adding 0.3, 0.6, 0.9, and 1.2 vol.% of MWCNTs to Cu- 10% Fe mixture using a mechanical mixer. The samples were compressed under a load of 700 MPa using a hydraulic press to compact the samples. Sintering was done at 900°C for 2 h at 5ºC/min heating rate. The microscopic structure was studied using a Scanning Electron Microscope (SEM). The effect of CNTs on the mechanical and wear properties, such as micro-hardness, dry sliding wear, density, and porosity were studied in detail. The wear tests were carried out at a fixed time of 20 minutes while the applied loads were varied (5, 10, 15, and 20 N). SEM images revealed that CNTs were uniformly distributed with relative agglomeration within the Cu/Fe matrix. The results showed that the hardness, density, and wear rates decreased while the percentage of porosity increased with increasing the CNT volume fraction. Furthermore, the wear rate for all the CNTs contents increased with the applied load.

Use of silica particles to improve dispersion of -COOH CNTs/carbon fibers to produce HyFRCC

The development of hybrid fiber reinforced cement composite that has high strength, scope to be used as cement-based sensors has been investigated in this study by using a combination of carbon fibers and carbon nanotubes (CNT) at low volume fraction. The dispersion of CNTs was enhanced by using polycarboxylate based superplasticizer that resulted in a homogeneous aqueous stable solution, and profoundly improved dispersion when integrated with the cementitious matrix. Different siliceous additives were also incorporated into the mixes to improve the dispersion of CNTs in the matrix, where micro-silica outperformed as compared to nano-silica, confirmed morphologically. On the other hand, nano-silica enhanced dispersion of milled carbon fibers in the aqueous state. The sensing behavior was determined by the measurement of bulk resistance of mixes and the samples were subjected to compressive loading to study the strength improvement with the incorporation of fibers. The experimental results reveal that hybrid combination of chopped carbon fibers, micro silica, and low volume fraction of CNTs in a cementitious matrix results in a stronger and durable concrete that holds the potential for sensing applications. Thus, laying a strong foundation for the future of low cost smart cement based materials.

Effect of CNT reinforcements on the flutter boundaries of cantilever trapezoidal plates under yawed supersonic fluid flow

A comprehensive study is presented on the supersonic flutter analysis of functionally graded carbon nanotube reinforced (FG-CNTRC) cantilever trapezoidal plates. First-order shear deformation theory (FSDT) is employed to model the structure, effective mechanical properties are calculated based on the extended rule of mixture, aerodynamic pressure is estimated according to the piston theory and the set of governing equations and boundary conditions are derived using Hamilton’s principle. A numerical solution is done using generalized differential quadrature method (GDQM) and natural frequencies, corresponding mode shapes, critical speed and flutter frequency are calculated. Convergence and accuracy of the presented solution are confirmed and effect of various parameters on the flutter boundaries are investigated including geometrical parameters, yaw angle, volume fraction, and distribution of carbon nanotubes (CNTs). In the near future, results of this article can be considered as a useful tool in design and analysis of aeronautic vehicles flying at supersonic speeds.

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.

Dynamic stability and bifurcation analysis of sandwich plate with considering FG core and FG-CNTRC face sheets

In this article, the dynamic stability and bifurcation analysis of sandwich plate made of functionally graded material (FGM) as a core and functionally graded carbon nanotubes-reinforced composite (FG-CNTRC) as face sheets at top and bottom of the core under lateral stochastic loads are investigated. The classical plate theory is employed as a suitable model in obtaining equilibrium equations using the variational principles. The material properties of each layer are considered as functions of the temperature-dependent environment. By applying the Fokker–Planck–Kolmogorov (FPK) equation on equilibrium equations of motion, the probability density function is obtained. Drawing probability density function and bifurcation diagrams indicates the influence of the aspect ratio of thickness ( h/hp), temperature changes, various distributions and volume fraction of carbon nanotube and power law index of functionally graded core on stability and bifurcation of sandwich plate. By enhancing volume fraction of carbon nanotube, length of the stable region (one equilibrium point) increases and this method can be employed for improving the stability of sandwich structures. The outcomes of this research could be employed to manufacture many composite structures in aircraft and automobiles.

Influence of multi-walled nanotubes on the fresh and hardened properties of a 3D printing PVA mortar ink

3D printing concrete has been accepted as a promising construction material which can realise formless construction and digital design. The fresh properties and the hardened strength of concrete ink are crucial for structural applications. In this study, different volume fractions of multi-walled carbon nanotubes (MWCNTs) were added to a 3D printing PVA fibre-reinforced mortar ink to modify its mechanical properties. To evaluate the effect of MWCNTs on the workability of 3D printing mortar, the buildability, shape stability, flowability and setting time of fresh mortar were tested. The improvement efficiency of MWCNTs on the mechanical properties of 3D printing PVA mortar ink was also experimentally studied. The test results indicate that a small amount of MWCNTs has almost no effect on the ink’s workability. The early age compressive and flexural strength of printing mortars with MWCNTs can be effectively improved, which benefits the requirements of 3D printing. The 3-d compressive strength of mortar with addition of 0.1 wt% of MWCNTs can be enhanced by 33.6%, while the 28-d strength was hardly affected. Agglomeration and poor dispersion of MWCNTs can generally be detected by SEM images as volume content of carbon nanotubes increases. Considering the influence of MWCNTs on the fresh and hardened properties of mortar and on the requirements of 3D printing, the optimum volume fraction of carbon nanotubes for 3D printing PVA fibre-reinforced mortar should be 0.02–0.05 wt%.

The vibration of the cylindrically curved sandwich plate with rheological core and nanocomposite face sheets rested on the Winkler–Pasternak foundation

In this research, the vibration analysis of a cylindrically curved sandwich plate rested on Winkler–Pasternak foundation is investigated. The curved sandwich plate consists of a rheological core and nanocomposite top and bottom layers which are included in polyvinylidene fluoride matrix and carbon nanotubes fiber. The core has electric properties, and it is affected by applying electric fields. At first, the governing relations for different layers are written, separately, in order to determine the constitutive equations of the cylindrically curved sandwich plate. Then, differential motion equations are derived by applying the energy method and Hamilton’s principle. With regard to achieving the set of coupled equations, an appropriate analytical approach is proposed to solve them which can be considered as SSCC and SSSS boundary conditions. Also, it is observed that increasing the volume fraction of carbon nanotubes in face sheets leads to increase in the stability of the electro-rheological sandwich plate. This finding can be employed to design building smart structures, military, aviation, marine and automotive.

Effects of carbon nanotubes distribution on the buckling of carbon nanotubes/fiber/polymer/metal hybrid laminates cylindrical shell

In this manuscript, buckling of carbon nanotubes reinforced circular cylindrical composite shell under hydrostatic presser with its ends closed by rigid disks is investigated, using Fourier decomposition and the Galerkin method. The accuracy of the utilized method is verified with previous research in buckling behavior of circular cylindrical shells. Both types of functionally graded and uniform distribution patterns of carbon nanotubes are studied. The novelty of this study is investigating the influence of carbon nanotubes distribution type and volume fraction on buckling resistance of carbon nanotubes reinforced circular cylindrical composite shell. Furthermore, the effect of material type and volume fraction of metal layers on fiber metal laminates is illustrated. The results show that buckling resistance of composite cylindrical shells increase about 10% by reinforcing with 5% carbon nanotubes. Also, it is shown that metal types Az91 and Ti6AlV have about same effect on buckling resistance of fiber metal laminates cylinders, and their effect are about 15% more than the effect of Al2024. With exploiting the executed analysis, pipes with optimum buckling resistance to weight ratio can be designed for hydrostatic loading.

Mechanical properties of CNT-reinforced Ni3Al composites: the role of chirality, temperature, and volume fraction

is an extremely significant reinforcing phase in nickel-based single crystal superalloys. As an alternative strengthening method to improve its mechanical properties, carbon nanotube (CNT)-reinforced composites have recently been synthesized in experiments. Here, in order to explore the corresponding influence factors and the underlying mechanism, tensile and compressive mechanical properties of CNT- composites are systematically investigated by using molecular dynamics simulations. It is shown that the dispersion of a minor fraction of a CNT into matrix leads to a sufficient enhancement in the stiffness of CNT- composites compared with the pure . It is demonstrated that CNT reinforcement takes effect in the elastic stage under compression while it works continuously during tension. Compared with armchair CNTs, zigzag CNTs are predicted to provide more strength for raising the elastic modulus while armchair CNTs can provide superior elongation. Particularly, CNTs are found to hinder the generation of slip bands under tensile loading owing to the robust interfacial interactions. Furthermore, quantitative analysis reveals that the impact of volume fraction of CNT is much more significant than the size effect. The role of chirality, temperature and volume fraction of CNT obtained in the present work could provide beneficial references for subsequent theoretical and experimental investigations, and shed some light on the design of CNT-reinforced composites in nanoscale engineering.

Vibration analysis of cantilever FG-CNTRC trapezoidal plates

In this paper, a numerical solution is presented for free vibration analysis of cantilever functionally graded carbon nanotube-reinforced trapezoidal plates. The plate is modeled based on the first-order shear deformation theory, effective mechanical properties are estimated according to extended rule of mixture, and the set of governing equations and boundary conditions are derived using Hamilton’s principle. Generalized differential quadrature method is employed, and natural frequencies and corresponding mode shapes are derived numerically. Convergence and accuracy of the solution are confirmed, and effect of various parameters on the natural frequencies is investigated including geometrical characteristics, volume fraction and distribution of carbon nanotubes. Because of similarity of the studied model with the wing, tail and fin of aircrafts and missiles, results of this paper can be useful in design and analysis of aeronautic vehicles in the near future. It is worth mentioning that results of this paper may serve as benchmarks for future studies.

Simulation of tensile modulus of polymer carbon nanotubes nanocomposites in the case of incomplete interfacial bonding between polymer matrix and carbon nanotubes by critical interfacial parameters

In this paper, we correlate the minimum length of carbon nanotubes (CNTs) vital for operative stress transferring between polymer matrix and nanoparticles (Lc) to the critical interfacial shear modulus between polymer and CNTs (Gc) and the interfacial shear modulus (Gi) in the case of imperfect interfacial adhesion between polymer and carbon nanotubes (CNTs). Both “Gc” and “Gi” define the effective aspect ratio and volume fraction of CNTs in nanocomposites. Moreover, the developed Hui-Shia model investigates the roles of “Lc”, “Gc” and “Gi” in the tensile modulus of nanocomposites. The impacts of various parameters on the “Lc” and effective terms are highlighted. Furthermore, the experimental results of modulus for several samples and the influences of all parameters on the modulus evaluate the developed model. The accurate agreement between experimental and theoretical results as well as the correct roles of all parameters in the modulus supports the current approach. There is a direct relationship between the modulus of nanocomposites and “Lc”. Low “Gc” and high “Gi” as well as thin and long CNTs positively control the “Lc” and effective terms producing a high modulus for nanocomposites.

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.

Definition of “b” exponent and development of power-law model for electrical conductivity of polymer carbon nanotubes nanocomposites

In this article, the conventional power-law model for electrical conductivity of polymer carbon nanotubes (CNT) nanocomposites (PCNT) is linked with a developed model. The main goal is to define the “b” exponent and develop the power-law model for conductivity of PCNT. The interphase region surrounding nanoparticles and the CNT waviness, which affect the percolation threshold, the fraction of networked CNT and the effective volume fraction of CNT are taken into account. The developed model expresses that CNT concentration, CNT length and interphase thickness positively handle the conductivity of PCNT, while thick and waved CNT cause the adverse effect. Moreover, the calculations of the developed model accurately follow the experimental results of conductivity and “b” raises as CNT concentration increases.

Development of Expanded Takayanagi Model for Tensile Modulus of Carbon Nanotubes Reinforced Nanocomposites Assuming Interphase Regions Surrounding the Dispersed and Networked Nanoparticles.

In this paper, we consider the interphase regions surrounding the dispersed and networked carbon nanotubes (CNT) to develop and simplify the expanded Takayanagi model for tensile modulus of polymer CNT nanocomposites (PCNT). The moduli and volume fractions of dispersed and networked CNT and the surrounding interphase regions are considered. Since the modulus of interphase region around the dispersed CNT insignificantly changes the modulus of nanocomposites, this parameter is removed from the developed model. The developed model shows acceptable agreement with the experimental results of several samples. “ER” as nanocomposite modulus per the modulus of neat matrix changes from 1.4 to 7.7 at dissimilar levels of “f” (CNT fraction in the network) and network modulus. Moreover, the lowest relative modulus of 2.2 is observed at the smallest levels of interphase volume fraction ( < 0.017), while the highest “” as 0.07 obtains the highest relative modulus of 11.8. Also, the variation of CNT size (radius and length) significantly changes the relative modulus from 2 to 20.

A molecular dynamics simulation of the glass transition temperature and volumetric thermal expansion coefficient of thermoset polymer based epoxy nanocomposite reinforced by CNT: A statistical study

A molecular dynamics simulation study is performed to predict the glass transition temperature ( Tg) and the volumetric coefficient of thermal expansion (CTE) of thermoset polymer based nanocomposite reinforced by carbon nanotube (CNT). An atomistic model of cross-linked Diglycidyl ether bisphenol A (DGEBA) epoxy and Diethylenetriamine (DETA) was built as a matrix by employingCondensed-phase optimized molecular potentials for atomistic simulation (COMPASS27) force field. Different molecular models were constructed with various types of CNT embedded in epoxy simulation boxes. Tg was determined based on density variation with temperature. Furthermore, a new method is proposed to compute the CTE based on density variation with temperature. The effects of CNT diameter, volume fraction and chirality on Tg and CTE of nanocomposites were investigated using molecular dynamics simulation. For all cases, studied and CTE were less than pure epoxy (between 3.77% to 10.05% for Tg and respectively 14.24% to 32.23% and 23.82% to 41.65% for CTE below and above of Tg ). Increasing the CNT diameter in nanocomposite increases Tg and CTE (5.0% for Tg and 20.0% for CTE when the diameter of CNT changed 7.8A0 to 15.6A0). On the other hand increasing volume fraction of CNT in the nanocomposite decreases Tg and CTE (2.7% for Tg and 13.8% for CTE when the volume fraction of CNT in the nanocomposites changed 3.36% to 5.23%). Chirality studies under constant weight fraction of nanocomposites show that applying armchair CNT instead of zigzag CNT, decreases Tg and increases CTE (2.1% for Tg and 5.8% for CTE)

A semi-empirical model for thermal conductivity of polymer nanocomposites containing carbon nanotubes

A new version of the semi-empirical Halpin–Tsai (H–T) model is presented to evaluate the effective thermal conductivity of general carbon nanotubes (CNTs)-reinforced polymer nanocomposites. The model captures the influences of the CNTs alignment, random orientation, aggregation, waviness, length, diameter and the CNT/polymer interfacial thermal resistance parameters. In order to verify the suitability of the new H–T model, the numerically calculated thermal conductivities are compared with existing experimentally measured ones. An excellent predictability is found of the modified H–T model over a wide range of the tests. The consideration of the CNT waviness and the interfacial thermal resistance parameters is seriously essential for a more realistic prediction in all conditions. For aligned CNT-reinforced polymer nanocomposites, considering the alignment factor seems to be very important. Moreover, in the case of well-dispersed CNTs into the matrix, it is necessary to incorporate the CNT random orientation parameter. Additionally, when CNTs are not well dispersed, the CNT aggregation and random orientation parameters must be incorporated in the analysis. The effects of the CNT volume fraction, length, diameter and non-straight shape on the nanocomposite thermal conducting behavior are estimated in details. The results clearly expose that it is needed to eliminate the aggregation, use the straight CNTs and form a strong interface if the full potential of CNT reinforcement is to be realized. Finally, the thermal conductivities of CNT-shape-memory polymer nanocomposites at different temperatures are obtained.

Modeling and Evaluation of Effective Elastic Properties of Carbon Nanotubes Reinforced Carbon Fiber/Epoxy Multiscale Composites

Abstract Carbon nanotubes (CNTs) are increasingly used as reinforcing materials in polymer matrix composites because of their high stiffness, strength and resilience, as well as excellent mechanical, electrical and thermal properties. Embedding CNTs in polymer matrix composites can increase the stiffness and strength of composites significantly. In this paper, the effective elastic properties of multiscale composites (Carbon Fiber/CNTs/Epoxy) at 5% volume fraction of CNTs are evaluated using finite element method. 3-D finite element models using representative volume element (RVE) applying necessary boundary conditions are developed. For validation the results are compared with classical theories of equivalent material properties. From the results it is observed that there is good agreement between the results of finite element method and classical theories of equivalent materials properties.

Atomistic behavior of nanoporous carbon nanotube-aluminum composite under compressive loading

Metal matrix nanocomposites have been actively studied to discover the characteristics of a new class of materials. In the present study, metal matrix nanocomposites are investigated using molecular dynamics simulations of the compressive behavior of nanoporous carbon nanotube (CNT)-aluminum (Al) composites that have a density of approximately 77% to that of pure Al. The weight-reduced nanocomposites exhibited an enhanced Young’s modulus of 138%, and a compressive strength degraded by 13% compared with pure Al. Through stress decomposition into CNT and Al constituents, it was observed that the Young’s modulus was enhanced due to the high stiffness of the CNTs; further, the reduced strength was primarily due to the early failure strain. The effects of CNT volume fractions and sizes are further analyzed using the rule of mixture, which is modified by the interphase area definition. In addition, the atomistic details of the structure and stress revealed a buckling behavior in the CNT as well as a massive slip behavior in the Al matrix during plastic deformation. The results presented in this study will have implications in the design and development of metal matrix nanocomposites for applications in high-performance lightweight materials.

Evaluation of the effect of adding carbon nanotubes on the effective mechanical properties of ceramic particulate aluminum matrix composites

In this study, a high-performance hybrid aluminum matrix composite (HAMC) reinforced with ceramic particles and carbon nanotubes (CNTs) is analyzed. A novel multi-step micromechanical approach, based on the Mori-Tanaka model and the generalized method of cell, is proposed in order to predict the effective elastic modulus and Poisson's ratio of the HAMCs. The influences of volume fraction, aspect ratio, waviness shape, alignment and agglomeration of CNTs, and ceramic particle volume fraction on the mechanical properties of CNT/ceramic particle-reinforced HAMCs are explored. Moreover, the role of aluminum carbide (Al4C3) which may be formed at the CNT/matrix interface in the mechanical behavior is micromechanically investigated. It is found that adding a small amount of CNTs into the microscale ceramic particle-reinforced aluminum matrix composites (AMCs) can significantly improve the effective mechanical properties of the resultant HAMCs. As compared to HAMCs, which contain the randomly dispersed CNTs, the alignment of CNTs into the HAMCs leads to a higher level of mechanical properties. However, the waviness and agglomeration of CNTs can decrease the HAMC elastic modulus. According to the obtained results, the CNT/matrix interfacial interaction may have significant effects on the effective properties of the particulate hybrid metal-based composites. The elastic properties estimated by the micromechanical model are compared to those measured by the experimental method. The outcomes of this research suggest that these hybrid metal-based composites, containing CNTs, have significant potential in diverse engineering applications as compared to the conventional metal-based composites.