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Abstract

This article presents different micromechanical modelling techniques based on analytical and numerical approaches to determine the effective elastic and piezoelectric (piezoelastic) properties of graphene-based composite materials. Different types, orientations and shapes as well as different geometrical parameters of fiber reinforcement are considered for estimating the effective properties. The effective properties of composite are predicted with and without considering the strong covalent bond which provides interaction and in-plane stability of 2Dcrystalline graphene or strong van der Wall forces formed between graphene layers and the matrix. It is revealed that the axial, transverse and shear effective piezoelastic properties of graphene reinforced piezoelectric composite (GRPC) are significantly enriched due to the incorporation of graphene into the epoxy matrix. The importance of incorporating graphene as nanofillers/interphase into the conventional epoxy matrix to form an advanced composite and its effective properties are illustrated while these results show excellent agreement with previously reported experimental estimates. These results reveal that due to incorporation of graphene nanofillers, there is a significant enhancement in effective properties of composite. The results would also help to recognize the most important material properties with respect to different shapes and orientation of reinforcements which influences the performance of system significantly. To confirm safety, robustness and sustainability of the structure, it is the most prior requirement to determine the effective properties of composites considering different parameters for the different static and structural analyses.

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... Even if the static and dynamic problem of conventional materials with their different structures were broadly studied by using theoretical, experimental or numerical approach, no previous study has been reported to investigate the electromechanical behavior of advanced layered hybrid piezoelectric composite structures. The effective properties of these advanced hybrid piezoelectric composites are predicted by using analytical and numerical models which are taken from Shingare and Naskar [36]. In this, they showed that electromechanical properties including elastic and piezoelectric properties of hybrid piezoelectric composite are enhanced due to addition of graphene nanofillers. ...
... In this article, hybrid graphene reinforced piezoelectric composite (GRPC) plate with combination of PZT and graphene (v g = 0.2v p ) into epoxy matrix was selected to investigate how the flexoelectricity influences the static and modal analysis, in which v g and v p denote the volume fraction of graphene nanofillers and PZT fiber. The elastic, piezoelectric and dielectric properties of GRPC are taken from Shingare and Naskar [36] and are summarized in Table 1. The mass density (ρ) of the hybrid GRPC is considered as 3798.4 ...
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Owing to their applications in devices such as in electromechanical sensors, actuators and nanogenerators, the consideration of size-dependent properties in the electromechanical response of composites is of great importance. In this study, a closed-form solution based on the linear piezoelectricity, Kirchhoff’s plate theory and Navier’s solution was developed, to envisage the electromechanical behaviors of hybrid graphene-reinforced piezoelectric composite (GRPC) plates, considering the flexoelectric effect. The governing equations and respective boundary conditions were obtained, using Hamilton’s variational principle for achieving static deflection and resonant frequency. Moreover, the different parameters considering aspect ratio, thickness of plate, different loadings (inline, point, uniformly distributed load (UDL), uniformly varying load (UVL)), the combination of different volume fraction of graphene and piezoelectric lead zirconate titanate are considered to attain the desired bending deflection and frequency response of GRPC. Different mode shapes and flexoelectric coefficients are also considered and the results reveal that the proper addition of graphene percentage and flexoelectric effect on the static and dynamic responses of GRPC plate is substantial. The obtained results expose that the flexoelectric effect on the piezoelastic response of the bending of nanocomposite plates are worth paying attention to, in order to develop a nanoelectromechanical system (NEMS). Our fundamental study sheds the possibility of evolving lightweight and high-performance NEMS applications over the existing piezoelectric materials.
... A significant number of mathematical models have been developed for bending, fracture and natural frequency investigation of functionally graded beams, rectangular plates, and shell structures. An extensive review of the work related to functionally graded structures, presented by Byrd [4], Wu et al. [5] and Swaminathan et al. [6], suggests that in most of the studies through-thickness gradation of properties is considered following deterministic and stochastic frameworks [7][8][9][10][11][12][13][14]. However, over the last few years, the focus is getting diverted toward the in-plane and multidirectional functionally graded structures because it gives more freedom to control the material properties of thin structures for meeting application-specific demands, such as specific stiffness, strength, impact and thermal resistance, high fatigue strength, corrosion resistance, and acoustic properties [5]. ...
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This paper proposes an accurate three-dimensional framework for elastic and viscoelastic free vibration investigation of in-plane functionally graded (IPFG) orthotropic rectangular plates integrated with piezoelectric sensory layers. The developed {analytical} framework is capable of considering layer-wise unidirectional linear functional gradation in both stiffness and density of the orthotropic composite layers. 3D piezoelasticity-based governing equations of motion are formulated in mixed form by employing Hamilton's principle, and further solved analytically for Levy-type support conditions using the power-series-based extended Kantorovich method (EKM) jointly with Fourier series. The displacements, stresses, and electrical variables (electric field and electric potential) are solved as the primary variables that ensure the point-wise interlayer continuity and electro-mechanical support conditions. The viscoelastic property of the orthotropic interlayer is defined by employing Biot model, which is similar to the standard linear viscoelastic model. The correctness and efficacy of the present mathematical model are established by comparing the present numerical results with published literature and 3D finite element results, obtained by utilizing user material subroutine in the commercial FE software ABAQUS. An extensive numerical study is performed for various configurations and thickness ratios to investigate the influences of in-plane gradation, viscoelasticity and their coupled effects on the free-vibration response of hybrid laminated plates. It is found that in-plane gradation of stiffness and density remarkably alters the flexural frequencies and corresponding mode shapes of the hybrid intelligent rectangular plates. The flexural frequencies and stresses in the plate can be modified by selecting suitable grading indexes. Another interesting observation is that the in-plane gradation shows a considerably less effect on the electrical response of piezoelectric layers, which can play a vital role in the design of sensors and actuators for dynamic applications. Further, the numerical study demonstrates a potential time-dependent structural behaviour based on the present viscoelastic modelling. The consideration of viscoelasticity could be crucial for analysing the mechanical behaviour of a wide range of polymer composites more realistically and for prospective temporal programming in smart structural systems by exploiting the viscoelastic effect. Although the present analytical solution has been proposed for the free-vibration investigation of smart in-plane functionally graded (IPFG) viscoelastic plates, it can also be utilized directly to analyze the symmetric and asymmetric laminated piezoelectric smart plates with constant properties.
... The effective properties of GRHC were evaluated using a three-phase MOM model with consideration of graphene volume fraction which is considered 0.2 times volume fraction of PZT-5H which is taken from Shingare and Naskar 57 and are enlisted in Table 2. ...
... (Kiani, 2018) examined the free vibration of composite plates incorporated with GPLs to study large amplitudes with the help of iso-geometric finite element (FE) modeling. Researchers (Karsh et al., 2019;Kundalwal, 2019, 2020;Shingare and Naskar, 2021a;Trinh et al., 2020;Vaishali et al., 2020;Naskar et al., 2017) studied the electromechanical response of hybrid graphene-based nanocomposites (GNC) including beam, plate, wire, and shell by incorporating piezoelectric graphene nanofiber in a polyimide matrix. In such studies, they assumed graphene as nanofiber and found the effect of size-dependent phenomena (piezoelectricity, flexoelectricity, and surface effect) on these non-FGM GNC structures. ...
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Owing to inhomogeneous strain and high surface-to-volume ratio in nanostructures, it is imperative to account for the flexoelectricity as well as surface effect while analyzing the size-dependent electromechanical responses of nano-scale piezoelectric materials. In this article, a semi-analytical ‘single-term extended Kantorovich method (EKM)’ and ‘Ritz method’ based powerful framework is developed for investigating the static and dynamic electromechanical responses of graphene reinforced piezoelectric functionally graded (FG) nanocomposite plates, respectively. The residual surface stresses, elastic and piezoelectric surface modulus, and direct flexoelectric effects are taken into account while developing the unified governing equations and boundary conditions. The modified Halpin Tsai model and rules of mixture are implemented to predict the effective bulk properties. Our results reveal that the static deflection and resonance frequency of the proposed FG nanoplates are significantly influenced due to the consideration of flexoelectricity and surface effects. While such outcomes emphasize the fact that such effects cannot be ignored, these also open up the notion of on-demand property modulation and active control. The effects are more apparent for nanoplates of lesser thickness, but they diminish as plate thickness increases, leading to the realization and quantification of a size-dependent behavior. Based on the developed unified formulation, a comprehensive numerical investigation is further carried out to characterize the electromechanical responses of nanoplates considering different critical parameters such as plate thicknesses, aspect ratios, flexoelectric coefficients, piezoelectric multiples, distribution, and weight fraction of graphene platelets along with different boundary conditions. With the recent advances in nano-scale manufacturing, the current work will provide the necessary physical insights in modeling size-dependent multifunctional systems for active control of mechanical properties and harvesting electromechanical energy.
... The properties of GHPC are chosen: C 11 = 112 GPa, C 12 = 3.34 GPa, C 66 = 2.04 GPa, e 31 = −6.933 Cm −2 and ∈ 33 = 3.24 × 10 −9 F/m for the bulk part [7]. The surface elastic moduli and piezoelectric constants for the present model is equal to the elastic moduli and piezoelectric constants of GHPC multiplied by its surface layer thickness, assumed as 1 nm. ...
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Woven fabric reinforced materials are are composite mediums commonly used in automotive industry. In this sector, high strength mechanical properties are required by the designers due to high loads during operation. Woven fabrics are modelled as orthotropic interlaced yarns within a polymeric matrix which can have additives. In this context, carbon nano-tubes are considered as reinforcing additives for the polymeric matrix, thus, giving to the resulting composite higher mechanical properties. However, the modelling of such composite material configuration is not trivial and it is not generally easy to find analytical formulations which accurately fit experimental results. Therefore, the aim of the present paper is to display a comparison among experimental and analytical mechanical properties predictions of carbon woven textile composites. In addition, some novel configurations have been proposed for further applications in this framework.
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This paper presents a unified solution for free vibration analysis of thick functionally graded porous graphene platelet reinforced composite (FGP-GPLRC) cylindrical shells embedded in elastic foundations. The three-dimensional (3-D) theory of shell theory is introduced for theoretical formulation. The Rayleigh-Ritz method in conjugation with artificial spring technique are employed, where the arbitrary boundary conditions can be conveniently obtained. A unified solution which comprises of six different displacement functions is developed. The calculation performances including convergence rate and calculating efficiency with respect to different displacement functions are compared extensively. Besides, three elastic foundations (Winkler/ Pasternak/ Kerr foundations), four types of porosity distributions and three categories of GPL patterns are considered. Some benchmark results are provided for free vibration of FGP-GPLRC cylindrical shells resting on elastic foundations. At last, the effects of different boundary conditions, elastic foundations with various parameters, porosity coefficient, GPL weight fraction and geometrical parameters on the vibration are elucidated.
Article
In this work, an analytical model was developed to study the distribution of electric potential in a graphene reinforced nanocomposite (GRNC) nanowire. The electromechanical responses such as electric potential and deflection of cylindrical GRNC cantilevered nanowire were investigated. Moreover, the conservative fully coupled finite element (FE) models were developed to validate the analytical predictions. Analytical solution shows that the piezoelectric potential in the GRNC nanowire depends on the transverse force, but it is not a function of the force acting along its axial direction. The electric potential in the tensile and compressive sections of nanowire is antisymmetric along its cross-section, making it as a “parallel plate capacitor” for nanopiezotronics applications such as nanogenerator and piezoelectric field effect transistor due to potential drop across the nanowire which assists as the gate voltage. The predictions of potential distributions across the GRNC nanowire considering piezoelectricity show better agreement with FE predictions. Outcomes of the current work reveal that the flexoelectric effect on the electromechanical behavior of GRNC nanowire is noteworthy and cannot be ignored.
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This chapter investigates both the mechanical properties as well as stress transfer characteristics of multiscale composites comprising nano- and microscale reinforcements. To improve the microfiber–matrix interfacial adhesion, carbon nanostructures (CNS) were incorporated into the epoxy around the continuous microscale fiber. These CNS are composed of aligned carbon nanotubes (A-CNTs). First, we evaluated the effective elastic properties of the interphase layer made of CNS and epoxy in conjunction with the Mori–Tanaka analytical model using the molecular dynamics simulations. Subsequently a micromechanical pull-out model was developed for a continuous fiber multiscale composite considering different CNS orientations accounting their perfect as well as imperfect interfacial bonding with the surrounding epoxy. The outcomes obtained from the pull-out model and finite element simulations were validated and were found to be in good coherence. Our outcomes revealed that the stress transfer behavior multiscale composite is significantly enhanced by governing the CNT morphology around the fiber, specifically, when it is parallel to the microscale fiber’s longitudinal direction.
Article
This paper quantifies the influence of uncertainty in the low-velocity impact responses of sandwich plates with composite face sheets considering the effects of obliqueness in impact angle and twist in the plate geometry. The stochastic impact analysis is conducted by using finite element (FE) modelling based on an eight nodded isoparametric quadratic plate bending element coupled with multivariate adaptive regression spline (MARS) in order to achieve computational efficiency. The modified Hertzian contact law is employed to model contact force and other impact parameters. Newmark's time integration scheme is used to solve the time-dependent equations. Comprehensive deterministic as well as probabilistic results are presented by considering the effects of location of impact, ply orientation angle, impactor velocity, impact angle, face-sheet material property, twist angle, plate thickness and mass of impactor. The relative importance of various input parameters is determined by conducting a sensitivity analysis. The results presented in this paper reveal that the impact responses of sandwich plates are significantly affected by the effect of source-uncertainty that in turn establishes the importance of adopting an inclusive stochastic design approach for impact modelling in sandwich plates.
Article
In present work, analysis of functionally graded carbon nanotube-reinforced composite laminates is investigated. Different types of functionally graded aligned reinforcement distributions of carbon nanotubes along the thickness of laminates are considered. A micro mechanical model using some effective parameters estimates material properties. The governing equations are developed based on third order shear deformation theory. A nine-node isoparametric finite element with seven unknowns at each node is used. The obtained results in terms of deflection and stresses are compared with available results in literature. The effects of carbon nanotube volume fraction. Length-to-thickness ratio, boundary conditions and other geometrical parameters are also examined.
Article
Three micromechanics approaches (method of cells, Fourier series analysis, and transformation field analysis) are formulated so that the final expressions relating the local sub-cell strain to the homogenized macro-strain in a unit cell are similar, although the three techniques and assumptions made to deduce them are different. This allows for a direct comparison of the three methods, and, more importantly, enables one to use the same algorithm for solving equations after the strain concentration and the strain transformation matrices have been determined from the three methods. Elastic constants found from the three approaches compare well with each other, and with those experimentally found. The micromechanics approaches are embedded in a finite element scheme to study elasto-plastic deformations of fiber-reinforced composites. The three sets of the axial stress-axial strain curves are found to correlate well with each other, and with the experimental ones. We use these micromechanics approaches to determine strains in each sub-cell from the macro-strains (i.e., dehomogenize global strains into local strains), find stresses in each constituent or sub-cell, and then employ the micromechanics technique to find macro-stresses (i.e., homogenize stresses) and stiffnesses.
Article
This paper presents a homogenization-based hybrid uncertain analysis method (HHUAM) for the prediction of the effective elastic tensor for microscopic material properties with uncertain‑but‑bounded parameters. For those uncertain‑but‑bounded parameters related to the microscopic material properties, the ones with sufficient statistic information are modelled as bounded random variables, and those without enough statistics to build the probability density functions are defined as interval variables. Based on the finite element framework for homogenization method, the effective elastic tensor with bounded hybrid uncertain parameters can be expanded by using Gegenbauer series expansion. The variation ranges of the expectation and variance of the effective elastic tensor can be obtained due to the orthogonality relationship of Gegenbauer polynomials. Two numerical cases are carried out to verify the effectiveness and the efficiency of the HHUAM. The influence of the bounded hybrid uncertainties in microstructures on homogenized macroscopic elastic properties of heterogeneous materials is also investigated.
Article
In the present study, finite element- and representative volume element (RVE)-based models for estimation of the effective elastic, thermal, and thermoelastic properties of the multi-phase spatially graded particulate composites have been developed. Efficient particle packing algorithms were utilized to create high-resolution graded microstructures with spatial (more than one direction) variation of the composites’ constituents. The so-called continuously graded RVEs were generated and accounted for spatially continuously graded microstructures. Numerical homogenization of these RVEs enabled to preserve the influence of the particle interactions resulting from continuous grading. The developed models were verified by comparing the predicted effective properties to those obtained using the previously existed models and were validated using available experimental data.
Article
This paper investigates the mechanical behaviors of functionally graded multilayer nanocomposite beams reinforced with a low content of single-layer graphene oxide powders (GOPs). The material properties of GOP nanocomposites are estimated. The first-order shear deformation theory and Hamilton's principle are employed to deal with the motion equations. Parametric studies are conducted to examine the effects of distribution pattern and weight fraction of GOPs, slenderness ratio and boundary condition on the bending, buckling, and vibration of GOP beams. The results show that GOP is superior to the single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) in reinforcing the mechanical behaviors of polymer nanocomposite.
Article
In the present work, extended finite element method (XFEM) in conjunction with multiscale finite element method (MsFEM) is employed to model heterogeneous materials i.e. matrix having particles and/or voids. This approach, named as multiscale extended finite element method (MsXFEM), is used to determine the effective elastic properties of heterogeneous materials. The elastic properties are calculated by analyzing a representative volume element (RVE) under periodic boundary conditions. Three cases of particles and voids in the matrix i.e. matrix with hard particles, matrix with voids, and matrix with voids and hard particles both, are considered for analysis. The particles and voids are randomly distributed in the matrix. A strain energy based homogenization is carried out numerically for reinforcement volume fractions up to 50%. RVEs containing large number of discontinuities are analyzed by the proposed MsXFEM. The evaluated effective properties of the heterogeneous material are compared with the results available in the literature. These simulations show that the use of MsXFEM leads to a significant reduction in the CPU time as compared with the standard XFEM.
Article
This paper studies the dynamic instability of functionally graded multilayer nanocomposite beams reinforced with a low content of graphene nanoplatelets (GPLs) and subjected to a combined action of a periodic axial force and a temperature change. The weight fraction of GPL nanofillers is assumed to be constant in each individual GPL-reinforced composite (GPLRC) layer but follows a layerwise variation across the beam thickness. The Halpin-Tsai micromechanics model is used to estimate the effective Young’s modulus of GPLRC layers. The differential quadrature method is employed to convert the partial differential governing equations into a linear system of Mathieu-Hill equations, from which the principle unstable region of functionally graded multilayer GPLRC beams is determined by Bolotin’s method. Special attention is given to the effects of GPL distribution pattern, weight fraction, geometry and dimension on the dynamic instability behaviour. The thermal buckling and free vibration are also discussed as subset problems. Numerical results show that distributing more GPLs near the top and bottom surfaces can effectively increase the natural frequency and reduce the size of the unstable region. The influences of GPL geometry and dimension tend to be insignificant when the GPL width-to-thickness ratio is larger than 10³.
Article
This paper presents a stochastic approach to study the natural frequencies of thin-walled laminated composite beams with spatially varying matrix cracking damage in a multi-scale framework. A novel concept of stochastic representative volume element (SRVE) is introduced for this purpose. An efficient radial basis function (RBF) based uncertainty quantification algorithm is developed to quantify the probabilistic variability in free vibration responses of the structure due to spatially random stochasticity in the micro-mechanical and geometric properties. The convergence of the proposed algorithm for stochastic natural frequency analysis of damaged thin-walled composite beam is verified and validated with original finite element method (FEM) along with traditional Monte Carlo simulation (MCS). Sensitivity analysis is carried out to ascertain the relative influence of different stochastic input parameters on the natural frequencies. Subsequently the influence of noise is investigated on radial basis function based uncertainty quantification algorithm to account for the inevitable variability for practical field applications. The study reveals that stochasticity/ system irregularity in structural and material attributes affects the system performance significantly. To ensure robustness, safety and sustainability of the structure, it is very crucial to consider such forms of uncertainties during the analysis.
Article
This paper presents the quantification of uncertain natural frequency for laminated composite plates by using a novel surrogate model. A group method of data handling in conjunction to polynomial neural network (PNN) is employed as surrogate for numerical model and is trained by using Latin hypercube sampling. Subsequently the effect of noise on a PNN based uncertainty quantification algorithm is explored in this study. The convergence of the proposed algorithm for stochastic natural frequency analysis of composite plates is verified and validated with original finite element method (FEM). Both individual and combined variation of stochastic input parameters are considered to address the influence on the output of interest. The sample size and computational cost are reduced by employing the present approach compared to direct Monte Carlo simulation (MCS).
Article
This paper presents the effect of noise on surrogate based stochastic natural frequency analysis of composite laminates. Surrogate based uncertainty quantification has gained immense popularity in recent years due to its computational efficiency. On the other hand, noise is an inevitable factor in every real-life design process and structural response monitoring for any practical system. In this study, a novel algorithm is developed to explore the effect of noise in surrogate based uncertainty quantification approaches. The representative results have been presented for stochastic frequency analysis of spherical composite shallow shells considering Kriging based surrogate model. The finite element formulation for laminated composite shells has been developed based on Mindlin’s theory considering transverse shear deformation. The proposed approach for quantifying the effect of noise is general in nature and therefore, it can be extended to explore other surrogates under the influence of noise.
Article
The Halpin-Tsai equations are based upon the ″self-consistent micromechanics method″ developed by Hill. Hermans employed this model to obtain a solution in terms of Hill's ″reduced moduli″ . Halpin and Tsai have reduced Hermans' solution to a simpler analytical form and extended its use for a variety of filament geometries. The development of these micromechanics relationships, which form the operational bases for the composite analogy of Halpin and Kardos for semi-crystalline polymers are reviewed.
Article
This paper presents the effect of twist and rotational speeds on free vibration characteristics of functionally graded conical shells employing finite element method. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of configuration of constituent materials on the frequencies. The equation of dynamic equilibrium is derived from Lagrange’s equation neglecting the Coriolis effect for moderate rotational speeds. The properties of the conical shell materials are presumed to vary continuously through their thickness with power-law distribution of the volume fractions of their constituents. The QR iteration algorithm is used for solution of standard eigenvalue problem. Computer codes developed are employed to obtain the numerical results concerning the combined effects of twist angle and rotational speed on the natural frequencies of functionally graded conical shells. The mode shapes for typical shells are also depicted. Numerical results obtained are the first known non-dimensional frequencies for the type of analyses carried out here.
Article
To improve the stress transfer and distribution of carbon fiber/epoxy interface, a gradient interphase reinforced by graphene oxide (GO) was designed in the composites. GO was introduced onto the surface of carbon fibers by physical adsorption, forming a gradient interphase in composite interface during the procedure of resin wetting. In order to improve the dispersion of GO in gradient interphase and chemical adhesion between GO and epoxy, GO was covalently functionalized with silane coupling agents and the silanized graphene oxide (SGO) was introduced into the gradient interphase as well. Compared with the base composites without nanosheets, the interfacial shear strength (IFSS), interlaminar shear strength (ILSS), flexural and tensile properties of hierarchical composites decreased seriously when 0.5 wt% GO was introduced on carbon fiber surface. However, hierarchical composites containing 0.5 wt% SGO showed a significant increase 60% in IFSS, 19% in ILSS, 15% in flexural strength and 16% in flexural modulus. A new stiffness phase between carbon fibers and matrix was found in the stiffness distribution curve of hierarchical composites by atomic force microscope in force mode. In addition, the stiffness of interphase was proved to change gradually from carbon fibers to epoxy, indicating the gradient dispersion of nanosheets in interphase.
Article
The preparation and characterisation of the different forms of graphene are reviewed first of all. The different techniques that have been employed to prepare graphene such as mechanical and solution exfoliation, and chemical vapour deposition are discussed briefly. Methods of production of graphene oxide by the chemical oxidation of graphite are then described. The structure and mechanical properties of both graphene and graphene oxide are reviewed and it is shown that although graphene possesses superior mechanical properties, they both have high levels of stiffness and strength. It is demonstrated how Raman spectroscopy can be used to characterise the different forms of graphene and also follow the deformation of exfoliated graphene, with different numbers of layers, in model composite systems. It is shown that continuum mechanics can be employed to analyse the behaviour of these model composites and used to predict the minimum flake dimensions and optimum number of layers for good reinforcement. The preparation of bulk nanocomposites based upon graphene and graphene oxide is described finally and the properties of these materials reviewed. It is shown that good reinforcement is only found at relatively low levels of graphene loading and that, due to difficulties with obtaining good dispersions, challenges still remain in obtaining good mechanical properties for high volume fractions of reinforcement.
Article
The imperfect contact conditions can be created by chemical reactions between the fiber and matrix materials or man-made interface design, such as surface modification of reinforced phase by using coating in order to enhance wetting property or due to environment effects. Although the problem of elastic properties of the composite materials with imperfect fiber–matrix interface has been addressed in a large number of research studies, in this work, there is an investigation about three different approaches, which have specific mathematical formulations and unique characteristics. Thus, the results provided by Asymptotic Homogenization Method (AHM) with some specific considerations, which are assumed, are compared to Semi Analytic Method (SAM) and Representative Volume Element (RVE) approach solved by Finite Element Method (FEM). The differences between the three approaches are normally less than 1%. Also, the results obtained by the investigated approaches are compared to the experimental data and literature, addressing a discussion about limitations and potentials of each one.
Article
In this study, multiscale homogenization modeling to characterize the thermal conductivity of polymer nanocomposites is proposed to account for the Kapitza thermal resistance at the interface and the polymer immobilized interphase. Molecular dynamics simulations revealed that the thermal conductivity dependent on the embedded particle size originated from the structurally altered interphase zone of surrounding matrix polymer in the vicinity of nanoparticles, and clearly indicate strong dominance of interfacial phonon scattering and dispersion. To account for both the thermal resistance and the immobilized interphase, a four-phase equivalent continuum model composed of spherical nanoparticles, Kapitza thermal interface, effective interphase, and bulk matrix phase is introduced in a finite element-based homogenization method. From the given thermal conductivity of the nanocomposites obtained from MD simulations, the thermal conductivity of the interphase is inversely and numerically obtained. Compared with the micromechanics-based multiscale model, the thermal conductivity of the interphase can be obtained more accurately from the proposed homogenization method. Using the thermal conductivity of the interphase, the random distribution and radius of nanoparticles to describe real nanocomposite microstructure are considered, and the results confirm the applicability of the proposed multiscale homogenization model for further stochastic approaches to account for geometric uncertainties in nanocomposites.
Article
This paper presents a three-dimensional elasticity solution for a simply supported, transversely isotropic functionally graded plate subjected to transverse loading, with Young’s moduli and the shear modulus varying exponentially through the thickness and Poisson’s ratios being constant. The approach makes use of the recently developed displacement functions for inhomogeneous transversely isotropic media. Dependence of stress and displacement fields in the plate on the inhomogeneity ratio, geometry and degree of anisotropy is examined and discussed. The developed three-dimensional solution for transversely isotropic functionally graded plate is validated through comparison with the available three-dimensional solutions for isotropic functionally graded plates, as well as the classical and higher-order plate theories.
Article
Graphene platelets (GP) are a novel class of nanofillers due to its good compatibility with most polymers, high aspect ratio, high absolute strength and cost-effectiveness. We in this study synthesised two types of epoxy/GP nanocomposites with different interface strength using the combination of sonication and chemical modification. Although the surface-modified graphene platelets (m-GP) formed clusters, a higher degree of dispersion and exfoliation of graphene was observed in each cluster owning to the improved interface by modification. The scrolling of graphene was found predominantly in the interface-modified nanocomposite. At 4 wt%, the modified nanocomposite shows fracture energy release rate G1c 613.4 J m−2, while the unmodified nanocomposite indicates 417.3 J m−2, in comparison with neat epoxy G1c 204.2 J m−2. The interface modification enhanced the glass transition temperature of neat epoxy from 94.7 to 108.6 °C, 14.7% increment. Toughening mechanisms are attributed to the voiding, microcracking and breakage of GP, while matrix may not consume as much fracture energy as m-GP do.
Article
A clear demonstration of the potential of ribbon shaped rein forcements in composite materials applications is presented. From a micromechanics analysis, supported by experimental results, we find that ribbon reinforcement offers superior stiffness properties in the plane of the lamina. The macromechanics analysis intro duces the concept of a hybrid composite in which the engineer may combine the outstanding strength properties of fibers with the superior stiffness properties offered by ribbon reinforcements. It is pointed out that the low strength observed for glass-ribbon com posites is a consequence of fabrication procedures and does not correspond to the theoretical limiting strength of ribbon rein forcements.