Effect of carbon nanotube (CNT) content on the mechanical properties of CNT-reinforced aluminium composites

The interest in carbon nanotubes (CNTs) as reinforcements for aluminium (Al) has been growing considerably. Efforts have been largely focused on investigating their contribution to the enhancement of the mechanical performance of the composites. The uniform dispersion of CNTs in the Al matrix has been identified as being critical to the pursuit of enhanced properties. Ball milling as a mechanical dispersion technique has proved its potential. In this work, we use ball milling to disperse up to 5 wt.% CNT in an Al matrix. The effect of CNT content on the mechanical properties of the composites was investigated. Cold compaction and hot extrusion were used to consolidate the ball-milled Al–CNT mixtures. Enhancements of up to 50% in tensile strength and 23% in stiffness compared to pure aluminium were observed. Some carbide formation was observed in the composite containing 5 wt.% CNT. In spite of the observed overall reinforcing effect, the large aspect ratio CNTs used in the present study were difficult to disperse at CNT wt.% greater than 2, and thus the expected improvements in mechanical properties with increase in CNT weight content were not fully realized.     

Stochastic multi-scale modeling of CNT/polymer composites

A full stochastic multi-scale modeling technique is developed to estimate mechanical properties of carbon nanotube reinforced polymers. Developing a full-range multi-scale technique to consider effective parameters of all nano, micro, meso and macro-scales and full stochastic implementation of integrated modeling procedures are the novelties of the present research. The length, orientation, agglomeration, curvature and dispersion of carbon nanotubes are taken into account as random parameters. It is proven that random distribution of carbon nanotube length and volume fraction can be replaced with corresponding mean values. The results of predictions are in a very good agreement with published experimental observations.     

Effects of CNT diameter on mechanical properties of aligned CNT sheets and composites

Drawing, winding, and pressing techniques were used to produce horizontally aligned carbon nanotube (CNT) sheets from free-standing vertically aligned CNT arrays. The aligned CNT sheets were used to develop aligned CNT/epoxy composites through hot-melt prepreg processing with a vacuum-assisted system. Effects of CNT diameter change on the mechanical properties of aligned CNT sheets and their composites were examined. The reduction of the CNT diameter considerably increased the mechanical properties of the aligned CNT sheets and their composites. The decrease of the CNT diameter along with pressing CNT sheets drastically enhanced the mechanical properties of the CNT sheets and CNT/epoxy composites. Raman spectra measurements showed improvement of the CNT alignment in the pressed CNT/epoxy composites. Research results suggest that aligned CNT/epoxy composites with high strength and stiffness are producible using aligned CNT sheets with smaller-diameter CNTs.     

Failure of carbon nanotube/polymer composites and the effect of nanotube waviness

This paper studies the failure of CNT/polymer composites by combining micromechanics model and finite element simulation. A computational model of composite of adequate size is employed so the interactions between nanotubes embedded in the matrix can be taken into account. The effects of nanotube waviness and random nanotube distribution relative to aligned straight nanotubes are investigated. The computational results indicate that the nanotube waviness tend to reduce the elastic modulus but increase the ultimate strain of a composite. The randomness of nanotube distribution tends to reduce both the composite elastic modulus and tensile strength. The damage initiation and evolution in composites with random wavy nanotubes have also been analyzed.     

Determining the power spectral density of the waviness of unidirectional glass fibres in polymer composites

A pilot study has been completed into the accurate measurement of 3D fibre waviness in high packing fraction, unidirectional, glass fibre reinforced polymer epoxy. It has been shown that the confocal laser scanning microscope (CLSM) can determine fibre waviness amplitudes,A40 µm andsimultaneously fibre wavelengths, 4 mm. Knowing the fibre-centre coordinates in 3D with sub-micron precision, the fibre waviness may be characterised in terms of the power spectral densitiesS _u andS _w orthogonal to the fibre direction (taken to be in they direction) and also in terms of the power spectral densities of fibre slopes,S _u andS _w. In future studies, these characterisation parameters will enable models linking random fibre waviness to compressive strength to be evaluated.     

The effective properties and local aggregation effect of CNT/SMP composites

A micromechanics model of the thermomechanical constitutive behavior and micro-structural inhomogeneity of carbon nanotubes (CNTs)/shape memory polymer (SMP) composites is presented. It is assumed that the CNTs are elastic and the SMP obeys a thermomechanical constitutive law. The effective properties of CNT/SMP composites are examined using a micro-mechanics method. The effect of CNT aggregation in the composite, frequently encountered in real engineering situations, is studied. The degree of aggregation is described by an aggregation coefficient, and the effective properties of SMP composites with aggregated CNTs are calculated using a stepping scheme. It is shown that the degree of CNT aggregation dramatically influences the effective properties of the CNT/SMP composites. A homogeneous microstructure leads to maximum levels of effective composite properties.     

Analysis of effective elastic modulus for multiphased hybrid composites

Short fiber reinforced composites inherently have fiber length distribution (FLD) and fiber orientation distribution (FOD), which are important factors in determining mechanical properties of the composites. Since the internal structure has a direct effect on the mechanical properties of the composites, a Micro-CT was used to observe the three dimensional structure of fibers in the composites and to acquire FLD and FOD. It was successful to investigate FLD, FOD, and fiber orientation states and to predict the elastic modulus of the hybrid system. Since hybrid composites used in this study consist of three phases of particles, glass fibers, and matrix, theoretical hybrid modeling is required to consider reinforcing effects of both particles and glass fibers. Interaction between the particles and matrix was considered by using a perturbed stress–strain theory, the Tandon–Weng model. In addition, the laminating analogy approach (LAA) was used to predict the overall elastic modulus of the composite. Theoretical prediction of hybrid moduli indicated that there was a possibility of poor adhesion between glass fibers and matrix. The poor interfacial adhesion was confirmed by morphological experiments. This theoretical and experimental platform is expected to provide more insightful understanding on any kinds of multiphased hybrid composites.     

Fast HdBNM for large-scale thermal analysis of CNT-reinforced composites

Because of their high thermal conductivities, carbon nanotubes (CNT) have promising potential in development of fundamentally new composites. To study the influence of CNTs distribution on the overall properties of a composite, the modeling of a Representative Volume Element (RVE) including a large number of CNTs that are randomly distributed and oriented is necessary. However, analysis of such a RVE using standard numerical methods faces two severe difficulties, namely the discretization of the geometry and a very large computational scale. In this paper, the first difficulty is alleviated by employing the Hybrid Boundary Node Method (HdBNM), which is a form of the boundary type meshless methods. To overcome the second difficulty, the Fast Multipole Method (FMM) is combined with the HdBNM to solve a simplified mathematical model. RVEs containing various numbers of CNTs with different lengths, shapes and alignments have been analyzed, resulting in valuable insights gained into the thermal behavior of the composite material.     

Modeling the effective elastic properties of nanocomposites with circular straight CNT fibers reinforced in the epoxy matrix

In the present study, the consistent effective elastic properties of straight, circular carbon nanotube epoxy composites are derived using the micromechanics theory. The CNT composites are known to provide high stiffness and elastic properties when the shape of the fibers is cylindrical and straight. Accordingly, in the present work, the effective elastic moduli of composite are newly obtained for straight, circular CNTs aligned in the specified direction as well as distributed randomly in the matrix. In this direction, novel analytical expressions are proposed for four cases of fiber property. First, aligned, and straight CNTs are considered with transverse isotropy in fiber coordinates, and the composite properties are also transversely isotropic in global coordinates. The short comings in the earlier developments are effectively addressed by deriving the consistent form of the strain tensor and the stiffness tensor of the CNT nanocomposite. Subsequently, effective relations for composites reinforced with aligned, straight CNTs but fibers isotropic in local coordinates are newly developed under hydrostatic loading. The effect of the unsymmetric Eshelby tensor for cylindrical fibers on the overall properties of the nanocomposite is included by deriving the strain concentration tensors. Next, the random distribution of CNT fibers in the matrix is studied with fibers being transversely isotropic as well as isotropic when CNT nanocomposites are subjected to uniform loading. The corresponding relations for the effective elastic properties are newly derived. The modeling technique is validated with results reported, and the variations in the effective properties for different CNT volume fractions are presented.     

Effect of inclusion shape on the effective elastic moduli for composites with imperfect interface

Summary Bounds on the effective elastic moduli for isotropic composites consisting of randomly oriented spheroidal inclusions with imperfect matrix-inclusion interface are proposed based on Hashin's extremum principle. Phenomenally, these bounds are the first-order ones for such composites, and contain the effect of the size and shape of inclusions, and the elastic properties of constituent phases and interfaces. In the limit cases, these bounds reduce to those known ones. The effect of inclusion shape and interface imperfection on the bounds is discussed with some numerical results for a WC/Co metal-matrix composite.     

Micromechanics models for the effective nonlinear electro-mechanical responses of piezoelectric composites

The nonlinear behavior of piezoelectric composites becomes prominent when the composites are subjected to high electric fields, which is often the case in actuator applications. Understanding the nonlinear behavior of piezoelectric composites is crucial in designing structures comprising of these materials. This study presents micromechanics models for predicting nonlinear electro-mechanical responses of polarized piezoelectric composites, comprising of a linear non-piezoelectric homogeneous medium (matrix) reinforced by either nonlinear piezoelectric fibers or particles, subjected to high electric fields. The maximum electric field applied is within the coercive electric field limit. The constitutive relations for the polarized piezoelectric inclusions consist of the third- and fourth-order electro-mechanical coupling tensors and the second- and third-order electric permeability tensors. The Mori–Tanaka micromechanics and simplified unit-cell micromechanics models are formulated to predict the effective nonlinear electro-mechanical responses of piezoelectric fiber reinforced and particle reinforced composites, respectively. Linearized micromechanical relations are first used to provide trial solutions followed by iterative schemes in order to correct errors from linearizing the nonlinear responses. Numerical results are presented to illustrate the performance of each micromechanics model.     

Effects of various fillers on the sliding wear of polymer composites

Short fibre reinforced polymer composites are nowadays used in numerous tribological applications. In spite of this fact, new developments are still under way to explore other fields of application for these materials and to tailor their properties for more extreme loading conditions. The references given at the end of this review describe some of these developments. In the present overview further approaches in designing polymeric composites in order to operate under low friction and low wear against steel counterparts are described. A particular emphasis is focused on special filler (including nanoparticle) reinforced thermoplastics and thermosets. Especially, the influence of particle size and filler contents on the wear performance is summarised. In some of the cases, an integration of traditional fillers with inorganic nanoparticles is introduced and presents an optimal effect. Furthermore, some new steps towards the development of functionally graded tribo-materials are illustrated.     

Differential scheme for the effective elastic properties of nano-particle composites with interface effect

The differential scheme is developed to evaluate the effective elastic properties of nano-composites with interface effect through the solution of an infinitely dilute dispersion of nano-particles in a matrix. The differential equations presented in this paper for overall modulus of composites extend the application of classic differential scheme to the nano-scale, and they are valid for both mono-sized and poly-sized nano-particle composites. Particle size distribution functions are introduced. Continuous and discrete size distributions are taken into consideration for poly-sized filled nano-particles. The numerical examples exhibit that the effective properties of mono-sized nano-particle composite are size dependent, which agrees well with previous studies. As for poly-sized particle composite, the results show that the elastic properties are dependent on particle size distributions. Some distribution parameters, such as the mean size and the standard deviation, may significantly affect the effective mechanical properties. The proposed differential equations can be reduced to the classic ones, and are supposed to be in wider application.     

Effects of higher-order interface stresses on the elastic states of two-dimensional composites

We propose a simple model to simulate higher-order interface stresses along the interface between two neighboring media in two dimensions. The interface behavior is modeled from a thin interphase of constant thickness by taking a proper limit process. In the formulation the deformation of the thin interphase is approximated by the Kirchhoff-Love assumption of thin shell. To incorporate the higher-order interface stresses, we consider the bending effects resulting from the non-uniform surface stress across the layer thickness. The stress equilibrium conditions is fulfilled by consideration of balance for forces as well as stress couples. Depending on the difference in stiffness and length scales of the interphase, we show that the interfaces can be classified into four different types. This findings, upon suitable definitions of material parameters, agree with a rigorous asymptotic analysis proposed by Benveniste and Miloh [Benveniste, Y., Miloh, T., 2001. Imperfect soft and stiff interfaces in two-dimensional elasticity. Mech. Mater. 33 309-323]. To illustrate the higher-order effects, we derive analytically the stress concentration factor of an infinite plate containing a circular cavity with interface stresses of different orders subjected to a remote transverse shear loading. The closed-form expressions show how the orders of interface stresses influence the concentration factor in a successive manner. In addition, we examine the effective shear modulus of composites with circular inclusions with higher-order interface effects. The effective transverse shear modulus is derived based on the generalized self-consistent method.     

Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities

Summary A micromechanical framework is proposed to investigate effective mechanical properties of elastic multiphase composites containing many randomly dispersed ellipsoidal inhomogeneities. Within the context of the representative volume element (RVE), four governing micromechanical ensemble-volume averaged field equations are presented to relate ensemble-volume averaged stresses, strains, volume fractions, eigenstrains, particle shapes and orientations, and elastic properties of constituent phases of a linear elastic particulate composite. A renormalization procedure is employed to render absolutely convergent integrals. Therefore, the micromechanical equations and effective elastic properties of a statistically homogeneous composite are independent of the shape of the RVE. Various micromechanical models can be developed based on the proposed ensemble-volume averaged constitutive equations. As a special class of models, inter-particle interactions are completely ignored. It is shown that the classical Hashin-Shtrikman bounds, Walpole's bounds, and Willi's bounds for isotropic or anisotropic elastic multiphase composites are related to the noninteracting solutions. Further, it is demonstrated that the Mori-Tanaka methodcoincides with the Hashin-Shtrikman bounds and the noninteracting micromechanical model in some cases. Specialization to unidirectionally aligned penny-shaped microcracks is also presented. An accurate, higher order (in particle concentration), probabilistic pairwise particle interaction formulation coupled with the proposed ensemble-volume averaged equations will be presented in a companion paper.     

On contribution of pores into the effective elastic properties of carbon/carbon composites

In this paper, we discuss the effect of porosity on the effective elastic properties of unidirectional carbon/carbon composites (carbon fibers in pyrolytic carbon matrix) densified by chemical vapor infiltration (CVI). It is shown that CVI treatment results in formation of irregularly shaped pores randomly oriented in the plane perpendicular to the direction of fiber (transverse plane). These pores are analyzed using numerical conformal mapping procedure, and their contribution to the effective elastic properties is expressed in terms of the cavity compliance contribution tensor. Components of this tensor are found for a variety of typical pores shapes.     

Effect of filler waviness and orientation on the damping behavior of CNF-reinforced epoxy composites

An ever increasing demand for material performance coupled with recent advances in the production and availability of nanoscale materials has led to a significant interest in the use of nanoscale fillers to augment and tailor material performance in nanocomposites. Specifically, the use of high aspect ratio fillers, such as carbon nanotubes and carbon nanofibers (CNF) to augment the viscoelastic performance of nanocomposites has been the focus of many studies. Previous study has shown the use of high aspect ratio fillers to significantly enhance the damping capacity at low frequencies by more than 100 %, relative to the neat epoxy. In light of the promise, this technology holds for use in engineered applications, requiring specific damping performance, there remains a fundamental lack in understanding of the precise mechanisms and thereby a lack of ability to accurately predict material performance, which is limiting application of the technology. This study looks at both the effect of the random filler orientation and the effect of filler waviness in examining the viscoelastic response of CNF-reinforced nanocomposites. Using a fundamental approach, this study employs experimental, analytical, and numerical modeling techniques to characterize the amount of strain energy transferred to the filler and the matrix, and to indirectly estimate the effective loss factor of the filler. Utilizing experimental investigation coupled with parametric inquiries using strain energy methods relative to both filler orientation and waviness, this study provides fundamental insight into the effect of imperfect geometries and random filler distributions seen in nanocomposites utilizing high aspect ratio fillers, such as CNF.     

Micromechanics and effective elastic moduli of particle-reinforced composites with near-field particle interactions

A micromechanical framework is proposed to predict effective elastic moduli of particle-reinforced composites. First, the interacting eigenstrain is derived by making use of the exterior-point Eshelby tensor and the equivalence principle associated with the pairwise particle interactions. Then, the near-field particle interactions are accounted for in the effective elastic moduli of spherical-particle-reinforced composites. On the foundation of the proposed interacting solution, the consistent versus simplified micromechanical field equations are systematically presented and discussed. Specifically, the focus is upon the effective elastic moduli of two-phase composites containing randomly distributed isotropic spherical particles. To demonstrate the predictive capability of the proposed micromechanical framework, comparisons between the theoretical predictions and the available experimental data on effective elastic moduli are rendered. In contrast to higher-order formulations in the literature, the proposed micromechanical formulation can accommodate the anisotropy of reinforcing particles and can be readily extended to multi-phase composites.