Influence of Matrix Stiffness, CNT Thickness, Poisson‘s Ratio and Interphase on Effective Longitudinal Modulus of CNT Based Composites for Square RVE (original) (raw)
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International Journal of Engineering Trends and Technology , 2017
The carbon nanotubes are well known for their superior material properties. They are effectively introducing in the composite to improve the material properties and therefore, it is necessary to understand the effect of carbon nanotubes on the mechanical properties of nanotube-based composite. In this paper, the effective Young’s modulus of the carbon nanotube-based composite is investigated by the finite element method for different matrix stiffness considering both long and short type carbon nanotubes. The effective Young’s modulus for different nanotube thickness in case of perfect bonding and interphase thickness for imperfect bonding is also determined. A 2-D axisymmetric model for the cylindrical representative volume element is considered in this work. For validation of the estimation considering the perfect bonding, finite element method results are compared with the analytical results. It is concluded that for both long and short type carbon nanotubes, the effective Young’s modulus of the composite material increases as the matrix stiffness, nanotube thickness, and interphase thickness increases.
Computational Materials Science, 2014
Carbon nanotubes (CNTs) possess extremely high stiffness, strength and resilience, and may provide ultimate reinforcing materials for the development of nanocomposites. CNT reinforced composite materials (CNTRC) can be effectively used in aircraft structures, due to their high strength to weight ratio. Accordingly, several experimental and analytical studies have been performed for evaluating effective mechanical properties of CNT-reinforced polymer matrix. However, several complex issues including sizes and forms of CNTs dispersed in a matrix, their distribution and orientation in the matrix make the simulations of the mechanical behaviour of these composites extremely complicated. One such issue is assessing the effect of nanotube curvature since embedded CNTs seldom remain straight inclusions. Nanotube curvature is often characterized by means of the waviness that accounts for the deviation from the straight particles assumption. In this paper, the effect of waviness of CNT is analyzed using a 3-D nanoscale representative volume element (RVE) based on continuum mechanics, and effective elastic modulus is calculated for two cases namely, a RVE with long CNT (CNT throughout the length of RVE) and a RVE with short CNT (CNT completely inside the RVE). Finite element method is used for the analysis. Further, a theoretical model based on the micromechanics of multi-phase composite and energy principles has also been developed to evaluate effective elastic constants of these RVEs. It is found that the reinforcing capacity of the CNTs reduces drastically even with a small waviness as compared to the straight CNTs. The effect of waviness is much more pronounced in case of long wavy CNT than short wavy CNT. The analysis is finally extended to predict the effective moduli of these composites embedded with completely randomly oriented CNTs of different waviness.
Journal of Mechanical Engineering, 2009
The aim of this research is to assess the effects of interphase property and matrix property on the tensile elastic modulus (TEM) of the carbon nanotube (CNT) using a 3-D nanoscale representative volume element (RVE) based on continuum mechanics and using the finite element method (FEM). Formulas to extract the effective material constants from solutions for the RVE is derived based on the elasticity theory. Based on the strength of materials theory, an extended rule of mixtures, for estimating the effective Young's modulus, is applied for comparisons with the numerical solutions based on the elasticity theory. Both long and short CNT embedded in matrix at a volume fraction of 2% and 5% respectively is considered for investigating the effects of interphase and matrix property variation. The results demonstrate that in both the cases, matrix property and interphase property significantly influence the TEM of the CNT based composite. These results suggest that a coating of harder polymer on the CNT or a surface treatment can significantly increase the TEM of CNT based composite.
Journal of Solid Mechanics, 2016
Predicting the effective elastic properties of carbon nanotube-reinforced nanocomposites is of great interest to many structural designers and engineers for improving material and configuration design in recent years. In this paper, a finite element model of a CNT composite has been developed using the Representative volume element (RVE) to evaluate the effective material properties of nanocomposites. Based on this model, the effects of geometrical characteristics such as the aspect ratio, orientation and volume fraction of the CNTs in conjunction with the interphase behavior on the mechanical properties of the nanocomposites are elucidated and the elastic properties of a complex polymeric nanofibrous structure are determined.
Evaluation of elastic modulus in PE/CNT composites subjected to axial loads
SN Applied Sciences
In this paper, a range of matrix materials from polymer to metal matrix were considered which have extensive applications in various industries. The effective mechanical properties of CNT-based composites were evaluated using a 3-D cylindrical representative volume element (RVE). Continuum mechanics model was used for estimating the effective Young's modulus in the axial direction of the RVE. The load transfer conditions between carbon nanotubes and matrix were modeled using a separated interfacial region. Numerical examples using FEM are presented which demonstrated that load carrying capacities of CNTs in a matrix were significant. With the addition of CNTs into a matrix at volume fractions of only about 2% and 5%, the stiffness of the composite was increase as high as 0.7 and 9.7 times for short and long CNTs, respectively. Also the effect of CNT addition to polyethylene matrix was studied. These simulation was performed using ABAQUS software and the obtained results were consistent with the experimental results reported in the literature.
Journal of Mechanical Engineering, 2010
In carbon nanotube (CNT) based composite, due to the small (micrometer) size of reinforcements a large amount of interphases is developed during the time of production. It is important to assess whether the interphase is responsible for the poor mechanical properties of CNT-reinforced composite. In this research, the effect of interphase property and characteristics on effective mechanical properties of CNT based composites is evaluated using a 3-D nanoscale representative volume element (RVE). The effect of both soft and stiff interphases on the Tensile Elastic Modulus (TEM) of nanocomposites is investigated using the Finite Element Method (FEM) for the case of both long and short CNTs. With the increase of thickness of stiff interphase, the stiffness of the composite increases significantly for both the short and long CNT cases. On the other hand the increase of thickness of soft interphase reduces the stiffness of the overall composite in a considerable amount.Key Words: Carbon n...
Journal of Materials Science, 2012
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 carbon nanotube orientation on the mechanical properties of nanocomposites
Composites Part B: Engineering, 2012
Carbon nanotubes (CNTs) have been regarded as ideal reinforcements of high-performance composites with enormous applications. In this paper, nano-structure is modeled as a linearly elastic composite medium, which consists of a homogeneous matrix having hexagonal representative volume elements (RVEs) and homogeneous cylindrical nanotubes with various inclination angles. Effects of inclined carbon nanotubes on mechanical properties are investigated for nano-composites using 3-D hexagonal representative volume element (RVE) with short and straight CNTs. The CNT is modeled as a continuum hollow cylindrical shape elastic material with different angles. The effect of the inclination of the CNT and its parameters is studied. Numerical equations are used to extract the effective material properties for the hexagonal RVE under axial as well as lateral loading conditions. The computational results indicated that elastic modulus of nano-composite is remarkably dependent on the orientation of the dispersed SWNTs. It is observed that the inclination significantly reduces the effective Young's modulus of elasticity under an axial stretch. When compared with lateral loading case, effective reinforcement is found better in axial loading case. The effective moduli are very sensitive to the inclination and this sensitivity decreases with the increase of the waviness. In the case of short CNTs, increasing trend is observed up to a specific value of waviness index. It is also found from the simulation results that geometry of RVE does not have much significance on stiffness of nano-structures. The results obtained for straight CNTs are consistent with ERM results for hexagonal RVEs, which validate the proposed model results.
Numerical Investigation of the Overall Stiffness of Carbon Nanotube-Based Composite Materials
Journal of Nano Research, 2011
In this study, a finite element model of a representative volume element that contains a hollow and filled single-walled Carbon nanotube (SWCNT) in two case studies was generated. It was assumed that the nanocomposites have geometric periodicity with respect to local length scale and the elastic properties can be represented by those of the representative volume element (RVE). Elastic properties in agreement with existing literature values for the Carbon nanotube and the matrix were assigned. Then for the two case studies, the tensile test was simulated to find the effect of the geometry, i.e. the volume fraction of matrix and SWCNT's properties variation, on the effective Young's modulus of the structure. In another approach, by applying perpendicular loading to the tube direction, the effect of matrix volume fraction on the transverse Young's modulus was studied. The investigations showed that for both RVEs with filled SWCNT and hollow SWCNT, the effective Young's modulus of the structure decreases approximately linear as the matrix volume fraction increases. The value of Young's modulus of the RVE with a filled Carbon nanotube was obtained to be higher than the RVE with the hollow Carbon nanotube. In addition, by increasing the tube diameter, the effective Young's modulus of the structure increases and the transverse Young's modulus decreases approximately linear for filled tubes but this parameter remains rather constant in the case of the hollow tube by increasing the matrix volume fraction. Lu [1] reported the Young's modulus of CNTs from 0.97 to 1.11 TPa, while Li and Chou [2] obtained the Young's modulus about 0.89 to 1.033 TPa. Chang and Gao [3] used molecular dynamics simulations to predict the mechanical properties of CNT. They obtained Young's modulus equal to 1.06 TPa, while Cho [4] reported Young's modulus about 1.024 TPa, based on continuum mechanics studies. Krishnan et al. [5] used TEM to measure Young's modulus for 27 isolated single-walled Carbon nanotubes in the range of 1.0-1.5 nm at room temperature and reported a mean value of 1.25-0.35/+0.45 TPa.