Evaluation of elastic modulus in PE/CNT composites subjected to axial loads (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.
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.
This paper presents a computational modeling approach for evaluating the mechanical behavior of CNT based nanocomposite. The CNT’s interaction with matrix material was modeled using the continuum mechanics theory and finite element approach. The effective mechanical properties of CNT based nanocomposite were then evaluated by using the finite element method (FEM) models. Two different models were constructed. The first model was a CNT through the length of the square representative volume element (RVE). The second model considers a CNT inside the square representative volume element (RVE). Several numerical examples were carried out to investigate the influence of Young’s modulus of matrix, CNT thickness, Poisson’s ratio and interphase on the effective modulus of CNT based nanocomposite in longitudinal direction. The computed results were compared with those obtained from the simple rule of mixture for validity.
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...
Evaluation of elastic properties of multi walled carbon nanotube reinforced composite
Computational Materials Science, 2014
Exceptional mechanical properties like high strength, stiffness and aspect ratio exhibited by carbon nanotubes, make them ideal reinforcements for nanocomposites. In this paper load transfer in multi-walled carbon nanotube (MWCNT) composites is studied under tension and compression loading conditions. Continuum mechanics model is used to evaluate the effective material properties using a representative volume element (RVE) approach. Numerical results are obtained using Finite Element Modeling (FEM) and these results have been validated with rule of mixture results. FEM results are found to be quite closer to the results obtained from rule of mixture. In the present work we have considered a range of matrix material, the range covers the matrix material from metal to polymer, i.e. taken in a form of the ratio of effective modulus of elasticity of CNT to that of matrix material E t /E m from 5 to 200. With the addition of the multi-walled CNT in a matrix at the volume fractions of 5.1%, the stiffness of the composite is increased by 46% for compressive loading and 14.9% for tensile loading, as compared with that of the matrix in the case of long CNT at E t /E m = 10. Multi-walled carbon nanocomposite are found to provide better value of young's modulus in compression as compared in tension, this is due to the higher inter-tube load transfer in compression. Comparative evaluation of material properties with single walled carbon nanocomposite is also done. It is established that multi-walled carbon nanotube composite provide a better resistance against compression as compared to single walled carbon nanotube composite. Effect of change in diameter and length of multi-walled carbon nanotube on stiffness of nanocomposite have also been investigated. Longer multiwalled carbon nanotubes are found to be more effective in reinforcing the composite as compared to shorter ones. FEM results are also found to be in close approximation with the experimental results, which validates the current model.
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.
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.
Elastic Behavior of Carbon Nanotubes Reinforced Composites: Micromechanical Modeling
2017
A micromechanical model is applied to examine the tensile properties of composite materials filled with multi-wall CNT oriented in in-plane and out-of-plane direction and a quantitative micromechanical model for the mechanical behavior of CNT-composites has been developed. Digimat-MF is used to generate a realistic three-dimensional microstructure for the current carbon nanotube/ epoxy composite. The Digimat model simulates a system of aligned carbon nanotubes arranged in-plane and another one having out of plane arrangement of reinforcements. A second model shows a representative volume element for the current nano-composite, in which the carbon nanotubes were simulated as a randomly (fully) dispersed, where all particles have been separated from each other. The predicted mechanical properties are compared with experimental tensile properties of composite materials reinforced with multi-wall CNTs arranged in in-plane and out-of-plane direction. A good agreement between the micromec...