A coarse-grained model for the elastic properties of cross linked short carbon nanotube/polymer composites (original) (raw)
Related papers
Composite Structures, 2015
Please cite this article as: Arash, B., Park, H.S., Rabczuk, T., Tensile fracture behavior of short carbon nanotube reinforced polymer composites: a coarse-grained model, Composite Structures (2015), doi: http://dx.Abstract Short-fiber-reinforced polymer composites are increasingly used in engineering applications and industrial products owing to their unique combination of superior mechanical properties, and relatively easy and low-cost manufacturing process. The mechanical behavior of short carbon nanotube (CNT) polymer composites, however, remains poorly understood due to size and time limitations of experiments and atomistic simulations. To address this issue, the tensile fracture behavior of short CNT reinforced poly (methyl methacrylate) (PMMA) matrix composites is investigated using a coarse-grained (CG) model. The reliability of the CG model is demonstrated by reproducing experimental results on the strain-stress behavior of the polymer material. The effect of the nanotube weight fraction on the mechanical properties, i.e. the Young's modulus, yield strength, tensile strength and critical strain, of the CNT/polymer composites is studied in detail. The dependence of the mechanical properties of the composites on the orientation and length-to-diameter aspect ratio of nanotube reinforcements is also examined.
Mechanics Research Communications, 2010
An embedded carbon nanotube in a polymer matrix is replaced with an equivalent long fiber for predicting the mechanical properties of the carbon nanotube/polymer composite. A 3-D finite element model consisting of a carbon nanotube, inter-phase and surrounding polymer is built. The inter-phase region is treated using van der Waals interactions. Comparing finite element analysis results and the rule of mixture we observed that the latter overestimates the properties of investigated composite and cannot capture the difference between the micro-and nanoscale. Developed equivalent fiber consisting of carbon nanotube and inter-phase region can be appropriately used in micromechanical equations.
Constitutive modeling of nanotube–reinforced polymer composites
Composites Science and Technology, 2003
In this study, a technique is presented for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Because the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties can no longer be determined through traditional micromechanical approaches that are formulated by using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber using an equivalentcontinuum modeling method. The effective fiber serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube shapes, sizes, concentrations, and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/LaRC-SI (with a PmPV interface) composite systems, one with aligned SWNTs and the other with three-dimensionally randomly oriented SWNTs. The Young's modulus and shear modulus have been calculated for the two systems for various nanotube lengths and volume fractions.
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...
International Journal of Performability Engineering, 2017
Discrepancy in reported elastic properties for nanocomposites is argued to be most likely a result of either variations in the size of reinforcement or lack of control of the composite microstructure. In general, there will be a size variation in nanotubes in a given composite, contribution from each nanotube diameter and the volume percentage that tubes of a definite diameter occupy within the composite toward the overall elastic modulus is modeled. In this work, Digimat-FE is used to generate a realistic three dimensional microstructure for the current carbon nanotube/ epoxy composite. A system of aligned carbon nanotubes embedded in epoxy matrix is modeled. In the system of aligned multi walled carbon nanotubes, the entire volume of the model has been divided into finite individual sub-composites, each one containing a specific nanotube diameter with a local volume fraction. A second model showed a single 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. Moreover, a micromechanical approach for modeling short fiber composites was developed to account for the structure of the multi-walled carbon nanotube reinforcement and predict the elastic modulus of the nanocomposite as a function of the constituent properties, reinforcement geometry and nanotube structure. Finite element results show increase in elastic modulus with increasing aspect ratio for composites with high filler loading (3 vol%). Micromechanical predictions highlight the structure or size influence of the nanotube reinforcement on the properties of the nanocomposite. The nanocomposite elastic properties were found to particularly be sensitive to the nanotube diameter, since larger diameter nanotubes showed a lower effective modulus and occupied a greater volume fraction in the composite relative to smaller-diameter nanotubes.
Composite Structures, 2010
The main goal of this research is to study the tensile behavior of embedded short carbon nanotubes (CNTs) in a polymer matrix in presence of van der Waals (vdW) interaction as inter-phase region. A 3D finite element model of a unit cell consisting of capped carbon nanotubes, inter-phase and surrounding polymer is built. The unit cell is subjected to tensile load case to obtain longitudinal Young's modulus of the investigated cell. A parametric study is carried out to investigate the effect of CNT's length on reinforcement. It is observed that improvement in the Young's modulus of CNT-composite is negligible for lengths smaller than 100 nm and saturation takes place in larger lengths on the order of 10 lm. Furthermore, a comparison between results obtained for short carbon nanotubes and long carbon nanotube is presented. The efficient length of CNT in form of (10, 10) is obtained at the order of 10 lm. Finally, it was shown that direct use of micromechanics equations for short fibers will overestimate the stiffness. However, employing effective stiffness of equivalent fiber comprising of CNT and its inter-phase instead of high modulus of CNT will lead us to more appropriate results, which are in an acceptable agreement with conventional semi-empirical micromechanics equations.
Polymer Composites, 2017
Multiscale modeling has been developed to calculate the Young's modulus of carbon nanotube (CNT) reinforced epoxy-based nanocomposites. Molecular dynamics was used to construct nanocomposite models consisting of crosslinked network structure of epoxy resin as the matrix material and CNT as the reinforcement at nanoscale. Transversely, isotropic stiffness matrices were calculated using constant strain method on four cases with different CNT chiralities. Effective fiber method was employed to scale bridging from nanoscale to microscale. In multiscale calculations, various types of micromechanical methods were investigated and Halpin-Tsai formulation was selected due to its more realistic predictions. The results showed that increasing CNT aspect ratio from 1 to 1,000 results in an increase in nanocomposite Young's modulus by about three times for nanocomposite reinforced with CNT(20,0). Comparing CNT(5,0) with CNT(20,0) reinforced polymer results, suggested that increasing the CNT radius resulted in a decrease in nanocomposite moduli to about one half. Multiscale results indicated that CNT agglomeration can decrease nanocomposite Young's modulus to one-third compared to the dispersed CNT case. Predicted results were compared with numerical and experimental results found in the literature and good agreement was observed.
Constitutive Modeling of Nanotube-Reinforced Polymer Composite Systems
2001
In this study, a technique has been proposed for developing constitutive models for polymer composite systems reinforced with single-walled carbon nanotubes (SWNT). Since the polymer molecules are on the same size scale as the nanotubes, the interaction at the polymer/nanotube interface is highly dependent on the local molecular structure and bonding. At these small length scales, the lattice structures of the nanotube and polymer chains cannot be considered continuous, and the bulk mechanical properties of the SWNT/polymer composites can no longer be determined through traditional micromechanical approaches that are formulated using continuum mechanics. It is proposed herein that the nanotube, the local polymer near the nanotube, and the nanotube/polymer interface can be modeled as an effective continuum fiber using an equivalentcontinuum modeling method. The effective fiber retains the local molecular structure and bonding information and serves as a means for incorporating micromechanical analyses for the prediction of bulk mechanical properties of SWNT/polymer composites with various nanotube sizes and orientations. As an example, the proposed approach is used for the constitutive modeling of two SWNT/polyethylene composite systems, one with continuous and aligned SWNT and the other with discontinuous and randomly aligned nanotubes.
Multi-scale modeling of tensile behavior of carbon nanotube-reinforced composites
Theoretical and Applied Fracture Mechanics, 2008
A multi-scale representative volume element (RVE) for modeling the tensile behavior of carbon nanotube-reinforced composites is proposed. The RVE integrates nanomechanics and continuum mechanics, thus bridging the length scales from the nano-through the mesoscale. A progressive fracture model based on the modified Morse interatomic potential is used for simulating the behavior of the isolated carbon nanotubes and the FE method for modeling the matrix and building the RVE. Between the nanotube and the matrix a perfect bonding is assumed until the interfacial shear stress exceeds the corresponding strength. Then, nanotube/matrix debonding is simulated by prohibiting load transfer in the debonded region. Using the RVE, a unidirectional nanotube/polymer composite was modeled and the results were compared with corresponding rule-of-mixtures predictions. A significant enhancement in the stiffness of the polymer owing to the adding of the nanotubes is predicted. The effect of interfacial shear strength on the tensile behavior of the nanocomposite was also studied. Stiffness is found to be unaffected while tensile strength to significantly decrease with decreasing the interfacial shear strength.