Multiscale modeling of compressive behavior of carbon nanotube/polymer composites
Introduction
It has been theoretically and experimentally confirmed that carbon nanotubes possess exceptional high stiffness and strength [1], [2], [3], [4], [5]. These properties as well as their high aspect ratio and low density suggest that carbon nanotubes may hold promise as the reinforcement for nanocomposites [6], [7]. The improvement in stiffness and strength due to the addition of carbon nanotubes in polymeric matrix materials have been demonstrated [8], [9], [10]. For the effective utilization of nanotubes as reinforcements in composites, various attempts have been made regarding the dispersion and alignment issues of nanotubes and well-dispersed and well-aligned nanotube reinforced composites are now feasible [11], [12], [13], [14], [15]. Meanwhile, some efforts have also been devoted to the study of the load transfer between nanotubes and the matrix [9], [10]. The transmission electron microscopy study of Ajayan et al. [16] indicated weak interfacial bonding between the nanotubes and resin matrix. The measurements of Schadler et al. [9] showed better load transferring efficiency when the composites are under compression than tension. For enhancing the load transfer capability, some researchers proposed the functionalization of carbon nanotubes to form chemical bonds between nanotubes and the matrix [17], [18].
Due to the difficulty in modeling nanotube reinforced composites, analytical studies on the mechanisms of load transfer between the matrix and nanotubes are still very limited. Among the available literature, Lordi and Yao [19] used force-field-based molecular mechanics to model the interactions between nanotubes and several different kind of polymers. Wise and Hinkley [20] used molecular dynamics simulation for addressing the local changes in the interface of a single-walled nanotube surrounded by polyethylene molecules. Odegard et al. [21] studied the effect of chemical functionalization on the mechanical properties of nanotube/polymer composites by using an equivalent-continuum modeling technique. More recently, Li and Chou [22] analyzed the stress distributions in carbon nanotube/polymer composites under tension by combining the atomistic molecular structural mechanics approach and the continuum finite element method. There is still a lack of extensive analytical studies of the behavior of nanotube/polymer composites under compression.
In this paper, we examine the compressive behavior of carbon nanotube/polymer composites using a multiscale modeling approach. Following the technique of Ref. [22], the nanotube is modeled at the atomistic scale by the molecular structural mechanics method, and the matrix deformation is analyzed at the macroscopic scale by the continuum finite element method. The nanotube and polymer matrix are assumed to be bonded by van der Waals interactions at the interface. The load transfer at the interface is considered first, followed by an examination of the buckling behavior of nanotube/polymer composites.
Section snippets
Modeling of nanotube/polymer composites
In this paper, we only considered nanocomposites reinforced by single-walled carbon nanotubes. Two cylindrical unit cells, as shown in Fig. 1, are chosen as computational models. One is the discontinuous reinforcement model where the nanotube is entirely embedded in the matrix (Fig. 1a). Another is the continuous reinforcement model, where the length of the nanotube is assumed to be the same as the length of the surrounding polymer matrix (Fig. 1b). The first model is used particularly for
Elastic buckling of nanotube/polymer composites
Under compressive loading, one of the failure modes of a structural component is elastic instability, namely, buckling. For understanding the performance of nanotube/polymer composites under compression, elastic buckling is a fundamental issue that needs to be addressed. According to the theory of structural stability [26], the buckling force of a structural element can be determined by the eigenvalue analysis, which requires the consideration of the geometrically nonlinear problem.
Assuming
Results
Using the molecular structural mechanics approach and finite element method, The computational modeling of a continuous nanotube- and a discontinuous nanotube-reinforced polymeric matrix composite has been carried out. The matrix is assumed to be an epoxy polymer with Young’s modulus and Poisson ratio of 2.41 GPa and 0.35, respectively. The nanotube is assumed to be zigzag type with end caps.
We consider two cases of loading, i.e., isostress and isostrain conditions, for the analysis of stress
Conclusions
In this paper, a multiscale modeling of carbon nanotube/polymer composites under compression is presented. The nanotube is modeled at the atomistic scale, and the matrix deformation is analyzed by the continuum finite element method. The nanotube and the polymer matrix are assumed to be bonded by van der Waals interactions at the interface. The simulations revealed the stress distributions at the nanotube/polymer interface under isostrain and isostress loading conditions. The buckling forces of
Acknowledgements
This work is supported by the Army Research Office (Grant No. DAAD 19-02-1-0264, Dr. Bruce LaMattina, Program Director) and the National Science Foundation (NIRT Program, Grant No. 0304506, Dr. Ken P. Chong, Program Director).
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