Mechanical characterization of graphite/epoxy nanocomposites by multi-scale analysis
Introduction
Graphite platelets are often used in polymeric matrices to enhance mechanical properties and impart physical functionalities such as electrical and thermal conductivities [1], [2], [3], [4]. However, it is not easy to intuitively predict the mechanical properties of the resulting nanocomposites due to the anisotropic properties and morphology of the particles. Thus, it is desirable to carry out analytical or numerical analyses to understand how the particles affect the mechanical behavior of the composite.
Multi-scale analyses have been conducted for nanoparticle reinforced polymeric composites by incorporating molecular mechanical models into continuum models in recent years [5], [6], [7], [8]. In general, the mechanical properties of nanostructured particles, expressed with atomic structures for the calculation, were evaluated by molecular mechanical analysis and subsequently, the nanoparticles were treated as equivalent solid particles, embedded in the polymeric matrix. The mechanical properties of the nanocomposite [5], [6] and the load-transfer between the particles and matrix [7], [8] were investigated with analytical and/or numerical micromechanical models.
In this study, following a similar analysis scheme, the elastic constants of graphite nanoplatelets were calculated based on molecular mechanics and subsequently, used in a micromechanical model based on the Mori–Tanaka method to calculate elastic constants of the nanocomposite [9]. We adopted the continuum approach because the dimensions of the platelet surface and edge are in the micrometer range, which allows for a large number of binding sites between the platelet and epoxy and justifies the continuum assumption. With the established model, the aspect ratio effect of the graphite particles on the elastic moduli of their composites was investigated. In addition, the effect of out-of-plane elastic constants of the nanoparticles was investigated, since, unlike in-plane elastic constants, there is a wide scatter in reported out-of-plane constants [10], [11], [12], [13], [14], [15], [16], [17], [18].
The experimental verification of the model was carried out with nanocomposites processed with two different types of particles, “as-received” and “intercalated and exfoliated”. They provided different aspect ratios for evaluation of their effect.
Section snippets
Structure of graphite
Graphite has a layered structure, as shown in Fig. 1. In a layer, carbon atoms are arranged in a hexagonal pattern with the shortest distance between atoms being 1.42 Å. The unit cell of the layer is hexagonal and comprises two atoms. In hexagonal graphite, the layers are stacked along the thickness direction (c-axis) in the so-called AB sequence. Each AB-layer is formed from an A layer by displacing it along the c-axis by half the crystallographic c-axis spacing of 3.35 Å and translating it in
Micromechanical analysis and parameter sensitivities
The stiffness of epoxy reinforced with a low concentration of graphite platelets can be calculated using a continuum mechanics approach. This has been demonstrated in a three-phase model [31] using Benveniste’s implementation [32] of Mori–Tanaka’s method [9] for epoxy reinforced by a low concentration of clay nanoplatelets in both intercalated and exfoliated form. In this study, the graphite platelets can be considered as ellipsoidal inclusions randomly distributed and oriented in the epoxy
Experimental verification
For the epoxy matrix, the stiffness properties (Young’s modulus = 3.27 GPa and Poisson’s ratio = 0.34) were obtained from tensile tests. The stiffness properties of graphite platelets were obtained from molecular mechanical calculations, with results listed in Table 1, Table 2. The graphite platelets were approximated as ellipsoidal inclusions with average lateral size (a1 = a2) and thickness (a3) obtained by scanning electronic microscopy. Three different batches of graphite platelet/epoxy composites
Conclusion
A set of elastic constants of graphite nanoplatelets was calculated based on their molecular force field. They were in good agreement with both experimental data and other published theoretical predictions, except for the out-of-plane shear modulus G13 and Poisson’s ratio ν13. It was confirmed that using the Lennard–Jones potential underestimates the shear modulus G13 for perfect graphite. Poisson’s ratio ν13 obtained in this study is positive and very small (0.006) and falls within the wide
Acknowledgement
We gratefully acknowledge the grant support from the NASA University Research, Engineering and Technology Institute on Bio Inspired Materials (BIMat) under award No. NCC-1-02037.
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