Mechanical characterization of graphite/epoxy nanocomposites by multi-scale analysis J. Cho, J.J. Luo, I.M. Daniel * Center for Intelligent Processing of Composites, McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA Received 12 September 2006; received in revised form 2 January 2007; accepted 11 January 2007 Available online 30 January 2007 Abstract Mechanical properties of nanocomposites consisting of epoxy matrix reinforced with randomly oriented graphite platelets were stud- ied by the Mori–Tanaka approach in conjunction with molecular mechanics. Elastic constants of graphite nanoplatelets, which are the inclusion phase in the micromechanical model, were calculated based on their molecular force field. The calculated elastic constants com- pared well with both experimental data and other published theoretical predictions. The results of the Mori–Tanaka micromechanical analysis, using the graphite platelet moduli calculated by molecular mechanics, were found to be insensitive to the variation of out-of- plane modulus E 3 and Poisson’s ratio m 13 . However, the nanocomposite modulus is sensitive to the in-plane modulus E 1 and out-of-plane shear modulus G 13 of the graphite platelets and less sensitive to the in-plane Poisson’s ratio m 12 for its small range of variation under consideration. The calculations confirm that the modulus of the nanocomposites studied here is strongly dependent on the aspect ratio of the reinforcing particles, but not on their size. The predicted moduli compare favorably with experimental results of several nanocom- posites with graphite particles of various aspect ratios and sizes. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: A. Nanostructures; A. Polymer–matrix composites; B. Mechanical properties; B. Modeling; C. Elastic properties 1. Introduction Graphite platelets are often used in polymeric matrices to enhance mechanical properties and impart physical functionalities such as electrical and thermal conductivities [1–4]. 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 nanoparti- cle reinforced polymeric composites by incorporating molecular mechanical models into continuum models in recent years [5–8]. In general, the mechanical properties of nanostructured particles, expressed with atomic struc- tures 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 par- ticles 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, 0266-3538/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2007.01.006 * Corresponding author. Tel.: +1 847 491 5649; fax: +1 847 491 5227. E-mail address: imdaniel@northwestern.edu (I.M. Daniel). www.elsevier.com/locate/compscitech Composites Science and Technology 67 (2007) 2399–2407 COMPOSITES SCIENCE AND TECHNOLOGY