Micro-mechanics based derivation of the materials constitutive relations for carbon-nanotube reinforced poly-vinyl-ester-epoxy based composites

The atomic-level computational results of the mechanical properties of Multi-Walled Carbon Nanotube (MWCNT) reinforced poly-vinyl-ester-epoxy obtained in our recent work [Grujicic M, Sun Y-P, Koudela KL (2006) Appl Surf Sci (accepted for publication, March)], have been utilized in the present work within a continuum-based micro-mechanics formulation to determine the effective macroscopic mechanical properties of these materials. Since the MWCNT reinforcements and the polymer-matrix molecules are of comparable length scales, the reinforcement/matrix interactions which control the matrix-to-reinforcement load transfer in these materials are accounted for through direct atomic-level modeling of the "effective reinforcement" mechanical properties. The term an "effective reinforcement" is used to denote a MWCNT surrounded by a layer of the polymer matrix whose thickness is comparable to the MWCNT radius and whose conformation is changed as a result of its interactions with the MWCNT. The micro-mechanics procedure yielded the effective continuum mechanical properties for the MWCNT-reinforced poly-vinyl-ester-epoxy matrix composite mats with a random in-plane orientation of the MWCNTs as a function of the following composite microstructural parameters: the volume fraction of the MWCNTs, their aspect ratio, the extent of covalent functionalization of the MWCNT outer walls as well as a function of the mechanical properties of the matrix and the reinforcements.