Mori-Tanaka-based statistical methodology to compute the effective Young modulus of polymer matrix nano-composites considering the experimental quantification of nanotubes dispersion and alignment degree

This paper presents a Mori-Tanaka-based statistical methodology to predict the effective Young modulus of carbon nanotubes (CNTs)-reinforced composites considering three variables: weight content, reinforcement dispersion and orientation. Last two variables are quantified by two parameters, namely, free-path distance between nano-reinforcements and orientation angle regarding the loading direction. To validate the present methodology, samples of multi-walled CNTs (MWCNTs)-reinforced polyvinyl alcohol (PVA)-matrix composite were manufactured by mixing solution. The MWCNT/PVA Young modulus was measured by nano-indentation, while the MWCNTs Young modulus was quantified by micro-Raman spectroscopy. Both stretched and unstretched composite specimens were fabricated. Transmission electron microscopy (TEM) and in-plane image analysis were used to obtain fitting coefficients of log-normal frequency distribution functions for the free-path distance and orientation angle. It was evidenced that numerical results fit well to measured values of effective Young modulus of MWCNTs and MWCNT/PVA, with exception of some particular cases where significant differences were found. Microstructural heterogeneities, cluster formation, polymer chains alignment, errors associated with the dispersion, orientation and mechanical characterization procedures, as well as idealization and statistical errors, were identified as possible causes of these differences. Finally, using the proposed methodology and the dispersion and orientation distribution functions experimentally obtained, the effective Young modulus is estimated for three kinds of thermoplastic matrices (polyvinyl alcohol, polyethylene ketone, and ultra-high molecular weight polyethylene) with different kinds of nanotubes (single wall, double wall, and multi-walled), at different weight contents, finding the superior mechanical performance for double-walled CNTs-reinforced composites and the lower one for multi-walled CNTs-reinforced ones.