Evaluation of the Mechanical Properties of PMMA Reinforced with Carbon Nanotubes - Experiments and Modeling

The effective mechanical properties of polymethyl-methacrylate (PMMA) reinforced with carbon nanotubes (CNTs) were evaluated by means of two approaches: experiments and a micromechanical model. With various concentrations of CNTs, two specimen fabrication processes were examined: hot pressing (HP) and injection molding (IM). Experiments included a series of uniaxial tensile tests guided by an ASTM standard. Using displacement control, tests were carried out while images were taken of the gage area. The in-plane displacement fields were evaluated by means of Digital Image Correlation (DIC). A MATLAB program was then used to calculate strains, create stress-strain and strain-force curves and determine Young’s modulus E, Poisson’s ratio ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\nu $\end{document}, the ultimate tensile stress σuts\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sigma _{uts}$\end{document} and the strain to failure εf\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\varepsilon _{f}$\end{document}. In addition, simulations were carried out using a micromechanical model (High-Fidelity Generalized Method of Cells or HFGMC). A Repeating Unit Cell (RUC) consisting of one CNT and PMMA surrounding it was modeled and analyzed in order to determine the effective mechanical properties of the composite. This method allows for imperfect bonding between the phases which is controlled by two parameters. These damage parameters decrease the stress-strain response of the material. However, the increase of the volume fraction increases the composite response. These two conflicting effects appear to provide the observed decrease in Young’s modulus for low volume fractions as discussed. The effects of CNT concentration, geometry and orientation, as well as the interface between the phases, were examined. It was seen from the experimental results, for HP specimens, that for low concentrations of CNTs, E initially decreases and then increases significantly as the weight fraction increases. This behavior of E was quantitatively predicted by the HFGMC model. For IM specimens, Young’s modulus is nearly constant for low weight fractions of CNTs and then increases with weight fraction.