Prediction a Range for Elastic Modulus of CNT Reinforced Polymer Composites using Analytical Method

Analytical and finite element models predict the elastic modulus of CNT-polymer nanocomposites greater than experimental results. This paper presents a theoretical full continuum model to define the upper and lower thresholds with small variations for elastic modulus in polymer nanocomposites، which the experimental results always place between these thresholds. For this purpose، the governing elasticity equations in polar coordinates have been solved for nanocomposite representative volume element (RVE) with shear-lag model by assuming perfect bond condition between CNT and matrix. In addition، the nanocomposite elastic modulus in perfect bond and debonding conditions between nanotube and matrix is calculated using finite element method in ANSYS software which confirms the accuracy of theoretical results. Also the obtained analytical and FEM results are compared with available experimental results، which indicates that the value of experimental results is always between the upper and lower thresholds of analytical and FEM results. finally by surveying the axial and von-mises stress in the matrix region، the new way for defining the elastic modulus of new nanocomposites with analytical method is proposed here which reduce the cost of experimental research.