A Three Dimensional Unit Cell Model for the Analysis of Thermal Residual Stresses in Polymer Composites Reinforced with
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MRS Advances © 2019 Materials Research Society DOI: 10.1557/adv.2019.440
A Three Dimensional Unit Cell Model for the Analysis of Thermal Residual Stresses in Polymer Composites Reinforced with Wavy Carbon Nanotubes Y. Zhang, A. Johnston, A. Yousefpour, J. Guan, B. Simard, C. Kingston National Research Council Canada, 1200 Montreal Road, Ottawa ON, Canada K1A 0R6
ABSTRACT
This paper presents a numerical approach to predict the thermal residual stresses in polymer nanocomposites reinforced with a periodic array of wavy carbon nanotubes. A three dimensional unit cell model is established to accurately account for the waviness of the nanotube. Periodic boundary conditions are determined for the unit cell with a pair of curved surfaces. Appropriate methods to evaluate the macroscopic stresses and strains are also determined for the unit cell model in which the interior pores of the nanotubes are explicitly included. It is demonstrated that the macroscopic behavior of the nanocomposites is orthotropic due to the symmetries manifested. By employing material properties of the two constituents, the thermal residual stresses and strains induced by high temperature curing and cooling-down are predicted for an epoxy/wavy-nanotube composite. It is also demonstrated that the curing process tends to increase the waviness of the nanotube and the waviness has a significant influence on the distribution of the microscopic residual stresses.
INTRODUCTION Polymeric nanocomposites incorporated carbon nanotubes (CNT) are one of the most promising materials in industrial applications where light-weight and high strength materials are increasingly demanded. Using only a few volume percentages of CNT, the mechanical properties of the composites can be significantly improved [1-3]. Due to their low bending stiffness and very high aspect ratio of length to diameter, most CNTs are highly wavy in a matrix and the overall mechanical properties of CNT/polymer composites are greatly influenced by the CNT waviness [4-5]. Analytical, numerical and experimental approaches have been extensively explored to investigate the waviness effect of the CNTs and micro-fibers on the elastic properties of composites [6-8].
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Finite element method based micromechanical approaches [9-11] have been utilized for the analysis of wavy nanotube reinforced nanocomposites [12-14], similar to the analysis of polymer composites with wavy micro-fibers (e.g., glass and carbon fibers) [15-16]. A few investigations have employed a repeated unit cell (RUC) model of wavy CNT reinforced polymer composites and periodic boundary conditions were explored to carry out the analyses. By using the micromechanical approach, not only the effective elastic constants of the composites can be predicted, but also the microscopic stress and s
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