A Shear-Lag Model for Nanotube Reinforced Piezoelectric Polymeric Composites Subjected to Electro-Thermo-Mechanical Loadings

Abstract

Understanding the stress transfer between nanotube reinforcements and surrounding matrix is an important factor in determining the overall mechanical properties of nanotube-reinforced composites. An efficient load transfer from the polymer matrix to the nanotube through interface is required to take the advantage of very high Young’s modulus and strength of carbon nanotubes in the composites. On the other hand, considerable energy dissipation can be obtained by interfacial slippage in the interface of nanotube and matrix which is beneficial in term of structural damping. In order to obtain a composite structure with tunable properties ranges from stiffer structure to better damper, we propose a semi-active control approach. In this method, applied electrical loading to piezoelectric polymeric matrix such as Polyvinylidene Fluoride (PVDF) reinforced with nanomaterials results in radial displacement of piezoelectric polymer corresponding to the direction and magnitude of electrical load. This leads to control of restriction effect of nanotube on the polymer segments, and consequently results in tunable interfacial adhesion between piezoelectric polymer and nanomaterials with faster response time. According to the concept of semi-active control, a shear lag model is obtained for a nanotube reinforced piezoelectric polymer under electro-thermo-mechanical loadings. As the adhesion in carbon nanotube (CNT) composite is universally present in the form of van der Waals interaction, and is the focus of this study, the shear stress and the axial displacement of nanotube and matrix in the interface zone can not be equal. This makes mathematical modeling of interface region more difficult. To solve this complexity, we propose to obtain the relative axial displacement between nanotube and polymer in the interface according to the Lennard-Jones potential function. Results indicate that as the electrical load increases, the relative displacement between nanotube and polymer increases which mean the possibility for slippage increases. Furthermore, results indicate that stiffer structures have more potential to show more switch stiffness capability.