Coupled electromechanical modeling of piezoresistive behavior of CNT-reinforced nanocomposites with varied morphology and concentration

Highlights

• Novel coupled electromechanical model of CNT composites with realistic morphologies.

• Percolating networks converted into equivalent electric circuits.

• Modified nodal analysis method used to determine conductivity of the composite.

• Sensor gauge factor increases with the increase in curvature of CNTs.

• Sensor gauge factor was highest at concentrations near percolation threshold.

Abstract

In this first time effort, we developed a coupled electromechanical model of CNT-reinforced composites with realistic morphologies. First, a Monte-Carlo based algorithm was developed to generate representative volume elements (RVEs) reinforced with different concentrations of straight and wavy CNTs. The percolating CNT networks were identified and transformed into an equivalent electric circuit consisting of tunneling and intrinsic resistances. The effective conductivity of the composite was then obtained using the modified nodal analysis method. Second, the structural response of each RVE was obtained using a novel embedded finite element model, where the composite constituents are meshed independently but solved simultaneously by coupling their equilibrium equations. Third, the displacements of the deformed CNTs were updated in the electrical model to calculate the corresponding tunneling distances and the resistance of the deformed system. The gauge factor of the nanocomposite was calculated from the strain-resistance curve. The obtained results indicated that the gauge factor increases with the increase in the curvature of the CNTs. The highest gauge factor of the sensor was attained at concentrations near the percolation threshold. Finally, the gauge factor was found to increase with the decrease in Poisson's ratio of the matrix.

Introduction

Due to their remarkable mechanical and electrical properties (Eatemadi et al., 2014; Tamura and Tsukada, 1997), carbon nanotubes (CNTs) are increasingly being viewed as an ideal choice of tailoring the properties for multifunctional polymer-based composites (Lee and Loh, 2017; Xu et al., 2019). It is well recognized that dispersing a small number of CNTs into an insulating polymeric matrix can significantly improve the electrical conductivity of the nanocomposite due to formation of percolating CNT networks spanning through the material (Bao et al., 2011; Chatterjee et al., 2011; Avilés et al., 2018). Such conductive nanocomposites have numerous potential applications in the area of flexible electronics, structural health monitoring, lightning strike protection for aerospace vehicles, and strain sensing (Hu et al., 2018; Namilae et al., 2019; Wang et al., 2018).

The electrical current is transmitted through the CNT-reinforced nanocomposite in two different mechanisms. The first is the ballistic transport of electrons along the CNT axis (Javey et al., 2003) and the second is the electron tunneling between closely located CNTs (Bao et al., 2012a, b; Li et al., 2007). If a mechanical load is applied on the nanocomposite, the dispersed CNTs are deformed and their relative positions change correspondingly. Therefore, the electromechanical behavior of the CNT-reinforced nanocomposite can be attributed to the change of the intrinsic resistance of a deformed CNT (Hadjiev et al., 2001) and the change of the tunneling resistance due to the redistribution of CNT network (Hu et al., 2010).

Over the past decade, CNT-based strain sensors have attracted considerable interest due to their higher gauge factor compared with traditional commercial metallic strain sensors (Oliva-Avilés et al., 2011). Several experimental (Avilés et al., 2016; Ma et al., 2018; Oliva-Avilés et al., 2011) and numerical (Alian and Meguid, 2019; Chaurasia and Seidel, 2017; Liu and Hu, 2010) studies were conducted to study their piezoresistive properties. Yasuoka et al. (2010) measured the piezoresistivity of the flexible-epoxy reinforced with different CNT concentrations. The experimental results showed that the strain gauge factor of the fabricated composite depends nonlinearly on the CNT volume fraction. Park et al. (2008) studied the strain-dependent resistance of polyethylene oxide reinforced by MWCNTs. Their results demonstrated that the effective resistance initially increases linearly with the strain and followed by a nonlinear behavior at high strain levels. Kang et al. (2009) found that CNT concentrations slightly above the percolation threshold demonstrated the maximum piezoresistive coefficient, which was two orders of magnitude higher than those of metal sensors. Oliva-Avilés et al. (2011) investigated the influence of CNT alignment on the piezoresistivity of MWCNT/polymer composites. Their results revealed that the alignment of CNTs results in an improvement of the strain sensing capabilities of the nanocomposite. More recently, Avilés et al. (2016) found that the electromechanical behavior of MWCNT/VER composites is strongly influenced by the mechanical properties of the matrix and the aspect ratio of the CNTs.

In addition to limited experimental studies, numerical simulations have also been conducted to investigate the piezoresistivity of CNT-reinforced nanocomposite. A two-dimensional model was developed by Li and Chou (2008) to study the damage sensing mechanism of CNT networks in fiber composites. In their model, the effective resistance was calculated by considering nanotube-matrix resistors network and employing the FE method for the equivalent electrical circuits. Hu et al. (2008) developed a three-dimensional (3D) model. In their model, the reorientation of CNTs under the applied strain was simplified as a rigid-body movement and used to determine the deformation effect on the tunneling resistance between the contacted CNTs and the overall piezoresistive properties of the composite. Later on, Liu and Hu (2010) considered both CNT's intrinsic and tunneling resistance in their 3D model but the CNTs new locations in the deformed RVEs were also calculated using a simplified reorientation models. The rigid-body assumption of the CNTs in these models oversimplifies the deformation mechanism of the composite at the nanoscale level (Simmons et al., 2009; Slobodian et al., 2012). Alian and Meguid (2019) proposed a coupled 3D electromechanical model which simulated the CNT movement using the FE model. However, due to the difficulties of creating the FE models for RVEs reinforced with complex CNT networks, they only managed to study the piezoresistivity of nanocomposites reinforced with very limited CNT volume fractions. All CNTs were considered to be straight and well dispersed in the RVEs, ignoring the actual morphology and dispersion state of the nanocomposites as imaged with an electron microscopy (Fisher et al., 2003). In spite of these earlier efforts, further work is still required to determine the governing mechanisms and the controlling parameters of the piezoresistive behaviour of nanocomposites at both nano and bulk levels.

In this work, we developed an advanced coupled electromechanical model to examine the piezoresistive properties of CNT/polymer-based nanocomposites. The influence of CNT volume fraction, CNT curvature, and matrix Poisson's ratio on the gauge factor of the composite is investigated. Understanding the influence if these parameters is essential in understanding the fundamental mechanism of the piezoresistivity at different length scales. The developed model consists of three sequential stages. In the first stage, we constructed RVEs containing dispersed CNTs with different volume fractions and curvatures, and identified the percolating CNT networks. The effective electrical conductivity of the RVE was then calculated by solving the equivalent electrical circuit using the modified nodal analysis method. In the second stage, the mechanical behavior of the RVE under different tensile and compression loads was simulated with the modified embedded finite element (mEFE) method. In the mEFE method, the grids of the CNT network and the polymer are created independently but solved simultaneously as a coupled system, which enabled us to overcome the difficulties of modeling RVEs with complex microstructures. In the third stage, the new positions of CNTs in the deformed RVEs were then updated in the electrical model to calculate the corresponding effective resistance of the RVE. The proposed coupled electromechanical model will help in developing nanocomposites-based sensors with reliable and predictable properties.