| The focus of this research has been to develop a validated computational framework to investigate the electro-mechanical-thermal behavior of carbon nanotube (CNT)-polymer composites. The computational framework included the development of both a new percolation approach and an electro-mechanical-thermal finite-element (FE) approach. The percolation approach addressed current shortcomings and inconsistencies of classical percolation theory, and it was used to predict the electrical conductivity of CNT-epoxy composite based on variations in tunneling resistances, aspect ratios, CNT volume fractions and distributions. This approach is based on an electrical network model and a junction-identifying search algorithm. For the search algorithm, the distances between all the generated CNTs were computed, and if the distance between two CNTs was smaller than a pre-determined maximum distance, the two CNTs were assumed to be in contact, and a junction can then be identified. The tunnel resistances at each junction and the overall electrical resistance of 3D CNT-polymer networks were then obtained. The predicted conductivity behavior was used to predict different percolation thresholds and the critical exponents for different CNT arrangements within an epoxy matrix, and this approach was validated with experimental observations and measurements.;The FE modeling method was then developed to investigate how the electro-mechanical-thermal behavior of CNT reinforced polymer composites is affected by electron tunneling distances, volume fraction, and physically realistic tube aspect ratios. A specialized Maxwell FE formulation with a Fermi-based tunneling resistance was then used to obtain current density evolution for different CNT-polymer dispersions and tunneling distances. Analyses based on coupled thermo-electrical and electro-mechanical FE approaches were used to investigate how temperatures, conductivities, stresses, and strains were affected by variations in tunneling distances and electro-thermo-mechanical loading conditions. In the coupled thermo-electrical analyses, the Maxwell equations were coupled to the heat conduction equations through Seebeck coefficients. The current flow, total current density, thermal distributions, and Joule heating were determined for different CNTs arrangements and tunnel distances. The analyses has indicated that tunneling has a dominant role in the overall electrical conductivity and thermal behavior of the composite. There was no clear correlation with tunneling distance, however, since the behavior is dominated by CNT orientation and distribution. This further underscores how the behavior of randomly distributed functionalized CNTs in an epoxy matrix with varying tunneling distances can be difficult to predict, since the physical scales range from tunnel lengths of a few nanometers to CNTs with lengths of hundreds of nanometers.;The coupled electro-mechanical FE approach was developed to investigate the piezoresistive response of the polymer composite. Gauge factors (GFs) and resistance variations of CNT-polymer composite systems were obtained by coupling Maxwell equations to mechanical loads and deformations through initial piezoresistive coefficients of the CNTs, the epoxy, and the tunnel regions, for different arrangements, percolated paths, tunnel distances, and loading conditions. The influences of loading conditions, such as tension, compression, and bending on the piezoresistivity of CNT polymer composites were investigated. A scaling relation between GFs and applied strains was obtained to understand how variations in loading and CNT arrangements affect sensing capabilities. These variations in GFs were then used to understand how the coupled strains, stresses and current densities vary for aligned and percolated paths for the different loading conditions, CNT arrangements, and tunnel distances. For the percolated path under tensile loading conditions, elastic strains as high as 16% and electrical conductivities that were four orders in magnitude greater than the initial matrix conductivity were obtained. Results for the three loading conditions clearly demonstrate that electrical conductivity and sensing capabilities can be optimized as a function of percolation, tunneling distance, orientation, and loading conditions for piezoresistive applications with large elastic strains and conductivities. |
