56th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference at AIAA SciTech 2015 Kissimmee, Florida, USA 5-9 January 2015

AIAA-2015-0393

Concurrent Multiscale Modeling of Coupling between Continuum Damage and Piezoresistivity in CNT-Polymer Nanocomposites

X. Ren and G. Seidel
Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061-0203, USA

The piezoresistive effect, i.e. the simultaneous relative change of resistance with the applied strain, has been widely observed in the CNT-polymer nanocomposites with a small loading of single-walled carbon nanotubes (SWCNTs) or multi-walled carbon nanotubes (MWCNTs). Researchers have also found that the piezoresistive response of the CNTpolymer nanocomposites can be an indicator of damage events within the material. It is therefore very attractive for the CNT-polymer nanocomposites to be directly embedded into vehicle structures to provide internal and in-situ strain and damage sensing, e.g. fuzzy fiber reinforced polymer composites.

The electrical tunneling (electron hopping) eect is found to be the main driving force for the macroscale piezoresistive response of the nanocomposites. It is a phenomenon that when the CNTs are close enough to the order of nanometers, electrical tunneling paths can form in the polymer matrix among the adjacent CNTs. The electrical tunneling effect is not only highly sensitive to the relative distances of the CNTs, but also guarantees the polymer nanocomposites to be electrically percolated at an extremely low loading of the CNT. As damage develops in the polymer matrix, the local electrical tunneling effect can be potentially in uenced by the evolution of microcracks and the change of relative distances of the CNT, and it is expected that the macroscale piezoresistive response of the CNT-polymer nanocomposites can capture the lower scale damage events. Among all the different damage phenomena, continuum damage is known to be an irreversible process, brought about by the nucleation, growth, extension, and coalescence of microcavities or microcracks, which can result in deterioration or full failure of mechanical properties. For fiber reinforced laminates, continuum damage in the polymer matrix can become important as it is usually the precedence of other damage events, such as fiber-matrix debonding and fiber breakage. In continuum damage mechanics, modeling the microscale damage is usually through prediction of stiffness reduction, and based on the damage initiation criteria, the continuum damage modeling work in the literature can be categorized into two classes. One is that the damage initiation is related to the strengthes of the material, such as the Christensen's or Hashin's failure criteria another is that the damage initiation is related to the internal state variables, such as Talreja et al.'s work. After damage is initiated, the damage evolution is usually formed by phenomenological laws that are proposed to be related to fracture toughness or internal state variables based on the dissipation rate of energy.

To better understand the damage and piezoresistivity coupled mechanisms within the CNT-polymer nanocomposites for SHM applications, a multiscale coupled continuum damage and piezoresistive modeling work is developed. The Christensen's failure criteria are applied to determine the initiation of damage within the polymer matrix, and a phenomenological law is used for damage evolution. Further by introducing the damage variables into the governing equation of the electrical tunneling effect, the one-way coupled continuum damage and piezoresistive response of the CNT-polymer nanocomposites is constructed.